[839] **viXra:1403.0981 [pdf]**
*submitted on 2014-03-31 16:42:09*

**Authors:** Marius Coman

**Comments:** 3 Pages.

I was playing with randomly formed formulas based on two distinct primes and the difference of them, when I noticed that the formula p + q + 2*(q – p) – 1, where p, q primes, conducts often to a result which is prime, semiprime, square of prime or product of very few primes. Starting from here, I made a conjecture about a way in which any square of a prime seems that can be written. Following from there, I made a conjecture about a possible infinite set of primes, a conjecture regarding the squares of primes and Poulet numbers and yet three other related conjectures.

**Category:** Number Theory

[838] **viXra:1403.0980 [pdf]**
*replaced on 2014-04-06 15:58:58*

**Authors:** Martin K. Dubreuil, Sergii Koliada

**Comments:** 30 Pages. This paper will be forwarded to a peer-reviewed journal after its completion. It was submitted here to invite people to review and criticise the paper.

Prompted by previous research results we analysed human decision processes for unconscious patterns. Like former studies [1, 2] we were able to find law-like patterns that were not consciously created. We calculated the residual uncertainty about the pattern to 1 : 1,000,000,000 and proved a high correlation ratio for the data source related to the found pattern through an intra class correlation test (3.2). We showed that conscious (3.3) and unconscious human behaviour and natural selection (3.4) are not able to explain this result. This includes the possibility to prove Intelligent Design (3.4).

**Category:** Mind Science

[837] **viXra:1403.0979 [pdf]**
*replaced on 2014-04-01 10:35:56*

**Authors:** S.C. Gaudie

**Comments:** 3 pages; A4 paper; portrait orientation; mostly font 11; UK English; Freelance scientist.

NEGATIVE ENERGY particles.
From S. Hawking:- “Particle Creation of Black Holes" two quotes.
“ Just outside the event horizon there will be virtual pairs of particles, one with negative energy and one with positive energy.”
AND
“It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally"
From a “standard physics point of view" the hypothetical NEGATIVE energy particle has, necessarily, other associated properties.
# = breaks “standard physics point of view" laws.
[A] Negative energy :: (1) # negative Kelvin temperature!
[B] Negative mass :: (1) # negative mass, which cannot be anti-matter because it has positive mass!
[C] Negative velocity (The space distance & time is self-referenced to the NEGATIVE energy particle.)
[C1] Negative space :: (1) # negative space distance, where all “normal space" has positive space distances.
[C2] Negative time :: (1) # negative time difference, where all “normal time" has positive time difference.
I suppose that tacyons would fit into the [C] category, but I’m not aware of any observation confirming the existence of [A], [B] or [C]. Of course the “standard physics point of view" does not apply inside a black hole! Theoretically, nothing but tacyons could escape from a black hole!
NEGATIVE INERTIA particles.
I, somewhat cynically, posit a similar NON-“standard physics point of view" property of matter [impossible in my understanding of the laws of physics]:-
NEGATIVE INERTIA particles.
[BUT, it does have some predicted properties that are compatible with experimental observations!]
Basic consequences
[1] If a group of negative inertia “particles” were hit by another they would go flying off in all directions immediately. [Normal matter would tend to have a “stay in the same place" tendency.]
[2] From the above, the negative inertia matter would not “clump together.
[3] It would be spread evenly, like a gas, throughout the universe.
[4] The negative inertia would also apply to how easy it is to add [or remove] angular momentum to [or from] a spinning body.
Possible assumptions (A) & conclusions (C)
[A1] It would be pushed away by photon pressure from stars & the accretion discs of galactic black holes much easier than normal matter.
[C1] The inner parts of galaxies would be emptied of negative inertia matter. The outer reaches of galaxies would have the “I want to go faster” type of negative inertia and, hence move faster!
[A2] Because the the negative inertia matter is so evenly and, hence “thinly” spread throughout the universe, its influence only becomes more noticeable as cosmic expansion increases. From our “newest time = greatest expansion", “localised viewpoint" of our universe we would see the greatest cosmic expansion around us.
[C2] [The normal matter is “spread out thinner & thinner” with time and also the greatest effect of negative inertia, because the negative inertia matter is initially, spread out fairly evenly [like a gas.]. The “I want to go faster” type negative inertia matter could cause the increased expansion of the universe. It would have a “pushing apart”, “increased velocity” effect!
[C3] The negative inertia matter could account for increased star rotation speeds on edges of galaxies and dark energy too. It’s an unexplored aspect of exotic matter!
[C4] The negative inertia matter could be viewed as “dark matter” or “shadow matter”.

**Category:** Relativity and Cosmology

[836] **viXra:1403.0978 [pdf]**
*submitted on 2014-03-31 21:51:21*

**Authors:** Shalender Singh, Vishnu Priya Singh Parmar

**Comments:** 20 Pages.

Lorentz transformations and special theory of relativity have existed for more than a century and mathematics related to them has been used and applied for innumerous times. Relativistic energy and relativistic momentum equations have been derived and proven to be conserved if energy/momentum transaction is seen from different frames of reference. The set of permissible inertial reference frame velocities from where the energy and momentum of a closed system of particles may be observed to be conserved forms a ball in the velocity vector space. In this paper we use the existing equations of special theory of relativity and Lorentz transformations and the mathematical structure of the observation velocity space to prove that the conservation of kinetic energy implies the conservation of momentum. We also prove that the conservation of momentum implies the conservation of kinetic energy. We further derive many more linearly independent conservation equations directly from the conservation of energy/ momentum. The derivation of the conservation of kinetic energy from the conservation of momentum implies that either potential energy has a momentum thus made of inertial particles or there cannot be a net conversion of potential energy to kinetic energy. Furthermore the existence of many equations lead to extremely strict form of transfers of energy and momentum. It highly restricts the set of states particles in any closed system can assume without changing the overall energy of the system. This has a strong impact on the particle mechanics and as an example we show that the relativistic explanation of the elastic collision of particles striking each other as used by Einstein in the 1934 two blackboard derivation of mass and energy is itself inconsistent and wrong.

**Category:** Relativity and Cosmology

[835] **viXra:1403.0977 [pdf]**
*submitted on 2014-03-31 12:36:51*

**Authors:** Richard J. Mathar

**Comments:** 6 Pages.

The solid angle of a circular sector specified by
circle radius, angle of the sector, and distance of the circle plane to the
observer is calculated in terms of various trigonometric and cyclometric
functions. This generalizes previous results for the full circle
that have appeared in the literature.

**Category:** Functions and Analysis

[834] **viXra:1403.0975 [pdf]**
*submitted on 2014-03-31 11:13:23*

**Authors:** editors Rajesh Singh, Florentin Smarandache

**Comments:** 71 Pages.

The purpose of writing this book is to suggest some improved estimators
using auxiliary information in sampling schemes like simple random sampling,
systematic sampling and stratified random sampling.
This volume is a collection of five papers, written by nine co-authors
(listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr.
Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil
Prajapati, Hemant Verma, and Viplav Kr. Singh.
In first paper dual to ratio-cum-product estimator is suggested and its
properties are studied. In second paper an exponential ratio-product type
estimator in stratified random sampling is proposed and its properties are
studied under second order approximation. In third paper some estimators are
proposed in two-phase sampling and their properties are studied in the
presence of non-response.
In fourth chapter a family of median based estimator is proposed in
simple random sampling. In fifth paper some difference type estimators are
suggested in simple random sampling and stratified random sampling and their
properties are studied in presence of measurement error.

**Category:** Statistics

[833] **viXra:1403.0974 [pdf]**
*replaced on 2014-11-23 10:46:58*

**Authors:** Jeffrey S. Keen

**Comments:** 14 Pages, 11 Figures, 3 Tables

The mind’s intuitive, noetic, or dowsable response to different situations are categorised to help understand its causes. In this paper, nine different subtle energy types have been identified and itemised together with some of their properties. They all have a connection to the earth’s environment and the laws of physics. This is convincingly demonstrated by using an abstract geometrical source that combines tetrahedral geometry and certain Pythagorean triangles allowing the mind to create the 9 subtle energy types. This technique enables the reader to fine-tune his or her noetic or dowsing skills, or use this paper for further serious scientific research into both the mind and its interaction with the cosmos.
Key words. Noetics, the mind, dowsing, intent, subtle energy, categorisation, Pythagorean triangles, structure of the universe

**Category:** Mind Science

[832] **viXra:1403.0973 [pdf]**
*replaced on 2014-07-04 02:00:54*

**Authors:** Sergey G. Fedosin

**Comments:** 33 pages. American Journal of Modern Physics. Vol. 3, No. 4, 2014, pp. 152-167. doi: 10.11648/j.ajmp.20140304.12

As a result of integration of the equations of motion with regard to the pressure field and acceleration field the system’s integral energy-momentum 4-vector is found. It is shown that this vector in the covariant theory of gravitation must be equal to zero. This allows us to explain the 4/3 problem and the problem of neutrino energy in an ideal spherical supernova collapse. At the same time, in order to describe the system’s state, instead of the integral 4-vector we must use the four-momentum, which is derived from the Lagrangian. The described approach differs substantially from the results of the general theory of relativity, in which the integral 4-vector serves as the system’s four-momentum, and the stress-energy tensor of the gravitational field is replaced by the corresponding pseudotensor.

**Category:** Relativity and Cosmology

[831] **viXra:1403.0972 [pdf]**
*replaced on 2014-03-30 09:57:09*

**Authors:** Nainan K. Varghese

**Comments:** 3 Pages.

Orbital speeds of stars, far from center of a galaxy, are found roughly constant, instead of reductions predicted by current gravitational theories (applied on galactic and cosmological scales). This is called the anomalous rotation of galaxies. This article intends to show that constant angular speeds of all macro bodies in a galaxy are natural phenomenon and there is no mystery about it.

**Category:** Astrophysics

[830] **viXra:1403.0971 [pdf]**
*replaced on 2014-08-21 09:47:30*

**Authors:** Keith Maxwell Hardy

**Comments:** 28 Pages.

All forces emerge from a simple field based on the analogy of waves rippling out from a source. New ideas are applied to this field such as plus and minus space and time, an absolute reference frame of nothingness, and origins of influence. This approach results in a basic unified field theory.

**Category:** High Energy Particle Physics

[829] **viXra:1403.0968 [pdf]**
*submitted on 2014-03-29 07:55:34*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper we present four conjectures, one of them regarding a possible infinite sequence of primes and three of them regarding three possible infinite sequences of Poulet numbers, each of them obtained starting from other possible infinite sequence of Poulet numbers.

**Category:** Number Theory

[828] **viXra:1403.0967 [pdf]**
*submitted on 2014-03-29 08:18:54*

**Authors:** Etkin V.A.

**Comments:** 6 Pages. In Russian

Existence of vector potential of rotating currents and unity of its analytical expression
with other potentials is shown. The sense of this potential as angular speed of rotation of a current is opened and its communication with work is found.
(Показано существование векторного потенциала вращающихся токов и единство его аналитического выражения с другими потенциалами. Вскрыт смысл этого потенциала как угловой скорости вращения тока и найдена его связь с работой)

**Category:** Classical Physics

[827] **viXra:1403.0966 [pdf]**
*submitted on 2014-03-28 18:21:30*

**Authors:** Stephen J. Crothers

**Comments:** 5 Pages.

These notes constitute a supplement to my paper ‘The Theological Basis of Big Bang Cosmology and the Failure of General Relativity’ and should therefore be read after that paper.

**Category:** Relativity and Cosmology

[826] **viXra:1403.0965 [pdf]**
*submitted on 2014-03-28 22:18:01*

**Authors:** Dhananjay P. Mehendale

**Comments:** 2 pages,

Reconstruction conjecture asks whether it is possible to reconstruct a unique (up to isomorphism) graph from set of its one vertex deleted subgraphs. We show here the validity of reconstruction conjecture for every connected graph which is uniquely reconstructible from the set of all its spanning trees. We make use of a well known result, namely, the reconstruction of a tree from the deck of its pendant point deleted subtrees.

**Category:** Combinatorics and Graph Theory

[825] **viXra:1403.0964 [pdf]**
*replaced on 2014-04-24 22:04:48*

**Authors:** Hsien-Pu Chen, Laszlo B. Kish, Claes-GÖran Granqvist, Gabor Schmera

**Comments:** 13 Pages. Version after Galley proof corrections in Fluctuation and Noise Letters

We refute a physical model, recently proposed by Gunn, Allison and Abbott (GAA) [http://arxiv.org/pdf/1402.2709v2.pdf], to utilize electromagnetic waves for eavesdropping on the Kirchhoff-law–Johnson-noise (KLJN) secure key distribution. Their model, and its theoretical underpinnings, is found to be fundamentally flawed because their assumption of electromagnetic waves violates not only the wave equation but also the Second Law of Thermodynamics, the Principle of Detailed Balance, Boltzmann’s Energy Equipartition Theorem, and Planck’s formula by implying infinitely strong blackbody radiation. We deduce the correct mathematical model of the GAA scheme, which is based on impedances at the quasi-static limit. Mathematical analysis and simulation results confirm our approach and prove that GAA’s experimental interpretation is incorrect too.

**Category:** Thermodynamics and Energy

[824] **viXra:1403.0962 [pdf]**
*submitted on 2014-03-29 03:04:16*

**Authors:** Keith Ferrer

**Comments:** 2 Pages.

The quantization of electromagnetic radiation can be interpreted based on the relativistic properties of light waves given its constant velocity relative to bodies that are slower than them.

**Category:** Quantum Physics

[823] **viXra:1403.0961 [pdf]**
*submitted on 2014-03-28 10:23:00*

**Authors:** Leonid Filippov

**Comments:** 41 Pages. in Russian

Lorentz transforms are derived and electrodynamic and optical effects of Special theory of relativity. A known formula for centrifugal force of inertia, which is a consequence of the emergence of gravitational interaction of the test body with all bodies of the Universe, is deduced. This corresponds to Mach’s principle, explaining the equivalence of inertial and gravitational masses.

**Category:** Relativity and Cosmology

[822] **viXra:1403.0960 [pdf]**
*submitted on 2014-03-28 11:27:39*

**Authors:** Joel M Williams

**Comments:** 5 Pages.

The bonding of the hydrogen atom in the B—H—B sequence of diborane is just a standard overlapping of atomic orbitals. With the MCAS model, hydrogen naturally has the capacity to form linear and non-linear bonds between two atoms, when necessary. There is no need for the nebulous 3-center, two-electron, bond that has been used to honor the unassailable s-orbital of the spdf-QM model.

**Category:** Quantum Physics

[821] **viXra:1403.0958 [pdf]**
*replaced on 2014-03-29 00:04:16*

**Authors:** Nikolay Dementev

**Comments:** 7 Pages.

The report suggests an approach to extend a concept of determinant to the systems of any order.

**Category:** Algebra

[820] **viXra:1403.0957 [pdf]**
*submitted on 2014-03-28 08:51:39*

**Authors:** A. A. Salama

**Comments:** 7 Pages.

Abstract: Mobile adhoc network is a special kind of wireless networks. It is a collection of mobile nodes without having aid of establish infrastructure. In mobile adhoc network, it is much more vulnerable to attacks than a wired network due to its limited physical security, Securing temporal networks like Mobile Ad-hoc Networks (MANETs) has been given a great amount of attention recently, though the process of creating a perfectly secured scheme has not been accomplished yet. MANETs has some other features and characteristics those are together make it a difficult environment to be secured. The bandwidth of MANET is another challenge because it is unlikely to consume the bandwidth in security mechanisms rather than data traffic. This paper proposes a security scheme based on Public Key infrastructure (PKI) for distributing session keys between nodes. The length of those keys is decided using intuitionistic fuzzy logic manipulation. The proposed algorithm of Security-model is an adaptive intuitionistic fuzzy logic based algorithm that can adapt itself according to the dynamic conditions of mobile hosts. Finally the Experimental results shows that the using of intuitionistic fuzzy based security can enhance the security of (MANETs).

**Category:** Data Structures and Algorithms

[819] **viXra:1403.0956 [pdf]**
*submitted on 2014-03-28 09:16:01*

**Authors:** A. A. Salama

**Comments:** 13 Pages.

The fundamental concepts of neutrosophic set, introduced by Smarandache in [9, 10] and
Salama et al. in [4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. In this paper we introduce and
study new types of neutrosophic concepts " cut levels , normal neutrosophic set, convex
neutrosophic set". Added to we will begin with a definition of neutrosophic relation and then
define the various operations and will study its main properties. Some types of neutrosophic
relations and neutrosophic database are gevine. Finaly we introduce and study neutrosophic
database (NDB for short). Some neutrosophic queries are gevine to a neutrosophic database .

**Category:** Data Structures and Algorithms

[818] **viXra:1403.0955 [pdf]**
*submitted on 2014-03-28 09:21:32*

**Authors:** A. A. Salama

**Comments:** 7 Pages.

Recommender systems are needed to find subject items of one’s interest. We review
recommender systems and recommendation methods. We propose a subject personalization
framework based on adaptive hypermedia for Computer Science ACM Curricula. We extend
Hermes framework with subject recommendation functionality. We combine TF-IDF term
extraction method with cosine similarity measure. Specialization and standard subject
database are incorporated into the knowledgebase. Based on the performed evaluation, we
conclude that semantic recommender systems in general outperform traditional recommenders
systems with respect to accuracy, precision, and recall, and that the proposed recommender
has a better F-measure than existing semantic recommenders.

**Category:** Digital Signal Processing

[817] **viXra:1403.0953 [pdf]**
*submitted on 2014-03-27 19:22:55*

**Authors:** Stephen J. Crothers

**Comments:** 11 Pages. This paper appeared in WSPC - Proceedings THE PHYSICS OF REALITY: SPACE, TIME, MATTER, COSMOS, VIGIER VIII - BCS 2012

It is shown in this paper that the Big Bang Cosmology has its basis in theology, not in science, that it pertains to a Universe entirely filled by a single spherically symmetric continuous indivisible homogeneous body and therefore models nothing, that it violates the physical principles of General Relativity, that it violates the conservation of energy, and that General Relativity itself violates the usual conservation of energy and momentum and is therefore in conflict with experiment on a deep level, rendering Einstein’s conception of the
physical Universe and the gravitational field invalid.

**Category:** Relativity and Cosmology

[816] **viXra:1403.0952 [pdf]**
*submitted on 2014-03-27 10:23:57*

**Authors:** Thomas Alexander Meyer

**Comments:** 6 Pages.

I present an analysis of the quantum erasing effect which categorizes the effect into attenuating and non-attenuating phenomena. It is shown that the attenuating quantum eraser is typically explained in a spurious fashion, and insight is given concerning the real phenomenon of interference between distinguishable states that would properly explain the attenuating eraser.

**Category:** Quantum Physics

[815] **viXra:1403.0951 [pdf]**
*submitted on 2014-03-27 10:50:26*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 9 Pages.

We give a survey on recent results
about the problem of approximating a real-valued function by means of suitable families of sampling type operators, which include both discrete and integral ones, and about
the order of approximation, and abstract
Korovkin-type theorems with respect to
different types of test functions,
in the context of filter convergence.
We give a unified approach, by
means of which it is possible to consider several
kinds of classical operators, for instance Urysohn integral operators, in particular Mellin-type convolution integrals, and generalized sampling series.
We obtain proper extensions of classical results.

**Category:** Functions and Analysis

[814] **viXra:1403.0950 [pdf]**
*submitted on 2014-03-27 12:09:57*

**Authors:** William O. Straub

**Comments:** 6 Pages.

In classical electrodynamics the vacuum is defined as a region where there are no electric or magnetic fields. In such a region, a charged particle (such as an electron) will feel no effect — the Lorentz force is zero. The space external to a perfect (i.e., infinite) solenoid can be considered an electromagnetic vacuum, since E and B vanish there. While a non-zero vector potential A does exist outside the solenoid, it can exert no influence on the particle, and thus cannot be directly detected or quantified classically. However, in 1959 Aharonov and Bohm predicted that a vector field would exert a purely quantum-mechanical effect on the phase of the particle’s wave function, which
in principle should be detectable. The predicted phase shift was not observed experimentally until 1986, when Tonomura brilliantly verified the effect using a microscopic solenoid. This paper provides a simplified explanation of the Aharonov-Bohm effect using a path-integral approach that is suitable for the advanced undergraduate.

**Category:** Quantum Physics

[813] **viXra:1403.0949 [pdf]**
*submitted on 2014-03-27 12:34:23*

**Authors:** Helmut Söllinger

**Comments:** 12 Pages.

The author's starting point is the axiom that the product of particle masses and the gravitational constant is constant and that the masses of the proton and the electron would increase while the gravitational constant would reduce over time. With this assumption, the author manages to explain the cosmic redshift without presupposing an expansion of the cosmos.
He presents an underlying relation between the fundamental natural constants, the Hubble constant and the two particle masses, which would describe in quantitative terms not just the beginning, but also – and this is what is momentously new about this model – the end of the universe as we know it. Via a mathematical link, the temporal change in the gravitational constant and the particle masses is described in relation to the Hubble constant. In this context, attention must also be paid to the way in which the change of the electron mass affects the definition of the SI units for length and time.
In addition, the author uses an analogy between magnetism and electricity in which the electron and the proton are considered as the two ends of an electrical dipole string. He develops a model for the elementary unit of the so-called dark matter through which the rotation characteristics of galaxies can be explained.
On the basis of this assumed fundamental relation, the author quantifies the mass and length of the supposed elementary electrets, thus estimating the number of elementary electrets that should cross a typical galaxy. With his model, the author is the first to design a concrete and compact proposal for solving the greatest mysteries of cosmology.

**Category:** Relativity and Cosmology

[812] **viXra:1403.0948 [pdf]**
*submitted on 2014-03-27 12:42:36*

**Authors:** Nigel B. Cook

**Comments:** 1 Page.

The occurrence of pi in formulae apparently unrelated to geometry was used by Eugene Wigner in his 1960 paper The unreasonable effectiveness of mathematics in the natural sciences. Wigner's example is the Gaussian/normal distribution law, which is an example of obfuscation. Laplace (1782), Gauss (1809), Maxwell (1860) and Fisher (1915) wrote the normal exponential distribution with the square root of pi in the normalization outside the integral. But Stigler in 1982 rewrote the equation with pi in the exponent, making the formula look less mysterious because the exponent is then the area of a circle (in other words, Poisson's exponential distribution, adapted to circular areas, with areas expressed in dimensionless form); if you think of the use of the normal distribution to model CEP error probabilities for missiles landing around a target point. (Please see paper for equations.)

**Category:** Statistics

[811] **viXra:1403.0947 [pdf]**
*submitted on 2014-03-27 08:07:08*

**Authors:** Hasmukh K. Tank

**Comments:** Seven-page-letter

The particle-interference-experiments, with the photons and electrons have clearly shown that they are always detected as localized ‘particles’; and the density of their detections exhibit a pattern similar to the interference of waves. This experimental-observation is now explained here, making the current, ‘probabilistic interpretation’, a past history. The ‘particle’ is first mathematically characterized as an ‘impulse function’ in space; and then Fourier-transformed into the wave-number-domain, as a wide band of constituent-waves as shown in the fig. 1&2. The ‘particle’ is explained as an ‘event’ of constructive-superimposition of a wide band of ‘pre-quantum-waves’. This ‘event’ occurs in space at regular distances; and at regular instances in time. We know that even the purest monochromatic laser source has a ‘line-width’ of a few Giga-Hertz, or at least a few kilo-Hertz. So in the particle-interference-experiments, they are these wide bands of waves which pass through both the slits, even in the case of single photon states, and interfere physically. This physical interference of the wide bands of pre-quantum-waves determines the position and time of emergence of the ‘particle’. Thus, form the theoretical view-point, there are only the waves, and waves alone; and the ‘particle’ is a specific situation of constructive-superimposition of all the spectral-components of pre-quantum-waves; so there is no wave-particle-duality.

**Category:** Quantum Physics

[810] **viXra:1403.0946 [pdf]**
*replaced on 2014-06-26 09:34:12*

**Authors:** Ray Hefferlin, Joshua Barrow

**Comments:** 20 Pages.

The objective of this work is to test whether vibration frequencies ν1 of free, ground-state, main-group triatomic molecules manifest a periodicity similar to those of atomic spectroscopic constants. This test and an earlier test on energies of atomization underscore the role of the periodic law as a foundation of chemistry. Using data from four data bases and from computation, we have collected and have mapped ν1 data in mathematical spaces of fixed-period molecules. These spaces are 8×8×8 atom cubes with rare-gas molecules on each face. The ν1 collected from various sources might be of use in searches for cold triatomics in interstellar space.

**Category:** Chemistry

[809] **viXra:1403.0945 [pdf]**
*submitted on 2014-03-27 09:46:20*

**Authors:** Yibing Qiu

**Comments:** 1 Page.

If there exists relationship between the “Zeeman effect” and “Stark effect”
with to “fine structure” and “hyperfine structure”.

**Category:** Nuclear and Atomic Physics

[808] **viXra:1403.0943 [pdf]**
*replaced on 2014-06-20 14:17:09*

**Authors:** Ray Hefferlin, Joshua Barrow

**Comments:** 20 Pages.

The objective of this work is to test whether vibration frequencies ν1 of free, ground-state, main-group triatomic molecules manifest a periodicity similar to those of atomic spectroscopic constants. This test and an earlier test on energies of atomization underscore the role of the periodic law as a foundation of chemistry. Using data from four data bases and from computation, we have collected and have mapped ν1 data in mathematical spaces of fixed-period molecules. These spaces are 8×8×8 atom cubes with rare-gas molecules on each face. The ν1 collected from various sources might be of use in optical or near-optical searches for cold triatomics in interstellar space.

**Category:** Chemistry

[807] **viXra:1403.0942 [pdf]**
*submitted on 2014-03-26 15:36:59*

**Authors:** A.Garcés Doz

**Comments:** 7 Pages.

Legendre’s conjecture, stated by Adrien-Marie Legendre ( 1752-1833 ), says there is always a prime between n2 and (n+1)2 . This conjecture is part of Landau’s problems. In this paper a proof of this conjecture is presented, using the method of generating prime numbers between consecutive squares, and proving that for every pair of consecutive squares with n >= 3 may be generated at least one prime number that belongs to the interval [n,(n+1)^2]

**Category:** Number Theory

[806] **viXra:1403.0941 [pdf]**
*replaced on 2014-03-30 09:16:38*

**Authors:** Florentin Smarandache

**Comments:** 96 Pages.

Dialoguri literare si stiintifice ale lui Florentin Smarandache cu Adrian Botez, Cora-Eliana Teodoru, Crenguţa Vişinescu, Eugen Evu, Alex Cetăţeanu, si Flavia Drăgan.
***
Literary and scientific dialogues of Florentin Smarandache with Adrian Botez, Cora-Eliana Teodoru, Crenguţa Vişinescu, Eugen Evu, Alex Cetăţeanu, and Flavia Drăgan.

**Category:** General Science and Philosophy

[805] **viXra:1403.0940 [pdf]**
*submitted on 2014-03-26 11:19:44*

**Authors:** Kailash Ch. Dash, Umakant Mishra

**Comments:** 13 Pages.

Although Information Systems and Information Technology (IS & IT) has become a major driving force for many of the current day organizations, the NGOs have not been able to utilize the benefits up to a satisfactory level. Most organizations use standard office tools to manage huge amount for field data and never feel the need for a central repository of data. While many people argue that an NGO should not spend too much money on information management, it is a fact that organizing the information requires more of a mindset and an organized behavior than a huge financial investment.

**Category:** Data Structures and Algorithms

[804] **viXra:1403.0939 [pdf]**
*submitted on 2014-03-26 07:30:09*

**Authors:** Raj C Thiagarajan

**Comments:** 5 Pages. An engineering proof to Beals Conjecture; This paper shows proof and highlights that finding a counter example is not possible due to the intrinsic nature of the equation which will have gcd greater than 1

In this paper, we provide computational results and a proof for Beal’s conjecture. We demonstrate that the common prime factor is intrinsic to this conjecture using the laws of powers. We show that the greatest common divisor is greater than 1 for the Beal’s conjecture.

**Category:** Number Theory

[803] **viXra:1403.0938 [pdf]**
*submitted on 2014-03-26 05:11:46*

**Authors:** Wan-Chung Hu

**Comments:** 43 Pages.

This study is to describe the defintion of space, time, light, and development of grand unified theories. Space has its smallest unit. Time is actually the inverse of unit space oscillation. Light is electromagnetic wave as well as gravitational wave. Light frequency can decicide unit space oscillation. By linking Stefan's law to Larmor formula, we can get a grand unified theory including electric field, magnetic field, gravity field(acceleration), momentity field(spinity/impelity filed)(angular momentum/linear momentum) and heat/temperature field. This equation is also the equation for heat-light transformation. Yukawa field can replace the electromagnetic fields to explain strong and weak force. Thus, all force fields are united!

**Category:** Relativity and Cosmology

[802] **viXra:1403.0937 [pdf]**
*submitted on 2014-03-26 07:13:03*

**Authors:** John R. Cipolla

**Comments:** 22 Pages.

A series of experiments and hydrodynamic analyses has been conducted to resolve the paradox that a viscous-flow distribution between concentric cylinders can be identical to a potential vortex (inviscid-flow) distribution at steady state. Where a potential vortex or tornado can be described as the flow around and through a drain hole at the bottom of a large container. As an approximation to this phenomenon, an experimental device to simulate a three dimensional potential vortex was fabricated that used a rapidly rotating central cylinder or rotating core located on the axis of a cylindrical basin filled with water. The fluid surface shape and velocity profile of an artificially generated potential vortex or free vortex was experimentally measured and compared with hydrodynamic models to define the viscid and inviscid nature of the potential vortex flow. A new program called VORTEX based on a finite difference solution of the Navier-Stokes equations was developed to determine the transient velocity profile and transient free surface shape of the potential vortex for comparison with experiment. From these experiments it is proposed the paradox is resolved because energy-momentum is conserved in a potential vortex under steady state conditions. This work can be applied to the measurement of the potential vortex flow generated by aircraft wing tips, interior flow of aircraft jet engines, rocket motor propellant tanks and natural phenomena like tornadoes, hurricanes and General Relativity.

**Category:** Classical Physics

[801] **viXra:1403.0936 [pdf]**
*submitted on 2014-03-25 21:57:34*

**Authors:** Pierre-Marie Robitaille

**Comments:** 5 Pages. First published in: Progress in Physics, 2014, v. 10(1), 116-120.

Kirchhoff’s law of thermal emission states that cavity radiation must always be black,
or normal, irrespective of the nature of the walls. Arbitrary cavity radiation must be
solely dependent upon the equilibrium temperature and the frequency of observation.
Despite such theoretical claims, it is well established that laboratory blackbodies are
not constructed from arbitrary materials, but rather from nearly perfect absorbers of
radiation over the frequency of interest. In the laboratory, arbitrary cavities do not
contain black radiation. This experimental fact stands in direct conflict with Kirchhoff’s
formulation. Nonetheless, Kirchhoff’s law of thermal emission endures, in part, due to
Gedanken experiments whose errors in logic are difficult to ascertain. In this work,
thought experiments are discussed in order to expose some logical shortcomings. It will
be demonstrated that Kirchhoff’s law cannot be supported in this context.

**Category:** Condensed Matter

[800] **viXra:1403.0935 [pdf]**
*replaced on 2014-12-26 16:34:37*

**Authors:** Pierre-Marie Robitaille

**Comments:** 2 Pages. First published in: Progress in Physics, 2014, v.2(10), 126-127 (revised December 26, 2014).

In this work, the equation which properly governs cavity radiation is presented. Given thermal equilibrium, the radiation contained within an arbitrary cavity depends upon the nature of its walls, in addition to its temperature and its frequency of observation. With this realization, the universality of cavity radiation collapses. The constants of Planck and Boltzmann can no longer be viewed as universal.

**Category:** Condensed Matter

[799] **viXra:1403.0934 [pdf]**
*replaced on 2015-12-29 04:15:12*

**Authors:** Sylwester Kornowski

**Comments:** 3 Pages.

Here, applying the Scale-Symmetric Theory (SST), we calculated sizes and described mechanism of production of the electron bubbles and the quantized vortices/twisters in liquid helium. Calculated size of the electron bubbles is 2.1 nm whereas of the twisters is of the order of an angstrom (0.1 nm). The mechanism of trapping the electron bubbles by the tangles-bundles composed of the quantized twisters (they are the cores of the electron bubbles) is described also. SST leads as well to electron bubbles with smaller core (4 times smaller) which exist at very low temperatures and explode at larger pressure. Such objects are referred to as the unidentified electron objects. Obtained results are consistent or very close to experimental data.

**Category:** Nuclear and Atomic Physics

[798] **viXra:1403.0932 [pdf]**
*submitted on 2014-03-25 12:17:13*

**Authors:** Barar Stelian Liviu

**Comments:** 9 Pages.

the method of determining if a number is prime up to a given number .

**Category:** Number Theory

[797] **viXra:1403.0931 [pdf]**
*submitted on 2014-03-24 16:51:30*

**Authors:** Mason A. Porter

**Comments:** 1 Page.

This note is my brief addendum to the opinion piece `Critical Truths About Power Laws' that Michael Stumpf and I published in 2012.

**Category:** General Mathematics

[796] **viXra:1403.0930 [pdf]**
*replaced on 2014-07-08 00:29:52*

**Authors:** Klinkerman R.V.

**Comments:** 3 Pages.

Annotation. An author considers that in DNA there can not be all information,
necessary for the construction of organism. It is suggested to consider a variant,
when complete information is contained in zero vibrations of birth-elimination of
microparticless, circumferential to organisms. On the gravity canals information is
passed to the center of Earth, where detailed pictures and classes of organisms are
formed. Center is provided by author with a capacity for creation, for participating in
the evolution of life. Informative connection of Center with organisms it is possible to
check experimentally.
Keywords: zero vibrations, microparticless, gravitation, information, Center,
creation, organisms, evolution.

**Category:** General Science and Philosophy

[795] **viXra:1403.0929 [pdf]**
*submitted on 2014-03-25 02:08:02*

**Authors:** Hasmukh K. Tank

**Comments:** Five-page-letter

While the experiments have shown similar wave-nature of matter-particles and photons, there are two different formulae for finding Relativistic-increase of energy of massive-particles and photons. This paper presents a unification of the two different formulae, in terms of Doppler-shifts of waves; leading to an insight that the ‘particles-of-matter’ seem to be the ‘standing-waves’; and de-Broglie’s ‘matter-waves’, and ‘quantum-mechanical-waves’ are ‘envelop-variations’ of the actual, more-fundamental waves.

**Category:** Quantum Physics

[794] **viXra:1403.0928 [pdf]**
*submitted on 2014-03-24 14:32:35*

**Authors:** Alexander Bolonkin

**Comments:** 20 Pages.

Designs of new forms of matter composed of nucleons (neutrons, protons), electrons, and other nuclear particles are detailed. This matter is measured in the femtometer (10-15 m) scale (“femtotechnology”), which is millions of times smaller than material on the nanometer (10-9 m) scale (“nanotechnology”). These new femto-needles, femto-tubes have extraordinary properties such as tensile strength, stiffness, hardness, critical temperature, superconductivity, super-transparency and zero friction. All of these properties are magnified millions of times in comparison to those of conventional molecular matter. Applications include concepts of design for aircraft, ships, transportation, thermonuclear reactors, constructions, and so on from nuclear matter. These vehicles will have unbelievable possibilities such as invisibility, ghost-like penetration through any walls and armor, protection from nuclear bomb explosions and any radiation flux.
But many readers asked about stability of the nuclear matter. It is well-known that the conventional nuclear matter having more than 92 protons or more than 238 nucleons became instable. In given work the author shows the special artificial forms of nuclear AB-matter which make its stability and give the fantastic properties. For example, by the offered AB-needle you can pierce any body without any damage, support motionless satellite, reach the other planet, and research Earth’s interior. These forms of nuclear matter are not in nature now, and nanotubes are also not in nature. That artificial matter is made by men. The AB-matter is also not natural now, but researching and investigating their possibility, stability and properties are necessary for creating them.

**Category:** Nuclear and Atomic Physics

[793] **viXra:1403.0927 [pdf]**
*replaced on 2014-10-14 00:19:16*

**Authors:** Yuri Heymann

**Comments:** 9 Pages.

The dichotomous cosmology is an alternative to the expanding Universe theory, and consists of a static matter Universe, where cosmological redshifts are explained by a tired-light model with an expanding luminous world. In this model the Hubble constant is also the photon energy decay rate, and the luminous world is expanding at a constant rate as in de Sitter cosmology for an empty Universe. The present model explains both the luminosity distance versus redshift relationship of supernovae Ia, and ageing of spectra observed with the stretching of supernovae light curves. Furthermore, it is consistent with a radiation energy density factor (1 + z)^4 inferred from the Cosmic Microwave Background Radiation.

**Category:** Astrophysics

[792] **viXra:1403.0926 [pdf]**
*replaced on 2014-06-22 10:34:14*

**Authors:** Shinsuke Hamaji

**Comments:** 11 Pages.

We know space expanding from the Hubble's law which Edwin Hubble and Milton Humason formulated first in 1929, and nearly 100 years passed, but Flat gravity caused by the expanding universe was covered in a short distance by Newtonian gravity according to inverse square law. It caused gravity anomalies such as the pioneer anomaly that a cause of the blue-shift indicating the slowdown to the sun direction is unclear as planetary probe pioneer 10-11 leaves the sun and the issue of galactic rotation curve which forms flat velocity distribution without rotational speed decreasing in galactic considerable penumbra known as physical unsolved problem. If expanding universe is premised, clause of the expansion that divided recession rate v=H0D in strain constant V0 is added, and Newtonian potential -GM/r(1) premising steady state cosmology be changes to -GM/r(1+v/V0). The clause of this expansion becomes constant G0=GH0/V0 which distance D and 1/r canceled and total gravitational mass of the universe M0=c3/(2GH0) which can be observed affects specific potential constant which multiplied gravitational mass for the observation and becomes -(G/r+G0)M. Flat gravity based on Hubble's law added to Newtonian gravity accords with the value of the gravity anomaly without assuming dark matter.

**Category:** Astrophysics

[791] **viXra:1403.0925 [pdf]**
*replaced on 2015-08-25 09:09:31*

**Authors:** Koji Nagata, Tadao Nakamura

**Comments:** 4 Pages. Open Access Library Journal, Volume 2 (2015), e1803/1--4, http://dx.doi.org/10.4236/oalib.1101803

We study about the metamathematics of Zermelo-Fraenkel set theory
with the axiom of choice.
We use the validity of Addition and Multiplication.
We provide an example that the two operations
Addition and Multiplication do not commute with each other.
All analyses are performed in a finite set of natural numbers.

**Category:** Mathematical Physics

[790] **viXra:1403.0924 [pdf]**
*submitted on 2014-03-24 08:59:31*

**Authors:** Koji Nagata, Tadao Nakamura

**Comments:** 4 pages

We discuss whether the
Stern-Gerlach experiment accepts hidden-variables theories.
We discuss that the existence of
two spin-1/2 pure states
$|\uparrow\rangle$ and $|\downarrow\rangle$ rules out
the existence of probability space of
specific quantum measurement.
If we detect $|\uparrow\rangle$, then measurement outcome is $+1$.
If we detect $|\downarrow\rangle$, then measurement outcome is $-1$.
This hidden-variables theory does not accept
the transition probability
$|\langle\uparrow|\downarrow\rangle|^2=0$.
Therefore we have to give up the hidden-variables theory.
This implies the Stern-Gerlach experiment cannot accept the specific
hidden-variables theory.
And we study whether quantum phase factor
accepts hidden-variables theories.
We use the transition probability for
two spin-1/2 pure states $(|\uparrow\rangle+|\downarrow\rangle)/\sqrt{2}$
and
$(|\uparrow\rangle+e^{i \theta}|\downarrow\rangle)/\sqrt{2}$.
It is $\cos^2(\theta/2)$.
We discuss that the phase factor does not accept another specific
hidden-variables theory.
We explore the phase factor is indeed a quantum effect, not classical.
Our research gives a new insight to the quantum information processing
which relies on quantum phase factor, such as Deutsch's algorithm.

**Category:** Quantum Physics

[789] **viXra:1403.0923 [pdf]**
*submitted on 2014-03-24 09:55:20*

**Authors:** Jeffrey Joseph Wolynski

**Comments:** 1 Page.

Since the Big Bang Model is a philosophically unsound construct violating cause and effect and laws of thermodynamics any deduction of the ages of stars based on it is also philosophically unsound. A seminal understanding is offered via stellar metamorphosis to replace it.

**Category:** Astrophysics

[788] **viXra:1403.0922 [pdf]**
*submitted on 2014-03-24 04:41:42*

**Authors:** Felice Russo

**Comments:** 8 Pages.

In this paper four Smarandache product sequences have been studied: Smarandache Square product sequence, Smarandache Cubic product sequence, Smarandache Factorial product sequence and Smarandache Palprime product sequence. In particular the number of primes, the convergence value for Smarandache Series, Smarandache Continued Fractions, Smarandache Infinite product of the mentioned sequences has been calculated utilizing the Ubasic software package. Moreover for the first time the notion of Smarandache Continued Radicals has been introduced. One conjecture about the number of primes contained in these sequences and new questions are posed too.

**Category:** General Mathematics

[787] **viXra:1403.0921 [pdf]**
*submitted on 2014-03-24 04:42:52*

**Authors:** Jozsef Sandor

**Comments:** 8 Pages.

The Smarandache function is a characterization of factorials...

**Category:** General Mathematics

[786] **viXra:1403.0920 [pdf]**
*submitted on 2014-03-24 04:45:12*

**Authors:** Clifford Singer

**Comments:** 3 Pages.

Of the branches of mathematics, geometry has, from the earliest Hellenic period, been given
a curious position that straddles empirical and exact science. Its standing Os an empirical and
approximate science stems from the practical pursuits of artistic drafting, land surveying and measuring in general.

**Category:** General Mathematics

[785] **viXra:1403.0919 [pdf]**
*submitted on 2014-03-24 07:18:57*

**Authors:** Richard L. Amoroso

**Comments:** 12 Pages. From 8th Vigier Symposium proceedings, "The Physics of Reality: Space, Time, Matter, Cosmos"

Newton claimed the influence of gravity is instantaneous; Einstein insisted no influence could propagate faster than the speed of light.
Recent experiments to test the speed of gravity have been controversial and inconclusive on technical grounds. Considerable effort is
currently expended in the search for a Quantum Gravity; but there is no a priori reason there should be one. We propose that is not the
regime of integration which instead occurs in the arena of the Unified Field, UF; further that a completed model of Geometrodynamics
inherently includes a Newton/Einstein duality which introduces shock effects in certain arenas. The unified theory predicts that there is
no graviton of the usual phenomenal form (an artifact of the incompleteness of Gauge Theory, i.e. gauge theory is only an approximation
suggesting new physics). A new Large Scale Additional Dimensional (LSXD) M-Theoretic topological charge alternative is presented.
We also attempt to show how the Titius-Bode Law for solar and exoplanetary configurations appears to provide indicia of this
multiverse gravitational model. Applications of the dual geometrodynamics formulation include an interpretation of quasar luminosity as
the result of gravitational shock waves in a manner countering explanations of large redshift, Z in Big Bang cosmology putatively based
on Doppler recession. Instead redshift occurs as the result of a periodic minute photon mass anisotropy caused by periodic coupling to a
covariant polarized Dirac vacuum.

**Category:** Relativity and Cosmology

[784] **viXra:1403.0918 [pdf]**
*replaced on 2015-04-29 22:11:31*

**Authors:** V.B. Smolenskii

**Comments:** 6 Pages.

Abstract: in may of this year will be published values of the fundamental physical constants (FPC), which CODATA recommended for international use. The article presents the predictive results of original theoretical research of the author in determining the numerical values of FPC, obtained using the analytical method of the PI-theory of the fundamental physical constants. Given a finite formulas and precise analytical results. Presents a table comparing the results of calculations with the data CODATA 2010.

**Category:** Nuclear and Atomic Physics

[783] **viXra:1403.0917 [pdf]**
*submitted on 2014-03-24 02:38:22*

**Authors:** Klinkerman R.V.

**Comments:** 6 Pages.

Abstract. An author considers that basic property of all living creatures is a
capacity for creation, that supposes the presence of consciousness, free will,
centralized structure. Drawn conclusion, that the indicated properties are inherent
not only biological objects but also microparticless, to the atoms. A man before
birth existed as an atom and will become such post mortem.
Key words: creation, consciousness, free will, centralization, electron, wave
function, atom, hypothalamus, information.

**Category:** General Science and Philosophy

[782] **viXra:1403.0915 [pdf]**
*submitted on 2014-03-24 03:08:10*

**Authors:** Zhong Li

**Comments:** 4 Pages.

In this paper we completely solve two questions concerning the divisor function and the pseudo - Smarandache function.

**Category:** General Mathematics

[781] **viXra:1403.0914 [pdf]**
*submitted on 2014-03-24 03:10:25*

**Authors:** E. Radescu

**Comments:** 4 Pages.

The Smarandache function and its principal properties are already known in the literature of speciality. Other functions were built
analogously, among which the following ones.

**Category:** General Mathematics

[780] **viXra:1403.0913 [pdf]**
*submitted on 2014-03-24 03:11:34*

**Authors:** E.Radescu, N.Radescu

**Comments:** 5 Pages.

The basic idee a of this paper is the algebraic construction of some functions representing prolongations of the Smarandache type functions to more complete sets already known and having specified properties.

**Category:** General Mathematics

[779] **viXra:1403.0912 [pdf]**
*submitted on 2014-03-24 03:13:12*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

There are an innumerable numbers of conjctures and WlSOlved problems in number theory predominantly on primes which have been giving sleepless nights to the mathematicians allover the world for centuries. Here are a few more to trouble them.

**Category:** General Mathematics

[778] **viXra:1403.0911 [pdf]**
*submitted on 2014-03-24 03:14:35*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

We have the well known result that n! divides the product of any set of consecutive numbers. Using this idea we define Smarandache LCM Ratio
Sequence...

**Category:** General Mathematics

[777] **viXra:1403.0910 [pdf]**
*submitted on 2014-03-24 03:16:10*

**Authors:** Marcela Popescu, Paul Popescu, Vasile Seleacu

**Comments:** 3 Pages.

In this pa.per we prove that the following numerical functions...

**Category:** General Mathematics

[776] **viXra:1403.0909 [pdf]**
*submitted on 2014-03-24 03:18:04*

**Authors:** M. Andrei, I. BaIaIcenoiu, C.Dumitrescu, V.Seleacu, L. Tutescu, St. Zanfir

**Comments:** 5 Pages.

On the method of ca1culus proposed by Florentin Smarandacbe...

**Category:** General Mathematics

[775] **viXra:1403.0907 [pdf]**
*submitted on 2014-03-24 03:20:39*

**Authors:** Emil Burton

**Comments:** 3 Pages.

The study of infinite series involving Smarandache function is one of the most interesting aspects of analysis.

**Category:** General Mathematics

[774] **viXra:1403.0906 [pdf]**
*submitted on 2014-03-24 03:21:50*

**Authors:** Henry Bottomley

**Comments:** 6 Pages.

This note considers eleven particular fimrilies of interrelated multiplicative functions, many of which are listed in Smarandache's problems.

**Category:** General Mathematics

[773] **viXra:1403.0905 [pdf]**
*submitted on 2014-03-24 03:24:21*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 2 Pages.

This new geometry is important because it generalizes and unites in the same time all together: Euclid, Lobachevsky/Bolyai/Gauss,
and Riemann geometries. And separates them as well!

**Category:** General Mathematics

[772] **viXra:1403.0904 [pdf]**
*submitted on 2014-03-24 03:25:21*

**Authors:** Fanel IACOBESCU

**Comments:** 4 Pages.

Thanks to C. Dumitrescu and Dr. V. Seleacu of the
University of Craiova, Department of Mathematics,
I became familiar with some of the Smarandache
Sequences. I list some of them, as well as questions
related to them. Now I'm working in a few conjectures involving these sequences.

**Category:** General Mathematics

[771] **viXra:1403.0903 [pdf]**
*submitted on 2014-03-24 03:26:33*

**Authors:** M.R. Popov

**Comments:** 3 Pages.

Let N be a positive integer with not all digits the same, and N' its digital reverse.

**Category:** General Mathematics

[770] **viXra:1403.0902 [pdf]**
*submitted on 2014-03-24 03:27:39*

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

First we need the following auxiliary proposition...

**Category:** General Mathematics

[769] **viXra:1403.0901 [pdf]**
*submitted on 2014-03-24 03:29:26*

**Authors:** Henry Ibstedt

**Comments:** 5 Pages.

It is shown that the sequence has an amusing oscillating behavior and that there are terms ...

**Category:** General Mathematics

[768] **viXra:1403.0900 [pdf]**
*submitted on 2014-03-24 03:31:04*

**Authors:** Emil Burton

**Comments:** 1 Page.

In this paper we define the S-Primality Degree of a Number, the S-Prime Numbers, and make some considerations on them.

**Category:** General Mathematics

[767] **viXra:1403.0899 [pdf]**
*submitted on 2014-03-24 03:40:35*

**Authors:** Felice Russo

**Comments:** 8 Pages.

In this paper, a problem posed in [1] by Smarandache concerning the prime gaps is analysed.

**Category:** General Mathematics

[766] **viXra:1403.0898 [pdf]**
*submitted on 2014-03-24 03:41:37*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let m be a positive integer with m > 1.

**Category:** General Mathematics

[765] **viXra:1403.0897 [pdf]**
*submitted on 2014-03-24 03:42:51*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we Smarandache factorial product sequence square 1.

**Category:** General Mathematics

[764] **viXra:1403.0896 [pdf]**
*submitted on 2014-03-24 03:44:23*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove that the Smarandache higeher power product sequences of the first kind and the second kind do not contain squares

**Category:** General Mathematics

[763] **viXra:1403.0895 [pdf]**
*submitted on 2014-03-24 03:45:34*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

The Smarandache Function is defined as Sen) = k . Where k is the smallest integer such that n divides k!

**Category:** General Mathematics

[762] **viXra:1403.0894 [pdf]**
*submitted on 2014-03-24 03:46:41*

**Authors:** Amarnath Murthy

**Comments:** 9 Pages.

Expression of unity as the sum of the reciprocals
of natural numbers is explored. And in this connection Smarandache Reciprocal partition of unity sets and sequences are defined. Some results and Inequalities are derived and a few open problems are proposed.

**Category:** General Mathematics

[761] **viXra:1403.0893 [pdf]**
*submitted on 2014-03-24 03:47:50*

**Authors:** Mihaly Bencze

**Comments:** 7 Pages.

Some Smarandache relationships between the terms of a given sequence are studied in the fIrst paragraph. In the second paragraph, are studied
Smarandache subsequences (whose terms have the same property as the initial sequence) . In the third paragraph are studied the Smarandache magic squares and cubes of order n and some conjectures in number
theory.

**Category:** General Mathematics

[760] **viXra:1403.0892 [pdf]**
*submitted on 2014-03-24 03:49:58*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let a1, a2 ,a3 ,... be a base sequence. We define a Smarandache Reverse Autocorrelated Sequence (SRACS) b1, b2 ,b3 ,... as follow...

**Category:** General Mathematics

[759] **viXra:1403.0891 [pdf]**
*submitted on 2014-03-24 03:50:53*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Consider a rectangular city with a mesh of tracks which are of equal length and which are either
horizontal or vertical and meeting at nodes.

**Category:** General Mathematics

[758] **viXra:1403.0889 [pdf]**
*submitted on 2014-03-24 03:53:30*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Absatract. Let p be a prime, and let k be a positive
integer. In this paper we prove that the Smarandache simple functions ...

**Category:** General Mathematics

[757] **viXra:1403.0888 [pdf]**
*submitted on 2014-03-24 03:55:32*

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

Let A be a Smarandache type sequence.
In this paper we show that if A is a positive integer sequence, then the simple continued fraction ... is convergent.

**Category:** General Mathematics

[756] **viXra:1403.0886 [pdf]**
*submitted on 2014-03-24 03:59:10*

**Authors:** I. Balacenoiu, Marcela Popescu, V. Seleacu

**Comments:** 7 Pages.

...is called the Smarandache square's complementary function.

**Category:** General Mathematics

[755] **viXra:1403.0885 [pdf]**
*submitted on 2014-03-24 04:00:49*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

The Significance of the above transfonnation will be clear when we consider the inverse transfonnation. It is evident that the star triangle is nothing but the Stirling Numbers ofthe Second kind ( Ref. [2] ).

**Category:** General Mathematics

[754] **viXra:1403.0884 [pdf]**
*submitted on 2014-03-24 04:02:19*

**Authors:** L. Seagull

**Comments:** 1 Page.

T. Yau proved that Smarandache function has the following property...

**Category:** General Mathematics

[753] **viXra:1403.0883 [pdf]**
*submitted on 2014-03-24 04:03:31*

**Authors:** J. Castillo

**Comments:** 3 Pages.

Inferior Smarandache Prime Part:
For any positive real number n one defines ISp(n) as the largest prime number less than or equal to n.

**Category:** General Mathematics

[752] **viXra:1403.0882 [pdf]**
*submitted on 2014-03-24 04:05:19*

**Authors:** E. Radescu, N. Radescu, C. Dumitrescu

**Comments:** 5 Pages.

It is sald that for every numerical function f it can be attashed the sumatory function.

**Category:** General Mathematics

[751] **viXra:1403.0881 [pdf]**
*submitted on 2014-03-24 04:06:24*

**Authors:** E.Radescu, N.Radescu

**Comments:** 3 Pages.

The sequence (1) is said to be a multiplicatively convergent to zero sequence (mcz) if:

**Category:** General Mathematics

[750] **viXra:1403.0880 [pdf]**
*submitted on 2014-03-24 04:08:18*

**Authors:** M. Andrei, C.Dumitrescu, E. RaIdescu, N. RaIdescu, V.Seleacu

**Comments:** 7 Pages.

From the definition it results that if...

**Category:** General Mathematics

[749] **viXra:1403.0879 [pdf]**
*submitted on 2014-03-24 04:10:13*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove that if the trailing
digit of a(n) is not zero for any n, then sum of
a(n)/Rev a(n)) is divergent.

**Category:** General Mathematics

[748] **viXra:1403.0878 [pdf]**
*submitted on 2014-03-24 04:11:16*

**Authors:** Henry Ibstedt

**Comments:** 6 Pages.

This is a simple study of expressions of positive integers as sums of consecutive integers.

**Category:** General Mathematics

[747] **viXra:1403.0877 [pdf]**
*submitted on 2014-03-24 04:12:16*

**Authors:** Felice Russo

**Comments:** 2 Pages.

In this paper a problem posed in [1J and concerning the number of primes in the Smarandache Unary sequence is analysed.

**Category:** General Mathematics

[746] **viXra:1403.0876 [pdf]**
*submitted on 2014-03-24 04:13:43*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let t be a positive integer with t> 1. In
this paper we give a necessary and sufficient condition for t to have the Smarandache uniform sequence.

**Category:** General Mathematics

[745] **viXra:1403.0875 [pdf]**
*submitted on 2014-03-24 04:14:51*

**Authors:** Jason WRIGHT

**Comments:** 5 Pages.

This brief paper was submitted as partial requirement for a Chemistry course. The topic was recommended to Dr. Kamala Sharrna.

**Category:** General Mathematics

[744] **viXra:1403.0874 [pdf]**
*submitted on 2014-03-24 04:16:08*

**Authors:** M. L. Perez

**Comments:** 2 Pages.

The American CRC Press, Boca Raton, Florida, published, in December 1998, a 2000 pages "CRC Concise Encyclopedia of Mathematics" , by Eric W. Weisstein.

**Category:** General Mathematics

[743] **viXra:1403.0873 [pdf]**
*submitted on 2014-03-24 04:17:38*

**Authors:** S.a. Yasinskiy, V.v. Shmagin, Y.v. Chebrakov

**Comments:** 13 Pages.

The system - graphical analysis results of some numerical Smarandache sequences are adduced. It is demonstrated that they possess of the big aesthetic.
cognitive and applied significance.

**Category:** General Mathematics

[742] **viXra:1403.0872 [pdf]**
*submitted on 2014-03-24 04:19:08*

**Authors:** Florian Luca

**Comments:** 9 Pages.

For every positive integer n let S(n) be the minimal positive integer m such that n I m !

**Category:** General Mathematics

[741] **viXra:1403.0871 [pdf]**
*submitted on 2014-03-24 04:23:39*

**Authors:** C. Dumitrescu, C. Rocsoreanu

**Comments:** 8 Pages.

From these properties we deduce that in fact on must consider....

**Category:** General Mathematics

[740] **viXra:1403.0870 [pdf]**
*submitted on 2014-03-24 04:24:39*

**Authors:** Zhu Weiyi

**Comments:** 3 Pages.

The main purpose of this paper is to study the asymptotic property of the divisor product sequences, and obtain two interesting asymptotic formulas.

**Category:** General Mathematics

[739] **viXra:1403.0869 [pdf]**
*submitted on 2014-03-24 04:25:58*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let S(a) be the Srnarandache function of a. In this paper we prove that the title equation has only the solution n= 1.

**Category:** General Mathematics

[738] **viXra:1403.0868 [pdf]**
*submitted on 2014-03-24 04:27:09*

**Authors:** Xigeng Chen

**Comments:** 2 Pages.

In this paper we prove that the residue sequence of Smarandache concatenated odd sequence mod 3 is periodical.

**Category:** General Mathematics

[737] **viXra:1403.0866 [pdf]**
*submitted on 2014-03-24 04:30:36*

**Authors:** Maohua Le

**Comments:** 2 Pages.

The number of distinct digits of n is called the length of Smarandache generalized period of n and denoted by Ig(n).

**Category:** General Mathematics

[736] **viXra:1403.0865 [pdf]**
*submitted on 2014-03-24 04:31:44*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we basically verify the third
Smarandache conjecture on prime.

**Category:** General Mathematics

[735] **viXra:1403.0864 [pdf]**
*submitted on 2014-03-24 04:33:03*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 6 Pages.

In the present note we prove the divergence of some series involving the Smarandache function, using an unitary method, and then we prove that the series...

**Category:** General Mathematics

[734] **viXra:1403.0863 [pdf]**
*submitted on 2014-03-24 04:33:57*

**Authors:** Charles Ashbacher

**Comments:** 5 Pages.

Welcome to the first installment of what is to be a regular feature in Smarandache Notions!

**Category:** General Mathematics

[733] **viXra:1403.0862 [pdf]**
*submitted on 2014-03-24 04:35:45*

**Authors:** Felice Russo

**Comments:** 3 Pages.

In this not we report the solution of an unsolved question on Smarandache Square-Partial-Digital Subsequence. We have found it by extesive computer search.

**Category:** General Mathematics

[732] **viXra:1403.0861 [pdf]**
*submitted on 2014-03-24 04:40:08*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 10 Pages.

The aim of this article is to introduce two functions and to give some simple properties for one of them. The function's properties are studied in connection v.ith the prime numbers. Finally, these functions are applied to obtain some inequalities concerning the Smarandache's function.

**Category:** General Mathematics

[731] **viXra:1403.0859 [pdf]**
*submitted on 2014-03-23 13:25:11*

**Authors:** Florian Luca

**Comments:** 2 Pages.

For any positive integer n let 5(n) be the minimal positive integer m.

**Category:** General Mathematics

[730] **viXra:1403.0857 [pdf]**
*submitted on 2014-03-23 13:27:30*

**Authors:** Amarnath Murthy

**Comments:** 5 Pages.

In [1] we define SMARANDACHE FACTOR
PARTITION FUNCTION, as follows:

**Category:** General Mathematics

[729] **viXra:1403.0856 [pdf]**
*submitted on 2014-03-23 13:29:14*

**Authors:** Ion Balacenoiu, Constantin Dumitrescu

**Comments:** 4 Pages.

The Smarandache functions of the second kind are defined in [1] thus:

**Category:** General Mathematics

[728] **viXra:1403.0855 [pdf]**
*submitted on 2014-03-23 13:30:30*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

Consider a chain having identical links (sticks) which can be bent at the hinges to give it
different shapes.

**Category:** General Mathematics

[727] **viXra:1403.0854 [pdf]**
*submitted on 2014-03-23 13:32:08*

**Authors:** Leonardo F. D. da Motta

**Comments:** 5 Pages.

In 1972 Smarandache proposed that there is not a limit speed on the Illlture, based on the EPR-Bell (Einstein, PodoLsky, Rosen, BeII) paradox. Although it appears that this paradox was solved recently, there are many other evidences that guide
us to believe that Smarandache Hypothesis is right on quanrum mechanics and even on the new unification theories.

**Category:** General Mathematics

[726] **viXra:1403.0853 [pdf]**
*submitted on 2014-03-23 13:33:05*

**Authors:** Henry Ibstedt

**Comments:** 14 Pages.

This paper deals with the analysis of a few Smarandache Integer Sequences which first appeared in Properties or the Numbers, F. Smarandache, University or Craiova Archives, 1975. The first four
sequences are recurrence generated sequences while the last three are concatenation sequences.

**Category:** General Mathematics

[725] **viXra:1403.0852 [pdf]**
*submitted on 2014-03-23 13:34:25*

**Authors:** Florian Luca

**Comments:** 2 Pages.

The Smarandache Irratioality Conjecture (see [lD claims:

**Category:** General Mathematics

[724] **viXra:1403.0851 [pdf]**
*submitted on 2014-03-23 13:35:29*

**Authors:** M.R. Mudge

**Comments:** 2 Pages.

The left-factorial function is defmed by D.Kurepa thus:

**Category:** General Mathematics

[723] **viXra:1403.0850 [pdf]**
*submitted on 2014-03-23 13:36:19*

**Authors:** Felice Russo

**Comments:** 3 Pages.

In this paper three problems posed in [1J and concerning the Smarandache LeM sequence have been analysed.

**Category:** General Mathematics

[722] **viXra:1403.0848 [pdf]**
*submitted on 2014-03-23 13:38:56*

**Authors:** Sabin Tabirca

**Comments:** 5 Pages.

The objective of this article is to investigate the existence of magic squares made with Smarandache's numbers [Tabirca, 1998]. Magic squares have been studied intensively and many aspects concerning them have been found.

**Category:** General Mathematics

[721] **viXra:1403.0847 [pdf]**
*submitted on 2014-03-23 13:40:26*

**Authors:** Raul Padilla

**Comments:** 3 Pages.

few notions are introduced in algebra in order to better study the congruences. Especially the Smarandache semigroups are very important
for the study of congruences.

**Category:** General Mathematics

[720] **viXra:1403.0846 [pdf]**
*submitted on 2014-03-23 13:43:11*

**Authors:** Muneer Jebreel Karama

**Comments:** 4 Pages.

In this article, I present the results of investigation of Smarandache Concatenate Magic Squares formed from the magic squares, and report some conjectures.

**Category:** General Mathematics

[719] **viXra:1403.0845 [pdf]**
*submitted on 2014-03-23 13:43:59*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

If the sum of any set of consecutive terms of a sequence = the product of the first and the last
number of the set then this pair is called a Smamdache Friendly Pair with respect to the
sequence.

**Category:** General Mathematics

[718] **viXra:1403.0843 [pdf]**
*submitted on 2014-03-23 13:45:48*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

We recall the definition of the Smarandache Function S(n): S(n) = the smallest positive integer such that S(n)! is divisible by n.

**Category:** General Mathematics

[717] **viXra:1403.0842 [pdf]**
*submitted on 2014-03-23 13:47:02*

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

An empirical study of Smarandache k-k additive
relationships and related data is tabulated and analyzed. It leads to the conclusion that the number of Smarandache 2-2 additive relations is infinite. It is also shown that Smarandache
k-k relations exist for large values ofk.

**Category:** General Mathematics

[716] **viXra:1403.0841 [pdf]**
*submitted on 2014-03-23 13:48:08*

**Authors:** Zhang Wenpeng

**Comments:** 6 Pages.

These sequences playa very important role in the studies of the theory and application of mathematics.

**Category:** General Mathematics

[715] **viXra:1403.0840 [pdf]**
*submitted on 2014-03-23 13:49:03*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Smarandache Maximum Reciprocal Representation
(SMRR) Function fsMRR(n) is defined as follows.

**Category:** General Mathematics

[714] **viXra:1403.0839 [pdf]**
*submitted on 2014-03-23 13:50:25*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 2 Pages.

All Euclid's five postulates are denied in this new geometry.

**Category:** General Mathematics

[713] **viXra:1403.0838 [pdf]**
*submitted on 2014-03-23 13:51:25*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

Given a sequence say Sb . We call it the base sequence.

**Category:** General Mathematics

[712] **viXra:1403.0837 [pdf]**
*submitted on 2014-03-23 13:52:20*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove that A(a,n) is a
Smarandache semigroup.

**Category:** General Mathematics

[711] **viXra:1403.0836 [pdf]**
*submitted on 2014-03-23 13:54:11*

**Authors:** Leonardo F. D. da Motta

**Comments:** 2 Pages.

Studying solutions of Maxwell and Dirac-Weyl equations, Waldyr Rodrigues Jr. and Jose Maiorino were able to propose a full-unified theory for
constructing of arbitrary speeds in nature...

**Category:** General Mathematics

[710] **viXra:1403.0835 [pdf]**
*submitted on 2014-03-23 13:55:18*

**Authors:** Maohua Le

**Comments:** 3 Pages.

In this paper, under the Smarandache algorithm ,we construct a class of commutative multiplicative semigroups.

**Category:** General Mathematics

[709] **viXra:1403.0834 [pdf]**
*submitted on 2014-03-23 13:56:27*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let n be a positive integer with n > 1 .
In this paper we prove that the remaining sequence of Smarandache n-ary sieve contains infinitely many composite numbers.

**Category:** General Mathematics

[708] **viXra:1403.0833 [pdf]**
*submitted on 2014-03-23 13:57:44*

**Authors:** Henry Ibstedt

**Comments:** 2 Pages.

The values of S(n) for n < 32000 are input from the file SN.DA T and the number of values falling
into each square of a 40 x 40 matrix are counted and displayed in a graph. An interresting
pattern is formed by large primes while the bottom layer mainly resulting form composite
numbers requires two lines in the graph.

**Category:** General Mathematics

[707] **viXra:1403.0832 [pdf]**
*submitted on 2014-03-23 13:58:57*

**Authors:** M. R. Mudge

**Comments:** 1 Page.

A number, q, is said to be near to prime if and only if either q+ I or q-l are primes it is said to be themean-of-a-prime-pair if and only if both q+ I and q-l are prime.

**Category:** General Mathematics

[706] **viXra:1403.0831 [pdf]**
*submitted on 2014-03-23 14:01:59*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 1 Page.

In the present note wesolve two diophantine eqations concerning the Smarandache function.

**Category:** General Mathematics

[705] **viXra:1403.0830 [pdf]**
*submitted on 2014-03-23 14:04:07*

**Authors:** Pal Gronas

**Comments:** 3 Pages.

This problem is closely connected to Problem 29916 in the first issue of the "Smarandache Function Journal".

**Category:** General Mathematics

[704] **viXra:1403.0829 [pdf]**
*submitted on 2014-03-23 10:14:21*

**Authors:** Micha Fleuren

**Comments:** 35 Pages.

This document will describe the current status on the search for factors of Smarandache consecutive numbers and their reverse.

**Category:** General Mathematics

[703] **viXra:1403.0828 [pdf]**
*submitted on 2014-03-23 10:15:37*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Russo's conjecture, prime, gap, Smarandache
constant.

**Category:** General Mathematics

[702] **viXra:1403.0827 [pdf]**
*submitted on 2014-03-23 10:16:38*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Abstract. Let k be an arbitrary large positive integer.

**Category:** General Mathematics

[701] **viXra:1403.0826 [pdf]**
*submitted on 2014-03-23 10:17:42*

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The function S is known as the Smarandache function and is defmed in the following way.

**Category:** General Mathematics

[700] **viXra:1403.0825 [pdf]**
*submitted on 2014-03-23 10:18:42*

**Authors:** Anthony Begay

**Comments:** 3 Pages.

In this paper some defmitions, examples and conjectures are exposed related to the Smarandache type functions, found in the Archives of the Arizona State University, Tempe, USA Special Collections.

**Category:** General Mathematics

[699] **viXra:1403.0824 [pdf]**
*submitted on 2014-03-23 10:19:57*

**Authors:** Leonardo Rubino

**Comments:** 22 Pages.

The cosmological constant as the biggest blunder of Einstein? I don’t think so. As I already said many times, his biggest blunder was that of taking into consideration a real fourth dimension. The Universe is three dimensional and will go on being so. All fourth components of relativity are those of the (three dimensional) falling towards the center of mass of the Universe. Below you can find the overwhelming proof from the well established atomic physics! Moreover, they go on supporting their full of holes Universe, with fourth dimensions, dark matter and energy, multidimensionality, multiple Universes (??), expansion contradicted by observations etc… My harmonic and oscillating Universe leads to a harmonic and oscillation based deduction of the Special Theory of Relativity and also of its extension (“Other Relativity”). Well, here below the overwhelming proof from the well established atomic physics!

**Category:** Nuclear and Atomic Physics

[698] **viXra:1403.0823 [pdf]**
*submitted on 2014-03-23 10:21:30*

**Authors:** Marcela Popescu, Vasile Seleacu

**Comments:** 11 Pages.

The function defined by the condition that n + c ( n ) = P, ...

**Category:** General Mathematics

[697] **viXra:1403.0821 [pdf]**
*submitted on 2014-03-23 12:49:21*

**Authors:** Helen Marirnutha

**Comments:** 2 Pages.

Professor Anthony Begay of Navajo Community College influenced me in writing this paper. I enjoyed the Smarandache concatenation. The sequences shown here have been extracted from the Arizona State University(Tempe) Archives. They are defmed as
follows:

**Category:** General Mathematics

[696] **viXra:1403.0820 [pdf]**
*submitted on 2014-03-23 12:52:45*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let d(a) denote the figure number of a in the decimal system.

**Category:** General Mathematics

[695] **viXra:1403.0819 [pdf]**
*submitted on 2014-03-23 12:55:37*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Then sequence C (A) ={ c} is called the Smarandache concatenated sequence of A.

**Category:** General Mathematics

[694] **viXra:1403.0818 [pdf]**
*submitted on 2014-03-23 12:56:37*

**Authors:** Felice Russo

**Comments:** 22 Pages.

In this paper some Smarandache conjectures and open questions will be analysed. The first three conjectures are related to prime numbers and formulated by F.

**Category:** General Mathematics

[693] **viXra:1403.0817 [pdf]**
*submitted on 2014-03-23 12:57:53*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Then the continued fraction is called a Smarandache general continued fraction associated with A
and B (see [1]).

**Category:** General Mathematics

[692] **viXra:1403.0816 [pdf]**
*submitted on 2014-03-23 12:59:02*

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

The theory of general continued fractions is developed to the extent required in order to calculate Smarandache continued fractions to a given number of decimal places. Proof is given for the fact that Smarandache general continued fractions built with positive integer Smarandache sequences baving only a finite number of terms equal to 1 is convergent. A few numerical results are given.

**Category:** General Mathematics

[691] **viXra:1403.0815 [pdf]**
*submitted on 2014-03-23 13:00:06*

**Authors:** Jose Castillo

**Comments:** 3 Pages.

Open problems are studied using Smarandache type sequences in the composition of simple and general continued fractions.

**Category:** General Mathematics

[690] **viXra:1403.0814 [pdf]**
*submitted on 2014-03-23 13:01:56*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 2 Pages.

All three axiom of the projective geometry are denied in this new geometry.

**Category:** General Mathematics

[689] **viXra:1403.0813 [pdf]**
*submitted on 2014-03-23 13:02:54*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In this note two types of Smarandache type determinant sequences are defined and studied.

**Category:** General Mathematics

[688] **viXra:1403.0812 [pdf]**
*submitted on 2014-03-23 13:04:03*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give a formula for Smarandache
divisor products.

**Category:** General Mathematics

[687] **viXra:1403.0811 [pdf]**
*submitted on 2014-03-23 13:05:03*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In the rising factorial (x+ 1) (x+2)(x+3) ... (x+n) , the coefficients of different powers ofx are the
absolute values of the Stirling numbers of the first kind. REF[1].

**Category:** General Mathematics

[686] **viXra:1403.0810 [pdf]**
*submitted on 2014-03-23 13:06:05*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 2 Pages.

Smarandache function is an irrational number (second constant of Smarandache).

**Category:** General Mathematics

[685] **viXra:1403.0809 [pdf]**
*submitted on 2014-03-23 13:08:30*

**Authors:** Tl3Ilg Zhengping, Xu Kanghua

**Comments:** 7 Pages.

A Smarandache sequence is studied completely in the first paragraph both Smarandache square-digital and partial-digital subsequence are studied.

**Category:** General Mathematics

[684] **viXra:1403.0808 [pdf]**
*submitted on 2014-03-23 13:10:09*

**Authors:** Ion Balacenoiu

**Comments:** 8 Pages.

Let p be a prime number.

**Category:** General Mathematics

[683] **viXra:1403.0806 [pdf]**
*submitted on 2014-03-23 13:21:16*

**Authors:** Shyam Sunder Gupta

**Comments:** 5 Pages.

In this article, we present the resuhs of investigation of Smarandache Concatenate Sequence
formed from the sequence of Happy Numbers and report some primes and other results fOlmd
from the sequence.

**Category:** General Mathematics

[682] **viXra:1403.0805 [pdf]**
*submitted on 2014-03-23 13:22:15*

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

A large number of sequences which originate from F. Smarandache or are of similar nature appear scattered in various notes and papers.

**Category:** General Mathematics

[681] **viXra:1403.0804 [pdf]**
*submitted on 2014-03-23 13:23:05*

**Authors:** Sebastian Martin Ruiz

**Comments:** 4 Pages.

This article lets out a law of recurrence in order to obtain the sequence of prime numbers.

**Category:** General Mathematics

[680] **viXra:1403.0803 [pdf]**
*submitted on 2014-03-23 07:29:29*

**Authors:** Steven R Finch

**Comments:** 2 Pages.

Given a positive integer n, let P(n) denote the largest prime factor of nand S(n) denote the
smallest integer m such that n divides m!

**Category:** General Mathematics

[679] **viXra:1403.0802 [pdf]**
*submitted on 2014-03-23 07:31:13*

**Authors:** M. E. Basher

**Comments:** 7 Pages.

A Smarandache k-tiling of the plane is a family of sets called k-tiles covering each point in the plane exactly k times.

**Category:** General Mathematics

[678] **viXra:1403.0801 [pdf]**
*submitted on 2014-03-23 07:32:23*

**Authors:** Ion Balacenoiu

**Comments:** 7 Pages.

Smarandache functions offirst kind are defined in (1) thus:

**Category:** General Mathematics

[677] **viXra:1403.0800 [pdf]**
*submitted on 2014-03-23 07:33:21*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP), as follows:

**Category:** General Mathematics

[676] **viXra:1403.0799 [pdf]**
*submitted on 2014-03-23 07:34:24*

**Authors:** Zhang Xiaobeng

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the m-power complement numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[675] **viXra:1403.0796 [pdf]**
*submitted on 2014-03-23 07:38:15*

**Authors:** Liu Yanni

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache multiplicative function, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[674] **viXra:1403.0794 [pdf]**
*submitted on 2014-03-23 07:40:12*

**Authors:** Jin Zhang, Pei Zhang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and the analytic methods
to study the mean value properties of a Smarandache multiplicative function, and give two
sharper asymptotic formulae for it.

**Category:** General Mathematics

[673] **viXra:1403.0793 [pdf]**
*submitted on 2014-03-23 07:41:22*

**Authors:** Lin Cheng

**Comments:** 4 Pages.

For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer k ...

**Category:** General Mathematics

[672] **viXra:1403.0792 [pdf]**
*submitted on 2014-03-23 07:42:35*

**Authors:** Xuhui Fan, Chengliang Tian

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of the function Zw(Z(n)), and give a sharper mean value formula for it.

**Category:** General Mathematics

[671] **viXra:1403.0790 [pdf]**
*submitted on 2014-03-23 07:45:06*

**Authors:** A. W. Vyawahare, K. M. Purohit

**Comments:** 20 Pages.

Near Pseudo Smarandache Function ( NPSF) K is defined as follows...

**Category:** General Mathematics

[670] **viXra:1403.0789 [pdf]**
*submitted on 2014-03-23 07:47:21*

**Authors:** Jozsef Sandor

**Comments:** 8 Pages.

Al and A3, A3 lies between A2 and A1, etc. and the
segments AAI, AIA2, A2A3, A3A4, ... are congruent to one another.
Then, among this series of points, not always there exists a certain point An such that B lies between A and An.

**Category:** General Mathematics

[669] **viXra:1403.0788 [pdf]**
*submitted on 2014-03-23 07:48:43*

**Authors:** Krassimir Atanassov, Hristo Aladjov

**Comments:** 6 Pages.

On an Example with a Smarandache Problem

**Category:** General Mathematics

[668] **viXra:1403.0787 [pdf]**
*submitted on 2014-03-23 07:50:29*

**Authors:** Angela Vasiu

**Comments:** 2 Pages.

Are remarked the new Geometries of Smarandache and it is given a relationship and an application of Smarandache Paradoxist Geometry to the ammejioration of human condition by a better understanding of ourselves and of others.

**Category:** General Mathematics

[667] **viXra:1403.0786 [pdf]**
*submitted on 2014-03-23 07:51:44*

**Authors:** Mihaly Bencze

**Comments:** 1 Page.

Let S be the Smarandache Function...

**Category:** General Mathematics

[666] **viXra:1403.0785 [pdf]**
*submitted on 2014-03-23 07:53:25*

**Authors:** G.l Waghmare, S.v. More

**Comments:** 3 Pages.

The aoditive identity of this linear space has nonzero components.

**Category:** General Mathematics

[665] **viXra:1403.0784 [pdf]**
*submitted on 2014-03-23 07:56:01*

**Authors:** Zhang Wenpeng

**Comments:** 4 Pages.

Let n be any positive integer, a(n) denotes the product of all non-zero digits in base 10.

**Category:** General Mathematics

[664] **viXra:1403.0783 [pdf]**
*submitted on 2014-03-23 07:57:29*

**Authors:** Kevin Ford

**Comments:** 6 Pages.

Let S(n) be the smallest integer k so that nIk!. This is known as the Smarandache function and has been studied by many authors.

**Category:** General Mathematics

[663] **viXra:1403.0782 [pdf]**
*submitted on 2014-03-23 07:59:15*

**Authors:** Mladen V. Vassilev - Missaha, Krassimir T. Atanassov

**Comments:** 5 Pages.

The solving of the Diophantine equation...

**Category:** General Mathematics

[662] **viXra:1403.0781 [pdf]**
*submitted on 2014-03-23 08:00:24*

**Authors:** Charles Ashbacher

**Comments:** 4 Pages.

In a brief paper passed on to the author[I], Michael R. Mudge used the definition of the
Primorial function.

**Category:** General Mathematics

[661] **viXra:1403.0780 [pdf]**
*submitted on 2014-03-23 08:01:38*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In [1] we define SMARANDACHE FACTOR PARTITION FUNCTION@@ (SFP) , as follows...

**Category:** General Mathematics

[660] **viXra:1403.0779 [pdf]**
*submitted on 2014-03-23 08:02:54*

**Authors:** A.A.K. Majumdar

**Comments:** 6 Pages.

This paper gives some properties of the Smarandache prime product sequence,(Pn ) , definded by...

**Category:** General Mathematics

[659] **viXra:1403.0778 [pdf]**
*submitted on 2014-03-23 08:05:17*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this note we discuss the primes in Smarandache
progressIons.

**Category:** General Mathematics

[658] **viXra:1403.0777 [pdf]**
*submitted on 2014-03-23 08:06:19*

**Authors:** Dviraj Talukdar

**Comments:** 8 Pages.

The notions of the Snmarandache group and the Smarandache Boolean ring are introduced here with the help of group action and ring action i.e. module respectively. The centre of the Smarandache groupoid is determined. These are very important for the study of Algebraic structures.

**Category:** General Mathematics

[657] **viXra:1403.0776 [pdf]**
*submitted on 2014-03-23 08:08:50*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Pseudo-Smarandache function was introduced by Kenichiro Kashihara in a book that is highly recommended.

**Category:** General Mathematics

[656] **viXra:1403.0775 [pdf]**
*submitted on 2014-03-23 08:09:59*

**Authors:** K. R. S. Sastry

**Comments:** 3 Pages.

Given a triangle in Euclidean geometry it is well known that there exist an infinity of triangles each of which is similar to the given one.

**Category:** General Mathematics

[655] **viXra:1403.0773 [pdf]**
*submitted on 2014-03-23 08:47:56*

**Authors:** Lru HONGYAN, Zhang Wenpeng

**Comments:** 5 Pages.

Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factorization of n!.

**Category:** General Mathematics

[654] **viXra:1403.0772 [pdf]**
*submitted on 2014-03-23 08:50:31*

**Authors:** Delfim F. M. Torres

**Comments:** 5 Pages.

Dando jus a matematica experimental, mostrarnos como 0 Maple pode ser usado na investigagao matematica de alg-wnas quest5es actualmente sern
resposta na Teoria dos Nlimeros. A tese defendida e que os alunos de urn curso de Matematica podem facilrnente usar a computador como urn lugar
ende Be excita e exercita a imaginacao.

**Category:** General Mathematics

[653] **viXra:1403.0770 [pdf]**
*submitted on 2014-03-23 08:51:45*

**Authors:** I. Balacenoiu, D. Bordea, V. Seleacu

**Comments:** 6 Pages.

This functions have the next properties...

**Category:** General Mathematics

[652] **viXra:1403.0768 [pdf]**
*submitted on 2014-03-23 08:54:40*

**Authors:** Zhu Weiyi

**Comments:** 4 Pages.

The main purpose of this paper is to study the distribution properties of k~power free numbers and k~power complement numbers, and give an interesting asymptotic formula.

**Category:** General Mathematics

[651] **viXra:1403.0767 [pdf]**
*submitted on 2014-03-23 08:56:35*

**Authors:** Sabin TABIRCA, Tatiana TABIRCA

**Comments:** 8 Pages.

The study of primality for the Smarandache sequences represents a recent research direction on the Smarandache type notions. A few articles that were published recently deal with the primality of the direct and reverse Smarandache sequences. The primality of Smarandache symmetric sequences has not been studied yet. This article proposes some results concerning the non-primality of these symmetric sequences and presents some interesting conclusions on a large computational test on these.

**Category:** General Mathematics

[650] **viXra:1403.0766 [pdf]**
*submitted on 2014-03-23 08:58:07*

**Authors:** Leonardo F. D. da Motta

**Comments:** 2 Pages.

The Smarandache Paradox is a very interesting paradox of logic because it has a background common sense. However, at the same time, it gets in a contradiction with itself. Although it may appear well cohesive, a careful look on the science definition and some logic can break down this paradox showing that it exist only when we are trying to mix two different universes, where in one we have two possibilities and in the other we have only one. When we try to understand the second possibility in the universe which has only one possibility, we end in the Smarandache Paradox.

**Category:** General Mathematics

[649] **viXra:1403.0765 [pdf]**
*submitted on 2014-03-23 08:59:18*

**Authors:** Zhang Wenpeng

**Comments:** 3 Pages.

The main purpose of this paper is to prove that there is only one prime among the symmetric sequence.

**Category:** General Mathematics

[648] **viXra:1403.0764 [pdf]**
*submitted on 2014-03-23 09:00:24*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

In general, in how many ways a number can be expressed as the product of its divisors?

**Category:** General Mathematics

[647] **viXra:1403.0763 [pdf]**
*submitted on 2014-03-23 09:01:25*

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Let Sen) be the Smarandache function. I propose the following open questions...

**Category:** General Mathematics

[646] **viXra:1403.0762 [pdf]**
*submitted on 2014-03-23 09:02:53*

**Authors:** Henry Ibstedt

**Comments:** 13 Pages.

This article ongmates from a proposal by M. L. Perez of American Research Press to carry out a study on Smarandache generalized palindromes [1]. The prime numbers were chosen as a fIrst )set of numbers to apply the development of ideas and computer programs on. The study begins by exploring regular pritlle number palindromes. To continue the study it proved useful to introduce a new concept, that of extended palindromes with the property that the union of regular
palindromes and extended palindromes form the set of Smarandache generalized palindromes. An interesting observation is proved in the article, namely that the only regular prime number palindrome with an even number of digits is 11.

**Category:** General Mathematics

[645] **viXra:1403.0761 [pdf]**
*submitted on 2014-03-23 09:03:58*

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

A number is said to be a palindrome if it reads the same forwards and backwards.

**Category:** General Mathematics

[644] **viXra:1403.0760 [pdf]**
*submitted on 2014-03-23 09:07:38*

**Authors:** Feng Liu

**Comments:** 4 Pages.

I came across one of the Smarandache divine paradoxes and felt very strongly that it is really our Buddhist's obligation to help understand the underlying truth. There seem a lot of toughest points in the cultural difference and it will be the most dificult job to reach the mutual point as neutrality. What I can do is to try our
best and find cooperation. Limited to the time, I just put a few as my first review.

**Category:** General Mathematics

[643] **viXra:1403.0759 [pdf]**
*submitted on 2014-03-23 09:10:04*

**Authors:** M. R. Mudge

**Comments:** 3 Pages.

Described by Charles T. Le as "The most paradoxist mathematician oF the world"

**Category:** General Mathematics

[642] **viXra:1403.0758 [pdf]**
*submitted on 2014-03-23 09:11:14*

**Authors:** Howard Iseri

**Comments:** 8 Pages.

paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into one space along with other non-Euclidean behaviors oflines that would seem to require a discrete space. A
class of continuous spaces is presented here together with specific examples that emibit almost all of these phenomena and suggest the prospect of a continuous paradoxist geometry.

**Category:** General Mathematics

[641] **viXra:1403.0757 [pdf]**
*submitted on 2014-03-23 09:12:29*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 8 Pages.

This article presents an application of the inferior Smarandache f-part function to a particular parallel loop-scheduling problem. The product between an upper diagonal matrix and a vector is analysed from parallel computation
point of view. An efficient solution for this problem is given by using the inferior Smarandache I-part function. Finally, the efficiency of our solution is proved experimentally by presenting some computational results.

**Category:** General Mathematics

[640] **viXra:1403.0756 [pdf]**
*submitted on 2014-03-23 09:13:24*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Smarandache's function may be defined as follows...

**Category:** General Mathematics

[639] **viXra:1403.0755 [pdf]**
*submitted on 2014-03-23 09:14:59*

**Authors:** Florian Luca

**Comments:** 18 Pages.

The proof of Theorem 1 is based on an idea of Lang

**Category:** General Mathematics

[638] **viXra:1403.0754 [pdf]**
*submitted on 2014-03-23 09:16:01*

**Authors:** Kejian Wu, Maohua Le

**Comments:** 2 Pages.

Let n be positive integer, and let sen) denote the
n-th Smarandache concatenated squre number.

**Category:** General Mathematics

[637] **viXra:1403.0752 [pdf]**
*submitted on 2014-03-23 09:18:16*

**Authors:** Henry Ibstedt

**Comments:** 10 Pages.

This paper is based on an article in Mathematical Spectru.m, VoL 29, No 1. It concerns what happens
when an operation applied to an n-digit integer results in an n digit integer. Since the number of ndigit integers is finite a repetition must occur after applying the operation a finite number of times. It was assumed in the above article that this would lead to a periodic sequence which is not always true because the process may lead to an invariant. The second problem with the initial article is that, say, 7
is considered as 07 or 007 as the case may be in order make its reverse to be 70 or 700. However, the reverse of 7 is 7. In order not to loose the beauty of these sequences the author has introduced stringent definitions to prevent the sequences from collapse when the reversal process is carried out.

**Category:** General Mathematics

[636] **viXra:1403.0751 [pdf]**
*submitted on 2014-03-23 09:19:37*

**Authors:** Zhang Wenpeng

**Comments:** 2 Pages.

The main purpose of this paper is to prove that there is no any perfect power among the permutation sequence...

**Category:** General Mathematics

[635] **viXra:1403.0750 [pdf]**
*submitted on 2014-03-23 09:20:33*

**Authors:** Maohua Le

**Comments:** 3 Pages.

Let P and Q denote the Smarandache cubic product sequences of the first kind and the second
kind respectively. In this paper we prove that P
contains only one power 9 and Q does not contain
any power.

**Category:** General Mathematics

[634] **viXra:1403.0749 [pdf]**
*submitted on 2014-03-23 09:21:33*

**Authors:** Felice Russo

**Comments:** 3 Pages.

In this paper the solution of two problems posed in [IJ and concerning the Smarandache Lucas-partial subsequence and the Smarandache Fibonacci-partial subsequence is reported.

**Category:** General Mathematics

[633] **viXra:1403.0748 [pdf]**
*submitted on 2014-03-23 09:22:28*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Let I s consider the function d(i) = number of divisors of the positive integer number i. We have found the following expression for this function:

**Category:** General Mathematics

[632] **viXra:1403.0747 [pdf]**
*submitted on 2014-03-23 09:23:45*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Smarandache power product sequence, fIrst
kind, prime.

**Category:** General Mathematics

[631] **viXra:1403.0745 [pdf]**
*submitted on 2014-03-23 09:25:50*

**Authors:** Maohua Le, Kejian Wu

**Comments:** 2 Pages.

For any positive integer k, let Ak be the Smarandache k -power product sequence.

**Category:** General Mathematics

[630] **viXra:1403.0744 [pdf]**
*submitted on 2014-03-23 09:26:50*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we completely determine the primes in the Smarandache power product sequences of the second kind.

**Category:** General Mathematics

[629] **viXra:1403.0743 [pdf]**
*submitted on 2014-03-23 09:28:03*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Smarandache symmetric sequence. In this paper we prove that if n is an even integer...

**Category:** General Mathematics

[628] **viXra:1403.0742 [pdf]**
*submitted on 2014-03-23 09:31:47*

**Authors:** Marcela Popescu, Paul Popescu

**Comments:** 5 Pages.

In our paper we prove that the 5marandache function S does not verify the Lipschitz condition, giving an answer to a problem proposed in (2] and we investigate also tbe possibility that some other functions, which involve the function S, verify
the Lipschitz condition.

**Category:** General Mathematics

[627] **viXra:1403.0741 [pdf]**
*replaced on 2015-07-21 10:58:36*

**Authors:** Koji Nagata, Tadao Nakamura

**Comments:** Journal of Applied Mathematics and Physics, Volume 3, No.7 (2015), Page 874--897.

We discuss the fact that there is a crucial contradiction within
Von Neumann's theory.
We derive a proposition concerning
a quantum expected value under an assumption of the existence
of the orientation of reference frames in
$N$ spin-1/2 systems ($1 \leq N < +\infty$). This assumption
intuitively depictures our physical world.
However, the quantum predictions within the formalism
of Von Neumann's projective measurement
violate the proposition with a magnitude that grows
exponentially with the number of particles.
We have to give up either the existence
of the directions or the formalism of Von Neumann's
projective measurement.
Therefore, Von Neumann's theory cannot depicture our
physical world with a violation factor that
grows exponentially with the number of particles.
The theoretical formalism of the implementation of
the Deutsch-Jozsa algorithm relies on Von Neumann's theory.
We investigate whether Von Neumann's theory meets the Deutsch-Jozsa algorithm.
We discuss the fact that the crucial contradiction
makes the quantum-theoretical formulation of Deutsch-Jozsa algorithm
questionable.
Further, we discuss the fact that projective measurement theory does
not meet an easy detector model for a single Pauli observable.
Especially, we systematically
describe our assertion
based on more mathematical analysis using raw data.
We propose a solution of the problem.
Our solution is equivalent to changing Planck's constant ($\hbar$) to a
new constant ($\hbar/\sqrt{2}$).
It may be said that a new type of the quantum theory early
approaches Newton's theory in the macroscopic scale
than the old quantum theory does.
We discuss how our solution is used in an implementation of
Deutsch's algorithm.

**Category:** Quantum Physics

[626] **viXra:1403.0740 [pdf]**
*submitted on 2014-03-23 09:32:49*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

Welcome to the inaugural version of what is to be a regular feature in Smarandache Notions!

**Category:** General Mathematics

[625] **viXra:1403.0739 [pdf]**
*submitted on 2014-03-23 09:34:12*

**Authors:** Florian Luca

**Comments:** 13 Pages.

Jose Castillo (see [2]) asks how many primes are of the Smarandache form...

**Category:** General Mathematics

[624] **viXra:1403.0738 [pdf]**
*submitted on 2014-03-23 09:35:03*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

Smarandache Distinct Reciprocal partition of unity for a given length '0' is defined as the number of ways in which unity can be expressed as the sum of
the reciprocals of '0' distinct numbers.

**Category:** General Mathematics

[623] **viXra:1403.0737 [pdf]**
*submitted on 2014-03-23 09:36:07*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

In [1] we have defined Pascalisation as follows:

**Category:** General Mathematics

[622] **viXra:1403.0736 [pdf]**
*submitted on 2014-03-23 09:37:53*

**Authors:** Pal Gronas

**Comments:** 2 Pages.

From this formula we see that it is essensial to determine S(pr), where p is a prime and r is a natural number.

**Category:** General Mathematics

[621] **viXra:1403.0735 [pdf]**
*submitted on 2014-03-23 09:38:52*

**Authors:** Zheng Jianfeng

**Comments:** 4 Pages.

The paper makes use of method of Mathematics Analytic to prove Functional Smarandache Iterations of three kinds.

**Category:** General Mathematics

[620] **viXra:1403.0734 [pdf]**
*submitted on 2014-03-23 09:41:34*

**Authors:** I. Balacenoiu, V. Seleacu, N. Varlan

**Comments:** 5 Pages.

In this paper are studied some properties of the numerical function.

**Category:** General Mathematics

[619] **viXra:1403.0733 [pdf]**
*submitted on 2014-03-23 09:43:00*

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Solve the following equations, where S is the Smarandache function.

**Category:** General Mathematics

[618] **viXra:1403.0732 [pdf]**
*submitted on 2014-03-23 09:45:28*

**Authors:** I. Balacenoiu, V. Seleacu

**Comments:** 5 Pages.

We consider the construction of Smarandache functions of the type...

**Category:** General Mathematics

[617] **viXra:1403.0731 [pdf]**
*submitted on 2014-03-23 09:46:55*

**Authors:** Amarnath Murthy

**Comments:** 7 Pages.

In [1] we defme SMARANDACHE FACTOR PARTITION
FUNCTION, as follows...

**Category:** General Mathematics

[616] **viXra:1403.0730 [pdf]**
*submitted on 2014-03-23 09:47:57*

**Authors:** Charles Ashbacher

**Comments:** 2 Pages.

In a paper that is scheduled to be published in volume 31 (3) of Journal of Recreational Mathematics,entitled "'On A Generalization of Perfect Nurnbers"[ll, Joseph L. Pe deflnes a generalization of the definition of perfect numbers. The standard definition is that a number n is pexfect if it is the sum of its proper divisors.

**Category:** General Mathematics

[615] **viXra:1403.0729 [pdf]**
*submitted on 2014-03-23 09:50:51*

**Authors:** Charles Ashbacher

**Comments:** 4 Pages.

The Pseudo-Smarandache function has the definition...

**Category:** General Mathematics

[614] **viXra:1403.0727 [pdf]**
*submitted on 2014-03-23 09:53:04*

**Authors:** David Gorski

**Comments:** 10 Pages.

The Pseudo-Smarandache Function is part of number theory.

**Category:** General Mathematics

[613] **viXra:1403.0724 [pdf]**
*submitted on 2014-03-23 09:55:56*

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

This study originates from questions posed on alternating iterations involving the pseudo-Smarandache function Z(n) and the Euler function.

**Category:** General Mathematics

[612] **viXra:1403.0722 [pdf]**
*submitted on 2014-03-23 09:58:33*

**Authors:** Henry Ibstedt

**Comments:** 3 Pages.

For a positive integer n. the Smarandache function S(n) is defined as the smallest positive
integer such that S(n)! is divisible by n.

**Category:** General Mathematics

[611] **viXra:1403.0721 [pdf]**
*submitted on 2014-03-23 09:59:38*

**Authors:** Maohua Le

**Comments:** 3 Pages.

In this paper we prove that there exist
infInitelv many disjoint sets of posItIve integers which the sum of whose reciprocals is equal to unity.

**Category:** General Mathematics

[610] **viXra:1403.0720 [pdf]**
*submitted on 2014-03-23 10:01:26*

**Authors:** Mihaly Bencze

**Comments:** 4 Pages.

Eight particular, Smarandache Recurrence Sequences and a Smarandache General-Recurrence Sequence are defined below and exemplified...

**Category:** General Mathematics

[609] **viXra:1403.0719 [pdf]**
*submitted on 2014-03-23 10:02:25*

**Authors:** A.a.k. Majumdar, H. Gunarto

**Comments:** 21 Pages.

In this paper, we study some properties of ten recurrence type Smarandache sequences, namely, the Smarandache odd, even, prime product, square product, higher-power product, permutation, consecutive, reverse, symmetric, and pierced chain sequences.

**Category:** General Mathematics

[608] **viXra:1403.0718 [pdf]**
*submitted on 2014-03-23 10:04:09*

**Authors:** Felice Russo

**Comments:** 5 Pages.

In this paper we report a recurrence formula to obtain the n-th prime in terms of (n-l)th prime and as a function of Smarandache or Totient
function.

**Category:** General Mathematics

[607] **viXra:1403.0716 [pdf]**
*submitted on 2014-03-23 10:07:18*

**Authors:** Maohua Le

**Comments:** 2 Pages.

THE REDUCED SMARANDACHE SQUARE-DIGITAL
SuBSEQUENCE IS INFINITE.

**Category:** General Mathematics

[606] **viXra:1403.0715 [pdf]**
*submitted on 2014-03-23 10:09:05*

**Authors:** Tomita Tiberiu Florin

**Comments:** 6 Pages.

The Smarandache function is a numerical function...

**Category:** General Mathematics

[605] **viXra:1403.0714 [pdf]**
*submitted on 2014-03-23 10:10:13*

**Authors:** Krassimir T. Atanassov

**Comments:** 17 Pages.

In 1996 the author of this remarks wrote reviews for "Zentralblatt fur Mathematik" for
books [1) and [2) and this was his first contact with the Smarandache's problems.

**Category:** General Mathematics

[604] **viXra:1403.0713 [pdf]**
*submitted on 2014-03-23 10:12:03*

**Authors:** Sebastian Martin Ruiz

**Comments:** 2 Pages.

Smarandache Function is defined as followed:

**Category:** General Mathematics

[603] **viXra:1403.0712 [pdf]**
*submitted on 2014-03-23 10:13:13*

**Authors:** Amarnath Murthy

**Comments:** 10 Pages.

we define SMARANDACHE FACTOR PARTITION FUNCTION, as follows:

**Category:** General Mathematics

[602] **viXra:1403.0711 [pdf]**
*submitted on 2014-03-23 02:41:23*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the asymptotic properties of the k-power part residue, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[601] **viXra:1403.0710 [pdf]**
*submitted on 2014-03-23 02:45:08*

**Authors:** Linfan Mao

**Comments:** 17 Pages.

This paper surveys the applications of Smarandache’s notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009.

**Category:** General Mathematics

[600] **viXra:1403.0709 [pdf]**
*submitted on 2014-03-23 02:46:44*

**Authors:** Dviraj Talukdar

**Comments:** 7 Pages.

Smarandache groupoid is not partly ordered under Smarandache inclusion relation but it contains some partly ordered sets, which are lattices under Smarandache union and intersection. We propose to establish the complemented and distributive lattices of Smarandache groupoid. Some properties of these lattices are discussed here.

**Category:** General Mathematics

[599] **viXra:1403.0708 [pdf]**
*submitted on 2014-03-23 02:48:16*

**Authors:** Chengliang Tian, Na Yuan

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL¤(n) and the mean value distribution
property of SL(n), obtain an exact calculating formula and a sharper asymptotic formula
for it.

**Category:** General Mathematics

[598] **viXra:1403.0706 [pdf]**
*submitted on 2014-03-23 02:50:29*

**Authors:** Zhongtian Lv

**Comments:** 4 Pages.

The main purpose of this paper is to use the elementary methods to study the mean value of the F.Smarandache LCM function SL(n), and give a
sharper asymptotic formula for it.

**Category:** General Mathematics

[597] **viXra:1403.0705 [pdf]**
*submitted on 2014-03-23 02:52:25*

**Authors:** Amarnath Murthy

**Comments:** 5 Pages.

In the present note we define two interesting parameters the length and extent of an SFP and study the interesting properties they exhibit for square free numbers.

**Category:** General Mathematics

[596] **viXra:1403.0704 [pdf]**
*submitted on 2014-03-23 02:53:44*

**Authors:** Qiuhong Zhao, Yang Wang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the convergent
properties of an in¯nity series involving S¤¤(n), and give an interesting limit formula for it.

**Category:** General Mathematics

[595] **viXra:1403.0703 [pdf]**
*submitted on 2014-03-23 02:54:57*

**Authors:** Vasile Seleacu, Narcisa VarIan

**Comments:** 2 Pages.

In this paper is studied the limit of the following sequence...

**Category:** General Mathematics

[594] **viXra:1403.0702 [pdf]**
*submitted on 2014-03-23 03:04:39*

**Authors:** Maohua Li

**Comments:** Pages.

In this paper we prove that the limit T(n)
of the Smarandache divisor sequence exists if and only if n is odd.

**Category:** General Mathematics

[593] **viXra:1403.0701 [pdf]**
*submitted on 2014-03-23 03:06:50*

**Authors:** M. Andrei, I. BaIaIcenoiu, C.Dumitrescu, E. RaIdescu, N. RaIdescu, V.Seleacu

**Comments:** 5 Pages.

In this paper we consider a numerical function
associated with a particular Smarandache Function S.

**Category:** General Mathematics

[592] **viXra:1403.0700 [pdf]**
*submitted on 2014-03-23 03:08:14*

**Authors:** Linfan Mao

**Comments:** 12 Pages.

We characterize curvature of s-line, particularly, Smarandachely embedded graphs and determine linear isometries on...

**Category:** General Mathematics

[591] **viXra:1403.0699 [pdf]**
*submitted on 2014-03-23 03:09:20*

**Authors:** P. Siva Kota Reddy, Kavita. S. Permi, B. Prashanth

**Comments:** 4 Pages.

In this note we define two generalizations of the line graph and obtain some results. Also, we mark some open problems.

**Category:** General Mathematics

[590] **viXra:1403.0698 [pdf]**
*submitted on 2014-03-23 03:11:53*

**Authors:** P. Siva Kota Reddy, K. M. Nagaraja, M. C. Geetha

**Comments:** 7 Pages.

Smarandachely symmetric n-marked graph.

**Category:** General Mathematics

[589] **viXra:1403.0696 [pdf]**
*submitted on 2014-03-23 03:16:09*

**Authors:** Yongga A., Zhiren Sun

**Comments:** 16 Pages.

Proves a conjecture of R. Shen and F. Tian, also related with the cyclic structures of
algebraically Smarandache multi-spaces.

**Category:** General Mathematics

[588] **viXra:1403.0695 [pdf]**
*submitted on 2014-03-23 03:18:24*

**Authors:** Charles Ashbacher

**Comments:** 1 Page.

The Smarandache Lucky Method/Algorithm/Operationietc. is said to be any incorrect method or algorithm or operation etc. wr.ich Leads to
a correct result. The wrong calculation should be fun, somehow similarly to the students' common mistakes, or to produce confusions or paradoxes.
Can someone give an example of a Smarandache Lucky Derivation, or Integration, or Solution to a Differential Equation?

**Category:** General Mathematics

[587] **viXra:1403.0694 [pdf]**
*submitted on 2014-03-23 03:20:13*

**Authors:** M. R. Mudge

**Comments:** 3 Pages.

Can you find a such magic square of order at least 3 or 4, when A is a set of prime numbers and 1 the addition?

**Category:** General Mathematics

[586] **viXra:1403.0693 [pdf]**
*submitted on 2014-03-23 03:21:29*

**Authors:** Xiang Ren, WeiLi He, Lin Zhao

**Comments:** 7 Pages.

Let G be a simple graph with diameter four,if G does not contain complete subgraph K3 of order three.

**Category:** General Mathematics

[585] **viXra:1403.0692 [pdf]**
*submitted on 2014-03-23 03:22:52*

**Authors:** R.Vasuki, S.Arockiaraj

**Comments:** 13 Pages.

Throughout this paper, by a graph we mean a finite, undirected, simple graph. Let G(V,E) be a graph with p vertices and q edges. For notations and terminology we follow [1].

**Category:** General Mathematics

[584] **viXra:1403.0690 [pdf]**
*submitted on 2014-03-23 03:25:20*

**Authors:** Liu Yanni, Gao Peng

**Comments:** 3 Pages.

The main purpose of this paper is using elementary method to study a new arithmetic function, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[583] **viXra:1403.0689 [pdf]**
*submitted on 2014-03-23 03:26:31*

**Authors:** Zhu Minhui

**Comments:** 5 Pages.

For any positive integer n, the Smarandache double factorial function Sdf(n)is defined as the least positive integer m such that m!! is divisible by n. In this paper, we study the mean value properties of Sdf(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[582] **viXra:1403.0688 [pdf]**
*submitted on 2014-03-23 03:27:29*

**Authors:** Xiaoying Du

**Comments:** 6 Pages.

The main purpose of this paper is to study the properties of the Smarandache LCM function SL(n), and give an asymptotic formula for its mean value.

**Category:** General Mathematics

[581] **viXra:1403.0687 [pdf]**
*submitted on 2014-03-23 03:28:38*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 5 Pages.

The main purpose of this paper is using the analytic method to study the asymptotic properties of the Near Pseudo Smarandache Function, and give two interesting asymptotic formulae for it.

**Category:** General Mathematics

[580] **viXra:1403.0686 [pdf]**
*submitted on 2014-03-23 03:29:45*

**Authors:** Jia Wang

**Comments:** 4 Pages.

In this paper, we use analytic method to study the mean value properties of Smarandache-Type Multiplicative Functions Km(n), and give its asymptotic formula . Finally, the convolution method is used to improve the error term.

**Category:** General Mathematics

[579] **viXra:1403.0685 [pdf]**
*submitted on 2014-03-23 03:31:00*

**Authors:** Yi Yuan, Zhang Wenpeng

**Comments:** 3 Pages.

In this paper, we study the mean value properties of the additive analogue of S(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[578] **viXra:1403.0684 [pdf]**
*submitted on 2014-03-23 03:32:27*

**Authors:** Jian Ge

**Comments:** 4 Pages.

For any positive integer n, the famous F.Smarandache function S(n) de¯ned as the smallest
positive integer m such that n / m!.

**Category:** General Mathematics

[577] **viXra:1403.0683 [pdf]**
*submitted on 2014-03-23 03:34:12*

**Authors:** Xiaoyan Li

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of P(n)SL(n) and p(n)SL(n), and give two
sharper asymptotic formulas for them.

**Category:** General Mathematics

[576] **viXra:1403.0682 [pdf]**
*submitted on 2014-03-23 03:35:53*

**Authors:** Wang Xiaoying

**Comments:** 3 Pages.

For any ¯fixed positive integer n, the Smarandache ceil function of order k is denoted by...

**Category:** General Mathematics

[575] **viXra:1403.0681 [pdf]**
*submitted on 2014-03-23 03:36:53*

**Authors:** B.Basavanagoud, Sunilkumar M. Hosamani

**Comments:** 8 Pages.

One related open problem is explored. Finally, some bounds on domination number of Dm(G) are obtained in terms of vertices and edges of G.

**Category:** General Mathematics

[574] **viXra:1403.0680 [pdf]**
*submitted on 2014-03-23 03:37:50*

**Authors:** Catalin Barbu

**Comments:** 6 Pages.

In this study, we present (i) a proof of the Menelaus theorem for quadrilaterals in
hyperbolic geometry, (ii) and a proof for the transversal theorem for triangles, and (iii) the
Menelaus's theorem for n-gons.

**Category:** General Mathematics

[573] **viXra:1403.0679 [pdf]**
*submitted on 2014-03-23 03:39:05*

**Authors:** A. E. El-Ahmady, H. Rafat

**Comments:** 7 Pages.

The concept of retraction and folding of zero dimension space-time will be obtained.The relation
between limit of folding and retraction presented.

**Category:** General Mathematics

[572] **viXra:1403.0678 [pdf]**
*submitted on 2014-03-23 03:40:20*

**Authors:** Dengju Ma, Han Ren

**Comments:** 8 Pages.

In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds.

**Category:** General Mathematics

[571] **viXra:1403.0677 [pdf]**
*submitted on 2014-03-23 03:41:17*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

This papers deals with the introduction and preliminary study of the Smarandache minimum
and maximum functions.

**Category:** General Mathematics

[570] **viXra:1403.0676 [pdf]**
*submitted on 2014-03-23 03:42:26*

**Authors:** S. Arumugam, S. Sudha

**Comments:** 8 Pages.

In this paper we present a dynamic programming algorithm for determining the min-max dom-
saturation number of a tree.

**Category:** General Mathematics

[569] **viXra:1403.0675 [pdf]**
*submitted on 2014-03-23 03:43:35*

**Authors:** Amarnath Murthy

**Comments:** 8 Pages.

In [1] we define SMARANDACHE FACTOR
PARTITION FUNCTION (SFP).

**Category:** General Mathematics

[568] **viXra:1403.0674 [pdf]**
*submitted on 2014-03-23 03:45:29*

**Authors:** Anghel N. Rugina

**Comments:** 2 Pages.

In this short paper I compare the Smarandache's Non-Euclidean Geometries with my Orientation Table For Any Science.

**Category:** General Mathematics

[567] **viXra:1403.0673 [pdf]**
*submitted on 2014-03-23 03:47:36*

**Authors:** Roberto Torretti

**Comments:** 14 Pages.

David Hilbert's Foundations of Geometry (1899) contain nineteen statements, labelled axioms, from which every theorem in Euclid's Elements can be derived by deductive inference, according to the classical rules of logic.

**Category:** General Mathematics

[566] **viXra:1403.0672 [pdf]**
*submitted on 2014-03-23 03:47:33*

**Authors:** Th. Guyer

**Comments:** 1 Page.

A + B = C
Rad(ABC) infinite < C
Number Example: 2*12p2 + 1 = 17p2

**Category:** Number Theory

[565] **viXra:1403.0671 [pdf]**
*replaced on 2014-10-23 16:34:50*

**Authors:** Emanuel Gluskin

**Comments:** 18 Pages. This is an important in its topic and unique in its treatment sociological work. In this version, Appendix 4, extending the topic of human thinking conformity, is added.

The basic role of Jews is defined as creating a motivating contrast between the mass of the people who often get into trouble, and the subsequently arising leader (prophet) who calls for conscience in order to help the people to survive the trouble. The words of the Old Testament: "You will bring the light to other nations" are understood as a reflection of the fact that such a prophet is important for the whole of humanity. The main reason for anti-Semitism is seen as some psychological incompatibility (perhaps, of some weak autistic nature) of Jews in their contacts with other people. This incompatibility, however, defends Jews against acquiring the feature of conformity of human society (psychology), -- the conformity that has caused serious moral problems over the world. Jews are thus presented as irritating, but positively thinking and contributing people. It is dangerous but interesting to be a Jew.

**Category:** Mind Science

[564] **viXra:1403.0670 [pdf]**
*submitted on 2014-03-22 14:03:46*

**Authors:** Alexander Bolonkin

**Comments:** 22 Pages.

In 1957 the new era of studying outer Space by space apparatus was ushered in. During this past half century, thousands of satellites, space ships and space stations were launched. The tens of thousands of slivers from old rockets remaining in Space represent a serious danger for new satellites, space craft, space stations and space travelers. Currently, about 19,000 pieces of debris larger than 5 cm (2.0 in) are tracked. Any of them can damage a space apparatus. This work delineates the problems of the space debris (amount, distribution, growth, danger and so on), reviews the old and contemporary methods of cleaning up the debris, and evaluates the relative efficiency of the current and new methods. This paper offers new methods and installations for cleaning outer space from space debris and specific protection of important space ships and stations from large space debris (SD). Advantages of the offered method and apparatus are the following: 1. Smaller size and weight by 2 -3 times than conventional SD Collector. 2. Greater efficiency by 2 -3 times. 3. Saves fuel by some times. 4. No limits in size for SD. 5. Can easily protect a space ship and station (for example, International Space Station) from SD.

**Category:** Classical Physics

[563] **viXra:1403.0669 [pdf]**
*submitted on 2014-03-22 14:14:37*

**Authors:** Alexander Bolonkin

**Comments:** 22 Pages.

Currently (2011), about 19,000 pieces of space debris larger than 5 cm (2.0 in) are tracked (for example: old non-working satellites, last stages of rockets and so on). Any of them can catastrophic damage the working space apparatus, space stations and space ship. The field of invention is a method and installation (space apparatus) for cleaning the outer Space from Space debris, protection current and future space station, ships, space apparatus from space debris, meteroids and enemy attack. Offered devices also can be installed on new space apparatus for returning them into the planet atmosphere after lifetime or in dangerous situation.
Author offers new method and installation for cleaning the outer space from space debris and individual protection the important space ship and stations from big space debris (SD). Advantages of the offered method and apparatus are following: 1. Less size and weight in 2 -3 times than conventional SD Collector. 2. More efficiency in 2 -10 times. 3. Save fuel in some times. 4. No limits in size for SD. 5. Can easy protect selected space ship and station (for example, International Space Station) from SD.

**Category:** Classical Physics

[562] **viXra:1403.0668 [pdf]**
*submitted on 2014-03-22 07:32:55*

**Authors:** Qing Tian

**Comments:** 5 Pages.

The main purpose of this paper is to study the distribution properties of the k-power free numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[561] **viXra:1403.0667 [pdf]**
*submitted on 2014-03-22 05:03:07*

**Authors:** Albert A. Mullin

**Comments:** 1 Page.

This brief note points out several basic connections between the Smarandache function, fixed-point theory [1] and prime-number theory.

**Category:** General Mathematics

[560] **viXra:1403.0666 [pdf]**
*submitted on 2014-03-22 05:04:10*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 6 Pages.

In the present paper we study some series concerning the following function of the
Numbers Theory.

**Category:** General Mathematics

[559] **viXra:1403.0665 [pdf]**
*submitted on 2014-03-22 05:08:40*

**Authors:** Adrian Vasiu, Angela Vasiu

**Comments:** 6 Pages.

The formalized theories in which are considered different types of logics give us an easier way of understanding of our own interpretations of the concepts and of the events of life.

**Category:** General Mathematics

[558] **viXra:1403.0664 [pdf]**
*submitted on 2014-03-22 05:10:03*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give a formula expressing the
Smarandache function S(n) by means of n without using the factorization of n.

**Category:** General Mathematics

[557] **viXra:1403.0663 [pdf]**
*submitted on 2014-03-22 05:11:06*

**Authors:** Krassimir T. Atanassov

**Comments:** 4 Pages.

F. Smarandache discussed the following particular cases of the well-know characteristic functions.

**Category:** General Mathematics

[556] **viXra:1403.0660 [pdf]**
*submitted on 2014-03-22 05:17:17*

**Authors:** Angela Vasiu, Nicolae Oprea

**Comments:** 5 Pages.

It is considered the notion of absolute Geometry in its evolution, from the first Non-euclidpan Geometry of Lobacewski, Bolyai and Gauss till that of Smaranclache Anti-Geometry,

**Category:** General Mathematics

[555] **viXra:1403.0659 [pdf]**
*submitted on 2014-03-22 05:18:43*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

Let us assume that m is a given prime p.

**Category:** General Mathematics

[554] **viXra:1403.0657 [pdf]**
*submitted on 2014-03-22 05:20:51*

**Authors:** Sebastian Martin Ruiz

**Comments:** 4 Pages.

Observe that this is a functional recurrence strictly closed too.

**Category:** General Mathematics

[553] **viXra:1403.0656 [pdf]**
*submitted on 2014-03-22 05:22:02*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

A number is said to be a Smarandache Lucky Number if an incorrect calculation leads to a correct result.

**Category:** General Mathematics

[552] **viXra:1403.0655 [pdf]**
*submitted on 2014-03-22 05:22:56*

**Authors:** Sayed Elagan

**Comments:** 7 Pages.

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

**Category:** General Mathematics

[551] **viXra:1403.0654 [pdf]**
*submitted on 2014-03-22 05:24:02*

**Authors:** Liang Fangchi

**Comments:** 4 Pages.

Let n be a positive integer...

**Category:** General Mathematics

[550] **viXra:1403.0653 [pdf]**
*submitted on 2014-03-22 05:25:28*

**Authors:** Yao Weili

**Comments:** 4 Pages.

The floor of the square root sequence is the natural sequence, where each number is repeated 2n+1 times. In this paper, we use analytic method to study the mean value properties of its generalization, and give an interesting asymptotic formula.

**Category:** General Mathematics

[549] **viXra:1403.0652 [pdf]**
*submitted on 2014-03-22 05:26:52*

**Authors:** Hailong Li

**Comments:** 4 Pages.

For any positive integer n, we define the function P(n) as the smallest prime p.

**Category:** General Mathematics

[548] **viXra:1403.0651 [pdf]**
*submitted on 2014-03-22 05:29:15*

**Authors:** Qianli Yang

**Comments:** 4 Pages.

In this paper, we use the elementary methods to study the properties of the constructive set S, and obtain some interesting properties for it.

**Category:** General Mathematics

[547] **viXra:1403.0650 [pdf]**
*submitted on 2014-03-22 05:40:20*

**Authors:** Chuan Lv

**Comments:** 3 Pages.

Let Q denotes the set of all rational numbers.

**Category:** General Mathematics

[546] **viXra:1403.0649 [pdf]**
*submitted on 2014-03-22 05:41:45*

**Authors:** George Gregory

**Comments:** 1 Page.

A generalized Smarandache Palindrome is a nnmber of the form.

**Category:** General Mathematics

[545] **viXra:1403.0648 [pdf]**
*submitted on 2014-03-22 05:42:38*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 4 Pages.

The aim of this article is to propose a generalisation for Euler's function.

**Category:** General Mathematics

[544] **viXra:1403.0647 [pdf]**
*submitted on 2014-03-22 05:43:39*

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

Partition function P(n) is defined as the number of ways that a positive integer can be expressed as the sum of positive integers.

**Category:** General Mathematics

[543] **viXra:1403.0646 [pdf]**
*submitted on 2014-03-22 05:44:45*

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

In this paper ,the result ( theorem-2.6) Derived in
REF. [2], the paper "Generalization Of Partition Function.

**Category:** General Mathematics

[542] **viXra:1403.0645 [pdf]**
*submitted on 2014-03-22 05:45:59*

**Authors:** Liangxia Wan, Hong-Jian Lai, Yanpei Liu

**Comments:** 11 Pages.

In this paper we develop the technique of a distribution decomposition for a graph. A formula is given to determine genus distribution of a cubic graph. Given any connected graph, it is proved that its genus distribution is the sum of those for some cubic graphs by using the technique.

**Category:** General Mathematics

[541] **viXra:1403.0644 [pdf]**
*submitted on 2014-03-22 05:47:00*

**Authors:** Adrian Vasiu, Angela Vasiu

**Comments:** 4 Pages.

TRANSGRESAREA FRONTIERELOR DINTRE DISCIPLINE

**Category:** General Mathematics

[540] **viXra:1403.0643 [pdf]**
*submitted on 2014-03-22 05:48:15*

**Authors:** Linfan Mao

**Comments:** 37 Pages.

Different from the system in classical mathematics, a Smarandache system is
a contradictory system in which an axiom behaves in at least two different ways within the
same system, i.e., validated and invalided, or only invalided but in multiple distinct ways.
Such systems exist extensively in the world, particularly, in our daily life. In this paper, we
discuss such a kind of Smarandache system, i.e., non-solvable ordinary differential equation
systems by a combinatorial approach, classify these systems and characterize their behaviors,
particularly, the global stability, such as those of sum-stability and prod-stability of such
linear and non-linear differential equations.

**Category:** General Mathematics

[539] **viXra:1403.0642 [pdf]**
*submitted on 2014-03-22 05:49:47*

**Authors:** M.A.Perumal, S.Navaneethakrishnan, A.Nagarajan

**Comments:** 19 Pages.

Smarandache-Fibonacci triple is a sequence S(n).

**Category:** General Mathematics

[538] **viXra:1403.0641 [pdf]**
*submitted on 2014-03-22 05:52:28*

**Authors:** S.somasundaram, A.nagarajan, G.mahadevan

**Comments:** 13 Pages.

[1] Acharya and Sampathkumar defined a graphoidal cover as a partition of edges into internally disjoint (not necessarily open) paths.

**Category:** General Mathematics

[537] **viXra:1403.0638 [pdf]**
*submitted on 2014-03-22 05:56:04*

**Authors:** D.D.Somashekara, C.R.Veena

**Comments:** 9 Pages.

A graph G is said to be Smarandachely harmonic graph with property P if its vertices can be labeled 1, 2, · · ·

**Category:** General Mathematics

[536] **viXra:1403.0637 [pdf]**
*submitted on 2014-03-22 05:57:37*

**Authors:** M.Seenivasan, A.Lourdusamy

**Comments:** 12 Pages.

Absolutely harmonious labeling f is an injection from the vertex set of a graph G...

**Category:** General Mathematics

[535] **viXra:1403.0636 [pdf]**
*submitted on 2014-03-22 05:59:16*

**Authors:** Leonardo F. D. da Motta

**Comments:** 4 Pages.

Em 1993, Smarandache propos que DaO hA uma velocidade limite na natureza, baseado no paradoxo EPR-Bell (Einstein, Podolsky, Rosen, Bell).

**Category:** General Mathematics

[534] **viXra:1403.0635 [pdf]**
*submitted on 2014-03-22 06:01:45*

**Authors:** I. Balacenoiu, V. Seleacu

**Comments:** 10 Pages.

This function is originated from the Romanian professor Florentin Smarandache.It is defined as follows...

**Category:** General Mathematics

[533] **viXra:1403.0634 [pdf]**
*submitted on 2014-03-22 06:03:09*

**Authors:** R.Rangarajan, M. S. Subramanya, P. Siva Kota Reddy

**Comments:** 8 Pages.

Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S...

**Category:** General Mathematics

[532] **viXra:1403.0633 [pdf]**
*submitted on 2014-03-22 06:04:45*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 8 Pages.

If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only if its holomorph is a Smarandache loop.

**Category:** General Mathematics

[531] **viXra:1403.0632 [pdf]**
*submitted on 2014-03-22 06:06:46*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 7 Pages.

By studying the holomorphic structure of automorphic inverse property quasigroups and loops...

**Category:** General Mathematics

[530] **viXra:1403.0631 [pdf]**
*submitted on 2014-03-22 06:07:43*

**Authors:** Chan Shi

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the hybrid
mean value properties of the Smarandache kn-digital sequence and Smarandache function, and
give an interesting asymptotic formula for it.

**Category:** General Mathematics

[529] **viXra:1403.0630 [pdf]**
*submitted on 2014-03-22 06:08:42*

**Authors:** Liu Huaning, Gao Jing

**Comments:** 3 Pages.

In this paper, we study the hybrid mean value of some Smarandache-type multiplicative functions and the Mangoldt function, and give two asymptotic formulae.

**Category:** General Mathematics

[528] **viXra:1403.0629 [pdf]**
*submitted on 2014-03-22 06:09:57*

**Authors:** Baohuai Shi

**Comments:** 3 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n m!.

**Category:** General Mathematics

[527] **viXra:1403.0628 [pdf]**
*submitted on 2014-03-22 06:10:56*

**Authors:** Le Huan

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method to study the hybrid mean value properties of the Smarandache kn digital sequence with SL(n) function and divisor function d(n), then give two interesting asymptotic formulae for it.

**Category:** General Mathematics

[526] **viXra:1403.0627 [pdf]**
*submitted on 2014-03-22 06:12:13*

**Authors:** R.Manoharan, R.Vasuki, R.Manisekaran

**Comments:** 6 Pages.

In this paper, we introduce ideal graph of a graph and study some of its properties. We characterize connectedness, isomorphism of graphs and coloring property of a graph using ideal graph. Also, we give an upper bound for chromatic number of a graph.

**Category:** General Mathematics

[525] **viXra:1403.0626 [pdf]**
*submitted on 2014-03-22 06:13:43*

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 9 Pages.

In this paper we analyze and study the Smarandache idempotents (S-idempotents).

**Category:** General Mathematics

[524] **viXra:1403.0625 [pdf]**
*submitted on 2014-03-22 06:15:13*

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 8 Pages.

In this paper we establish the existence of S-idempotents in case of loop rings...

**Category:** General Mathematics

[523] **viXra:1403.0624 [pdf]**
*submitted on 2014-03-22 06:17:00*

**Authors:** Yu Wang

**Comments:** 8 Pages.

function. The main purpose of this paper is using the elementary method to study the properties and obtain some interesting identities involving function...

**Category:** General Mathematics

[522] **viXra:1403.0623 [pdf]**
*submitted on 2014-03-22 06:18:20*

**Authors:** Xiaowei Pan, Pei Zhang

**Comments:** 4 Pages.

The main purpose of this paper is to study the relationship between the Riemann zeta-function and an infinite series involving the Smarandache function.

**Category:** General Mathematics

[521] **viXra:1403.0622 [pdf]**
*submitted on 2014-03-22 06:19:59*

**Authors:** Henry Ibstedt

**Comments:** 2 Pages.

The cover illustration is a representation of the values of the Smarandache function.

**Category:** General Mathematics

[520] **viXra:1403.0621 [pdf]**
*submitted on 2014-03-22 06:20:57*

**Authors:** Jon Perry

**Comments:** 3 Pages.

The sum of factorials function, also known as the left factorial function, is defined as...

**Category:** General Mathematics

[519] **viXra:1403.0620 [pdf]**
*submitted on 2014-03-22 06:23:05*

**Authors:** Germina K.A., Beena Koshy

**Comments:** 12 Pages.

A Smarandachely uniform 1-graph is abbreviated to a complementary distance pattern uniform graph, i.e.,
CDPU graphs. This paper studies independent CDPU graphs.

**Category:** General Mathematics

[518] **viXra:1403.0619 [pdf]**
*submitted on 2014-03-22 06:24:39*

**Authors:** Florian Luca

**Comments:** 5 Pages.

Inequality (1) was suggested by Balacenoiu at the First International Conference on Smarandache Notions in Number Theory.

**Category:** General Mathematics

[517] **viXra:1403.0618 [pdf]**
*submitted on 2014-03-22 06:25:37*

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

Our aim is to shmv that certain results from om recent paper [3] can be obtained in a simpler way from a generalization of relation (1).

**Category:** General Mathematics

[516] **viXra:1403.0617 [pdf]**
*submitted on 2014-03-22 06:27:03*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 9 Pages.

The object that is researched is Smarandache's function.

**Category:** General Mathematics

[515] **viXra:1403.0616 [pdf]**
*submitted on 2014-03-22 06:28:33*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer a, let S(a) be the Smarandache function. Bencze proposed the following problem.

**Category:** General Mathematics

[514] **viXra:1403.0615 [pdf]**
*submitted on 2014-03-22 06:30:32*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer n, let S(n) denote the
Smarandache function of n.

**Category:** General Mathematics

[513] **viXra:1403.0614 [pdf]**
*submitted on 2014-03-22 06:31:26*

**Authors:** Chaoping Chen

**Comments:** 5 Pages.

We present some inequalities for the polygamma funtions.

**Category:** General Mathematics

[512] **viXra:1403.0613 [pdf]**
*submitted on 2014-03-22 06:32:38*

**Authors:** Weiyi Zhu

**Comments:** 4 Pages.

For any positive integer n, the famous Smarandache function S(n) is defined as the smallest positive integer m such that njm!.

**Category:** General Mathematics

[511] **viXra:1403.0612 [pdf]**
*submitted on 2014-03-22 06:33:27*

**Authors:** Zheng Jianfeng

**Comments:** 4 Pages.

For any positive integer n, let a{n) and b{n) denote the inferior and superior k-th power
part of n respectively.

**Category:** General Mathematics

[510] **viXra:1403.0611 [pdf]**
*submitted on 2014-03-22 06:34:50*

**Authors:** Pantelimon Stanica, Gabriela Stanica

**Comments:** 5 Pages.

A number is said to be a Smarandache Lucky Number (see [3, 1, 2]) if an incorrect calculation leads to a correct result. In general, a Smarandache Lucky Method or Algorithm is said to be any incorrect method or algorithm, which leads to a correct result. In this note we find an infinite sequence of distinct lucky fractions.

**Category:** General Mathematics

[509] **viXra:1403.0609 [pdf]**
*submitted on 2014-03-22 06:37:35*

**Authors:** Vasile Seleacu, Constantin A. Dumitrescu

**Comments:** 7 Pages.

Next we will study two diophantine equations which contain the Smarandache function.
Reminding of two of the features of Smarandache' s function which we will need further...

**Category:** General Mathematics

[508] **viXra:1403.0608 [pdf]**
*submitted on 2014-03-22 06:38:45*

**Authors:** Jing Li

**Comments:** 4 Pages.

In this paper, we using the elementary method to study the convergent property of one class Dirichlet series involving a special sequences, and give several interesting identities for it.

**Category:** General Mathematics

[507] **viXra:1403.0607 [pdf]**
*submitted on 2014-03-22 06:40:06*

**Authors:** Gheorghe Dinulescu-Campina

**Comments:** 2 Pages.

In my own work "The Modelling of the Rationality" under the basis of the MESER licence, I have enlightened a new spiritual doctrine sustained by scientific and logical hypotheses.

**Category:** General Mathematics

[506] **viXra:1403.0606 [pdf]**
*submitted on 2014-03-22 06:41:16*

**Authors:** Zhang Tianping

**Comments:** 4 Pages.

For any positive integer m, let a(m) denotes the integer part of the k-th root of m.

**Category:** General Mathematics

[505] **viXra:1403.0605 [pdf]**
*submitted on 2014-03-22 06:42:17*

**Authors:** Xiaoying Du

**Comments:** 7 Pages.

The main purpose of this paper is using the elementary methods to study the properties of the integer part of the m-th root and the largest m-th power not exceeding n,and give some interesting identities involving these numbers.

**Category:** General Mathematics

[504] **viXra:1403.0604 [pdf]**
*submitted on 2014-03-22 06:43:44*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method and analytic method to study the asymptotic properties of the integer part of the k-th root positive integer, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[503] **viXra:1403.0603 [pdf]**
*submitted on 2014-03-22 06:44:48*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let k, n be distinct positive integers

**Category:** General Mathematics

[502] **viXra:1403.0602 [pdf]**
*submitted on 2014-03-22 06:45:35*

**Authors:** Kang Xiaoyu

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the property of
the Smarandache function, and give an interesting result.

**Category:** General Mathematics

[501] **viXra:1403.0601 [pdf]**
*submitted on 2014-03-22 06:47:02*

**Authors:** Linfan Mao

**Comments:** Pages.

In recent decades, Smarandache’s notions of multispace and multistructure were widely
spread and have shown much importance in sciences around the world. Organized by Prof.Linfan Mao, a professional conference on multispaces and multistructures, named the First International Conference on Smarandache Multispace and Multistructure was held in Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was announced by American Mathematical Society in advance.

**Category:** General Mathematics

[500] **viXra:1403.0599 [pdf]**
*submitted on 2014-03-22 06:54:50*

**Authors:** Linfan Mao

**Comments:** 27 Pages.

These Smarandache spaces are right theories for objectives by logic. However,the mathematical combinatorics is a combinatorial theory for branches in classical mathematics motivated by a combinatorial speculation.

**Category:** General Mathematics

[499] **viXra:1403.0598 [pdf]**
*submitted on 2014-03-22 07:05:39*

**Authors:** Felice Russo

**Comments:** 10 Pages.

In this paper we will study this function and several examples, theorems,conjectures and problems will be presented. The behaviour of this function is
similar to the other Srnarandache functions introduced in the chapter I.

**Category:** General Mathematics

[498] **viXra:1403.0597 [pdf]**
*submitted on 2014-03-22 07:07:21*

**Authors:** A.A.K. Majumdar

**Comments:** 6 Pages.

In a recent paper, Muneer [1] introduced the Smarandache inversion sequence. In this paper, we study some properties of the Smarandache inversion sequence.

**Category:** General Mathematics

[497] **viXra:1403.0596 [pdf]**
*submitted on 2014-03-22 07:08:38*

**Authors:** Y.v. Chebrakov, V.v. Shmagin

**Comments:** 20 Pages.

In this paper we investigate some properties of Smarandache sequences of the 2nd kind and demonstrate that these numbers are near prime numbers.

**Category:** General Mathematics

[496] **viXra:1403.0595 [pdf]**
*submitted on 2014-03-22 07:11:09*

**Authors:** Jianbin Chen

**Comments:** 6 Pages.

F.Smarandache multiplicative function.

**Category:** General Mathematics

[495] **viXra:1403.0594 [pdf]**
*submitted on 2014-03-22 07:12:59*

**Authors:** Jozsef Sandor

**Comments:** 3 Pages.

Let S(n) be the Smarandache function.

**Category:** General Mathematics

[494] **viXra:1403.0593 [pdf]**
*submitted on 2014-03-22 07:14:26*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 9 Pages.

The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past.

**Category:** General Mathematics

[493] **viXra:1403.0592 [pdf]**
*submitted on 2014-03-22 07:16:33*

**Authors:** Temitope Gbolahan Jaiyeola

**Comments:** 12 Pages.

The pair is called a special loop if is a loop with an arbitrary subloop called its special subloop. A special loop is called a second Smarandache Bol
loop.

**Category:** General Mathematics

[492] **viXra:1403.0591 [pdf]**
*submitted on 2014-03-22 07:17:35*

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The Pseudo-Smarandache function was recently defined in a book by Kashihara.

**Category:** General Mathematics

[491] **viXra:1403.0590 [pdf]**
*submitted on 2014-03-22 07:18:57*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 13 Pages.

The aim of this article is to propose a Java concurrent program for the Smarandache fimction based on the equation...

**Category:** General Mathematics

[490] **viXra:1403.0589 [pdf]**
*submitted on 2014-03-22 07:20:39*

**Authors:** Guanghua Dong, Ning Wang, Yuanqiu Huang, Yanpei Liu

**Comments:** 12 Pages.

The vertex v of a graph G is called a 1-critical-vertex for the maximum genus of the graph, or for simplicity called 1-critical-vertex.

**Category:** General Mathematics

[489] **viXra:1403.0588 [pdf]**
*submitted on 2014-03-22 07:22:36*

**Authors:** H. A.Malathi, H. C.Savithri

**Comments:** 3 Pages.

The notion of jump symmetric n-sigraphs was
introduced by E. Sampathkumar, P. Siva Kota Reddy and M. S. Subramanya [Proceedings of the Jangjeon Math. Soc., 11(1) (2008), 89-95].

**Category:** General Mathematics

[488] **viXra:1403.0587 [pdf]**
*submitted on 2014-03-21 19:45:41*

**Authors:** U.V.S. Seshavatharam

**Comments:** 2 Pages. Global Journal of Computer Science and Technology Volume XIII Issue VII Version I Year 2013

To promote advanced low fees high quality education among the people of India within their reach
and to promote continuous research program in all areas of Science & Technology

**Category:** Education and Didactics

[487] **viXra:1403.0586 [pdf]**
*replaced on 2014-04-04 20:07:04*

**Authors:** Victor Christianto

**Comments:** 12 Pages. This article has not been submitted to any journal. This file is written in order to stimulate further observation/experiment. Comments are welcome.

For years, scientists have assumed that the sun is an enormous mass of hydrogen. Galileo was the first to propose that the sun is filled with gas. But Dr. Oliver Manuel says iron, not hydrogen, is the sun's most abundant element. IF his suggestion is true then it may imply that the source of solar energy is different of the presently held theory of hydrogen fusion.

**Category:** Nuclear and Atomic Physics

[486] **viXra:1403.0585 [pdf]**
*submitted on 2014-03-21 22:39:07*

**Authors:** Klinkerman R.V.

**Comments:** 3 Pages.

In the given work attempt to understand the nature of gravitation on the basis
of quantum concepts is done. It supposed, that in a basis of gravitation lay zero
fluctuations of quantum fields which are identified with the chaos "surrounding"
the Universe. The gravitational field is result of transformation by a physical body
of distant chaos in near chaos.
Key words: gravitation, particles, zero fluctuations, « phantoms of particles
», chaos, transformation.

**Category:** Quantum Physics

[485] **viXra:1403.0584 [pdf]**
*submitted on 2014-03-22 01:34:24*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

Considerations about the Smarandache, Pseudo-Smarandache, resp. Smarandache-simple functions.

**Category:** Number Theory

[484] **viXra:1403.0583 [pdf]**
*submitted on 2014-03-22 01:35:30*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

We now define the following" additive analogue" , which is defined on a subset of real numbers.

**Category:** General Mathematics

[483] **viXra:1403.0582 [pdf]**
*submitted on 2014-03-22 01:38:49*

**Authors:** E.Radescu, N.Radescu, C.Dumitrescu

**Comments:** 5 Pages.

Of course the algebraic usual operations "+" and "." play also an important role in the description of the properties of S.

**Category:** General Mathematics

[482] **viXra:1403.0581 [pdf]**
*submitted on 2014-03-22 01:40:01*

**Authors:** Amarnath Murthy

**Comments:** 4 Pages.

we define SMARANDACHE FACTOR PARTITION FUNCTION (SFP) , as follows:

**Category:** General Mathematics

[481] **viXra:1403.0580 [pdf]**
*submitted on 2014-03-22 02:07:30*

**Authors:** Mohammed Javed, P. Nagabhushan, B.B. Chaudhuri

**Comments:** 6 Pages. Direct processing of compressed data, compressed document, TIFF Document Processing

Extracting a block of interest referred to as segmenting a specified block in an image and studying its characteristics is of general research interest, and could be a challenging if such a segmentation task has to be carried out directly in a compressed image. This is the objective of the present research work. The proposal is to evolve a method which would segment and extract a specified block, and carry out its characterization without decompressing a compressed image, for two major reasons that most of the image archives contain images in compressed format and 'decompressing' an image indents additional computing time and space. Specifically in this research work, the proposal is to work on run-length compressed document images.

**Category:** Digital Signal Processing

[480] **viXra:1403.0579 [pdf]**
*submitted on 2014-03-22 02:06:48*

**Authors:** Charles Ashbacher

**Comments:** 6 Pages.

The number of divisors function den), is a classic function of number theory, having been defined centuries ago. In contrast, the Smarandache function Sen), was defined only a few decades ago. The purpose of this paper is to tind all solutions to a simple equation involving both functions.

**Category:** General Mathematics

[479] **viXra:1403.0578 [pdf]**
*submitted on 2014-03-22 02:08:29*

**Authors:** Florian Munteanu, Octavian Mustafa

**Comments:** 4 Pages.

Some splitting lemma of topological nature provides fundamental information when dealing with dynamics (see [1], pg.79).

**Category:** General Mathematics

[478] **viXra:1403.0577 [pdf]**
*submitted on 2014-03-22 02:09:43*

**Authors:** Mohammed Javed, P. Nagabhushan, B.B. Chaudhuri

**Comments:** 8 Pages. Automatic font size detection, compressed document processing, compressed domain

Automatic detection of font size finds many applications in the area of intelligent OCRing and document image analysis, which has been traditionally practiced over uncompressed documents, although in real life the documents exist in compressed form for efficient storage and transmission. It would be novel and intelligent if the task of font size detection could be carried out directly from the compressed data of these documents without decompressing, which would result in saving of considerable amount of processing time and space. Therefore, in this paper we present a novel idea of learning and detecting font size directly from run-length compressed text documents at line level using simple line height features, which paves the way for intelligent OCRing and document analysis directly from compressed documents. In the proposed model, the given mixed-case text documents of different font size are segmented into compressed text lines and the features extracted such as line height and ascender height are used to capture the pattern of font size in the form of a regression line, using which the automatic detection of font size is done during the recognition stage. The method is experimented with a dataset of 50 compressed documents consisting of 780 text lines of single font size and 375 text lines of mixed font size resulting in an overall accuracy of 99.67%.

**Category:** Digital Signal Processing

[477] **viXra:1403.0576 [pdf]**
*submitted on 2014-03-22 02:10:21*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

Let S(n) be @@the Smarandache function.

**Category:** General Mathematics

[476] **viXra:1403.0575 [pdf]**
*submitted on 2014-03-22 02:11:33*

**Authors:** Y.v. Chebrakov. V.v. Shmagin

**Comments:** 10 Pages.

In this paper we study the properties of some six numerical Smarandache sequences. As result we present a set of analytical formulae for the computation of numbers in these Smarandache series and for constructing Magic squares.

**Category:** General Mathematics

[475] **viXra:1403.0574 [pdf]**
*submitted on 2014-03-22 02:12:55*

**Authors:** Y.v. Chebrakov. V.v. Shmagin

**Comments:** 9 Pages.

We discuss the theme on translating different descriptions of computative algorithms
into high-level programming languages, enumerate some advantages of analytical descriptions and demonstrate that logical functions may be used effectively to create analytical formulae available for describing a set of combinatorial and number-theoretic computative algorithms.

**Category:** General Mathematics

[474] **viXra:1403.0573 [pdf]**
*submitted on 2014-03-22 02:14:03*

**Authors:** Y.v. Chebrakov

**Comments:** 18 Pages.

In this paper we seek for an answer on Smarandache type question: may one create the theory of Magic squares 4x4 in size without using properties of some
concrete numerical sequences? As a main result of this theoretical investigation we adduce the solution of the problem on decomposing the general algebraic formula of Magic squares 4x4 into two complete sets of structured and fourcomponent
analytical formulae.

**Category:** General Mathematics

[473] **viXra:1403.0572 [pdf]**
*submitted on 2014-03-22 02:15:03*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

Let us define the following arithmetic function...

**Category:** General Mathematics

[472] **viXra:1403.0570 [pdf]**
*submitted on 2014-03-22 02:18:17*

**Authors:** Sandy P. Chimienti, Mihaly Bencze

**Comments:** 15 Pages.

This is an experimental geometry. All Hilbert's 20 axioms of the Euclidean GGeometry are denied in this vanguardist geometry of the real chaos: What is even more intriguing? F.Smarandache[5] has even found in 1969 a model of it.

**Category:** General Mathematics

[471] **viXra:1403.0569 [pdf]**
*submitted on 2014-03-22 02:20:09*

**Authors:** Y.v. Chebrakov

**Comments:** 12 Pages.

By developing F. Smarandache (algebraic) approach to solving systems of Diophantine equations we elaborate a set of new computative algorithms and
analytical formulae, which may be used for finding numerical solutions of some combinatorial and number-theoretic problems.

**Category:** General Mathematics

[470] **viXra:1403.0568 [pdf]**
*submitted on 2014-03-22 02:21:25*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 3 Pages.

The aim of this article is to establish the complexity order of the Erdos function average. This will be studied based on some recent results about the Smarandache function.

**Category:** General Mathematics

[469] **viXra:1403.0567 [pdf]**
*submitted on 2014-03-22 02:22:30*

**Authors:** Steven R. Finch

**Comments:** 2 Pages.

Given a positive integer n, let P(n) denote the largest@@ prime factor of n and S(n) denote
the smallest integer m such that n divides m!

**Category:** General Mathematics

[468] **viXra:1403.0566 [pdf]**
*submitted on 2014-03-22 02:23:24*

**Authors:** Maohua Le

**Comments:** 4 Pages.

In this paper we prove that there are only fmitely many Balu numbers.

**Category:** General Mathematics

[467] **viXra:1403.0565 [pdf]**
*submitted on 2014-03-22 02:24:20*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

Definition of the Smarandache function S(n).

**Category:** General Mathematics

[466] **viXra:1403.0564 [pdf]**
*submitted on 2014-03-22 02:25:12*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

In the book [1] by Smarandache (see also [2]) appears the following generalization of the well-known bisector theorem.

**Category:** General Mathematics

[465] **viXra:1403.0563 [pdf]**
*submitted on 2014-03-22 02:26:20*

**Authors:** Mark Farris, Patrick Mitchell

**Comments:** 6 Pages.

This observation illustrates the importance
of being able to calculate the Smarandache function for prime powers. This paper will be considering that process.

**Category:** General Mathematics

[464] **viXra:1403.0562 [pdf]**
*submitted on 2014-03-22 02:27:22*

**Authors:** Henry Ibstedt

**Comments:** 4 Pages.

This briefnote on Smarandache 2-2 subtractive relationships should be seen in relation
to the article on Smarandache k-k additive relationships in this issue of SNJ [1].

**Category:** General Mathematics

[463] **viXra:1403.0560 [pdf]**
*submitted on 2014-03-22 02:30:50*

**Authors:** C. Dumitrescu

**Comments:** 4 Pages.

New References concerninig this function.

**Category:** General Mathematics

[462] **viXra:1403.0559 [pdf]**
*submitted on 2014-03-22 02:32:06*

**Authors:** J.R. Sutton

**Comments:** 5 Pages.

This paper presents an alternative algorithm for use when S is to be calculated for all integers up to n. The integers are synthesised by combining all the prime powers in the range up to n.

**Category:** General Mathematics

[461] **viXra:1403.0558 [pdf]**
*submitted on 2014-03-22 02:33:01*

**Authors:** J.R. Sutton

**Comments:** 3 Pages.

The Smarandache function is an integer function.

**Category:** General Mathematics

[460] **viXra:1403.0557 [pdf]**
*submitted on 2014-03-22 02:42:06*

**Authors:** Jon Perry

**Comments:** 4 Pages.

The process involved is fairly simple, and we need to know the factorisation of n.From this factorisation, it is possible to exactly calculate by which m each prime is satisfied, i.e. the correct number of exponents appears for the first time. The largest of these values gives a(n).

**Category:** General Mathematics

[459] **viXra:1403.0556 [pdf]**
*submitted on 2014-03-22 02:43:28*

**Authors:** Jozsef Sandor

**Comments:** 2 Pages.

In the recent book [1] there appf'ar certain arithmetic functions which are similar to
the Smarandache function. In a rf'("ent paper [2} we have considered certain generalization
or duals of the Smarandache fnnct:ion 8(11).

**Category:** General Mathematics

[458] **viXra:1403.0555 [pdf]**
*submitted on 2014-03-22 02:44:44*

**Authors:** J. Sandor

**Comments:** 11 Pages.

This arithmetical function is connected to the number of divisors of n, and other important number theoretic functions.

**Category:** General Mathematics

[457] **viXra:1403.0554 [pdf]**
*submitted on 2014-03-22 02:45:42*

**Authors:** Jozsef Sandor

**Comments:** 4 Pages.

The Smarandache function satisfies certain elementary inequalities which have importance in the deduction of properties of this (or related) functions. We quote here the following relations which have appeared in the Smarandache Function Journal.

**Category:** General Mathematics

[456] **viXra:1403.0552 [pdf]**
*submitted on 2014-03-22 02:49:05*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we construat a class of commutaive rings tmder the Smarandache algorithm.

**Category:** General Mathematics

[455] **viXra:1403.0551 [pdf]**
*submitted on 2014-03-22 02:50:40*

**Authors:** Y. v. CHEBRAKOV, V. V. Shmagin

**Comments:** 20 Pages.

By developing F. Smarandache thema on paradoxes in mathematics it is stated, firstly, ifin measurement (natural science) experiments the best solutions are found by using methods of modem data analysis theory, then some difficulties with the interpretation of the computation results are liable to occur; secondly, one is not capable to overcome these difficulties without a data analysis theory modification, consisted in the translation of this theory from Aristotelian "binary logic" into more progressive "fuzzy logic".

**Category:** General Mathematics

[454] **viXra:1403.0550 [pdf]**
*submitted on 2014-03-22 03:02:35*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 5 Pages.

The note presents an algorithm for the Smarandache's function computation. The complexity of algorithm is studied using the main properties of function. An interesting inequality is found giving the complexity of thefunction on the set {1.2 •...• n}.

**Category:** General Mathematics

[453] **viXra:1403.0549 [pdf]**
*submitted on 2014-03-22 03:04:43*

**Authors:** Y ongdong Guo, Maohua Le

**Comments:** 1 Page.

In this paper we prove that all Smarandache concatenated k-power decimals are irrational numbers.

**Category:** General Mathematics

[452] **viXra:1403.0548 [pdf]**
*submitted on 2014-03-22 03:07:23*

**Authors:** Henry Ibstedt

**Comments:** 11 Pages.

This article has been inspired by questions asked by C11ar1es Ashbacbcr in the Journal of Rereational Mathemdics, vol. 29.2.

**Category:** General Mathematics

[451] **viXra:1403.0547 [pdf]**
*submitted on 2014-03-22 03:08:18*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

Smarandache's function is defined thus:

**Category:** General Mathematics

[450] **viXra:1403.0546 [pdf]**
*submitted on 2014-03-22 03:09:12*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Smarandache Square-Partial-Digital Subsequence(SSPDS) is the sequence of square integers which can be partitioned so that each element of the partition is a perfect square[l][2][3].

**Category:** General Mathematics

[449] **viXra:1403.0545 [pdf]**
*submitted on 2014-03-22 03:10:31*

**Authors:** I. Prodanescu, L. Tutescu

**Comments:** 2 Pages.

Then the following Diophantine equation has no solution.

**Category:** General Mathematics

[448] **viXra:1403.0544 [pdf]**
*submitted on 2014-03-22 03:11:28*

**Authors:** Wang Yang, Zhang Hong Li

**Comments:** 1 Page.

The main purpose of this paper is to solve a problem generated by Professor F.Smarandache.

**Category:** General Mathematics

[447] **viXra:1403.0543 [pdf]**
*submitted on 2014-03-22 03:12:40*

**Authors:** Constantin Dunutrescu, Cannen Rocsoreanu

**Comments:** 11 Pages.

This paper is aimed to provide generalizations of the Smarandache function. They will be constructed by means of sequences more general than the sequence of the factorials.

**Category:** General Mathematics

[446] **viXra:1403.0542 [pdf]**
*submitted on 2014-03-22 03:13:42*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 5 Pages.

The aim oj this article is to study the convergence oj the Euler harmonic series. Firstly, the results concerning the convergence oj the Smaralldache and Erdos harmonic junctions are reviewed Secondly, the Euler harmonic series is proved to be convergent jor a> I, and divergent otherwise. Finally, the slims of the Euler harmonic series are given.

**Category:** General Mathematics

[445] **viXra:1403.0541 [pdf]**
*submitted on 2014-03-22 03:16:18*

**Authors:** E. Burton, I. Cojocaru, S. Cojocaru, C. Dwnittcscu

**Comments:** 8 Pages.

In this paper we consider same series attached to Smarandache function.

**Category:** General Mathematics

[444] **viXra:1403.0540 [pdf]**
*submitted on 2014-03-22 03:17:41*

**Authors:** Emil Burton

**Comments:** 3 Pages.

S(n) is the smallest integer m with the property that m! is divisible by n R set of real numbers.

**Category:** General Mathematics

[443] **viXra:1403.0539 [pdf]**
*submitted on 2014-03-22 03:18:39*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 9 Pages.

The studies concerning the series with Smarandache numbers have been done recently and represents an important research direction on Smarandache' s
notions.

**Category:** General Mathematics

[442] **viXra:1403.0538 [pdf]**
*submitted on 2014-03-22 03:19:46*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we consider the convergence
value and the simple continued fraction of some
Smarandache sequeces.

**Category:** General Mathematics

[441] **viXra:1403.0537 [pdf]**
*submitted on 2014-03-22 03:20:57*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we prove Smarandache cube-partial-digital subsequence is infinite.

**Category:** General Mathematics

[440] **viXra:1403.0536 [pdf]**
*submitted on 2014-03-22 03:22:11*

**Authors:** Marcela Popescu, Mariana Nicolescu

**Comments:** 9 Pages.

If we take into account of the above definition of the function g, it is easy to prove the
above properties.

**Category:** General Mathematics

[439] **viXra:1403.0535 [pdf]**
*submitted on 2014-03-22 03:23:35*

**Authors:** Zhang Tianping

**Comments:** 6 Pages.

The main purpose of this paper is to study the asymptotic property of the the cubic residues and k-power complement numbers and obtain some interesting asymptotic formulas.

**Category:** General Mathematics

[438] **viXra:1403.0534 [pdf]**
*submitted on 2014-03-22 03:25:02*

**Authors:** Henry Ibstedt

**Comments:** 8 Pages.

In a recent study of the PrimaIity oj the Smarandache Symmetric Sequences Sabin and Tatiana Tabirca [1] observed a very high frequency of the prime factor 333667 in the factorization of the terms of the second order sequence. The question if this prime factor occurs peridically was raised. The odd behaviour of this and a few other primefadors of this sequence will be explained
and details of the periodic occurence of this and of several other prime factors will be given.

**Category:** General Mathematics

[437] **viXra:1403.0533 [pdf]**
*submitted on 2014-03-22 03:26:04*

**Authors:** Charles Ashbacher

**Comments:** 3 Pages.

The Smarandache Deconstructive Sequence (SDS(n)) of integers is constructed by sequentially repeating the digits 1-9 in the following way:

**Category:** General Mathematics

[436] **viXra:1403.0532 [pdf]**
*submitted on 2014-03-22 03:27:49*

**Authors:** Amarnath Murthy

**Comments:** 3 Pages.

We call the process of extracting the base sequence from the Pascal derived sequence as Depascalisation.

**Category:** General Mathematics

[435] **viXra:1403.0531 [pdf]**
*submitted on 2014-03-22 03:29:22*

**Authors:** Dviraj Talukdar

**Comments:** 11 Pages.

Let m be a positive integer greater than one...

**Category:** General Mathematics

[434] **viXra:1403.0530 [pdf]**
*submitted on 2014-03-22 03:30:45*

**Authors:** Maohua Le

**Comments:** 1 Page.

In this paper, we prove that there exist infmitely many positive integers n satisfying...

**Category:** General Mathematics

[433] **viXra:1403.0529 [pdf]**
*submitted on 2014-03-22 03:32:29*

**Authors:** Lamarr Widmer

**Comments:** 2 Pages.

The Smarandache Square-Partial-Digital Subsequence (SPDS) is the sequence of square integers which admit a partition for which each segment is a square integer.

**Category:** General Mathematics

[432] **viXra:1403.0528 [pdf]**
*submitted on 2014-03-22 03:34:21*

**Authors:** Lucian Tulescu, Emil Burton

**Comments:** 2 Pages.

Let S(n) be defined as the smallest integer such that (S(n))! is divisible by n (Smarandache Function).

**Category:** General Mathematics

[431] **viXra:1403.0527 [pdf]**
*submitted on 2014-03-22 03:35:12*

**Authors:** Maohua Le

**Comments:** 2 Pages.

Let S( n) denote the Smarandache function of n.
In this paper we prove that Sen) = n if and only if
n = 1, 4 or p, where p is a prime.

**Category:** General Mathematics

[430] **viXra:1403.0526 [pdf]**
*submitted on 2014-03-22 03:36:44*

**Authors:** S.M.Tabirca, I.Pitt, D.Murphy

**Comments:** 7 Pages.

The aim of this article is to present a discrete model for histogram shaping. This is an important image transformation with several practical applications. The model that is proposed is based on a generalization of the inferior part function. Finally, an algorithm based on this model is developed.

**Category:** General Mathematics

[429] **viXra:1403.0525 [pdf]**
*submitted on 2014-03-22 03:38:05*

**Authors:** Florian Luca

**Comments:** 3 Pages.

For any positive integer n let S(n) be the minimal positive integer m such that n m!.

**Category:** General Mathematics

[428] **viXra:1403.0524 [pdf]**
*submitted on 2014-03-22 03:39:07*

**Authors:** Amarnath Murthy

**Comments:** 2 Pages.

Are there an infinite number of primes in this sequence?

**Category:** General Mathematics

[427] **viXra:1403.0523 [pdf]**
*submitted on 2014-03-22 03:40:51*

**Authors:** Liu HONGYAN, Zhang Wenpeng

**Comments:** 6 Pages.

Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n...

**Category:** General Mathematics

[426] **viXra:1403.0522 [pdf]**
*submitted on 2014-03-22 03:42:05*

**Authors:** Jozsef Sandor

**Comments:** 6 Pages.

In paper [3] we have defined certain generalizations and extensions of the Smarandache
function.

**Category:** General Mathematics

[425] **viXra:1403.0521 [pdf]**
*submitted on 2014-03-22 03:43:17*

**Authors:** E. R.a.descu, N. R.a.descu, C. Dumitrescu

**Comments:** 8 Pages.

In this paper we continue the algebraic consideration begun in [2]. As it was sun,
two of the proprieties of Smarandache's function are hold.

**Category:** General Mathematics

[424] **viXra:1403.0520 [pdf]**
*submitted on 2014-03-22 03:44:23*

**Authors:** C. Dumitrescu, R. Muller

**Comments:** 16 Pages.

Studying the properties of the proportions the peoples of the antiquity could build using the ruler and the compasses. For example if instead of a square of side a it was required the construction of another square. of side x determined by
the condition that the new square has a double area.

**Category:** General Mathematics

[423] **viXra:1403.0519 [pdf]**
*submitted on 2014-03-22 03:45:25*

**Authors:** Zhang Wenpeng

**Comments:** 3 Pages.

Let Q denotes the set of @@all rational numbers.

**Category:** General Mathematics

[422] **viXra:1403.0518 [pdf]**
*submitted on 2014-03-22 03:46:46*

**Authors:** F. Saidak

**Comments:** 7 Pages.

An old conjecture of Paul Erdos [6] states that there exist only 7 integers.

**Category:** General Mathematics

[421] **viXra:1403.0517 [pdf]**
*submitted on 2014-03-22 03:49:18*

**Authors:** Tatiana Sabirca, Sabin Tabirca

**Comments:** 4 Pages.

The purpose of this article is to study the convergence of a few series with the Erdos function. The work is based on results concerning the convergence of some series with the Smarandache function.

**Category:** General Mathematics

[420] **viXra:1403.0516 [pdf]**
*submitted on 2014-03-22 03:50:36*

**Authors:** Sabin Tabirca

**Comments:** 5 Pages.

The starting point of this article is represented by a recent work of Finch [2000]. Based on two
asymptotic results concerning the Erdos function, he proposed some interesting equation concerning the moments of the Smarandache function. The aim of this note is give a bit modified proof and to show some computation results for one of the Finch equation.

**Category:** General Mathematics

[419] **viXra:1403.0515 [pdf]**
*submitted on 2014-03-22 03:51:43*

**Authors:** Sabin Tabirca, Tatiana Tabirca

**Comments:** 5 Pages.

The starting point of this article is represented by a recent work of Finch [2000]. Based on two
asymptotic results concerning the Erdos function, he proposed some interesting equations concerning the moments of the· Smarandache function. The aim of this note is give a bit modified proof and to show some computation results for one of the Finch equation.

**Category:** General Mathematics

[418] **viXra:1403.0512 [pdf]**
*submitted on 2014-03-22 03:56:03*

**Authors:** Amarnath Murthy

**Comments:** 7 Pages.

DEFINITION of SMARANDACHE TERM

**Category:** General Mathematics

[417] **viXra:1403.0511 [pdf]**
*submitted on 2014-03-22 03:57:02*

**Authors:** Sebastian Martin Ruiz

**Comments:** 2 Pages.

Smarandache Coprime Function is defined this way:

**Category:** General Mathematics

[416] **viXra:1403.0510 [pdf]**
*submitted on 2014-03-22 03:58:00*

**Authors:** Felice Russo

**Comments:** 4 Pages.

In this note v.e report the results regarding ,he check of the third Smarandache conjecture on
primes.

**Category:** General Mathematics

[415] **viXra:1403.0509 [pdf]**
*submitted on 2014-03-22 03:59:07*

**Authors:** Amarnath Murthy

**Comments:** 13 Pages.

In this article I have defined a number of
SMARANDACHE type sets ,sequences which I found very
interesting. The problems and conjectures proposed would give food for thought and would pave ways for more work in this field.

**Category:** General Mathematics

[414] **viXra:1403.0508 [pdf]**
*submitted on 2014-03-22 04:00:04*

**Authors:** Maohua Le

**Comments:** 3 Pages.

In this paper we verify two conjectures concerning extents of Smarandache factor partitions.

**Category:** General Mathematics

[413] **viXra:1403.0507 [pdf]**
*submitted on 2014-03-22 04:19:55*

**Authors:** Vera W. de Spinadel

**Comments:** 36 Pages.

The family of Metallic Means comprises every quadratic irrational number that is the positive solution of algebraic equations of the types.

**Category:** General Mathematics

[412] **viXra:1403.0505 [pdf]**
*submitted on 2014-03-22 04:23:52*

**Authors:** Stefan Porubsky

**Comments:** 16 Pages.

In the paper it is shown how a form of the classical FERMAT-EULER Theorem discovered by F • SMARANDACHE fits into the generalizations found
by S.SCHWARZ, M.LASSAK and the author. Then we show how SMARANDACHE'S algorithm can be used to effective computations of the so called group membership.

**Category:** General Mathematics

[411] **viXra:1403.0504 [pdf]**
*submitted on 2014-03-22 04:25:20*

**Authors:** Ion Cojocaru, Sorin Cojocaru

**Comments:** 3 Pages.

In this note we prove that the series ... is convergent to a real number.

**Category:** General Mathematics

[410] **viXra:1403.0503 [pdf]**
*submitted on 2014-03-22 04:29:52*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we completely determine the
first digit and the trailing digit of every term in the Smarandache deconstructive sequence.

**Category:** General Mathematics

[409] **viXra:1403.0502 [pdf]**
*replaced on 2018-06-15 11:14:46*

**Authors:** Michael John Sarnowski

**Comments:** 15 Pages.

Originally. I had worked on an equation for charge and gravity. I had found that charge was mostly related to the electron mass, I since found out that gravity is most related to the proton mass. The realization came when I was working on “The Answer to the Universe, the Life and Everything is Still 42” I had an extra term for the mass ratio of the proton to the neutron. To get rid of that term, I came to the realization that Gravity was related to the mass ratio of the proton to the neutron. This paper is then an up dated version of “The Aether Found, Discrete Calculations of Charge and Gravity with Planck Spinning Spheres and Kaluza Spinning Spheres”, which are the previous versions of this update.
This paper shows that the force of charge and gravity can be modeled from a sphere, indicating granulated granular spacetime. Planck Spinning Spheres, (Planck) packed in a cuboctahedron structure, where many spheres are combined to produce the fabric of space. The Planck would be made of smaller Spheres called Kaluza Spinning Spheres (Kaluza). See images below for an example of a sphere made of spheres.

**Category:** Quantum Gravity and String Theory

[408] **viXra:1403.0501 [pdf]**
*replaced on 2015-12-29 04:10:36*

**Authors:** Sylwester Kornowski

**Comments:** 5 Pages.

Here, on base of the lacking part of ultimate theory, i.e. the Scale-Symmetric Theory, we described the production of the E- and B-modes in the CMB. The obtained result 0.22 for the ratio of amplitudes of the B-modes to E-modes (i.e. the tensor-to-scalar ratio) for the beginning of expansion of the very early Universe, for multipole moment equal to 384, is close to the central value in the BICEP2 data. The tensor-to-scalar ratio depends on density of the Einstein-spacetime and is higher for higher densities. The calculated energies carried by the Einstein-spacetime components the spreading condensates were built of (such condensates produced the B-modes in the CMB), were in approximation the sixteen powers of ten of GeV.

**Category:** Quantum Gravity and String Theory

[407] **viXra:1403.0500 [pdf]**
*submitted on 2014-03-21 12:00:09*

**Authors:** Glenn A. Baxter

**Comments:** 40 Pages

Dr. Diederik Aerts joins us this issue with a serious challenge to Quantum Physics as understood by the mainstream, as we call them. Also Jim Marsen, MSME, with his TRON theory as developed with his dad.
The Institute has formally accepted a proposed alliance with the NPA, the Natural Philosophy Alliance. NPA, in turn is working toward an alliance with The Electric Universe organization. The ramifications of this would be huge. See www.k1man.com/Springer130319A.pdf

**Category:** Quantum Physics

[406] **viXra:1403.0499 [pdf]**
*submitted on 2014-03-21 07:24:19*

**Authors:** P.Selvaraju, P.Balaganesan, J.Renuka

**Comments:** 6 Pages.

Vertex graceful graphs.

**Category:** General Mathematics

[405] **viXra:1403.0498 [pdf]**
*submitted on 2014-03-21 07:25:59*

**Authors:** A.Lourdusamy, M.Seenivasan

**Comments:** 7 Pages.

In this paper, we obtain necessary conditions for a
graph to be V-mean and study V-mean behaviour of certain classes of graphs.

**Category:** General Mathematics

[404] **viXra:1403.0497 [pdf]**
*submitted on 2014-03-21 07:27:38*

**Authors:** Pinar DUNDAR, Tufan TURACI, Derya DOGAN

**Comments:** 7 Pages.

In this paper we introduce the weak reinforcement number which is the minimum number of added edges to reduce the weak dominating number. We give some boundary of this new parameter and trees.

**Category:** General Mathematics

[403] **viXra:1403.0496 [pdf]**
*submitted on 2014-03-21 07:28:51*

**Authors:** Ranjini P.S., V.Lokesha

**Comments:** 10 Pages.

Many researchers have studied several operators on a connected graph in which one make an attempt on subdivision of its edges. In this paper, we show how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators.

**Category:** General Mathematics

[402] **viXra:1403.0495 [pdf]**
*submitted on 2014-03-21 07:30:02*

**Authors:** W.B.Vasantha, Moon K.Chetry

**Comments:** 13 Pages.

In this paper we ¯nd the number of smarandache zero divisors.

**Category:** General Mathematics

[401] **viXra:1403.0494 [pdf]**
*submitted on 2014-03-21 07:34:15*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we consider the convergence for two Smarandache senes.

**Category:** General Mathematics

[400] **viXra:1403.0493 [pdf]**
*submitted on 2014-03-21 07:35:42*

**Authors:** I. Balacenoiu, V. Seleacu

**Comments:** 5 Pages.

In this paper we define the numerical functions and we prove some propenies of these functions.

**Category:** General Mathematics

[399] **viXra:1403.0491 [pdf]**
*submitted on 2014-03-21 07:37:36*

**Authors:** Sabin Tabirca

**Comments:** 2 Pages.

The main objective of this note is to introduce the notion of the S-multiplicative function and to give some simple properties concerning it. The name ofS-multiplicative is short for Smarandache-multiplicative and reflects the main equation of the Smarandache function.

**Category:** General Mathematics

[398] **viXra:1403.0490 [pdf]**
*submitted on 2014-03-21 07:39:23*

**Authors:** Leonardo Rubino

**Comments:** 14 Pages.

Nothing is still in this Universe ant there is also another alternative relativity, for those objects which look not moving.

**Category:** Relativity and Cosmology

[397] **viXra:1403.0489 [pdf]**
*submitted on 2014-03-21 07:38:37*

**Authors:** Csaba Biro

**Comments:** 3 Pages.

In this paper we will discuss about a problem that I asked about 8 years ago, when I was interested mainly in computer science.

**Category:** General Mathematics

[396] **viXra:1403.0488 [pdf]**
*submitted on 2014-03-21 07:40:30*

**Authors:** Mihaly Bencze

**Comments:** 1 Page.

There exists infinitely many n e N such that
S(n) = S(n - S)), where S is the Smarandache function.

**Category:** General Mathematics

[395] **viXra:1403.0487 [pdf]**
*submitted on 2014-03-21 04:59:23*

**Authors:** Han Ren, Jing Ren

**Comments:** 9 Pages.

In this paper we investigate the structure of the shortest co-cycle base(or SCB in short) of connected graphs, which are related with map geometries, i.e., Smarandache 2-dimensional manifolds.

**Category:** General Mathematics

[394] **viXra:1403.0486 [pdf]**
*submitted on 2014-03-21 05:00:24*

**Authors:** P.Siva Kota Reddy

**Comments:** 10 Pages.

Several variations and characterizations of directionally n-signed graphs have been proposed and studied. These include the various notions of balance and others.

**Category:** General Mathematics

[393] **viXra:1403.0485 [pdf]**
*submitted on 2014-03-21 05:02:05*

**Authors:** P. Siva Kota Reddy, M. S. Subramany

**Comments:** 5 Pages.

A Smarandachely k-signed graph...

**Category:** General Mathematics

[392] **viXra:1403.0484 [pdf]**
*submitted on 2014-03-21 05:03:33*

**Authors:** Yang Qianli

**Comments:** 3 Pages.

A positive integer n is called simple number if the product of its all proper divisors is less than or equal to n.

**Category:** General Mathematics

[391] **viXra:1403.0483 [pdf]**
*submitted on 2014-03-21 05:04:58*

**Authors:** S. Arumugam, I. Sahul Hamid

**Comments:** 11 Pages.

A simple path cover of a graph G is a collection of paths in G such that every edge of G is in exactly one path in and any two paths in have at most one vertex in common.

**Category:** General Mathematics

[390] **viXra:1403.0482 [pdf]**
*submitted on 2014-03-21 05:06:30*

**Authors:** H.B. Walikar, Shailaja S. Shirkol, Kishori P.Narayankar

**Comments:** 4 Pages.

In this paper, some properties related
signed total domatic number and signed total domination number of a graph are studied
and found the sign total domatic number of certain class of graphs such as fans, wheels and
generalized Petersen graph.

**Category:** General Mathematics

[389] **viXra:1403.0481 [pdf]**
*submitted on 2014-03-21 05:07:30*

**Authors:** Muneer Jebreel Karama

**Comments:** 14 Pages.

We study the Smarandache inversion sequence which is a new concept, related sequences, conjectures, properties, and problems.

**Category:** General Mathematics

[388] **viXra:1403.0480 [pdf]**
*submitted on 2014-03-21 05:08:37*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 10 Pages.

The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops.

**Category:** General Mathematics

[387] **viXra:1403.0479 [pdf]**
*submitted on 2014-03-21 05:09:46*

**Authors:** Jiao Chen

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the Smarandache adjacent number sequences, and give several interesting asymptotic formula for it.

**Category:** General Mathematics

[386] **viXra:1403.0478 [pdf]**
*submitted on 2014-03-21 05:10:47*

**Authors:** Wang Yongxing

**Comments:** 5 Pages.

In this paper, we use the elementary methods to study the arithmetical properties of Sk(n),
and give some identities involving the Smarandache ceil function.

**Category:** General Mathematics

[385] **viXra:1403.0477 [pdf]**
*submitted on 2014-03-21 05:11:53*

**Authors:** Jason Earls

**Comments:** 3 Pages.

Florentin Smarandache has posed many problems that deal with perfect powers.

**Category:** General Mathematics

[384] **viXra:1403.0476 [pdf]**
*submitted on 2014-03-21 05:13:37*

**Authors:** S. Balasubramanian, C. Sandhya, P. Aruna Swathi Vyjayanthi

**Comments:** 13 Pages.

In this paper Smarandache V−connectedness and Smarandache locally−connectedness in topological space are introduced, obtained some of its basic properties and interrelations are verified with other types of connectedness.

**Category:** General Mathematics

[383] **viXra:1403.0475 [pdf]**
*submitted on 2014-03-21 05:14:37*

**Authors:** Melih Turgut, Suha Yilmaz

**Comments:** 5 Pages.

A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve.

**Category:** General Mathematics

[382] **viXra:1403.0474 [pdf]**
*submitted on 2014-03-21 05:15:38*

**Authors:** A. C. F. Bueno

**Comments:** 4 Pages.

In this paper, the concept of Smarandache cyclic geometric determinant sequence was introduced and a formula for its nth term was obtained using the concept of right and left circulant matrices.

**Category:** General Mathematics

[381] **viXra:1403.0473 [pdf]**
*submitted on 2014-03-21 05:17:41*

**Authors:** Cuncao Zhang, Yanyan Liu

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the convergent properties of the infinite series involving the Smarandache kn-digital subsequence f Sk(n)g , and obtain some interesting conclusions.

**Category:** General Mathematics

[380] **viXra:1403.0472 [pdf]**
*submitted on 2014-03-21 05:19:09*

**Authors:** S. M. Khairnar, Anant W. Vyawahare, J. N. Salunke

**Comments:** 8 Pages.

One approach to Smarandache friendly numbers is given by A.Murthy, who defined them Ref [1]. Another approach is presented here.

**Category:** General Mathematics

[379] **viXra:1403.0471 [pdf]**
*submitted on 2014-03-21 05:20:16*

**Authors:** A. A. K. Majumdar

**Comments:** 4 Pages.

The Smarandache friendly numbers have been de¯ned by Murthy [1]. This paper ¯nds the Smarandache friendly numbers by solving the associated Pell's equation.

**Category:** General Mathematics

[378] **viXra:1403.0468 [pdf]**
*submitted on 2014-03-21 05:23:34*

**Authors:** Guoping Feng

**Comments:** 4 Pages.

The main purpose of this paper is using
the elementary methods to study the value distribution properties of the function SL(n), and
give an interesting asymptotic formula for it.

**Category:** General Mathematics

[377] **viXra:1403.0467 [pdf]**
*submitted on 2014-03-21 05:24:54*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 13 Pages.

The concept of Smarandache Bryant Schneider Group of a Smarandache loop is introduced.

**Category:** General Mathematics

[376] **viXra:1403.0466 [pdf]**
*submitted on 2014-03-21 05:26:24*

**Authors:** P. Siva Kota Reddy, B. Prashanth, M. Ruby Salestina

**Comments:** 5 Pages.

A Smarandachely k-signed digraph (Smarandachely k-marked digraph) is an ordered pair...

**Category:** General Mathematics

[375] **viXra:1403.0465 [pdf]**
*submitted on 2014-03-21 05:28:02*

**Authors:** P. Devadas Rao, B. Sooryanarayana, M. Jayalakshmi

**Comments:** 13 Pages.

A Smarandachely k-constrained labeling of a graph.

**Category:** General Mathematics

[374] **viXra:1403.0464 [pdf]**
*submitted on 2014-03-21 05:29:28*

**Authors:** S. M. Khairnar, Anant W. Vyawahare, J. N. Salunke

**Comments:** 2 Pages.

This paper contains a magic square. A square array of natural numbers in which the sum of each row and each column is same is a magic square. Smarandache magic square has been defined by Sabin Tabirca [1].

**Category:** General Mathematics

[373] **viXra:1403.0463 [pdf]**
*submitted on 2014-03-21 05:30:49*

**Authors:** Ma Jinping

**Comments:** 4 Pages.

In this paper, we study the mean value properties of
f(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[372] **viXra:1403.0462 [pdf]**
*submitted on 2014-03-21 05:31:52*

**Authors:** Muneer Jebreel Karama

**Comments:** 4 Pages.

I study Smarandache numbers partitions, and the partitions set of these numbers. This study conducted by Computer Algebra System namely, Maple 8.

**Category:** General Mathematics

[371] **viXra:1403.0461 [pdf]**
*submitted on 2014-03-21 05:33:05*

**Authors:** Liu Huaning

**Comments:** 2 Pages.

In this paper, we use the elementary methods to give a sharp lower bound estimate for r.

**Category:** General Mathematics

[370] **viXra:1403.0459 [pdf]**
*submitted on 2014-03-21 05:35:36*

**Authors:** Yanrong Xue

**Comments:** 3 Pages.

In this paper, some elementary methods are used to study the property of the Smarandache-Riemann zeta sequence and obtain a general result.

**Category:** General Mathematics

[369] **viXra:1403.0457 [pdf]**
*submitted on 2014-03-21 05:47:08*

**Authors:** Yuan Yi

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary method to study the value
distribution property of the Smarandache multiplicative function, and give an interesting
asymptotic formula for it.

**Category:** General Mathematics

[368] **viXra:1403.0456 [pdf]**
*submitted on 2014-03-21 05:48:21*

**Authors:** Wenjing Xiong

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the parity of U(n), and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[367] **viXra:1403.0455 [pdf]**
*submitted on 2014-03-21 05:50:15*

**Authors:** V.Balaji

**Comments:** 3 Pages.

In this paper, we prove a conjecture that the three stars,a skolem mean graph.

**Category:** General Mathematics

[366] **viXra:1403.0454 [pdf]**
*submitted on 2014-03-21 05:51:30*

**Authors:** Lu Yaming

**Comments:** 4 Pages.

In this paper, we discussed the solutions of the following equation involving the Smarandache function.

**Category:** General Mathematics

[365] **viXra:1403.0453 [pdf]**
*submitted on 2014-03-21 05:52:46*

**Authors:** Weiguo Duan, Yanrong Xue

**Comments:** 10 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is defined as the
smallest positive integer m such that n divides m!.

**Category:** General Mathematics

[364] **viXra:1403.0452 [pdf]**
*submitted on 2014-03-21 05:53:53*

**Authors:** Xu Zhefeng

**Comments:** 4 Pages.

The main purpose of this paper is to study the arithmetical properties of the primitive numbers of power p by using the elementary method, and give some interesting identities and asymptotic formulae.

**Category:** General Mathematics

[363] **viXra:1403.0451 [pdf]**
*submitted on 2014-03-21 05:54:53*

**Authors:** Sebastian Martin Ruiz

**Comments:** 3 Pages.

The main purpose of this paper is using elementary arithmetical functions to give some expressions of the Smarandache Prime Function P(n).

**Category:** General Mathematics

[362] **viXra:1403.0450 [pdf]**
*submitted on 2014-03-21 05:55:53*

**Authors:** Sayed Khalil Elagan

**Comments:** 12 Pages.

The main purpose of this paper is to study the existence of a fixed points in fuzzy n-normed spaces. we proved our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings on
fuzzy n-normed spaces. Also we gave some remarks on fuzzy n-normed spaces.

**Category:** General Mathematics

[361] **viXra:1403.0448 [pdf]**
*submitted on 2014-03-21 05:59:06*

**Authors:** Muneer Jebreel Karama

**Comments:** 2 Pages.

The purpose of this article is to presents 23 Smarandache Identities (SI) (or Facts) with second, three, four, and five degrees. These SI have been obtained by the help of Maple 8(Programming language, see [1]).

**Category:** General Mathematics

[360] **viXra:1403.0447 [pdf]**
*submitted on 2014-03-21 06:00:36*

**Authors:** Caijuan Li

**Comments:** 9 Pages.

In this paper, we use the elementary method to study the properties of pseudo Smarandache function.

**Category:** General Mathematics

[359] **viXra:1403.0446 [pdf]**
*submitted on 2014-03-21 06:01:41*

**Authors:** Yanni Liu, Jinping Ma

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the calculating problem of one kind infinite series involving the k-th power complements, and obtain several interesting identities.

**Category:** General Mathematics

[358] **viXra:1403.0445 [pdf]**
*submitted on 2014-03-21 06:03:13*

**Authors:** Pei Zhang

**Comments:** 4 Pages.

Professor F.Smarandache asked us to study the properties of the k-power complement number sequence.

**Category:** General Mathematics

[357] **viXra:1403.0444 [pdf]**
*submitted on 2014-03-21 06:05:28*

**Authors:** M. Perez

**Comments:** 6 Pages.

Remarks on some problems regarding Inferior Smarandache Prime Part, Smarandache Prime Base, triple Smarandache function etc.

**Category:** Number Theory

[356] **viXra:1403.0442 [pdf]**
*submitted on 2014-03-21 06:07:32*

**Authors:** R. Vasuki, A. Nagaraj

**Comments:** 16 Pages.

Such a labeling is usually called a super mean labeling. A graph that admits a Smarandachely
super mean m-labeling is called Smarandachely super m-mean graph.

**Category:** General Mathematics

[355] **viXra:1403.0440 [pdf]**
*submitted on 2014-03-21 06:10:33*

**Authors:** Junliang Cai, Xiaoli Liu

**Comments:** 13 Pages.

Connected simple graph, k-partite graph, complete graph...

**Category:** General Mathematics

[354] **viXra:1403.0439 [pdf]**
*submitted on 2014-03-21 06:11:48*

**Authors:** Ahmad T. Ali

**Comments:** 7 Pages.

In this work, we introduce some special Smarandache curves in the Euclidean space. We study Frenet-Serret invariants of a special case. Besides, we illustrate examples of our main results.

**Category:** General Mathematics

[353] **viXra:1403.0438 [pdf]**
*submitted on 2014-03-21 06:13:23*

**Authors:** Melih Turgut, Suha Yilmaz

**Comments:** 6 Pages.

In this work, a system of differential equation on Minkowski space-time E41, a special case of Smarandache geometries ([4]), whose solution gives the components of a space-like curve on Frenet axis is constructed by means of Frenet equations. In view of some special solutions of this system, characterizations of some special space-like curves are presented.

**Category:** General Mathematics

[352] **viXra:1403.0437 [pdf]**
*submitted on 2014-03-21 06:25:30*

**Authors:** P.Jeyanthi, D.Ramya

**Comments:** 9 Pages.

Smarandachely super m-mean labeling.

**Category:** General Mathematics

[351] **viXra:1403.0435 [pdf]**
*submitted on 2014-03-21 06:27:58*

**Authors:** Chengliang Tian, Xiaoyan Li

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the solutions of the equation...

**Category:** General Mathematics

[350] **viXra:1403.0434 [pdf]**
*submitted on 2014-03-21 06:29:08*

**Authors:** Juanli Su

**Comments:** 3 Pages.

We using the elementary methods to study these problems, and prove that the problem
(B) is true.

**Category:** General Mathematics

[349] **viXra:1403.0433 [pdf]**
*submitted on 2014-03-21 06:30:10*

**Authors:** Yanchun Guo

**Comments:** 2 Pages.

The Smarandache prime additive complement, sequence.

**Category:** General Mathematics

[348] **viXra:1403.0432 [pdf]**
*submitted on 2014-03-21 06:31:07*

**Authors:** Xiaoxia Yan

**Comments:** 4 Pages.

Smarandache superior prime part, Smarandache inferior prime part, mean value,asymptotic formula.

**Category:** General Mathematics

[347] **viXra:1403.0431 [pdf]**
*submitted on 2014-03-21 06:32:00*

**Authors:** Zhang Wenpeng

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache function, and give an interesting asymptotic formula.

**Category:** General Mathematics

[346] **viXra:1403.0430 [pdf]**
*submitted on 2014-03-21 06:33:00*

**Authors:** Yanyan Han

**Comments:** 5 Pages.

This article uses the hyperbolic summation and the convolution method to obtain a better error term.

**Category:** General Mathematics

[345] **viXra:1403.0429 [pdf]**
*submitted on 2014-03-21 06:34:17*

**Authors:** Bin Cheng

**Comments:** 4 Pages.

We study the solvability of an equation
involving the Pseudo Smarandache Square-free function, and prove that it has infinity positive
integer solutions.

**Category:** General Mathematics

[344] **viXra:1403.0428 [pdf]**
*submitted on 2014-03-21 06:35:11*

**Authors:** Ren Dongmei

**Comments:** 3 Pages.

The main purpose of this paper is to study the number of the square-free number sequence,
and give two interesting asymptotic formulas for it. At last, give another asymptotic formula and a
corollary.

**Category:** General Mathematics

[343] **viXra:1403.0427 [pdf]**
*submitted on 2014-03-21 06:36:18*

**Authors:** Hai Yang, Ruiqin Fu

**Comments:** 8 Pages.

The main purpose of this paper is using the elementary methods to study the number of the
solutions of the equation...

**Category:** General Mathematics

[342] **viXra:1403.0426 [pdf]**
*submitted on 2014-03-21 06:37:24*

**Authors:** Liping Ding

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the
mean value distribution properties of Sc(n), and give two interesting mean value formulas for
it.

**Category:** General Mathematics

[341] **viXra:1403.0425 [pdf]**
*submitted on 2014-03-21 06:38:37*

**Authors:** W.B.Vasantha Kandasamy, M. Khoshnevisan, K.Ilanthenral

**Comments:** 16 Pages.

Here we for the first time define Smarandache representation of ¯nite S-bisemigroup.

**Category:** General Mathematics

[340] **viXra:1403.0424 [pdf]**
*submitted on 2014-03-21 06:39:40*

**Authors:** Yanting Yang

**Comments:** 4 Pages.

In this paper, we use the elementary method to study the convergence of the Smarandache alternate consecutive, reverse Fibonacci sequence and Smarandache multiple sequence.

**Category:** General Mathematics

[339] **viXra:1403.0422 [pdf]**
*submitted on 2014-03-21 06:41:55*

**Authors:** Han Ren, Yun Bai

**Comments:** 13 Pages.

In this paper, we investigate the structures of cycle bases with extremal properties which are related with map geometries, i.e., Smarandache 2-dimensional manifolds.

**Category:** General Mathematics

[338] **viXra:1403.0421 [pdf]**
*submitted on 2014-03-21 06:43:18*

**Authors:** W. B. Vasantha Kandasamy, A. Praveen Prakash, K. Thirusangu

**Comments:** 8 Pages.

In this paper we find the interrelations and the hidden pattern of the problems faced by the PWDs and their caretakers using Fuzzy Relational Maps (FRMs).

**Category:** General Mathematics

[337] **viXra:1403.0420 [pdf]**
*submitted on 2014-03-21 06:44:25*

**Authors:** Anant W. Vyawahare

**Comments:** 8 Pages.

This paper deals with the sums of products of ¯rst n natural numbers, taken r at a time. Many interesting results about the summations are obtained. Mr. Ramasubramanian [1] has already made some work in this direction. This paper is an extension of his work.

**Category:** General Mathematics

[336] **viXra:1403.0419 [pdf]**
*submitted on 2014-03-21 06:45:41*

**Authors:** R. Sridevi, S.Navaneethakrishnan, K.Nagarajan

**Comments:** 19 Pages.

We prove that these graphs are super Fibonacci graceful graphs.

**Category:** General Mathematics

[335] **viXra:1403.0418 [pdf]**
*submitted on 2014-03-21 06:46:57*

**Authors:** P.Jeyanthi, P.Selvagopal

**Comments:** 16 Pages.

In this paper we show that edge amalgamation of a finite collection of graphs isomorphic to any
2-connected simple graph H is H-supermagic.

**Category:** General Mathematics

[334] **viXra:1403.0417 [pdf]**
*submitted on 2014-03-21 06:47:55*

**Authors:** Yanpei Liu

**Comments:** 6 Pages.

This paper provides a way to observe embedings of a graph on surfaces based on join trees and then characterizations of orientable and nonorientable embeddabilities of a graph with given genus.

**Category:** General Mathematics

[333] **viXra:1403.0416 [pdf]**
*submitted on 2014-03-21 06:48:58*

**Authors:** Yanpei Liu

**Comments:** 7 Pages.

On the basis of reductions, polyhedral forms of Jordan axiom on closed curve in the plane are extended to establish characterizations for the surface embeddability of a graph.

**Category:** General Mathematics

[332] **viXra:1403.0415 [pdf]**
*submitted on 2014-03-21 06:50:04*

**Authors:** P.Siva Kota Reddy, M.C.Geetha, K.R.Rajanna

**Comments:** 6 Pages.

We give the relation between antipodal symmetric n-sigraphs and S-antipodal symmetric n-sigraphs. Further, we discuss structural characterization of S-antipodal symmetric n-sigraphs.

**Category:** General Mathematics

[331] **viXra:1403.0414 [pdf]**
*submitted on 2014-03-21 06:51:23*

**Authors:** Emin OZYILMAZ

**Comments:** 10 Pages.

A pseudo-Euclidean space, or Smarandache space is a pair.

**Category:** General Mathematics

[330] **viXra:1403.0413 [pdf]**
*submitted on 2014-03-21 06:52:33*

**Authors:** Suha Yılmaz, Melih Turgut

**Comments:** 6 Pages.

A regular curve with more than 2 breadths in Minkowski 3-space is called a Smarandache breadth curve. In this paper, we study a special case of Smarandache breadth curves.

**Category:** General Mathematics

[329] **viXra:1403.0412 [pdf]**
*submitted on 2014-03-21 06:53:39*

**Authors:** Linfan Mao

**Comments:** 9 Pages.

Topological groups, particularly, Lie groups are very important in differential geometry, analytic mechanics and theoretical physics. Applying Smarandache multi-spaces, topological spaces, particularly, manifolds and groups were generalized to combinatorial manifolds and multi-groups underlying a combinatorial structure in references.

**Category:** General Mathematics

[328] **viXra:1403.0411 [pdf]**
*submitted on 2014-03-21 06:54:48*

**Authors:** Shengxiang Lv, Tang Ling, Yuanqiu Huang

**Comments:** 12 Pages.

In this paper, we study the crossing number of the complete bipartite graph.

**Category:** General Mathematics

[327] **viXra:1403.0410 [pdf]**
*submitted on 2014-03-21 06:55:46*

**Authors:** A.Vijayalekshmi

**Comments:** 7 Pages.

Let G be a graph without isolated@@ vertices.

**Category:** General Mathematics

[326] **viXra:1403.0409 [pdf]**
*submitted on 2014-03-21 06:57:04*

**Authors:** A.Vijayalekshmi

**Comments:** 5 Pages.

Let G be a graph without isolated vertices.

**Category:** General Mathematics

[325] **viXra:1403.0408 [pdf]**
*submitted on 2014-03-21 06:58:17*

**Authors:** P.Siva Kota Reddy, S. Vijay

**Comments:** 6 Pages.

A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S.

**Category:** General Mathematics

[324] **viXra:1403.0407 [pdf]**
*submitted on 2014-03-21 06:59:41*

**Authors:** Manjunath Prasad K B, Venkanagouda M Goudar

**Comments:** 6 Pages.

In this paper, the concept of Total semirelib graph of a planar graph is introduced. We present a characterization of those graphs whose total semirelib graphs are planar, outer planar, Eulerian, hamiltonian with crossing number one.

**Category:** General Mathematics

[323] **viXra:1403.0406 [pdf]**
*submitted on 2014-03-21 07:01:20*

**Authors:** Yanting Yang, Min Fang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic method to study the convergence of the function ...

**Category:** General Mathematics

[322] **viXra:1403.0405 [pdf]**
*submitted on 2014-03-21 07:02:38*

**Authors:** P. Siva Kota Reddy, B. Prashanth, V. Lokesha

**Comments:** 4 Pages.

In this paper we characterize signed graphs which are switching equivalent to their Smarandachely 3-path step signed graphs.

**Category:** General Mathematics

[321] **viXra:1403.0404 [pdf]**
*submitted on 2014-03-21 07:04:05*

**Authors:** You Qiying

**Comments:** 4 Pages.

We study the hybrid mean value of the Smarandache triple factorial function and the Mangoldt function, and give a sharp asymptotic formula.

**Category:** General Mathematics

[320] **viXra:1403.0403 [pdf]**
*submitted on 2014-03-21 07:05:37*

**Authors:** G.Mahadevan, Selvam Avadayappan, J.Paulraj Joseph, T.Subramanian

**Comments:** 12 Pages.

The concept of triple connected graphs with real life application was introduced in [7] by considering the existence of a path containing any three vertices of a graph G. In this paper, we introduce a new domination parameter, called Smarandachely triple connected domination number of a graph.

**Category:** General Mathematics

[319] **viXra:1403.0402 [pdf]**
*submitted on 2014-03-21 07:06:58*

**Authors:** Akbar Ali.M.M, S.Panayappan, Vernold Vivin.J

**Comments:** 10 Pages.

In this paper we find the tulgeity of line, middle and total graph of wheel graph, Gear graph and Helm graph.

**Category:** General Mathematics

[318] **viXra:1403.0400 [pdf]**
*submitted on 2014-03-21 07:09:10*

**Authors:** Shen Hong

**Comments:** 4 Pages.

The main purpose of this paper is to study the distributive properties of k + 1-power free
numbers, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[317] **viXra:1403.0399 [pdf]**
*submitted on 2014-03-21 07:10:07*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

Arithmetic functions, inequalities.

**Category:** General Mathematics

[316] **viXra:1403.0398 [pdf]**
*submitted on 2014-03-21 07:11:56*

**Authors:** Chengliang Tian

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method to study the number of the solutions of two equations involving the Smarandache LCM dual function SL¤(n), and give their all positive integer solutions.

**Category:** General Mathematics

[315] **viXra:1403.0397 [pdf]**
*submitted on 2014-03-21 07:13:01*

**Authors:** Xu Zhefeng

**Comments:** 5 Pages.

The main purpose of this paper is to study the asymptotic property of the k-power complement numbers.

**Category:** General Mathematics

[314] **viXra:1403.0396 [pdf]**
*submitted on 2014-03-21 07:13:55*

**Authors:** Jason Earls

**Comments:** 3 Pages.

Two subsets of generalized Smarandache palindromes are constructed to determine some of their properties. New sequences, conjectures, and unsolved
questions are given.

**Category:** General Mathematics

[313] **viXra:1403.0395 [pdf]**
*submitted on 2014-03-21 07:14:55*

**Authors:** Yizhi Chen

**Comments:** 6 Pages.

In this paper, Smarandache U-liberal semigroup structure is given. It is shown that a semigroup S is Smarandache U-liberal semigroup if and only if it is a strong semilattice of some rectangular monoids.

**Category:** General Mathematics

[312] **viXra:1403.0393 [pdf]**
*submitted on 2014-03-21 07:17:56*

**Authors:** J.John, S.Panchali

**Comments:** 7 Pages.

Smarandachely k-monophonic path, Smarandachely k-monophonic number,monophonic path, monophonic number.

**Category:** General Mathematics

[311] **viXra:1403.0392 [pdf]**
*submitted on 2014-03-21 07:19:22*

**Authors:** Jianping Wang

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the value
distribution properties of SDF(n), and give an interesting mean value formula for it.

**Category:** General Mathematics

[310] **viXra:1403.0391 [pdf]**
*submitted on 2014-03-21 07:20:39*

**Authors:** Jianbin Chen

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the value distribution properties of the function SL(n), and give a sharper
value distribution theorem.

**Category:** General Mathematics

[309] **viXra:1403.0390 [pdf]**
*submitted on 2014-03-21 07:21:50*

**Authors:** Ismail Sahul Hamid, Mayamma Joseph

**Comments:** 11 Pages.

In this paper we introduce and initiate a study of a new variation of decomposition namely equiparity induced path decomposition of a graph which is defined to be a decomposition in which all the members are induced paths having same parity.

**Category:** General Mathematics

[308] **viXra:1403.0388 [pdf]**
*replaced on 2015-11-10 20:45:52*

**Authors:** Reginald T Cahill

**Comments:** 8 Pages. Minor correction re alpha decay

The discovery that the electron current fluctuations through Zener diode pn junctions in
reverse bias mode, which arise via quantum barrier tunnelling, are completely driven by
space fluctuations, has revolutionised the detection and characterisation of gravitational
waves, which are space fluctuations, and also has revolutionised the interpretation of
probabilities in the quantum theory. Here we report very simple and cheap table-top
gravitational wave experiments using Zener diode detectors, and reveal the implications
for the nature of space and time, and for the quantum theory of “matter”, and the
emergence of the “classical world” as space-induced wave function localisation. The
dynamical space posses an intrinsic inflation epoch.

**Category:** Relativity and Cosmology

[307] **viXra:1403.0387 [pdf]**
*replaced on 2014-04-03 17:42:58*

**Authors:** Reginald T Cahill

**Comments:** 8 Pages.

The discovery that the electron current fluctuations through Zener diode $pn$ junctions in reverse bias mode, which arise via quantum barrier tunnelling, are completely driven by space fluctuations, has revolutionised the detection and characterisation of gravitational waves, which are space fluctuations, and also has revolutionised the interpretation of probabilities in the quantum theory. Here we report new data from the very simple and cheap table-top gravitational wave experiment using Zener diode detectors, and reveal the implications for the nature of space and time, and for the quantum theory of ``matter", and the emergence of the ``classical world" as space-induced wave function localisation. The dynamical space posses an intrinsic inflation epoch with associated fractal turbulence: gravitational waves, perhaps as observed by the BICEP2 experiment in the Antarctica.

**Category:** Relativity and Cosmology

[306] **viXra:1403.0386 [pdf]**
*submitted on 2014-03-20 22:39:22*

**Authors:** S.C. Gaudie

**Comments:** 4 pages; mostly font 11; A4 paper; UK English; Freelance scientist.

This looks at black holes from a different viewpoint. The black holes and normal space are viewed as two parts to a single closed system.
the ideas are:-
[1] As electrons and protons have mass they cannot travel at the velocity of light. This would mean that there must be three event horizons.
(a) The electro-magnetic event horizon.
(b) The electron - positron event horizon
(c) The proton - anti-proton event horizon
[2] If a black hole is in empty space the only influence is that the pairs formed from virtual particles are pulled apart at the last two event horizons. The infalling particles will have more kinetic energy than the emitted particles.
From the E = m * c^2 equivalence principle,
the kinetic energy differences will add mass to the black hole.
[3] Infalling photons should gain energy from the gravity gradient and the “emitted” photon (Hawking radiation from inside the e - p event horizon) should lose energy because of the gravity gradient. Overall photons falling into the black hole would have higher photonic energy than the “emitted” photons.
the photon energy differences will add mass to the black hole.
[2] & [3] = The original mass of the black hole does not reduce! [Unless bombarded with antimatter!]
[4] Black holes have a massive “footprint” in our “normal space” [NS].
Because of this we must consider black holes & “normal space” together, as two parts of “closed system” both from a thermodynamic and a quantum point of view.
Properties in & around black holes, including polarisation [polarization] of the cosmic microwave background radiation, are considered from this new viewpoint.

**Category:** Relativity and Cosmology

[305] **viXra:1403.0385 [pdf]**
*submitted on 2014-03-21 02:44:35*

**Authors:** H.B.Walikar, Kishori P. Narayankar, Shailaja S. Shirakol

**Comments:** 5 Pages.

A set S of vertices in a graph G is said to be a Smarandachely k-dominating set if each vertex of G is dominated by at least k vertices of S.

**Category:** General Mathematics

[304] **viXra:1403.0384 [pdf]**
*submitted on 2014-03-21 02:46:31*

**Authors:** Jon Perry

**Comments:** 6 Pages.

We consider the sum of digits function which maps an integer to the sum of it’s digits, for example 142 is mapped to 1 + 4 + 2 = 7. This papers examines the question of how many other integers are mapped to a given digit in the range 1 to 10z.

**Category:** General Mathematics

[303] **viXra:1403.0383 [pdf]**
*submitted on 2014-03-21 02:47:59*

**Authors:** Li Congwei

**Comments:** 3 Pages.

Let Fk denotes the set of k-free number.

**Category:** General Mathematics

[302] **viXra:1403.0382 [pdf]**
*submitted on 2014-03-21 02:50:33*

**Authors:** Ren Ganglian

**Comments:** 4 Pages. 4

The author had used the analytic method to consider the special case: p1 and p2 are two fixed distinct primes.

**Category:** General Mathematics

[301] **viXra:1403.0381 [pdf]**
*submitted on 2014-03-21 02:52:09*

**Authors:** S.K.Vaidya, N.H.Shah

**Comments:** 8 Pages.

The labeling of discrete structures is a potential area of research due to its wide range of applications. The present work is focused on one such labeling called odd harmonious labeling.

**Category:** General Mathematics

[300] **viXra:1403.0380 [pdf]**
*submitted on 2014-03-21 02:53:23*

**Authors:** Yao Weili

**Comments:** 3 Pages.

The odd sieve sequence is the sequence, which is composed of all odd numbers that are not equal to the difference of two primes. In this paper, we use analytic method to study the mean value properties of this sequence, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[299] **viXra:1403.0379 [pdf]**
*submitted on 2014-03-21 02:54:46*

**Authors:** F. Salama

**Comments:** 10 Pages.

In this paper we will define a new type of graph. The idea of this definition is based on when we illustrate the cardiovascular system by a graph we find that not all vertices have the same important so we define this new graph and call it 1- mother vertex graph.

**Category:** General Mathematics

[298] **viXra:1403.0378 [pdf]**
*submitted on 2014-03-21 02:57:44*

**Authors:** N.Jafari Rad, H.Rezazadeh

**Comments:** 7 Pages.

A defensive alliance in a graph G = (V,E) is a set of vertices S ⊆ V satisfying the condition that for every vertex v ∈ S, the number of v’s neighbors is at least as large as the number of v’s neighbors in V − S.

**Category:** General Mathematics

[297] **viXra:1403.0377 [pdf]**
*submitted on 2014-03-21 02:59:41*

**Authors:** Bibin K. Jose

**Comments:** 13 Pages.

All graphs considered in this paper are finite, simple, undirected and connected. For graph
theoretic terminology we refer to Harary.

**Category:** General Mathematics

[296] **viXra:1403.0375 [pdf]**
*submitted on 2014-03-21 03:02:20*

**Authors:** Henry Ibstedt

**Comments:** 16 Pages.

This article originates from a proposal by M. L. Perez of American Research Press to carry out a study on Smarandache generalized palindromes [1]. The prime numbers were chosen as a rst set of numbers to apply the development of ideas and computer programs on. The study begins by exploring regular prime number palindromes. To continue the study it proved useful to introduce a new concept, that of extended palindromes with the property that the union of regular palindromes and extended palindromes form the set of Smarandache generalized palindromes. An interesting observation is proved in the article, namely that the only regular prime number palindrome with an even number of digits is 11.

**Category:** General Mathematics

[295] **viXra:1403.0371 [pdf]**
*submitted on 2014-03-21 03:07:31*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 6 Pages.

The study of the Smarandache concept in groupoids was initiated by W.B. Vasantha Kandasamy in [18].

**Category:** General Mathematics

[294] **viXra:1403.0370 [pdf]**
*submitted on 2014-03-21 03:08:52*

**Authors:** Keerthi G.Mirajkar, Iramma M.Kadakol

**Comments:** 8 Pages.

The concept of pathos of a graph G was introduced by Harary [1] as a collection of minimum number of line disjoint open paths whose union is G.

**Category:** General Mathematics

[293] **viXra:1403.0369 [pdf]**
*submitted on 2014-03-21 03:10:31*

**Authors:** Muddebihal M. H., Syed Babajan

**Comments:** 15 Pages.

In this communications, the concept of pathos semitotal and total block graph of a graph is introduced. Its study is concentrated only on trees. We present a characterization of those graphs whose pathos semitotal block graphs are planar, maximal outer planar, non-minimally non-outer planar, non-Eulerian and hamiltonian.

**Category:** General Mathematics

[292] **viXra:1403.0368 [pdf]**
*submitted on 2014-03-21 03:11:54*

**Authors:** Muddebihal M. H., Syed Babajan

**Comments:** 13 Pages.

In this communication, the concept of pathos total semitotal and entire total block graph of a tree is introduced. Its study is concentrated only on trees. We present a characterization of graphs whose pathos total semitotal block graphs are planar, maximal outerplanar, minimally nonouterplanar, nonminimally nonouterplanar, noneulerian and hamiltonian.

**Category:** General Mathematics

[291] **viXra:1403.0367 [pdf]**
*submitted on 2014-03-21 03:13:20*

**Authors:** P. Siva Kota Reddy S. Vijay, H. C. Savithri

**Comments:** 5 Pages.

For standard terminology and notion in digraph theory, we refer the reader to the classic text-
books of Bondy and Murty [2]and Harary et al. [4]; the non-standard will be given in this paper
as and when required.

**Category:** General Mathematics

[290] **viXra:1403.0366 [pdf]**
*submitted on 2014-03-21 03:15:05*

**Authors:** A.Lourdusamy, S.Samuel Jeyaseelan, Loyola T.Mathivanan

**Comments:** 4 Pages.

Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move (or pebbling step) is defined as the removal of two pebbles from a vertex and placing one pebble on an adjacent vertex.

**Category:** General Mathematics

[289] **viXra:1403.0365 [pdf]**
*submitted on 2014-03-21 03:16:01*

**Authors:** Catalin Barbu

**Comments:** 4 Pages.

In this note, we present a proof of the hyperbolic a Smarandache's pedal polygon theorem in the Poincar¶e disc model of hyperbolic geometry.

**Category:** General Mathematics

[288] **viXra:1403.0364 [pdf]**
*submitted on 2014-03-21 03:17:21*

**Authors:** Sharada B.

**Comments:** 5 Pages.

In this paper we introduce the concept of
perfect domination excellent graph as a graph in which every vertex belongs to some perfect
dominating set of minimum cardinality. We also provide a constructive characterization of
perfect domination excellent trees.

**Category:** General Mathematics

[287] **viXra:1403.0363 [pdf]**
*submitted on 2014-03-21 03:18:34*

**Authors:** Maohua Le

**Comments:** 7 Pages.

Let N be the set of all positive integer. For any positive integer a, let S(a) denote the Smarandache function of a. Let n be a postivie integer.

**Category:** General Mathematics

[286] **viXra:1403.0361 [pdf]**
*submitted on 2014-03-21 03:21:26*

**Authors:** Muneer Jebreel Karama

**Comments:** 11 Pages.

In [1] I studied the concept of Smarandache n-expressions, for example I proposed
formulas, found solutions, proposed open questions, and conjectured, but all for the ¯xed 3,
and 2 numbers, but what will happen if these equations have di®erent ¯xed numbers such as
7? This paper will answer this question.

**Category:** General Mathematics

[285] **viXra:1403.0360 [pdf]**
*submitted on 2014-03-21 03:22:28*

**Authors:** M.A. Gungor, A.Z. Pirdal, M. Tosun

**Comments:** 10 Pages.

In this paper we have given the canonical
relative systems of a plane with respect to other planes so that the plane has a curve on
it, which is spacelike or timelike under homothetic motion.

**Category:** General Mathematics

[284] **viXra:1403.0359 [pdf]**
*submitted on 2014-03-21 03:23:45*

**Authors:** B.Basavanagoud, V.R.Kulli

**Comments:** 8 Pages.

In this paper, we deduce a necessary and sufficient condition for graphs whose plick graphs have crossing number 1. We also obtain a necessary and sufficient condition for plick graphs to have crossing number 1 in terms of forbidden subgraphs.

**Category:** General Mathematics

[283] **viXra:1403.0358 [pdf]**
*submitted on 2014-03-21 03:25:00*

**Authors:** Zhao Xiaopeng, Ren Zhibin

**Comments:** 3 Pages.

In this paper, we using the elementary method to study the convergent property of one class Dirichlet series involving a special sequences, and give an interesting identity for it.

**Category:** General Mathematics

[282] **viXra:1403.0357 [pdf]**
*submitted on 2014-03-21 03:26:12*

**Authors:** Liu Yanni, Gao Peng

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of a new arithmetical function involving the m-power free part of an integer, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[281] **viXra:1403.0356 [pdf]**
*submitted on 2014-03-21 03:28:14*

**Authors:** Li Junzhuang, Gao Peng

**Comments:** 3 Pages.

we use the elementary method to study the asymptotic properties of log and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[280] **viXra:1403.0355 [pdf]**
*submitted on 2014-03-21 03:29:23*

**Authors:** Ma Yuankui, Zhang Tianping

**Comments:** 4 Pages.

The main purpose of this paper is to study the distribution properties ofm-power residues numbers, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[279] **viXra:1403.0354 [pdf]**
*submitted on 2014-03-21 03:31:23*

**Authors:** P. Siva Kota Reddy, S. Vijay, V. Lokesha

**Comments:** 6 Pages.

In this paper, we present solutions of some
signed graph switching equations involving the line signed graph, complement and n-th power signed graph operations.

**Category:** General Mathematics

[278] **viXra:1403.0353 [pdf]**
*submitted on 2014-03-21 03:32:50*

**Authors:** Sayed Elagan

**Comments:** 6 Pages.

It is shown that linear functional on topological vector spaces are Smarandachely precontinuous. Prebounded, totally prebounded and precompact sets in topological vector spaces are identified.

**Category:** General Mathematics

[277] **viXra:1403.0352 [pdf]**
*submitted on 2014-03-21 03:34:13*

**Authors:** Songye Shang, Juanli Su

**Comments:** 3 Pages.

The main purpose of the paper is using the elementary method to study the properties of the Smarandache Prime-Digital Subsequence, and give an interesting limit Theorem.This solved a problem proposed by Charles.

**Category:** General Mathematics

[276] **viXra:1403.0351 [pdf]**
*submitted on 2014-03-21 03:35:39*

**Authors:** Yahui Yu, Lixiang Cai

**Comments:** 3 Pages.

In this paper, we de¯ned some determinants involving the Smarandache prime part sequences, and introduced two conjectures proposed by professor Zhang Wenpeng.

**Category:** General Mathematics

[275] **viXra:1403.0350 [pdf]**
*submitted on 2014-03-21 03:45:33*

**Authors:** Yi Yuan

**Comments:** 3 Pages.

About this problem, Professor Zhang and Liu in [2] have studied it and obtained an interesting asymptotic formula. That is, for any fixed prime p and any positive integer n...

**Category:** General Mathematics

[274] **viXra:1403.0349 [pdf]**
*submitted on 2014-03-21 03:46:45*

**Authors:** Ding Liping

**Comments:** 3 Pages.

The problem is interesting because it can help us to calculate the Smarandache function.

**Category:** General Mathematics

[273] **viXra:1403.0348 [pdf]**
*submitted on 2014-03-21 03:48:55*

**Authors:** Weiyi Zhu

**Comments:** 4 Pages.

For any positive integer n and prime p, let Sp(n) denotes the smallest positive integer m such that m! is divisible by ...

**Category:** General Mathematics

[272] **viXra:1403.0347 [pdf]**
*submitted on 2014-03-21 03:51:15*

**Authors:** Mingshun Yang

**Comments:** 3 Pages.

For any positive integer n, the famous Euler function is defined as the number of all integers m...

**Category:** General Mathematics

[271] **viXra:1403.0346 [pdf]**
*submitted on 2014-03-21 03:52:44*

**Authors:** Xiaojun Qi

**Comments:** 7 Pages.

In his book "Only problems, not solutions", professor F.Smarandache introduced many
functions, sequences and unsolved problems, many authors had studied it.

**Category:** General Mathematics

[270] **viXra:1403.0345 [pdf]**
*submitted on 2014-03-21 03:54:13*

**Authors:** Baoli Liu, Xiaowei Pan

**Comments:** 3 Pages.

For any positive integer n, the famous@@ F.Smarandache function S(n) is defined
as the smallest positive integer m such that n divides m!.

**Category:** General Mathematics

[269] **viXra:1403.0344 [pdf]**
*submitted on 2014-03-21 03:55:06*

**Authors:** Jozsef Sandor

**Comments:** 6 Pages.

Let T(n) denote the product of divisors of the positive integer n.

**Category:** General Mathematics

[268] **viXra:1403.0342 [pdf]**
*submitted on 2014-03-21 03:57:08*

**Authors:** Claudiu Coanda

**Comments:** 4 Pages.

In this article we prove the Smarandache-Patrascu's theorem in relation to the inscribed orthohomological triangles using the barycentric coordinates.

**Category:** General Mathematics

[267] **viXra:1403.0341 [pdf]**
*submitted on 2014-03-21 03:58:28*

**Authors:** A.A.A.Agboola

**Comments:** 10 Pages.

The purpose of this paper is to present some properties of bialgebraic structures.

**Category:** General Mathematics

[266] **viXra:1403.0340 [pdf]**
*submitted on 2014-03-21 04:00:00*

**Authors:** Wei Qin

**Comments:** 3 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is de¯ned as
the smallest positive integer m such that n / m!.

**Category:** General Mathematics

[265] **viXra:1403.0338 [pdf]**
*submitted on 2014-03-21 04:02:51*

**Authors:** Anant W. Vyawahare

**Comments:** 6 Pages.

"A natural number n is a Happy Number if the sum of squares of its digits, when added iteratively, terminates to 1."

**Category:** General Mathematics

[264] **viXra:1403.0336 [pdf]**
*submitted on 2014-03-21 04:05:14*

**Authors:** Li Zhanhu

**Comments:** 3 Pages.

The main purpose of this paper is using elementary method to study the main value of the
m-th power mean of the sum of all digits in the Smarandache pseudo-number sequence, and give some
interesting asymptotic formulae for them.

**Category:** General Mathematics

[263] **viXra:1403.0335 [pdf]**
*submitted on 2014-03-21 04:06:09*

**Authors:** A.A.K. Majumdar

**Comments:** 25 Pages.

This paper gives some results and observations related to the Pseudo-Smarandache function Z(n). Some explicit expressions of Z(n) for some particular cases of n are also given.

**Category:** General Mathematics

[262] **viXra:1403.0334 [pdf]**
*submitted on 2014-03-21 04:07:22*

**Authors:** A.A.K. Majumdar

**Comments:** 11 Pages.

The Smarandache function, denoted by S(n), is de¯ned as follows...

**Category:** General Mathematics

[261] **viXra:1403.0332 [pdf]**
*submitted on 2014-03-21 04:09:44*

**Authors:** Yuanbing Lou

**Comments:** 3 Pages.

For any positive integer n, the famous pseudo Smarandache function Z(n) is de¯ned as the smallest positive integer m such that n evenly divides...

**Category:** General Mathematics

[260] **viXra:1403.0331 [pdf]**
*submitted on 2014-03-21 04:10:54*

**Authors:** Xuhui Fan

**Comments:** 5 Pages.

The main purpose of this paper is using the elementary methods to study the mean value properties of the Pseudo-Smarandache-Squarefree function and Smarandache function, and give two sharper asymptotic formulas for it.

**Category:** General Mathematics

[259] **viXra:1403.0328 [pdf]**
*submitted on 2014-03-21 04:14:23*

**Authors:** B. Sooryanarayana, Vishu Kumar M., Manjula K.

**Comments:** 25 Pages.

Let G be a connected graph.

**Category:** General Mathematics

[258] **viXra:1403.0326 [pdf]**
*submitted on 2014-03-21 04:16:35*

**Authors:** Zhibin Ren

**Comments:** 3 Pages.

This solved a problem posed by Zhang Wenpeng during the Fourth International Conference on Number Theory and the Smarandache Problems.

**Category:** General Mathematics

[257] **viXra:1403.0325 [pdf]**
*submitted on 2014-03-21 04:19:11*

**Authors:** Jason Earls

**Comments:** 3 Pages.

In [1] Recursive Prime Numbers were studied and shown to be finite. This article deals with the same "recursive" topic, but applies the method to numbers whose Smarandache value, S(n), gives a palindromic number.

**Category:** General Mathematics

[256] **viXra:1403.0324 [pdf]**
*submitted on 2014-03-21 04:21:04*

**Authors:** Weiyi Zhu

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary methods to study the relationship between Sp(n) and Sp(kn), and give an interesting identity.

**Category:** General Mathematics

[255] **viXra:1403.0323 [pdf]**
*submitted on 2014-03-21 04:23:03*

**Authors:** Mladen V. Vassilev-Missana, Krassimir T. Atanassov

**Comments:** 26 Pages.

In 1999, the second author of this remarks published a book over 30 of Smarandache's
problems in area of elementary number theory (see [1, 2]). After this, we worked over new 20
problems that we collected in our book [28]. These books contain Smarandache's problems, described in [10, 16]. The present paper contains some of the results from [28].

**Category:** General Mathematics

[254] **viXra:1403.0322 [pdf]**
*submitted on 2014-03-21 04:24:38*

**Authors:** Jason Earls

**Comments:** 3 Pages.

In 1987, Mike Keith introduced "repfigits" (replicating Fibonacci-like digits) [1].
In this paper two generalizations of repfigits are presented in which Smarandache type functions are applied to the digits of n. Some conjectures and unsolved questions are then proposed.

**Category:** General Mathematics

[253] **viXra:1403.0321 [pdf]**
*submitted on 2014-03-21 04:26:04*

**Authors:** R. Ponraj, J. Vijaya Xavier Parthipan, R. Kala

**Comments:** 9 Pages.

Here we study about the pair sum labeling of some standard graphs.

**Category:** General Mathematics

[252] **viXra:1403.0320 [pdf]**
*submitted on 2014-03-21 04:27:43*

**Authors:** S.K.Vaidya, C.M.Barasara

**Comments:** 8 Pages.

A graph labeling is an assignment of integers to the vertices or edges or both subject to certain condition(s). If the domain of the mapping is the set of vertices (or edges) then the labeling is called a vertex labeling (or an edge labeling).

**Category:** General Mathematics

[251] **viXra:1403.0319 [pdf]**
*submitted on 2014-03-21 04:28:41*

**Authors:** Maohua Le

**Comments:** 2 Pages.

In this paper we give an explicit formula for the n times Smarandache reverse auto correlated sequence of natural numbers.

**Category:** General Mathematics

[250] **viXra:1403.0318 [pdf]**
*submitted on 2014-03-21 04:29:39*

**Authors:** Jason Earls

**Comments:** 2 Pages.

A computer program was written and a search through the first 1000SRPS numbers yielded several useful results.

**Category:** General Mathematics

[249] **viXra:1403.0317 [pdf]**
*submitted on 2014-03-21 04:30:51*

**Authors:** Fu Yuhua, Fu Anjie

**Comments:** 7 Pages.

According to Smarandache’s neutrosophy, the G¨odel’s incompleteness theorem
contains the truth, the falsehood, and the indeterminacy of a statement under consideration.
It is shown in this paper that the proof of G¨odel’s incompleteness theorem is faulty, because
all possible situations are not considered (such as the situation where from some axioms
wrong results can be deducted, for example, from the axiom of choice the paradox of the
doubling ball theorem can be deducted; and many kinds of indeterminate situations, for
example, a proposition can be proved in 9999 cases, and only in 1 case it can be neither
proved, nor disproved).

**Category:** General Mathematics

[248] **viXra:1403.0315 [pdf]**
*replaced on 2014-04-13 07:58:49*

**Authors:** Michael Muteru

**Comments:** 09 Pages.

With the current global human population surpassing the 7 billon mark, energy requirements exponentially rise (shift) with demographics. Living in a planetary system of finite natural resources the Biosphere in turn overstretched. Humanity has to think outside the box to satisfy / quench this first for energy within our technology means. I herein apply the notion of harnessing the energy of the sun (star using green Biomass as the only efficient means that not only ‘cleans’ our planet of a biotic factors upsetting the planet’s climate, but provide sustainable energy to power the rising population while also promoting biodiversity but providing all life forms on planet suitable Biomes for we all need one another for successful co-existence. The reader of this work is left with the meditative task of answering on where we lie on the cosmic energy scale (Kardashev scale) our obligations, where we should be. The leader should derive methods which he/she can personal apply in life making the best out of the scenarios within, with the ultimate goal making the planet for all life (not only humans) with one foot on earth and the other in the heavens(Cosmos) we set forth.

**Category:** Quantum Gravity and String Theory

[247] **viXra:1403.0314 [pdf]**
*submitted on 2014-03-20 07:32:04*

**Authors:** Syed Afsar Abbas

**Comments:** 4 Pages.

Half a century old Okamoto-Nolen-Schiffer anomaly,
has not been properly resolved as of now.
We revive here, an old model of Sacks of a phenomenological exchange potential,
which uses Majorana exchange potential idea to obtain the electric charge switching back and forth between a neutron-proton
pair, thereby producing a current along the line joining them.
Thus a modified charge current is required to fulfil a new continuity equation.
This introduces a new term, completely missed out so far, in the binding energy difference in the mirror nuclei.
Thus the above anomaly is resolved consistently within a completely nuclear physics framework.

**Category:** Nuclear and Atomic Physics

[246] **viXra:1403.0313 [pdf]**
*replaced on 2018-07-03 12:14:44*

**Authors:** Osvaldo Domann

**Comments:** 71 Pages. Copyright. The content of the present work, its ideas, axioms, postulates, definitions, derivations, results, findings, etc., can be reproduced only by making clear reference to the author.

The methodology of today's theoretical physics consists in introducing first all known forces by separate definitions independent of their origin, arriving then to quantum mechanics after postulating the particle's wave, and is then followed by attempts to infer interactions of particles and fields postulating the invariance of the wave equation under gauge transformations, allowing the addition of minimal substitutions. The origin of the limitations of our standard theoretical model is the assumption that the energy of a particle is concentrated at a small volume in space. The limitations are bridged by introducing artificial objects and constructions like particles wave, gluons, strong force, weak force, dark matter, dark energy, big bang, etc. The proposed approach models subatomic particles such as electrons and positrons as focal points in space where continuously fundamental particles are emitted and absorbed, fundamental particles where the energy of the electron or positron is stored as rotations defining longitudinal and transversal angular momenta (fields). Interaction laws between angular momenta of fundamental particles are postulated in that way, that the basic laws of physics (Coulomb, Ampere, Lorentz, Maxwell, Gravitation, bending of particles and interference of photons, Bragg, etc.) can be derived from the postulates. This methodology makes sure, that the approach is in accordance with the basic laws of physics, in other words, with well proven experimental data. Due to the dynamical description of the particles the proposed approach has not the limitations of the standard model and is not forced to introduce artificial objects or constructions. All forces are the product of electronagnetic interactions described by QED. Interactions like QCD and Gauge/Gravity Duality are simply the product of the insufficiencies of the SM and not required.

**Category:** Classical Physics

[245] **viXra:1403.0312 [pdf]**
*submitted on 2014-03-20 09:46:46*

**Authors:** Jeffrey Joseph Wolynski

**Comments:** 2 Pages. 2 illustrations, 3 references

It is explained in easy to understand language and pictures the main differences between GTSM’s (The General Theory of Stellar Metamorphosis) location for accretion and the establishment’s location for accretion.

**Category:** Astrophysics

[244] **viXra:1403.0310 [pdf]**
*submitted on 2014-03-20 00:14:06*

**Authors:** David Eelbode, Eckhard Hitzer

**Comments:** Submitted to Publications of Research Institute for Mathematical Sciences (PRIMS), March 2014, 18 pages.

This paper briefly reviews the notion of Clifford's geometric algebras and vector to multivector functions; as well as the field of Clifford analysis (function theory of the Dirac operator). In Clifford Fourier transformations (CFT) on multivector signals the complex unit $i\in \mathbb{C}$ is replaced by a multivector square root of $-1$, which may be a pseudoscalar in the simplest case. For these transforms we derive, via a multivector function representation in terms of monogenic polynomials, the operator representation of the CFTs by exponentiating the Hamilton operator of a harmonic oscillator.

**Category:** Functions and Analysis

[243] **viXra:1403.0309 [pdf]**
*replaced on 2014-03-23 01:58:55*

**Authors:** francis M. Sanchez

**Comments:** 2 Pages. Note to the Editor of Nature (12 March 2013), rejected without justification

A generalization of the virial theorem, using the basic quantum proportionality between energy and frequency, leads to a Coherence Principle which applies both in atomistics, astrophysics and cosmology, with the determination of several so-called 'free cosmic parameters'. An application in biology is also proposed

**Category:** General Science and Philosophy

[242] **viXra:1403.0308 [pdf]**
*submitted on 2014-03-20 03:50:42*

**Authors:** Mustafa Salti

**Comments:** 7 Pages. Eur.Phys.J. Plus (2014) 129:42

In literature, a large number of approaches have been done to reconstruct the potential and dynamics of the scalar fields by establishing a connection between holographic/Ricci/new agegraphic/ghost energy density and a scalar eld model of dark energy. In most of these attempts, the analytical form of the potentials in terms of the scalar eld have not been reconstructed due to the complexity of the equations involved. In the present work, we establish a correspondence between ghost dark energy and quintessence, tachyon and dilaton scalar eld models in anisotropic Bianchi type-I universe to reconstruct the dynamics of these scalar fields.

**Category:** Relativity and Cosmology

[241] **viXra:1403.0307 [pdf]**
*submitted on 2014-03-20 03:53:06*

**Authors:** Mustafa Salti

**Comments:** 6 Pages. Commun. Theor. Phys. 61 (2014) 171–176.

In the present study, using the Fourier analyze method and considering the Bianchi-type I spacetime, we investigate
the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give the same results.
Furthermore, we also discuss the harmonic oscillator behavior of the solutions.

**Category:** Relativity and Cosmology

[240] **viXra:1403.0306 [pdf]**
*submitted on 2014-03-20 03:57:40*

**Authors:** Mustafa Salti

**Comments:** 5 Pages. Int.J.Theor.Phys. 52 (2013) 4583-4591

The main goal of the present work is to investigate the validity of the second law of gravitational
thermodynamics in an expanding Godel-type universe filled with generalized Chaplygin gas interacting
with cold dark matter. By assuming the Universe as a thermodynamical system bounded by the
apparent horizon, and calculating separately the entropy variation for generalized Chaplygin gas,
cold dark matter and for the horizon itself, we obtained an expression for the time derivative of the
total entropy. We conclude that the 2nd law of gravitational thermodynamics is conditionally valid
in the cosmological scenario where the generalized Chaplygin gas interacts with cold dark matter.

**Category:** Relativity and Cosmology

[239] **viXra:1403.0305 [pdf]**
*submitted on 2014-03-19 17:12:04*

**Authors:** Leszek w. Guła

**Comments:** 3 Pages. I woul like to request publish my work.

Elementarny dowód Wielkiego Twierdzenia Fermata (Elementary proof of The Fermat's Last Theorem).

**Category:** Number Theory

[238] **viXra:1403.0304 [pdf]**
*submitted on 2014-03-19 18:07:58*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 3 Pages.

We present some new convergence and
boundedness theorem with respect to
filter convergence for lattice
group-valued measures, whose techniques
are based on sliding hump
arguments.

**Category:** Functions and Analysis

[237] **viXra:1403.0303 [pdf]**
*submitted on 2014-03-19 14:56:28*

**Authors:** John A. Gowan

**Comments:** 1 Page.

Diagram with text presents major stages of the gravitational take-over of the electromagnetic metric and its functions at increasing matter densities and local gravitational field strengths.

**Category:** Relativity and Cosmology

[236] **viXra:1403.0302 [pdf]**
*replaced on 2014-03-21 03:08:46*

**Authors:** Shunichi Katoh

**Comments:** 4 Pages. Opportunity for Finding a Simple Proof of FLC.

This paper presents AAC conjecture for a simple and finer version of FLT (Fermat's Last Theorem) which had been FLC (Fermat's Last Conjecture) for more than 350 years since 1637 and was finally proved in the end of the 20th cencury in a profoundly sophisticated and complex way. However complex the proof is, FLC itself is very simple. It conjectures that a simple equation has no solutions. AAC conjecture comes from a pursuit of a simpler proof of FLC. It conjectures that two simple equations have no solutions except some evident ones. It is shown, in a rigorous and step-by-step way, that if AAC is true then FLC is true, and that AAC is a finer version of FLC. AAC conjecture will give us a finer view and an opportunity for finding a simple proof of FLC. If AAC conjecture is proved without using FLT, then AAC theorem will be a theorem for itself, and FLT will be a beautiful specialization of AAC theorem.

**Category:** Number Theory

[235] **viXra:1403.0300 [pdf]**
*replaced on 2015-05-30 10:35:44*

**Authors:** Frank Dodd Tony Smith Jr

**Comments:** 20 Pages.

B-mode CMB polarization observed by BICEP2 is consistent with the Octonionic Inflation of E8 Physics that does not use a conventional inflaton field but instead uses NonAssociative Non-Unitary Octonionic Quantum Processes. V2 adds details such as inflation producing a matter-dominated Universe. V3 corrects and expands material about matter-antimatter and generation-antigeneration. V4 add some details about Octonionic Inflation. V5 adds discussion of gravity fluctuations leading to cosmological structure.

**Category:** High Energy Particle Physics

[234] **viXra:1403.0296 [pdf]**
*submitted on 2014-03-18 09:18:23*

**Authors:** Joel M Williams

**Comments:** 4 Pages.

Diamonds and silicon wafers are prized materials that share a common crystal structure. Tetrahedral atom interactions are the basis for their properties: hardness, thermal conductivity, electrical non-conductivity, etc. sp3-Hybrid orbitals provide the current explanation for the interatomic “bond” connections. These covalent bonds, however, do not provide an adequate mechanism for these materials acting as semiconductors. Ionic bonding between atoms with the crystal lattice fully connected via overlapped, but “unoccupied”, orbitals does provide a logical structure to explain how semiconductor doping works, however.

**Category:** Quantum Physics

[233] **viXra:1403.0295 [pdf]**
*replaced on 2014-03-19 01:04:07*

**Authors:** Carlos Castro

**Comments:** 14 Pages. Submitted to Physics Letters B

We improve our earlier work in [14] and derive the minimal length
string/membrane uncertainty relations by imposing momentum slices in flat Clifford spaces. The Jacobi identities associated with the modified Weyl-Heisenberg algebra require noncommuting spacetime coordinates, but commuting momenta, and which is compatible with the notion of curved momentum space. Clifford Phase Space Relativity requires the introduction of a maximal scale which can be identified with the Hubble scale and is a consequence of Born's Reciprocal Relativity Principle.

**Category:** Quantum Gravity and String Theory

[232] **viXra:1403.0294 [pdf]**
*submitted on 2014-03-17 17:45:38*

**Authors:** Leszek W. Guła

**Comments:** 3 Pages. Thanks

**Category:** Number Theory

[231] **viXra:1403.0293 [pdf]**
*submitted on 2014-03-17 18:13:49*

**Authors:** Richard A. Marsen, James R. Marsen

**Comments:** 10 Pages.

The Tron Theory is proposed for unifying physical science. It presents a new fundamental particle called the tron. The tron is several orders of magnitude smaller than the electron. Trons are premised to be everywhere, their physical involvement thorough. Each tron is composed of even smaller particles called rons. Adjacent trons attract each other with an elemental force that is neutral of charge. The inter-tron force is inversely proportional to the distance between tron cores. The fundamental particles are constructed with trons closely pressed together. Tenuous arrays of trons cohere to form the respective imponderable physical fields. Micro-particle action is revealed as a causal discipline. Particles are presented in determinate activity. The composition and dynamic properties of the tron and ron are set forth in seven axiom forming the Tron Postulate.

**Category:** Classical Physics

[230] **viXra:1403.0292 [pdf]**
*replaced on 2014-03-18 08:24:35*

**Authors:** Rodney Bartlett

**Comments:** Replaced because I left out about 5 pages that try to answer questions.

What do you think of today's attention to so-called echoes of the big bang (imprints of gravitational waves from the time of the big bang that have left their trace in the cosmic microwave background)? It's obviously an amazing discovery but my fear is that it's going to be used more for alleged confirmation of present theories than for investigation of the questions it raises (especially in the short term). A starting point for these questions is, "If the universe expanded to about the size of a football in 10^-36 second, what was outside the football?" Many people will say this is an invalid question because no space or time existed outside the football. But I think that's mere evasion of the question (understandable if there are no other ideas to fall back on).
There's a simple alternative which says there was space and time outside the football, and this alternative is supported by the modern idea of a multiverse. I'll take a lazy approach to the last sentence and copy/paste relevant sections from a couple of my recent vixra articles - "Defining Division by Zero (Making it not Just Possible, But Essential) and Relating Zero to Infinity" (http://vixra.org/abs/1402.0087) and "Connecting Bioscience, Atoms, Gravitation, Black Holes, and Strings” (http://vixra.org/abs/1403.0149). I heard a short talk with Dr. Lawrence Krauss, a theoretical physicist at Arizona State University in the US (http://www.abc.net.au/newsradio/content/s3965819.htm), whose comments about gravity being a quantum theory and the universe originating from “absolutely nothing” are addressed by my articles. If the binary digits of 1 and 0 are the basis for manufacturing space-time (whose curves and warps are gravity), this is in firm agreement with gravity being a quantum theory. And electronic bits could easily avoid Dr. Krauss’s “supernatural shenanigans” by being a product of human technology – we know this much to be true – that is recycled to 13.8 billion years ago by our future discovery of how to time travel into the past (a hypothesis explaining this is presented).
It seems unfortunate that no science journal is interested in my ideas (maybe it’s the way I write?) because I’m certain I’m correct, even if my ideas sound too strange to be true. I don’t think I’ll bother sending these thoughts to Dr. Krauss (professional scientists don’t answer my emails) – but I just might, if I get impulsive.

**Category:** Quantum Gravity and String Theory

[229] **viXra:1403.0290 [pdf]**
*replaced on 2015-02-24 05:57:49*

**Authors:** John R. Cipolla, Usha Raut

**Comments:** 25 Pages.

An attempt is made to simulate the curved space-time of General Relativity by comparison with the characteristics of a potential vortex at steady state sometimes called a free vortex. In this paper, we present results of our study of the potential vortex as an analogy with gravity and General Relativity. Analyses of potential vortex characteristics demonstrate that an analogy exists between potential vortex flow, General Relativity and the gravitational fields around massive objects. An analogue model of gravity is developed which simulates the potential vortex model of space-time observed by Gravity Probe-B experiments. Statements by Gravity Probe-B researchers that the region around Earth resembles a “space-time vortex” lend credibility to the premise of this paper that potential vortex flow and gravity are related. Albert Einstein introduced the first analogue model for General Relativity that describes space-time as a membrane upon which objects move along geodesics. Analogue models provide a unique and viable means of analyzing complex space-time in situations that would normally be beyond our means to explore using conventional methods. Further, by exploring the dynamics of the analogue model, we are able to recover the equivalent form of the Einstein field equation starting from the usual equations of hydrodynamics and vector dynamics and make predictions about space-time and gravity using these observations. An implication for the existence of an analogy between space-time and the potential vortex is the possibility that space-time can be considered a superfluid forming the surface of our universe.

**Category:** Relativity and Cosmology

[228] **viXra:1403.0289 [pdf]**
*submitted on 2014-03-17 08:20:44*

**Authors:** Leszek W. Guła

**Comments:** 1 Page. Dedicated to my Parents and my Brother

**Category:** Number Theory

[227] **viXra:1403.0288 [pdf]**
*submitted on 2014-03-17 09:33:40*

**Authors:** Alejandro A. Torassa

**Comments:** 3 Pages.

In classical mechanics, this paper presents a new principle of conservation of energy which is invariant under transformations between reference frames and which can be applied in any reference frame (rotating or non-rotating) (inertial or non-inertial) without the necessity of introducing fictitious forces.

**Category:** Classical Physics

[226] **viXra:1403.0287 [pdf]**
*submitted on 2014-03-17 09:36:43*

**Authors:** Albert Zotkin

**Comments:** 3 Pages.

I'm going to prove in this brief paper that actually there is not a so called "cosmic inflation", because that so called "cosmic inflation" is just an artifact of an incorrect theoretic model of Doppler effect for electromagnetic waves in remote sources.

**Category:** Astrophysics

[225] **viXra:1403.0286 [pdf]**
*replaced on 2014-07-02 12:52:37*

**Authors:** Arm Boris Nima

**Comments:** 14 Pages.

Did you ever wondered what is the Taylor formula for an arbitrary chosen basis ? The answer of this question is the Arm theory introduced in this article.

**Category:** Mathematical Physics

[224] **viXra:1403.0285 [pdf]**
*submitted on 2014-03-17 06:10:06*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We introduce the p-Arm theory which give rise to a new mathematical
object that we call the "p-exponential" which is invariant under
p derivation. We calculate its derivate and we use this new
function to solve dierential equations. Next, we
dene its real and imaginary part which are
the p-cosinus and the p-sinus respectively.

**Category:** Mathematical Physics

[223] **viXra:1403.0284 [pdf]**
*submitted on 2014-03-17 06:11:48*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We introduce the Arm prime factors decomposition
which is the equivalent of the Taylor formula
for decomposition of integers on the basis
of prime numbers. We make the link
between this decomposition and
the p-adic norm known in the
p-adic numbers theory.
To see how it works,
we give examples
of these two
formulas.

**Category:** Mathematical Physics

[222] **viXra:1403.0283 [pdf]**
*submitted on 2014-03-17 06:13:24*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We construct the equivalent of the Taylor
formula in the basis of all roots
fx kgK when K is Z iZ,
Q iQ and C.

**Category:** Mathematical Physics

[221] **viXra:1403.0282 [pdf]**
*submitted on 2014-03-17 06:15:09*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We give the developpment of functions in C[z] C[z
1
] with a scalar product which
involves an integral and a residue calculus. Then we give some examples
of those developpments and nd new 'representations' of the
exponential and the logarithm function . We draw those
representations and we see that there are
similar to their original
representations

**Category:** Mathematical Physics

[220] **viXra:1403.0281 [pdf]**
*submitted on 2014-03-17 06:17:47*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We developp the Arm-Lie group theory which is a theory based
onthe exponential of a changing of matrix variable u(X).
We dene a corresponding u-adjoint action, the
corresponding commutation relations in the
Arm-Lie algebra and the u-Jacobi identity.
Throught the exponentiation, Arm-Lie
algebras become Arm-Lie groups.
We give the example of pp
so(2) and
pp
su(2).

**Category:** Mathematical Physics

[219] **viXra:1403.0280 [pdf]**
*submitted on 2014-03-17 06:19:35*

**Authors:** Arm Boris Nima

**Comments:** 6 Pages.

After diagonalizing the Lorentz Matrix,
we nd the frame where the Dirac
equation is one derivation and
we calculate the 'speed' of
the Schwarschild metric

**Category:** Mathematical Physics

[218] **viXra:1403.0279 [pdf]**
*submitted on 2014-03-17 06:20:51*

**Authors:** Arm Boris Nima

**Comments:** 10 Pages.

We calculate the Poisson-Lie sigma model for every 4-dimensional
Manin triples (function of its structure constant) and we
give the 6-dimensional models for the Manin triples
(sl(2; C) sl(2; C)
; sl(2; C); sl(2; C)
),
(sl(2; C) sl(2; C)
; sl(2; C)
); sl(2; C),
(sl(2; C); su(2; C); sb(2; C)) and
(sl(2; C); sb(2; C); su(2; C))

**Category:** Mathematical Physics

[217] **viXra:1403.0278 [pdf]**
*submitted on 2014-03-17 06:22:13*

**Authors:** Arm Boris Nima

**Comments:** 16 Pages.

We calculate the torsion free spin connection on the quantum group Bq[SU2]
at the fourth root of unity. From this we deduce the covariant derivative
and the Riemann curvature. Next we compute the Dirac operator
of this quantum group and we give numerical
approximations of its eigenvalues.

**Category:** Mathematical Physics

[216] **viXra:1403.0277 [pdf]**
*submitted on 2014-03-17 06:24:03*

**Authors:** Arm Boris Nima

**Comments:** 22 Pages.

We study the noncommutative geometry of the dihedral group D6
using the tools of quantum group theory. We explicit the
torsion free regular spin connection and the
corresponding 'Levi-Civita' connection.
Next, we nd the Riemann curvature
and its Ricci tensor. The main
result is the Dirac operator
of a representation of the
group which we nd the
eigenvalues and the
eigenmodes

**Category:** Mathematical Physics

[215] **viXra:1403.0276 [pdf]**
*submitted on 2014-03-17 06:25:21*

**Authors:** Arm Boris Nima

**Comments:** 16 Pages.

We study the Borel algebra dene by [xa; xb] = 2a;1xb
as a noncommutative manifold R
3
. We calculate its
noncommutative dierential form relations. We deduce
its partial derivative relations and the derivative
of a plane wave. After calculating its de Rham
cohomology, we deduce the wave operator and
its corresponding magnetic solution

**Category:** Mathematical Physics

[214] **viXra:1403.0275 [pdf]**
*submitted on 2014-03-16 16:59:21*

**Authors:** Leszek Włodzimierz Guła

**Comments:** 2 Pages. My the short proofs are true.

The short proofs of the Fermat's Last Theorem for even n≥4.

**Category:** Number Theory

[213] **viXra:1403.0274 [pdf]**
*submitted on 2014-03-16 17:36:38*

**Authors:** Leszek Włodzimierz Guła

**Comments:** 3 Pages. My proof is true.

1. The hypothetical Fermat's proof of FLT.
2. Elementary proof of The fermat's Last Theorem.

**Category:** Number Theory

[212] **viXra:1403.0273 [pdf]**
*submitted on 2014-03-16 20:23:48*

**Authors:** S. J. Nettleton

**Comments:** 15 Pages. A presentation at auSakai 2010.

Four years experience in the use of Type 3 student eportfolios for assessment in undergraduate and postgraduate courses.

**Category:** Social Science

[211] **viXra:1403.0272 [pdf]**
*replaced on 2014-06-05 14:38:07*

**Authors:** Jay R. Yablon

**Comments:** 225 Pages. Revision 3 updates section 14, adds new sections 15 through 20.

We develop in detail, the classical magnetic monopoles of non-abelian Yang-Mills gauge theory and show how these monopoles, when analyzed using Gauss’ / Stokes’ theorem, appear to confine their gauge fields, and also, appear to be composite objects. Of course, baryons, which include the protons and neutrons at the heart of nuclear physics, also confine their gauge fields and are similarly-composite objects. This raises the question whether the magnetic monopoles of Yang-Mills theory are in some fashion related to the observed physical baryons. After developing inverse solutions for the non-abelian electric charge densities while carefully examining uniqueness and gauge fixing, we use these solutions together with Dirac theory to “populate” these classical monopoles with fermions. Applying the Fermi-Dirac-Pauli Exclusion Principle to these fermions forces the selection of a dimension-3 gauge group initially chosen to be SU(3). We then find that these non-abelian magnetic monopoles have the exact chromodynamic symmetries of baryons and interact via colored magnetic fields with the exact chromodynamic symmetries of mesons. We show that a required U(1) factor ensures that these monopoles are topologically stable, and also “flavors” these monopole as protons and neutrons. Because this exposition is classical, we also discuss the extent to which classical field theory can be used to effectively analyze baryons and confinement. We point out how a recursive aspect of the non-abelian electric charge solution may be used to perform an analytically-exact quantum path integration for Yang-Mills theory, proving the existence of a non-trivial quantum Yang–Mills theory on R4 for any simple gauge group G. Finally, we use the results of this path integration to develop four examples of the application of analytical non-linear quantum field theory, which includes a quantum field explanation of confinement, a fitting of the running QCD curve to the known empirical data within experimental error bars, and a careful review of single and double slit experiments.

**Category:** High Energy Particle Physics

[210] **viXra:1403.0271 [pdf]**
*replaced on 2014-12-09 12:37:03*

**Authors:** Rami Mehrem

**Comments:** 7 Pages.

Triangular properties of associated Legendre
functions are derived using the Vectorial Addition Theorem of spherical harmonics

**Category:** Mathematical Physics

[209] **viXra:1403.0270 [pdf]**
*replaced on 2014-03-17 04:35:06*

**Authors:** Nikolay V. Dibrov .

**Comments:** 3 Pages.

Abstract. Based on the Shadow-Gravity theory a dependency of bodyweight on speed is analysed.

**Category:** Classical Physics

[208] **viXra:1403.0269 [pdf]**
*replaced on 2014-04-13 04:00:40*

**Authors:** Marius Coman

**Comments:** 82 Pages.

It is always difficult to talk about arithmetic, because those who do not know what is about, nor do they understand in few sentences, no matter how inspired these might be, and those who know what is about, do no need to be told what is about.Arithmetic is the branch of mathematics that you keep it in you’re soul and you’re mind not in you’re suitcase or laptop. It also will not help you to gain money (unless you will prove Fermat’s last theorem without using complex numbers or you will prove Beal’s conjecture which is unlikely) but it will give you something more important than that. Part One of this book of collected papers aims to show new applications of Smarandache function in the study of some well known classes of numbers, like prime numbers, Poulet numbers, Carmichael numbers, Sophie Germain primes etc. Beside the well known notions of number theory, we defined in these papers the following new concepts: “Smarandache-Coman divisors of order k of a composite integer n with m prime factors”, “Smarandache-Coman congruence on primes”, “Smarandache-Germain primes”, “Coman-Smarandache criterion for primality”, “Smarandache-Korselt criterion”, “Smarandache-Coman constants”. Part Two of this book brings together several articles regarding primes, submitted by the author to the preprint scientific database Vixra.

**Category:** Number Theory

[207] **viXra:1403.0268 [pdf]**
*submitted on 2014-03-16 09:56:34*

**Authors:** Ray Fleming

**Comments:** 4 Pages.

In a previous paper the author showed that the Casimir force between protons is strong enough to account for the nuclear force. The purpose of this paper is to investigate if the Casimir force between two electrons computed by using a proximity force approximation is also strong enough to overcome Coulomb repulsion. The electrons are approximated as shells on the scale of the Compton wavelength, since their mass-energy has been shown to be consistent with a shell structure on that scale. It was determined that the Casimir force between two electrons is strong enough to overcome Coulomb repulsion such that there is a strong attraction between them. This is important as it gives us a mechanism to explain electron charge clustering.

**Category:** Nuclear and Atomic Physics

[206] **viXra:1403.0267 [pdf]**
*submitted on 2014-03-15 20:58:17*

**Authors:** Michael Snyder

**Comments:** 8 Pages.

This document is an update to my paper "Photonic Dipole Contours of Ferrofluid Hele-Shaw Cell" arXiv:0805.4364v2 . Photographs are the primary datasets and makeup the majority of the document. The overall argument is that the ferrofluid cells are basically spin based radar systems that show photon scatter off of electron flows inside of the
ferrofluid cell; induced by external magnetic fields. In other words, we are watching sparks cascading through an irregular lattice like lighting jumping cloud to cloud. They build up static electricity like a solar cell.

**Category:** High Energy Particle Physics

[205] **viXra:1403.0266 [pdf]**
*replaced on 2014-03-20 03:58:31*

**Authors:** Hasmukh K. Tank

**Comments:** Nine-page paper

This paper makes use of some astronomical-observations to gain deeper insight into the fundamental questions of physics and astrophysics. Alternative-interpretations of cosmological-red-shift are generally rejected on the ground that ‘tired-light-interpretations’ are inconsistent with the observations of time-dilation of super-nova-light-curves; whereas it is shown here that these curves are time-domain-representations of amplitude of light. So, these curves can be Fourier-transformed into wave-number-domain, and it is this wide band of waves which propagates in inter-galactic-space, and reaches us after millions of years. These Fourier-transformed-components, being electromagnetic-waves, get red-shifted by any mechanism that can cause spectral-shift, and when transformed back into time-domain, show time-dilation. Thus, time-dilation of super-nova light-curves, or the relativistic-time-dilation, means ‘red-shift of light’ due to any mechanism. Similarly, the relativistic-length-contraction is also explained using wave-theory. With this explanation, this letter presents five new possible-mechanisms for the ‘cosmological-red-shift’; which will also give some insight into pure physics. These alternative-interpretations are: (i) Inter-galactic-photons can also get red-shifted due to vacuum-polarization-mechanism; (ii) Spherically-expanding-wave-front of light can be viewed as a spherically-expanding cavity, continuously changing its impedance, causing around -400 dB reflected-power back to the source; (iii) Cumulative-phase-alteration of extra-galactic-photons caused by the cosmic-microwave-background; (iv) Electric-field and magnetic-field of extra-galactic-light in the transverse-directions, causing virtual-electrons to oscillate, and generating gravitational-field in the longitudinal-direction; losing part of their energy in the form of ‘gravitational-waves’; (v) Though the rest-mass of photon is zero, it has a ‘relativistic-mass’ equal to its momentum-divided-by-its-speed (h f / c^2); so this ‘relativistic-mass’ of the photon can radiate gravitational-waves, branching-out its energy into gravitational-wave and electromagnetic-wave; and as a supportive-evidence, it is shown here that the energy lost by ‘cosmologically-red-shifting-photons’ is strikingly proportional to the strength-ratio of gravitational and electric forces. These new alternative explanations also explain the non-linearity of red-shift-distance-curve, observed by Perlmutter and Reiss, without any need for ‘dark-energy’.

**Category:** Astrophysics

[204] **viXra:1403.0265 [pdf]**
*submitted on 2014-03-15 11:38:55*

**Authors:** Jeffrey Joseph Wolynski

**Comments:** 3 Pages. 2 diagrams, 1 reference

A short analysis of the Jerusalem Extraterrestrial Spaceship is presented.

**Category:** General Science and Philosophy

[203] **viXra:1403.0264 [pdf]**
*submitted on 2014-03-14 18:32:50*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I present the notion of “chameleonic numbers”, a set of composite squarefree numbers not divisible by 2, 3 or 5, having two, three or more prime factors, which have the property that can easily generate primes with a certain formula, other primes than they own prime factors but in an amount proportional with the amount of these ones.

**Category:** Number Theory

[202] **viXra:1403.0263 [pdf]**
*replaced on 2014-03-15 13:36:18*

**Authors:** William O. Straub

**Comments:** 5 Pages. Computer program didn't typeset correctly; third attempt

The problem of angular momentum addition requires the calculation of Clebsch-Gordan coefficients. While systems involving small values of momenta and spin present no special problem, larger systems require extensive computational effort. This paper describes a straightforward method for computing the coefficients for any two-particle problem exactly by means of a simplified form of the recursion formula in a notation that is particularly accessible to the third- or fourth-year student. The method is summarized in a brief BASIC program.

**Category:** Quantum Physics

[201] **viXra:1403.0262 [pdf]**
*submitted on 2014-03-14 21:51:47*

**Authors:** Shreyak Chakraborty

**Comments:** 8 Pages.

Crowds are generally analyzed in the regime of sociology- where
they are studied and classified on the basis of crowd psychology.
This analysis arises from the study of collective behavior and treats
crowds as dependent on psychology of humans in the crowd. In this
introductory paper we show a generalized treatment of crowds as a
set of living objects: called members of the crowd. We classify
crowds based on various parameters and study some general and
specific characteristics of crowd of humans and study the response
of a simple crowd to an external situation or stimulus by deriving the
solution of the generalized crowd equation. We also define some
terminology regarding the mathematical description of crowds and
hence arrive at some useful conjectures.

**Category:** Functions and Analysis

[200] **viXra:1403.0261 [pdf]**
*submitted on 2014-03-15 02:33:25*

**Authors:** Jing Fu, Yu Wang

**Comments:** 3 Pages.

For any positive integer n, we define a new Smarandache function G(n) as the smallest positive integer m such...

**Category:** General Mathematics

[199] **viXra:1403.0260 [pdf]**
*submitted on 2014-03-15 02:37:42*

**Authors:** Maohua Le

**Comments:** 2 Pages.

For any positive integer n, let S(n) and Z(n) denote the Smarandache function and the
pseudo Smarandache function respectively. In this paper we prove that the equation S(n) = Z(n) has
infinitely many positive integer solutions n.

**Category:** General Mathematics

[198] **viXra:1403.0259 [pdf]**
*submitted on 2014-03-15 02:39:25*

**Authors:** Yao Weili

**Comments:** 3 Pages.

For any positive integer n, let S(n) denotes the Smarandache function, then S(n) is defined as the smallest m 2 N+ with njm!. In this paper, we study the asymptotic property of a hybrid mean value of the Smarandache function and the Mangoldt function, and give an interesting hybrid mean value formula for it.

**Category:** General Mathematics

[197] **viXra:1403.0258 [pdf]**
*submitted on 2014-03-15 02:40:54*

**Authors:** Yanrong Xue

**Comments:** 3 Pages.

In this paper, we de¯ne a new arithmetical function SL¤(n), which is related with the famous F.Smarandache LCM function SL(n). Then we studied the properties of SL¤(n), and solved a conjecture involving function SL¤(n).

**Category:** General Mathematics

[196] **viXra:1403.0257 [pdf]**
*submitted on 2014-03-15 02:42:39*

**Authors:** Sayed Elagan

**Comments:** 10 Pages.

The purpose of this paper is to introduce finite convergence sequences and functions preserving convergence of series in fuzzy n-normed spaces.

**Category:** General Mathematics

[195] **viXra:1403.0256 [pdf]**
*submitted on 2014-03-15 02:44:46*

**Authors:** Talal Ali AL-Hawary

**Comments:** 9 Pages.

The aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy C-flats, fuzzy alternative-sets and fuzzy i-flats. Moreover, we characterize some peculiar fuzzy matroids via these notions. Finally, we provide a decomposition of fuzzy strong maps.

**Category:** General Mathematics

[194] **viXra:1403.0255 [pdf]**
*submitted on 2014-03-15 02:46:15*

**Authors:** Rong Ma

**Comments:** 4 Pages.

In this paper, we use the elementary methods to study the F.Smarandache LCM ratio sequence, and obtain three interesting recurrence relations for it.

**Category:** General Mathematics

[193] **viXra:1403.0254 [pdf]**
*submitted on 2014-03-15 02:47:24*

**Authors:** Hailong Li, Qianli Yang

**Comments:** 8 Pages.

The main purpose of this paper is using the elementary method to study the properties of the Smarandache LCM sequence, and give some interesting identities.

**Category:** General Mathematics

[192] **viXra:1403.0253 [pdf]**
*submitted on 2014-03-15 02:49:05*

**Authors:** S.M. Khairnar, Anant W. Vyawahare, J.N.Salunke

**Comments:** 8 Pages.

Smarandache LCM function and LCM ratio are already de¯ned in [1]. This paper gives some additional properties and obtains interesting results regarding the ¯gurate numbers.
In addition, the various sequaences thus obtained are also discussed with graphs and their
interpretations.

**Category:** General Mathematics

[191] **viXra:1403.0252 [pdf]**
*submitted on 2014-03-15 02:50:42*

**Authors:** Handan BALGETIR OZTEKIN, Mahmut ERGUT

**Comments:** 7 Pages.

In this paper, we study the Euler-Savary's formula for the planar curves in the lightlike cone. We ¯rst de¯ne the associated curve of a curve in the two dimensional lightlike cone Q2:Then we give the relation between the curvatures of a base curve, a rolling curve and a roulette which lie on two dimensional lightlike cone Q2.

**Category:** General Mathematics

[190] **viXra:1403.0251 [pdf]**
*submitted on 2014-03-15 02:52:17*

**Authors:** M.A.Perumal, S.Navaneethakrishnan, A.Nagarajan

**Comments:** 19 Pages.

Let G be a (p, q) - graph. An injective function f : V (G) → {l0, l1, l2, · · · , la}, (a ǫ N), is said to be Lucas graceful labeling if...

**Category:** General Mathematics

[189] **viXra:1403.0250 [pdf]**
*submitted on 2014-03-15 02:53:25*

**Authors:** Jiao Chen

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of the Smarandache repetitional sequence, and give two asymptotic formulas for it.

**Category:** General Mathematics

[188] **viXra:1403.0249 [pdf]**
*submitted on 2014-03-15 02:54:21*

**Authors:** Zhang Xiaobeng

**Comments:** 6 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the SCBF function on simple numbers, and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[187] **viXra:1403.0248 [pdf]**
*submitted on 2014-03-15 02:55:46*

**Authors:** Yiren Wang

**Comments:** 5 Pages.

The main purpose of this paper it to studied the mean value properties of the Smarandache Superior m-th power part sequence SSMP(n) and the Smarandache Inferior m-th power part sequence SIMP(n), and give several interesting asymptotic formula for them.

**Category:** General Mathematics

[186] **viXra:1403.0247 [pdf]**
*submitted on 2014-03-15 02:57:12*

**Authors:** Taekyun Kim

**Comments:** 5 Pages.

The additive analogues of Pseudo-Smarandache, Smarandache-simple functions and their duals have been recently studied by J. Sandor. In this note, we obtain q-analogues of Sandor's theorems [6].

**Category:** General Mathematics

[185] **viXra:1403.0246 [pdf]**
*submitted on 2014-03-15 02:58:50*

**Authors:** A. Nagarajan, A. Nellai Murugan, S. Navaneetha Krishnan

**Comments:** 6 Pages.

Let G = (V,E) be a graph with p vertices and q edges and let f : V (G) → {0, 1, 2, . . . , q − 1, q + 1} be an injection. The graph G is said to have a near mean labeling if for each edge, there exist an induced injective map f : E(G) → {1, 2, . . . , q} ...

**Category:** General Mathematics

[184] **viXra:1403.0245 [pdf]**
*submitted on 2014-03-15 03:00:10*

**Authors:** Yongfeng Zhang

**Comments:** 4 Pages.

For any positive integer n, the near pseudo Smarandache function K(n) is defined as...

**Category:** General Mathematics

[183] **viXra:1403.0244 [pdf]**
*submitted on 2014-03-15 03:02:10*

**Authors:** P.Siva Kota Reddy, K.Shivashankara, K. V.Madhusudhan

**Comments:** 6 Pages.

A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair...

**Category:** General Mathematics

[182] **viXra:1403.0243 [pdf]**
*submitted on 2014-03-15 03:04:29*

**Authors:** Mihaly Bencze

**Comments:** 2 Pages.

It is not very common for a young PhD aspirant to select a topic for his dissertation that makes exploratory forays into a fiedgling science | one that is still in the process of finding feet within the ramparts of academia. It would be considered a highly risky venture to say the least given that through his dissertation the PhD aspirant would need to not only convince his examiners on the merit of his own research on the topic but also present a strong case on behalf of the topic itself.

**Category:** General Mathematics

[181] **viXra:1403.0242 [pdf]**
*submitted on 2014-03-15 03:06:55*

**Authors:** Agboola A.A.A., Akwu A.D., Oyebo Y.T.

**Comments:** 9 Pages.

This paper is devoted to the study of eutrosophic groups and neutrosophic subgroups. Some properties of neutrosophic groups and neutrosophic subgroups are pre-sented. It is shown that the product of a neutrosophic subgroup and a pseudo neutrosophic subgroup of a commutative neutrosophic group is a neutrosophic subgroup and their union is also a neutrosophic subgroup even if neither is contained in the other. It is also shown that all neutrosophic groups generated by the neutrosophic element I and any group isomorphic to Klein 4-group are Lagrange neutrosophic groups. The partitioning of neutrosophic groups is also presented.

**Category:** General Mathematics

[180] **viXra:1403.0241 [pdf]**
*submitted on 2014-03-15 03:08:18*

**Authors:** Agboola A.A.A., Akinola A.D., Oyebola O.Y.

**Comments:** 14 Pages.

In this paper, we present some elementary properties of neutrosophic rings. The structure of neutrosophic polynomial rings is also presented. We provide answers to the questions raised by Vasantha Kandasamy and Florentin Smarandache in [1] concerning principal ideals, prime ideals, factorization and Unique Factorization Domain in neutrosophic polynomial rings.

**Category:** General Mathematics

[179] **viXra:1403.0240 [pdf]**
*submitted on 2014-03-15 03:10:02*

**Authors:** Agboola A.A.A., Akinola A.D., Oyebola O.Y.

**Comments:** 8 Pages.

This paper is the continuation of the work started in [12]. The present paper is devoted to the study of ideals of neutrosophic rings. Neutrosophic quotient rings are also studied.

**Category:** General Mathematics

[178] **viXra:1403.0239 [pdf]**
*submitted on 2014-03-15 03:11:21*

**Authors:** Yanchun Guo

**Comments:** 10 Pages.

For any positive integer n, we de¯ne the arithmetical function F(n) as F(1) = 0.

**Category:** General Mathematics

[177] **viXra:1403.0238 [pdf]**
*submitted on 2014-03-15 03:12:27*

**Authors:** Jason Earls

**Comments:** 2 Pages.

The purpose of this note is to report on the discovery of some new prime numbers that were built from factorials, the Smarandache Consecutive Sequence, and the Smarandache Reverse Sequence.

**Category:** General Mathematics

[176] **viXra:1403.0237 [pdf]**
*submitted on 2014-03-15 03:13:44*

**Authors:** Fanbei Li

**Comments:** 3 Pages.

For any positive integer n ¸ 3, if n and n + 2 both are primes, then we call that n and n + 2 are twin primes. In this paper, we using the elementary method to study the relationship between the twin primes and some arithmetical function, and give a new critical method for twin primes.

**Category:** General Mathematics

[175] **viXra:1403.0236 [pdf]**
*submitted on 2014-03-15 03:15:16*

**Authors:** Selvam Avadayappan, R. Vasuki

**Comments:** 13 Pages.

Let G(V,E) be a graph with p vertices and q edges.

**Category:** General Mathematics

[174] **viXra:1403.0235 [pdf]**
*submitted on 2014-03-15 03:16:40*

**Authors:** Ding Liping

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the mean value properties of a new function for n, and give a sharp asymptotic formula for it.

**Category:** General Mathematics

[173] **viXra:1403.0234 [pdf]**
*submitted on 2014-03-15 03:19:03*

**Authors:** Weili Yao, Tieming Cao

**Comments:** 5 Pages.

For any positive integer n, we define the arithmetical function G(n) as G(1) = 0.
The main purpose of this paper is using the elementary method and the prime distribution theory to study the mean value properties of G(n) in Smarandache divisor product sequences fpd(n)g and fqd(n)g, and give two sharper asymptotic formulae for them.

**Category:** General Mathematics

[172] **viXra:1403.0233 [pdf]**
*submitted on 2014-03-15 03:20:15*

**Authors:** Xiaowei Pan

**Comments:** 4 Pages.

The main purpose of this paper is using the elementary method to study the LCM Sequence, and give an asymptotic formula about this sequence.

**Category:** General Mathematics

[171] **viXra:1403.0232 [pdf]**
*submitted on 2014-03-15 03:21:49*

**Authors:** S.K.Vaidya

**Comments:** 7 Pages.

A vertex labeling of G is an assignment f : V (G) → {1, 2, 3, . . . , p + q} be an injection.

**Category:** General Mathematics

[170] **viXra:1403.0231 [pdf]**
*submitted on 2014-03-15 03:23:30*

**Authors:** Yulin Lu

**Comments:** 2 Pages.

For any positive integer n, the famous F.Smarandache function S(n) is defined as
the smallest positive integer m such that njm!. That is, S(n) = minfm : m 2 N; njm!g.
The main purpose of this paper is to introduce some new unsolved problems involving the Smarandache function and the related functions.

**Category:** General Mathematics

[169] **viXra:1403.0230 [pdf]**
*submitted on 2014-03-15 03:25:48*

**Authors:** Marius Coman

**Comments:** 1 Page.

In this paper I present a conjecture about primes with an extremely simple enunciation, but very interesting despite (or on the contrary, because of) its simplicity.

**Category:** Number Theory

[168] **viXra:1403.0229 [pdf]**
*submitted on 2014-03-15 03:26:22*

**Authors:** Linfan Mao

**Comments:** 16 Pages.

Different from the homogenous systems, a Smarandache system is a contra-dictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple distinct ways. Such systems widely exist in the world. In this report, we discuss such a kind of Smarandache sys-tem, i.e., non-solvable equation systems, such as those of non-solvable algebraic equations,non-solvable ordinary differential equations and non-solvable partial differential equations by topological graphs, classify these systems and characterize their global behaviors, partic-ularly, the sum-stability and prod-stability of such equations. Applications of such systems to other sciences, such as those of controlling of infectious diseases, interaction fields and flows in network are also included in this report.

**Category:** General Mathematics

[167] **viXra:1403.0228 [pdf]**
*submitted on 2014-03-15 03:27:51*

**Authors:** Linfan Mao

**Comments:** 16 Pages.

A Smarandache system (;R) is such a mathematical system that has at least one Smarandachely denied rule in R, i.e., there is a rule in (;R) that behaves in at least two different ways within the same set , i.e., validated and invalided, or only invalided but in multiple distinct ways. For such systems, the linear equation systems without solutions, i.e., non-solvable linear equation systems are the most simple one.

**Category:** General Mathematics

[166] **viXra:1403.0227 [pdf]**
*submitted on 2014-03-15 03:29:09*

**Authors:** Chandrashekar Adiga, Shrikanth A. S., Shivakumar Swamy C.S.

**Comments:** 5 Pages.

Let G be a graph with vertex set V and edge set E, and Z2 = {0, 1}.

**Category:** General Mathematics

[165] **viXra:1403.0226 [pdf]**
*submitted on 2014-03-15 03:31:37*

**Authors:** Jozsef Sandor

**Comments:** 5 Pages.

EXPONENTIAL DIVISORS AND RELATED ARITHMETIC FUNCTIONS.

**Category:** General Mathematics

[164] **viXra:1403.0225 [pdf]**
*submitted on 2014-03-15 03:32:53*

**Authors:** A.A.K. Majumdar

**Comments:** 8 Pages.

Vyawahare and Purohit [1] introduced the near pseudo Smarandache function, K(n). In this paper, we derive some more recurrence formulas satis¯ed by K(n). We also derive some new series, and give an expression for the sum of the ¯rst n terms of the sequence fK(n)g.

**Category:** General Mathematics

[163] **viXra:1403.0224 [pdf]**
*submitted on 2014-03-15 03:34:25*

**Authors:** Wei Huang, Jiaolian Zhao

**Comments:** 6 Pages.

For any positive integer n, the Smarandache power function SP(n) is defined as the smallest positive integer m such that...

**Category:** General Mathematics

[162] **viXra:1403.0223 [pdf]**
*submitted on 2014-03-15 03:35:54*

**Authors:** Juan Lopez Gonzalez

**Comments:** 7 Pages.

In this note I prove using an algebraic identity and Wilson's Theorem...

**Category:** General Mathematics

[161] **viXra:1403.0222 [pdf]**
*submitted on 2014-03-15 03:37:42*

**Authors:** H. Gunarto, A.A.K. Majumdar

**Comments:** 6 Pages.

The pseudo Smarandache function, denoted by Z(n), has been introduced by Kashihara.

**Category:** General Mathematics

[160] **viXra:1403.0221 [pdf]**
*submitted on 2014-03-15 03:39:05*

**Authors:** Jin Zhang, Pei Zhang

**Comments:** 6 Pages.

In reference [2], we used the elementary method to study the mean value properties of a new arithmetical function, and obtained two mean value formulae for it, but there exist some errors in that paper. The main purpose of this paper is to correct the errors in reference [2], and give two correct conclusions.

**Category:** General Mathematics

[159] **viXra:1403.0220 [pdf]**
*submitted on 2014-03-15 03:40:21*

**Authors:** Melih Turgut

**Comments:** 8 Pages.

A regular curve with more than 2 breadths in Minkowski 3-space is called a Smarandache Breadth Curve [8].

**Category:** General Mathematics

[158] **viXra:1403.0219 [pdf]**
*replaced on 2014-03-18 07:07:14*

**Authors:** George Rajna

**Comments:** 9 Pages.

The gravitational force attracting the matter, causing concentration of the matter in a small space and leaving much space with low matter concentration: dark matter and energy.
There is an asymmetry between the mass of the electric charges, for example proton and electron, can understood by the asymmetrical Planck Distribution Law. This temperature dependent energy distribution is asymmetric around the maximum intensity, where the annihilation of matter and antimatter is a
high probability event. The asymmetric sides are creating different frequencies of electromagnetic radiations being in the same intensity level and compensating each other. One of these compensating ratios is the electron –
proton mass ratio. The lower energy side has no compensating intensity level, it is the dark energy and the corresponding matter is the dark matter.

**Category:** Relativity and Cosmology

[157] **viXra:1403.0218 [pdf]**
*submitted on 2014-03-14 12:26:59*

**Authors:** Nikolay Samofatov

**Comments:** 3 Pages.

In this article we examine mathematical properties of discrete universe models in their most general form and propose a special technique (universe self-programming with recursive self-virtualization) which can be used to guide evolution within the model.

**Category:** Quantum Gravity and String Theory

[156] **viXra:1403.0217 [pdf]**
*submitted on 2014-03-14 07:34:53*

**Authors:** Rodney Bartlett

**Comments:** 3 Pages.

Disorder (entropy) increases over time. This is known as the 2nd law of thermodynamics. In the 1860s, physicist James Clerk Maxwell invented the hypothetical "Maxwell's Demon" - this classic thought experiment could break the law by sorting hot and cold gas particles without expending any energy. 150 years later, a research team in the USA has published a mathematical model envisioning a machine which really could decrease entropy without using energy. It would only need a supply of bits – the binary digits of 0 and 1 – with which to encode information about the particles. Such a machine may supply infinite energy in the future, according to team member Dibyendu Mandal. But it would require about 200 x 10^18 bytes to heat a gram of water by just a single degree Celsius – at present, an overwhelming demand on data storage. (from “Conquering a Demon” by Shannon Palus – Discover Magazine, March 2014, p.17). My vixra article seeks to show how to delete that overwhelming demand.

**Category:** Thermodynamics and Energy

[155] **viXra:1403.0216 [pdf]**
*submitted on 2014-03-14 05:28:33*

**Authors:** Said Broumi

**Comments:** Pages.

The Smarandache's Synonymity Test: similar to, and an extension of, the antonym test in psychology,
is a verbal test where the subject must supply as many as possible synonyms of a given word within a as short as possible period of time.
How to measure it?

**Category:** General Mathematics

[154] **viXra:1403.0214 [pdf]**
*submitted on 2014-03-14 05:31:29*

**Authors:** Said Broumi

**Comments:** Pages.

The Smarandache Sequences. 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, …

**Category:** General Mathematics

[153] **viXra:1403.0212 [pdf]**
*submitted on 2014-03-14 05:34:11*

**Authors:** Mircea Selariu

**Comments:** Pages.

Plot#+0.1 t/ Cos#t'sSqrt#1 Sin#t'^2 ' 0.25Pit, t, 0, 10Pi'

**Category:** General Mathematics

[152] **viXra:1403.0211 [pdf]**
*submitted on 2014-03-14 05:35:33*

**Authors:** Claudia Coanda

**Comments:** 4 Pages.

In this article we prove the Smarandache–Pătraşcu’s Theorem in relation to the inscribed orthohomological triangles using the barycentric coordinates.

**Category:** General Mathematics

[151] **viXra:1403.0210 [pdf]**
*submitted on 2014-03-14 05:37:39*

**Authors:** Florentin Smarandache

**Comments:** 10 Pages.

Florentin Smarandache has introduced the notion of “unmatter” and related concepts such as “unparticle,” “unatom,” “unmolecule” in a manuscript from 1980 according to the CERN web site, and he uploaded articles about unmatter starting with year 2004 to the CERN site and published them in various journals in 2004, 2005, 2006.

**Category:** General Mathematics

[150] **viXra:1403.0209 [pdf]**
*submitted on 2014-03-14 05:39:08*

**Authors:** Adrian Vasiu

**Comments:** 6 Pages.

The fulfilled euclidean plane is the real projective plane completed with the infinite point of its infinite line denoted c. This new incidence structure is a structure with neighbouring elements, in which the unicity of the line through two distinct points is not assured. This new Geometry is a Smarandacheian structure introduced in [10] and [11], which generalizes and unites in the same time: Euclid, Bolyai Lobacewski Gauss and Riemann Geometries.

**Category:** General Mathematics

[149] **viXra:1403.0207 [pdf]**
*submitted on 2014-03-14 06:06:49*

**Authors:** Krassimir T. Atanassov

**Comments:** 3 Pages.

Treating a problem on Smarandache circular sequence.

**Category:** Number Theory

[148] **viXra:1403.0206 [pdf]**
*submitted on 2014-03-14 06:10:03*

**Authors:** Wenpeng Zhangy, Ling Liy

**Comments:** 3 Pages.

For any positive integer n, the famous pseudo Smarandache function Z(n) is de¯ned as the smallest positive integer m such that n j
m(m + 1)2 . That is, Z(n) = min ½ m : n j m(m + 1)
2 ; n 2 N. The Smarandache reciprocal function Sc(n) is de¯ned as Sc(n) = max fm : y j n! for all 1 · y · m; and m + 1 y n!g. That is, Sc(n) is the largest positive integer m such that y j n! for all integers 1 · y · m. The main purpose of this paper is to study the solvability of some equations involving the pseudo Smarandache function Z(n)and the Smarandache reciprocal function Sc(n), and propose some interesting conjectures.

**Category:** General Mathematics

[147] **viXra:1403.0205 [pdf]**
*submitted on 2014-03-14 06:11:21*

**Authors:** Mladen V. Vassilev

**Comments:** 4 Pages.

Remarks on a problem regarding Smarandache's simple number.

**Category:** Number Theory

[146] **viXra:1403.0204 [pdf]**
*submitted on 2014-03-14 06:12:39*

**Authors:** Fu Ruiqin

**Comments:** 3 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the integer part of the k-th root positive integer, and give two interesting asymptotic formulae.

**Category:** General Mathematics

[145] **viXra:1403.0203 [pdf]**
*submitted on 2014-03-14 06:14:24*

**Authors:** Gao Nan

**Comments:** 5 Pages.

For any positive integer n, let mq(n) denote the integer part of k-th root of n. That is, mq(n) =
h n 1k i. In this paper, we study the properties of the sequences fmq(n)g, and give an interesting asymptotic formula.

**Category:** General Mathematics

[144] **viXra:1403.0202 [pdf]**
*submitted on 2014-03-14 06:18:45*

**Authors:** Yi Yuan

**Comments:** 3 Pages.

The main purpose of this paper is using the analytic method to study the n-ary sieve sequence, and solved one conjecture about this sequence.

**Category:** General Mathematics

[143] **viXra:1403.0201 [pdf]**
*submitted on 2014-03-14 06:19:59*

**Authors:** F. Ayatollah Zadeh Shiraziy, A. Hosseini

**Comments:** 4 Pages.

In the following text, the main aim is to distinguish some relations between Smarad-
che semigroups and (topological) transformation semigroups areas. We will see that a transfor-
mation group is not distal if and only if its enveloping semigroup is a Smarandache semigroup.
Moreover we will ¯nd a classifying of minimal right ideals of the enveloping semigroup of a
transformation semigroup.

**Category:** General Mathematics

[142] **viXra:1403.0200 [pdf]**
*submitted on 2014-03-14 06:21:23*

**Authors:** Jon Perry

**Comments:** 4 Pages.

F. Smarandache defines a k-factorial as n(n¡k)(n¡2k) ¢ ¢ ¢, terminating when n ¡ xk is positive and n ¡ (x + 1)k is 0 or negative. Smarandacheials extend this definition into the negative numbers such that the factorial terminates when jn ¡ xkj is less than or equal to n and jn ¡ (x + 1)kj is greater than n. This paper looks at some relations between these numbers.

**Category:** General Mathematics

[141] **viXra:1403.0199 [pdf]**
*submitted on 2014-03-14 06:22:55*

**Authors:** Zhang Xiaobeng

**Comments:** 2 Pages.

The main purpose of this paper is using the elementary method to study the asymptotic properties of the Smarandache factorial sequence, and give an interesting asymptotic formula.

**Category:** General Mathematics

[140] **viXra:1403.0198 [pdf]**
*submitted on 2014-03-14 06:24:22*

**Authors:** Y. B. Jun

**Comments:** 5 Pages.

The notion of Smarandache fantastic ideals is introduced, examples are given, and related properties are investigated. Relations among Q-Smarandache fresh ideals, Q-Smarandache clean ideals and Q-Smarandache fantastic ideals are given. A characterization of a Q-Smarandache fantastic ideal is provided. The extension property for Q-Smarandache fantastic ideals is established.

**Category:** General Mathematics

[139] **viXra:1403.0197 [pdf]**
*submitted on 2014-03-14 06:26:27*

**Authors:** R.Sridevi, S.Navaneethakrishnan, K.Nagarajan

**Comments:** 14 Pages.

A Smarandache-Fibonacci Triple is a sequence S(n), n ≥ 0 such that S(n) = S(n − 1) + S(n − 2), where S(n) is the Smarandache function for integers n ≥ 0. Certainly, it is a generalization of Fibonacci sequence. A Fibonacci graceful labeling and a super Fi-bonacci graceful labeling on graphs were introduced by Kathiresan and Amutha in 2006.
Generally, let G be a (p, q)-graph and S(n)|n ≥ 0 a Smarandache-Fibonacci Triple. An bi-jection f : V (G) → {S(0), S(1), S(2), . . . , S(q)} is said to be a super Smarandache-Fibonacci graceful graph if the induced edge labeling f∗(uv) = |f(u) −f(v)| is a bijection onto the set
{S(1), S(2), . . . , S(q)}. Particularly, if S(n), n ≥ 0 is just the Fibonacci sequence Fi, i ≥ 0, such a graph is called a super Fibonacci graceful graph. In this paper, we show that some
special class of graphs namely Ftn, Ctn and St
m,n are super fibonacci graceful graphs.

**Category:** General Mathematics

[138] **viXra:1403.0196 [pdf]**
*submitted on 2014-03-14 06:30:18*

**Authors:** T.Ramaraj, N.Kannappa

**Comments:** 3 Pages.

In this paper we study the Finite Smarandache-2-algebraic structure of Finite-near-ring, namely, Finite-Smarandache-near-ring, written as Finite-S-near-ring. We de¯ne Finite Smarandache near-ring with examples. We introduce some equivalent conditions for Finite S-near-ring and obtain
some of its properties.

**Category:** General Mathematics

[137] **viXra:1403.0195 [pdf]**
*submitted on 2014-03-14 06:31:55*

**Authors:** Yanrong Xue

**Comments:** 5 Pages.

For any positive integer n, the famous .Smarandache LCM function SL(n) is de¯ned as the smallest positive integer k such that n j [1; 2; ¢ ¢ ¢ ; k], where [1; 2; ¢ ¢ ¢ ; k] denotes the least common multiple of 1; 2; ¢ ¢ ¢ ; k. The main purpose of this paper is using the elemen-tary methods to study the mean value distribution property of (P(n)¡p(n))SL(n), and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[136] **viXra:1403.0194 [pdf]**
*submitted on 2014-03-14 06:34:11*

**Authors:** Jozsef Sandor

**Comments:** 4 Pages.

For a given arithmetical function f : N ! N, let F : N ! N be de¯ned byF(n) = minfm ¸ 1 : njf(m)g, if this exists. Such functions, introduced in [4], will be called as the f-minimum functions. If f satis¯es the property a · b =) f(a)jf(b), we shall prove that F(ab) = maxfF(a); F(b)g for (a; b) = 1. For a more restrictive class of functions, we
will determine F(n) where n is an even perfect number. These results are generalizations of
theorems from [10], [1], [3], [6].

**Category:** General Mathematics

[135] **viXra:1403.0193 [pdf]**
*submitted on 2014-03-14 06:36:18*

**Authors:** H.Abdollahzadeh Ahangar

**Comments:** 5 Pages.

A set of vertices S in a graph G is called to be a Smarandachely dominating k-set, if each vertex of G is dominated by at least k vertices of S. Particularly, if k = 1, such a set is called a dominating set of G. The Smarandachely domination number k(G) of G is the minimum cardinality of a Smarandachely dominating set of G. For abbreviation, we denote 1(G) by (G). In 1996, Reed proved that the domination number (G) of every n-vertex graph G with minimum degree at least 3 is at most 3n/8. Also, he conjectured that
(H) ≥ ⌈n/3⌉ for every connected 3-regular n-vertex graph H. In [?], the authors presented
a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this
paper we study forcing domination number for those graphs.

**Category:** General Mathematics

[134] **viXra:1403.0192 [pdf]**
*submitted on 2014-03-14 06:38:14*

**Authors:** K.Palani, A.Nagarajan

**Comments:** 6 Pages.

In [7], we introduced the new concept (G,D)-set of graphs. Let G = (V,E) be any graph. A (G,D)-set of a graph G is a subset S of vertices of G which is both a dominating and geodominating(or geodetic) set of G. The minimum cardinality of all (G,D)-sets of G is
called the (G,D)-number of G and is denoted by γG(G). In this paper, we introduce a new
parameter called forcing (G,D)-number of a graph G. Let S be a γG-set of G. A subset T of
S is said to be a forcing subset for S if S is the unique γG-set of G containing T. A forcing
subset T of S of minimum cardinality is called a minimum forcing subset of S. The forcing
(G,D)-number of S denoted by fG,D(S) is the cardinality of a minimum forcing subset of S.
The forcing (G,D)-number of G is the minimum of fG,D(S), where the minimum is taken
over all γG-sets S of G and it is denoted by fG,D(S).

**Category:** General Mathematics

[133] **viXra:1403.0191 [pdf]**
*submitted on 2014-03-14 06:40:27*

**Authors:** J.John, V.Mary Gleeta

**Comments:** 10 Pages.

For a connected graph G = (V,E), let a set M be a minimum monophonic hull set of G. A subset T ⊆ M is called a forcing subset for M if M is the unique minimum monophonic hull set containing T. A forcing subset for M of minimum cardinality is a
minimum forcing subset of M. The forcing monophonic hull number of M , denoted by
fmh(M), is the cardinality of a minimum forcing subset of M. The forcing monophonic hull number of G, denoted by fmh(G), is fmh(G) = min fmh(M)}, where the minimum is taken over all minimum monophonic hull sets in G. Some general properties satisfied by this concept are studied. Every monophonic set of G is also a monophonic hull set of G and so mh(G) ≤ h(G), where h(G) and mh(G) are hull number and monophonic hull number of a connected graph G. However, there is no relationship between fh(G) and fmh(G), where
fh(G) is the forcing hull number of a connected graph G. We give a series of realization
results for various possibilities of these four parameters.

**Category:** General Mathematics

[132] **viXra:1403.0190 [pdf]**
*submitted on 2014-03-14 06:43:19*

**Authors:** A.P.Santhakumaran, S.Athisayanathan

**Comments:** 8 Pages.

For two vertices u and v in a graph G = (V,E), the distance d(u, v) and detour distance D(u, v) are the length of a shortest or longest u − v path in G, respectively, and the Smarandache distance di S(u, v) is the length d(u, v)+ i(u, v) of a u−v path in G, where 0 ≤ i(u, v) ≤ D(u, v) − d(u, v). A u − v path of length di
S(u, v), if it exists, is called a
Smarandachely u − v i-detour. A set S ⊆ V is called a Smarandachely i-detour set if every
edge in G has both its ends in S or it lies on a Smarandachely i-detour joining a pair of vertices
in S. In particular, if i(u, v) = 0, then di
S(u, v) = d(u, v); and if i(u, v) = D(u, v) − d(u, v), then di S(u, v) = D(u, v). For i(u, v) = D(u, v) − d(u, v), such a Smarandachely i-detour
set is called a weak edge detour set in G. The weak edge detour number dnw(G) of G is
the minimum order of its weak edge detour sets and any weak edge detour set of order dnw(G) is a weak edge detour basis of G. For any weak edge detour basis S of G, a subset T ⊆ S is called a forcing subset for S if S is the unique weak edge detour basis containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing weak edge detour number of S, denoted by fdnw(S), is the cardinality of a minimum forcing subset for S. The forcing weak edge detour number of G, denoted by fdnw(G), is
fdnw(G) = min{fdnw(S)}, where the minimum is taken over all weak edge detour bases S in G. The forcing weak edge detour numbers of certain classes of graphs are determined. It is proved that for each pair a, b of integers with 0 ≤ a ≤ b and b ≥ 2, there is a connected graph G with fdnw(G) = a and dnw(G) = b.

**Category:** General Mathematics

[131] **viXra:1403.0189 [pdf]**
*submitted on 2014-03-14 06:45:02*

**Authors:** Wang Ting

**Comments:** 5 Pages.

In this paper, a reduction formula for Smarandache LCM ratio sequences SLR(6)and SLR(7) are given.

**Category:** General Mathematics

[130] **viXra:1403.0188 [pdf]**
*submitted on 2014-03-14 06:46:29*

**Authors:** Wenji Guan

**Comments:** 3 Pages.

For any positive integer n, the Pseudo-Smarandache-Squarefree function Zw(n)is de¯ned as the smallest positive integer m such that mn is divisible by n. That is,Zw(n) = min fm : m 2 N; n j mng. In reference [2], Felice Russo proposed many problems
and conjectures related to the Pseudo-Smarandache-Squarefree function Zw(n). The main
purpose of this paper is using the elementary methods to study several problems in [2], and
four of them are solved.

**Category:** General Mathematics

[129] **viXra:1403.0187 [pdf]**
*submitted on 2014-03-14 06:47:47*

**Authors:** Muneer Jebreel Karama

**Comments:** 3 Pages.

The main purpose of this paper is to introduce new concepts of Smarandache numbers, namely Smarandache Friendly Cube Numbers, and give definitions,
curious note, theorem, conjectures, proposed future studies, and ask open problems.

**Category:** General Mathematics

[128] **viXra:1403.0186 [pdf]**
*submitted on 2014-03-14 06:49:31*

**Authors:** Mingdong Xiao

**Comments:** 4 Pages.

Let n be any positive integer, Pd(n) denotes the product of all positive divisors of n. The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of a new arithmetical function S (Pd(n)), and give an interesting asymptotic formula for it.

**Category:** General Mathematics

[127] **viXra:1403.0185 [pdf]**
*submitted on 2014-03-14 06:51:39*

**Authors:** Yani Zheng

**Comments:** 3 Pages.

For any positive integer n, the famous Pseudo Smarandache function Z(n) is de¯ned as the smallest integer m such that n evenly divides
Xm k=1 k. That is, Z(n) = min ½ m : nj m(m + 1)
2; m 2 N¾, where N denotes the set of all positive integers. The main purpose of this paper is using the elementary method to study the properties of the Pseudo Smarandache function Z(n), and solve two conjectures posed by Kenichiro Kashihara in ref-
erence [2].

**Category:** General Mathematics

[126] **viXra:1403.0184 [pdf]**
*replaced on 2015-06-22 08:12:02*

**Authors:** T.Nakashima

**Comments:** 5 Pages.

This paper is the answer of the Riemann Hypothesis about the sum of the mebius function.

**Category:** Number Theory

[125] **viXra:1403.0183 [pdf]**
*replaced on 2014-03-24 16:43:40*

**Authors:** Rodolfo Sergio González Castro

**Comments:** 12 Pages. hal.archives-ouvertes.fr:hal-00947254

In this paper I derive an equation relating the gravitational acceleration with the gravitational wavelength corresponding to the “gravitational energy” density at a point in space and with the speed of light, without using the gravitational constant of Newton (G), derive an equation of the Energy-Momentum of Einstein suppressing this constant, and further I set the foundations for new theory of gravity “Energy-Wave”.

**Category:** Quantum Gravity and String Theory

[124] **viXra:1403.0182 [pdf]**
*submitted on 2014-03-13 19:42:37*

**Authors:** Aleksandr V. Bukalov

**Comments:** 7 Pages. Proc. 11-th Gamov Odessa Astronomical Conftrence, - Odessa,2011

It is shown, that the Earth biosphere main parameters, such as the alive matter total mass, the
DNA and peptides length, are connected with the observed Universe parameters. In particular,
the length of the integral genome DNA of the Earth biosphere is equal to the Hubble radius. The
consideration of humanity as the biosphere matter especial part provides us to value the human
mass limit and extremal quantity; the obtained results coincide with the ones, calculated by the
demography specialists. The obtained relations are explained by the author conception of the
synergistical evolutioning Universe, where the nonequilibrium structures, including the alive ones,
are created under the action of the observed energy forms as well as of the dark energy. The
connection between the biosphere and Universe parameters provides us to extend the Anthropic
principle notion as well as the observer conception because the biosphere is an adaptation tracing
system, which adjusts itself under the Universe evolution to be the one unit with it.
Keywords: biosphere, cosmological parameters, Hubble radius, DNA length, humanity mass, Earth biosphere
mass, Universe mass, Hubble radius, P. Dirac Big Numbers, ﬁne structure constant, synergetical Universe,
biospheres number in the Universe.

**Category:** Relativity and Cosmology

[123] **viXra:1403.0181 [pdf]**
*submitted on 2014-03-13 22:21:39*

**Authors:** Nigel B. Cook

**Comments:** 15 Pages.

Concise, brief 15-page fallout prediction model, covering both land surface and underwater nuclear explosions, radiation shielding by buildings, fallout solubility as function of particle size, retention on vegetation, gamma ray spectrum versus time, fractionation of fission products, salting by cobalt-60 etc., and effects of environmental neutron induced activities in fallout. Includes literature summaries and data reductions to formulae based on many reports.

**Category:** Nuclear and Atomic Physics

[122] **viXra:1403.0180 [pdf]**
*submitted on 2014-03-13 23:16:44*

**Authors:** Hyoyoung Choi, Prabir Rudra

**Comments:** 23 pages, 16 figures

Departing from the abstract aversion of the concept of negative
mass (energy), we propose a pair creation model of the universe
taking into account the possibility of co-existence of both
positive and negative mass particles. Nature of negative mass has
been given a fair thought and the possible dynamics is studied.
The existence of negative mass has been theoretically justified.
The birth of the universe is explained and the future is predicted
using the pair creation model. Various cosmological problems have
been discussed and it has been shown that the model presents an
obvious solution to all of them. Einstein's field equations of
General Relativity have been modified in the light of the model.
The energy ratio of the components of the universe (matter, dark
matter and dark energy) is studied using the model and found to be
comparable with the experimental data obtained from WMAP and
Planck. Finally it is concluded that the model deserves a serious
consideration, given its consistency with the observational data.

**Category:** Relativity and Cosmology

[121] **viXra:1403.0179 [pdf]**
*submitted on 2014-03-14 01:24:12*

**Authors:** Richard Blaber.

**Comments:** 9 Pages. 14 equations; 36 footnotes.

We revisit the Milne cosmological model and examine Melia’s argument for a ‘cosmic horizon’ in relation to that model, before dismissing both in favour of the standard Lambda-CDM view.

**Category:** Astrophysics

[120] **viXra:1403.0178 [pdf]**
*replaced on 2014-05-16 14:30:57*

**Authors:** Frank Dodd Tony Smith Jr

**Comments:** 17 Pages.

Cosmos (2014) with Neil deGrasse Tyson discusses Giordano Bruno's MultiVerse. David Deutch defines the MultiVerse in terms of SnapShots that are equivalent to Cl(16) E8 Local Lagrangian Regions that can be combined by completing the union of all tensor products of all copies of Cl(16) for such E8 Local Lagrangian SnapShot Regions to produce a generalization of the Hyperfinite II1 von Neumann factor that is a realistic Algebraic Quantum Field Theory for E8 Physics. Ramon Llull's 13th Century Quaternary Phase Art gives a remarkably detailed picture of the Structure of E8 Physics. In the 16th Century Giordano Bruno had access only to Llull's Ternary Art which was far less detailed than the earlier Quaternary Art, but even so was able to see that Llull's Art was, as Anthony Bonner said, "… a way to explore the connections among his infinity of worlds …", a way that can now in the 21st Century be seen to be consistent with the realistic E8 Physics model. V2 adds Vico, Joyce and Finnegans Wake

**Category:** History and Philosophy of Physics

[119] **viXra:1403.0177 [pdf]**
*submitted on 2014-03-14 03:05:32*

**Authors:** Fu Yuhua, Fu Anjie, Zhao Ge

**Comments:** 2 Pages.

Besides the existing four fundamental interactions there must exist six neutral
fundamental interactions (as six new forms of interaction) in accordance with the neutrosophy theory. For example, between strong interaction and weak interaction there exists intermediate interaction, namely neutral strong-weak fundamental interaction, it’s neither strong interaction nor weak interaction, but something in between. Similarly, other five neutral fundamental interactions are neutral strong-electromagnetic fundamental interaction, neutral strong-gravitation fundamental interaction, neutral weak-electromagnetic fundamental interaction, neutral weak-gravitation fundamental
interaction and neutral electromagnetic-gravitation fundamental interaction. Thus, there
are ten fundamental interactions all together.

**Category:** General Mathematics

[118] **viXra:1403.0175 [pdf]**
*submitted on 2014-03-14 03:09:15*

**Authors:** Jason Earls

**Comments:** 3 Pages.

In Smarandache Sequences Vol. I at the Smarandache web site[1], item #12 is a “Smarandache car” in which the figure of a vehicle can be seen as a
picture outlined in a block of digits. In this note I report on some primes that were found using the “Smarandache car” as the initial segment of their
decimal expansions.

**Category:** General Mathematics

[117] **viXra:1403.0174 [pdf]**
*submitted on 2014-03-14 03:10:57*

**Authors:** Charles T. Le

**Comments:** 3 Pages.

The three kinds of paradoxes are equivalent. They are called: The Smarandache Class of Paradoxes.

**Category:** General Mathematics

[116] **viXra:1403.0173 [pdf]**
*submitted on 2014-03-14 03:13:09*

**Authors:** Said Broumi

**Comments:** Pages.

The Smarandache Cómplex (with the accent on the first syllable): is a collection of fears.

**Category:** General Mathematics

[115] **viXra:1403.0172 [pdf]**
*submitted on 2014-03-14 03:15:02*

**Authors:** M. Khoshnevisan

**Comments:** Pages.

In this short paper, as an extension and
consequence of Einstein-Podolski-Rosen paradox
and Bell’s inequality, one promotes the hypothesis that: There is no speed barrier in the universe and one can construct arbitrary speeds, and also one asks if it's possible to have an infinite speed (instantaneous transmission)?

**Category:** General Mathematics

[114] **viXra:1403.0170 [pdf]**
*submitted on 2014-03-14 03:19:02*

**Authors:** N. Kannappa, Mr. K. Suresh

**Comments:** 10 Pages.

In this paper we have introduced smarandache - 2 - Algebraic structure of lattice namely smarandache lattice. A smarandache 2- algebraic structure on a set N means a weak algebraic structure Ao on N such that there exists a proper subset M of N which is embedded with a stronger algebraic structure A1, Stronger algebraic structure means that it is satisfying more axioms, by proper subset one understands a subset different from the empty set, from the unit element if any, and from the whole set. we define smarandache lattice and obtain some of its characterization through Pseudo complemented .For
basic concept we refer to PadilaRaul[4].

**Category:** General Mathematics

[113] **viXra:1403.0169 [pdf]**
*submitted on 2014-03-14 03:20:40*

**Authors:** A. A. Salama

**Comments:** Pages.

Classes of linguistic paradoxes are introduced with examples and explanations. The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such paradoxes one grammatically adjusts the sentences.

**Category:** General Mathematics

[112] **viXra:1403.0168 [pdf]**
*submitted on 2014-03-14 03:22:42*

**Authors:** M. Khoshnevisan

**Comments:** Pages.

In any domain of knowledge, a Smarandache -structure, for , on a set means a weak structure on such that there exists a chain of proper
subsets whose corresponding structures satisfy the inverse inclusion chain , where signifies strictly stronger (i.e., structure satisfying more axioms).

**Category:** General Mathematics

[111] **viXra:1403.0167 [pdf]**
*submitted on 2014-03-14 03:23:52*

**Authors:** M. Khoshnevisan

**Comments:** Pages.

In a democracy should the non-democratic ideas be allowed?

**Category:** General Mathematics

[110] **viXra:1403.0166 [pdf]**
*submitted on 2014-03-14 03:25:05*

**Authors:** A. A. Salama

**Comments:** Pages.

As in the Primitive Society, the modern society is making for MATRIARCHATE – the woman leads in the industrialized societies.

**Category:** General Mathematics

[109] **viXra:1403.0165 [pdf]**
*submitted on 2014-03-14 03:26:30*

**Authors:** Celestin Lele, Jean B. Nganou

**Comments:** 10 Pages.

Using some new characterizations of ideals in BL-algebras, we revisit the paper of A. Borumand, and al.[1] recently published in this Journal. Using the concept of MV-center of a BL-algebra, we give a very simple characterization of
Smarandache BL-algebra. We also restate some of the results and provide much simpler proofs. Among other things, we notice that Theorem 3.17 and Theorem 3.18 of [1] are not true and they aect a good portion of the paper. Since Deni-
tion 3.19, Examples 3.20, 3.21, Theorem 3.22, Remark 3.23 and Remark 3.24 are based on a wrong Theorem, they are completely irrelevant.

**Category:** General Mathematics

[108] **viXra:1403.0161 [pdf]**
*submitted on 2014-03-14 03:32:26*

**Authors:** J. Dezert

**Comments:** 2 Pages.

Let n>k≥1 be two integers. Then the Smarandacheial is defined as:

**Category:** General Mathematics

[107] **viXra:1403.0159 [pdf]**
*submitted on 2014-03-14 03:35:00*

**Authors:** Mihai Dicu

**Comments:** 1 Page.

The Smarandache-Pătrașcu Theorem of orthohomological Triangles is the folllowing:
If P1,P2 are isogonal points in the triangle ABC , and if 1 1 1 ABC and 2 2 2 A B C are their
pedal triangles such that the triangles ABC and 1 1 1 ABC are homological (the lines 1 1 1 AA , BB , CC are concurrent), then the triangles ABC and 2 2 2 A B C are also homological.

**Category:** General Mathematics

[106] **viXra:1403.0157 [pdf]**
*submitted on 2014-03-14 03:38:13*

**Authors:** A. A. Salama

**Comments:** Pages.

In order to save the colorless combinations prevailed in the Theory of Quantum Chromodynamics (QCD) of quarks and antiquarks in their combinations when binding, we devise the following formula.

**Category:** General Mathematics

[105] **viXra:1403.0154 [pdf]**
*submitted on 2014-03-14 03:42:40*

**Authors:** Xingsen Li

**Comments:** Pages.

Since Venn diagram is very hard to draw and to read for the cases when the number of sets becomes big (say n = 8, 9, 10, 11, …), Smarandache has proposed a generalization of Venn diagram through an algebraic representation for the intersection of sets.

**Category:** General Mathematics

[104] **viXra:1403.0153 [pdf]**
*submitted on 2014-03-14 03:43:56*

**Authors:** Xingsen Li

**Comments:** Pages.

Suppose you travel to a third world country, for example Romania.

**Category:** General Mathematics

[103] **viXra:1403.0152 [pdf]**
*submitted on 2014-03-14 03:45:17*

**Authors:** Xingsen Li

**Comments:** Pages.

Is is an improvement of Weber's and Fechner's Laws on sensations and stimuli.

**Category:** General Mathematics

[102] **viXra:1403.0151 [pdf]**
*submitted on 2014-03-14 03:46:59*

**Authors:** Xingsen Li

**Comments:** Pages.

Is characterized by nose frequently bleeding under stress, fear,restlessness, tiredness, nervousness, prolonged unhappiness.

**Category:** General Mathematics

[101] **viXra:1403.0150 [pdf]**
*submitted on 2014-03-14 03:48:38*

**Authors:** Said Broumi

**Comments:** Pages.

Classes of linguistic tautologies are introduced with examples and explanations.
The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such tautologies one grammatically adjusts the sentences.

**Category:** General Mathematics

[100] **viXra:1403.0149 [pdf]**
*submitted on 2014-03-14 03:54:42*

**Authors:** Rodney Bartlett

**Comments:** 6 Pages.

I'm studying Bioscience externally with Charles Darwin University in Australia, and the textbook for this unit is "Essentials of Human Anatomy and Physiology" (Tenth Edition) by Elaine N. Marieb - Pearson Education Limited, 2014. In the textbook on p.35, Review Question 3 asks "Which is not essential to survival? (Water, Oxygen, Gravity, Atmospheric pressure, Nutrients)" Of course, the answer is supposed to be "gravity". For years, I've firmly believed (based on neglected theories of Einstein's, that I've built on) that gravity is as essential as any of the other items (without gravity, there would be no atoms and no water, oxygen, atmosphere etc.) My question is - If I'm asked this as a multiple choice in a test (meaning there'e no space for lengthy explanation), what should I do? Stick to the beliefs I've spent years developing, and get marked "wrong"? Or conform to tradition, answer "gravity" even though I don't want to, and get marked "right"?

**Category:** Relativity and Cosmology

[99] **viXra:1403.0148 [pdf]**
*submitted on 2014-03-14 03:50:06*

**Authors:** Mihaly Bencze

**Comments:** 3 Pages.

Through one of the intersecting points of two circles we draw a line that intersects a
second time the circles in the points 1 M and 2 M respectively. Then the geometric locus of the
point M which divides the segment 1 2 M M in a ratio k (i.e. M1M = k⋅MM2) is the circle of center
O (where O is the point that divides the segment of line that connects the two circle centers O1
and respectively O2 into the ratio k, i.e. O1O = k ⋅OO2 ) and radius OA, without the points A and
B.

**Category:** General Mathematics

[98] **viXra:1403.0147 [pdf]**
*submitted on 2014-03-14 03:52:16*

**Authors:** R. Padilla

**Comments:** 2 Pages.

A Smarandache Strong Structure on a set S means a structure on S that has a proper subset P with a stronger structure.
By proper subset of a set S, we mean a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.

**Category:** General Mathematics

[97] **viXra:1403.0146 [pdf]**
*submitted on 2014-03-14 03:53:43*

**Authors:** R. Padilla

**Comments:** 1 Page.

A Smarandache Strong-Weak Structure on a set S means a structure on S that has two proper subsets: P with a stronger structure, and Q with a weaker structure.

**Category:** General Mathematics

[96] **viXra:1403.0145 [pdf]**
*submitted on 2014-03-14 03:55:13*

**Authors:** Mihaly Bencze

**Comments:** 2 Pages.

Let n>k≥1 be two integers. Then a Smarandache Summand is defined as:

**Category:** General Mathematics

[95] **viXra:1403.0144 [pdf]**
*submitted on 2014-03-14 03:57:08*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 1 Page.

A Smarandache Weak Structure on a set S means a structure on S that has a proper subset P with a weaker structure.
By proper subset of a set S, we mean a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.

**Category:** General Mathematics

[94] **viXra:1403.0143 [pdf]**
*submitted on 2014-03-14 03:58:17*

**Authors:** Said Broumi

**Comments:** Pages.

A Smarandache-Wellin Number, SWN(n), in a given base b, is a number resulted from the concatenation of first consecutive prime numbers.

**Category:** General Mathematics

[93] **viXra:1403.0140 [pdf]**
*submitted on 2014-03-14 04:01:51*

**Authors:** Micha Fleuren

**Comments:** 6 Pages.

SmBackConodd(1): 1
PRIME!
SmBackConodd(2): 31
PRIME!

**Category:** General Mathematics

[92] **viXra:1403.0137 [pdf]**
*submitted on 2014-03-14 04:05:07*

**Authors:** Young Bae Jun

**Comments:** 6 Pages.

The Smarandache structure of generalized BCK-algebras is considered. Several examples of a qS-gBCK-algebra are provided. The notion of SΩ-ideals and qSΩ-ideals is introduced, and related properties are investigated.

**Category:** General Mathematics

[91] **viXra:1403.0128 [pdf]**
*submitted on 2014-03-14 04:17:17*

**Authors:** Navin Kashyap, Alexander Vardy

**Comments:** 8 Pages.

In this paper, we present characterizations of annihilator polynomials over the ring, Zn =
Z=nZ, of integers modulo n. These characterizations are used to derive an expression for the number of annihilator polynomials of degree k over Zn, as well as one for the number of monic annihilators of degree k.

**Category:** General Mathematics

[90] **viXra:1403.0127 [pdf]**
*submitted on 2014-03-14 04:18:50*

**Authors:** Taekyun Kim, C. Adiga, Jung Hun Han

**Comments:** 8 Pages.

The additive analogues of Pseudo-Smarandache, Smarandache-simple func-tions and their duals have been recently studied by J. S´andor. In this note,
we obtain q-analogues of S´andor’s theorems

**Category:** General Mathematics

[89] **viXra:1403.0126 [pdf]**
*submitted on 2014-03-14 04:22:33*

**Authors:** Linfan Mao

**Comments:** 15 Pages.

A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2-manifolds on surfaces, called map geome-
tries was presented by the author in [9]−[10] and [12]. However, few observations for cases of n ≥ 3 are found on the journals. As a kind of Smarandache geometries, a general way for constructing dimensional n pseudo-manifolds are
presented for any integer n ≥ 2 in this paper. Connection and principal fiber bundles are also defined on these manifolds. Following these constructions, nearly all existent geometries, such as those of Euclid geometry, Lobachevshy-
Bolyai geometry, Riemann geometry, Weyl geometry, K¨ahler geometry and Finsler geometry, ...,etc., are their sub-geometries.

**Category:** General Mathematics

[88] **viXra:1403.0125 [pdf]**
*submitted on 2014-03-14 04:24:52*

**Authors:** Jaiyeola Temitope Gbolahan

**Comments:** 15 Pages. 15

Smarandache quasigroup(loop) is shown to be universal if all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f, g-principal isotopes are Smarandache f, g-
principal isotopes. Conversely, it is shown that if these weak Smarandache loops of Bol-Moufang type are universal, then some autotopisms are true in the weak Smaran- dache sub-loops of the weak Smarandache loops of Bol-Moufang type relative to some Smarandache elements. Futhermore, a S in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is shown to be universal if and only if it is a Smarandache left(right) Bol loop in which all its
f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, it is established
that a Smarandache inverse property loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes is universal if and only if it is a Smarandache Moufang loop in which all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Hence, some of the autotopisms earlier mentioned are found to be true in the Smarandache sub-loops of universal Smarandache: left(right) inverse property loops
and inverse property loops.

**Category:** General Mathematics

[87] **viXra:1403.0123 [pdf]**
*submitted on 2014-03-14 04:35:30*

**Authors:** Linfan Mao

**Comments:** 16 Pages.

A tendering is a negotiating process for a contract through by a tenderer issuing an invitation, bidders submitting bidding documents and the tenderer accepting a bidding by sending out a notification of award. As a useful way of purchasing, there are many norms and rulers for it in the purchasing guides of the World Bank, the Asian Development Bank, · · ·, also
in contract conditions of various consultant associations. In China, there is a law and regulation system for tendering and bidding. However, few works on the mathematical model of a tendering and its evaluation can be found in publication. The main purpose of this paper is to construct a Smarandache multi-space model for a tendering, establish an evaluation system for bidding based on those ideas in the references [7] and [8] and analyze its solution by
applying the decision approach for multiple objectives and value engineering.
Open problems for pseudo-multi-spaces are also presented in the final section.

**Category:** General Mathematics

[86] **viXra:1403.0122 [pdf]**
*submitted on 2014-03-14 04:37:15*

**Authors:** Sukanto Bhattacharya

**Comments:** 3 Pages.

{w0} on S such that there exists a chain of proper subsets Pn-1 < Pn-2 < … < P2 < P1 < S, where '<' means 'included in', whose corresponding structures
verify the inverse chain {wn-1} > {wn-2} > … > {w2} > {w1} > {w0}, where '>' signifies 'strictly stronger' (i.e., structure satisfying more axioms).

**Category:** General Mathematics

[85] **viXra:1403.0119 [pdf]**
*submitted on 2014-03-14 04:41:07*

**Authors:** Ralph E. Griswold

**Comments:** 3 Pages.

All kinds of things can be found among integer
sequences, including the weird and nonsensical.
Enter Smarandache sequences (S. sequences,
for short), which are integer sequences due to
Florentin Smarandache and his disciples.

**Category:** General Mathematics

[84] **viXra:1403.0118 [pdf]**
*submitted on 2014-03-13 06:54:12*

**Authors:** Hideki Mutoh

**Comments:** 4 Pages.

The electromagnetic field model including Nakanishi-Lautrup (NL) field of quantum electrodynamics (QED) can easily treat creation and annihilation of positive and negative charge pairs, although it is difficult for Maxwell's equations to treat them. However, the model does not directly satisfy the charge conservation equation and permits single charge creation and annihilation. It is shown that the potential energy of NL field for a pair of charge creation and annihilation centers is proportional to their distance. It causes the confinement of charge creation and annihilation centers, which means the charge conservation for this model. The quark confinement might be also explained by the energy of NL field.

**Category:** High Energy Particle Physics

[83] **viXra:1403.0117 [pdf]**
*submitted on 2014-03-13 00:43:56*

**Authors:** Madhukar Shivajirao Dama

**Comments:** 20 Pages.

Sexual dimorphism of human body size starts as early as first trimester of fetal development [1].
Compared to daughters, sons develop faster [2] and weigh 2-3% higher at birth [3]. This
dimorphism is believed to create an investment dimorphism for mothers, such that, women
bearing sons tend to incur higher physiological investment costs. Further, analysis of human
populations has shown that mothers bearing more sons require longer time to reproduce again
[4]. These observations lead to the prediction that mothers bearing more sons may need to trade
the physiological investments with lifespan [5].

**Category:** Quantitative Biology

[82] **viXra:1403.0116 [pdf]**
*submitted on 2014-03-13 00:41:51*

**Authors:** Victor Christianto

**Comments:** 3 Pages. This article has not been submitted to any journal. Comments are welcome

Sarah Becker et al. just released a new paper (arXiv: 1402.2833) where she and her colleagues including Mark Jacobson suggest a new plan for fully renewable US electricity system. Their title is: Features of a fully renewable US electricity system: Optimized mixes of wind and solar PV and transmission grid extensions. So I think it is worth to discuss their proposal.

**Category:** General Science and Philosophy

[81] **viXra:1403.0115 [pdf]**
*submitted on 2014-03-13 01:10:34*

**Authors:** Madhukar Shivajirao Dama

**Comments:** 18 Pages.

Balanced sex ratio evolves by a process known as frequency-dependent selection of the minority sex. Efforts to test this theory have focused mainly on experimental populations. Heterogametic sex has greater influence over the sex of the offspring. We tested the prediction that a smaller human population should favor male offspring. Our findings reveal that size of the population has significant inverse correlation with male proportion. We also present evidence for frequency-dependent selection of the minority sex and evolution of balanced sex ratio in isolated human population.

**Category:** Quantitative Biology

[80] **viXra:1403.0114 [pdf]**
*replaced on 2014-06-07 23:11:27*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 6 Pages.

The Principle of Equivalence is a central concept of Einstein's theory of gravitation, which makes generally covariant presentation of that theory extremely convenient for working out and communicating its dynamical detail. Weinberg has pointed out, however, that part of the base physics content of the theory, e.g., its overall stress-energy and conserved four-momentum, is inaccessible to formulations which maintain strict general covariance. Feynman, whose lectures on gravitation initially pursue an order-by-order construction of the theory, as a by-product arrived at a revelatory insight into the dynamical character of the gravitational field that reaches one step beyond Weinberg's not yet theory-stipulating separation of the Einstein tensor into its physically dissimilar linear and nonlinear parts. While Einstein's gauge-imposition of a local conservation principle is a common theme in physical theory, permitting it to spill over into outright solution nonuniqueness clearly isn't acceptable classical physics. Thus stipulation of Feynman's gravitational Lorentz condition, which pins down the dynamical character of the gravitational field, is fundamental to physically sensible application of Einstein's gravity theory.

**Category:** Relativity and Cosmology

[79] **viXra:1403.0112 [pdf]**
*submitted on 2014-03-13 03:18:26*

**Authors:** L. Kuciuk, M. Antholy

**Comments:** 4 Pages.

In această lucrare facem o prezentare a acestor geometrii inovatoare şi prezentăm
un model pentru una particulară.

**Category:** General Mathematics

[78] **viXra:1403.0111 [pdf]**
*submitted on 2014-03-13 03:20:23*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 5 Pages.

In this paper we study the Smarandache Semi-Automaton and
Automaton using Smarandache free groupoids.

**Category:** General Mathematics

[77] **viXra:1403.0110 [pdf]**
*submitted on 2014-03-13 03:22:15*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 7 Pages.

This paper aims to study the Smarandache cosets and derive some interesting
results about them. We prove the classical Lagranges theorem for
Smarandache semigroup is not true and that there does not exist a one-to-one
correspondence between any two right cosets. We also show that the classical
theorems cannot be extended to all Smarandache semigroups. This leads to the
definition of Smarandache Lagrange semigroup, Smarandache p Sylow
subgroup and Smarandache Cauchy elements. Further if we restrict ourselves
to the subgroup of the Smarandache semigroup all results would follow
trivially hence the Smarandache coset would become a trivial definition.

**Category:** General Mathematics

[76] **viXra:1403.0109 [pdf]**
*submitted on 2014-03-13 03:24:38*

**Authors:** C. Le

**Comments:** 4 Pages.

Die drei Arten der Paradoxe sind äquivalent. Man nennt sie: die Smarandache'sche Klasse von Paradoxen.

**Category:** General Mathematics

[75] **viXra:1403.0108 [pdf]**
*submitted on 2014-03-13 03:27:44*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 5 Pages.

In this paper we study the notion of Smarandache-Galois fields and homomorphism and the Smarandache quotient ring. Galois fields are nothing but fields having only a finite number of elements. We also propose some interesting problems.

**Category:** General Mathematics

[74] **viXra:1403.0107 [pdf]**
*submitted on 2014-03-13 03:31:59*

**Authors:** T`emitope Gbolahan Jaiyeola

**Comments:** 14 Pages.

The idea of left(right) palindromic permutations(LPPs,RPPs) and left(right) gen-
eralized Smarandache palindromic permutations(LGSPPs,RGSPPs) are introduced in
symmetric groups Sn of degree n. It is shown that in Sn, there exist a LPP and a RPP
and they are unique(this fact is demonstrated using S2 and S3). The dihedral group
Dn is shown to be generated by a RGSPP and a LGSPP(this is observed to be true in
S3) but the geometric interpretations of a RGSPP and a LGSPP are found not to be rotation and reflection respectively. In S3, each permutation is at least a RGSPP or a LGSPP. There are 4 RGSPPs and 4 LGSPPs in S3, while 2 permutations are both RGSPPs and LGSPPs. A permutation in Sn is shown to be a LPP or RPP(LGSPP or RGSPP) if and only if its inverse is a LPP or RPP(LGSPP or RGSPP) respectively.
Problems for future studies are raised.

**Category:** General Mathematics

[73] **viXra:1403.0106 [pdf]**
*submitted on 2014-03-13 03:33:49*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 9 Pages.

In this paper we study the concept of Smarandache Groupoids, subgroupoids, ideal of groupoids, semi-normal subgroupoids, Smarandache-Bol groupoids and Strong Bol groupoids and obtain many interesting results about them.

**Category:** General Mathematics

[72] **viXra:1403.0105 [pdf]**
*submitted on 2014-03-13 03:35:23*

**Authors:** Howard Iseri

**Comments:** 8 Pages.

A paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into
one space along with other non-Euclidean behaviors of lines that would seem to require a discrete space. A class of continuous spaces is presented here together with specific examples that exhibit almost all of these phenomena and suggest the prospect of a continuous paradoxist geometry.

**Category:** General Mathematics

[71] **viXra:1403.0104 [pdf]**
*submitted on 2014-03-13 03:37:02*

**Authors:** Howard Iseri

**Comments:** 6 Pages.

A model of a cone can be constructed from a piece of paper by removing a wedge and taping the edges together. The paper models discussed here expand on this idea (one or more wedges are added and/or removed). These models are flat everywhere, except at the “cone points,” so the geodesics are locally straight lines in a natural sense. Non-Euclidean “effects” are easily quantifiable using basic geometry, the Gauss-Bonnet theorem is a naturally intuitive concept, and the connection between hyperbolic and elliptic geometry and curvature is clearly seen.

**Category:** General Mathematics

[70] **viXra:1403.0103 [pdf]**
*submitted on 2014-03-13 03:38:56*

**Authors:** Howard Iseri

**Comments:** 11 Pages.

In Riemannian (differential) geometry, the differences between Euclidean geometry, elliptic geometry, and hyperbolic geometry are understood in terms of curvature. I think Gauss and Riemann captured the essence of geometry in their studies of surfaces and manifolds, and their point of view is spectacularly illuminating. Unfortunately, curvature is highly non-trivial to work with. I will talk about a more accessible version of curvature that dates back to Descartes.

**Category:** General Mathematics

[69] **viXra:1403.0097 [pdf]**
*submitted on 2014-03-13 03:52:39*

**Authors:** Fu Yuhua, Fu Anjie

**Comments:** 7 Pages.

Based on the combined method in Chinese ancient I-Ching and theory of Taiji, this paper presents the Neutrosophic combinatorics by means of the combinations of the truth, the falsehood, and the indeterminacy in Smarandache’s Neutrosophy. For the Neutrosophic combinatorics we can say that “Changes originate in the Taiji; from the
Taiji come the 3 spheres. From the 3 spheres come the 9 elements, and from the 9 elements come the 27 diagrams.” As the application examples, discussing the further revision to Gödel's Incompleteness Theorem; Based on one divides into two, three, more than three, pointing out that one can divide into the mixed fraction parts even
hypercomplex numbers parts, such as one divides into two point five parts, one divides into (1+9i+25000j+1700k) parts; By using Neutrosophic combinatorics, also presents the digitized Taiji figure, fractal Taiji figure and the special digitized Taiji figure (one kind of asymmetry Taiji figure). Finally, discussing the rule in the application of Neutrosophic combinatorics, namely the truth uniqueness, for example, if considering that the principle of conservation of energy is a truth, then the principle of conservation of momentum or the principle of conservation of angular momentum no longer can be
considered as a truth.

**Category:** General Mathematics

[68] **viXra:1403.0096 [pdf]**
*submitted on 2014-03-13 03:54:15*

**Authors:** T. Srinivas, A.K.S. Chandra Sekhar Rao

**Comments:** 14 Pages.

It is proved that a ring R in which for every x ∈ R there exists a (and hence the smallest) natural number n(x) > 1 such that xn(x) = x is always a Smarandache Ring. Two examples are provided for justification.

**Category:** General Mathematics

[67] **viXra:1403.0095 [pdf]**
*submitted on 2014-03-13 03:57:57*

**Authors:** Ovidiu Șandru

**Comments:** 3 Pages.

În spațiul euclidian tridimensional considerăm două plane paralele și distincte 1 α și 2 α . Spațiul Smarandache Σ , pe care îl definim, este alcătuit din punctele acestor două plane, sau altfel zis,Σ =α1 ∪α 2 . Tot prin definiție, considerăm că dreptele acestui spațiu sunt date de reuniunea tuturor dreptelor (euclidiene) incluse în 1 α , sau 2 α . În legătură cu elementele modelului geometric Σ enunțăm următoarele definiții :

**Category:** General Mathematics

[66] **viXra:1403.0094 [pdf]**
*submitted on 2014-03-13 04:00:02*

**Authors:** V. Christianto

**Comments:** 7 Pages.

A new theory is proposed: poly-emporium theory. A search done in Google on May 3rd, 2008, for the term “poly-emporium” returned no entry, so
we introduce it for the first time.

**Category:** General Mathematics

[65] **viXra:1403.0093 [pdf]**
*submitted on 2014-03-13 04:02:41*

**Authors:** Paulo D. F. Gouveia, Delm F. M. Torres

**Comments:** 18 Pages.

We study Smarandache sequences of numbers, and related problems, via a Computer Algebra System. Solutions are discovered, and some conjectures presented.

**Category:** General Mathematics

[64] **viXra:1403.0092 [pdf]**
*submitted on 2014-03-13 04:04:34*

**Authors:** L. Perez

**Comments:** 3 Pages.

Any odd integer n can be expressed as a combination
of three primes as follows.

**Category:** General Mathematics

[63] **viXra:1403.0089 [pdf]**
*replaced on 2014-04-24 06:33:00*

**Authors:** Gordon Watson

**Comments:** 12 Pages.

With Bell (1964) and his EPR-based mathematics contradicted by experiments, at least one step in his supposedly commonsense theorem must be false. Defining commonsense local realism as the fusion of local-causality (no causal influence propagates superluminally) and physical-realism (some physical properties change interactively), we eliminate all such contradictions and make EPR correlations intelligible by completing the quantum mechanical account in a classical way. Thus refuting the famous inequality at the heart of Bell's mathematics, we show that Bell's theorem is limited by Bell's use of naive realism. Validating the classical mantra that correlated tests on correlated things produce correlated results without mystery, we conclude that Bell's theorem and related experiments negate naive realism, not commonsense local realism.

**Category:** Quantum Physics

[62] **viXra:1403.0088 [pdf]**
*submitted on 2014-03-13 04:15:19*

**Authors:** Mircea Eugen Selariu

**Comments:** 9 Pages.

Teorema liniilor concurente a lui Florentin Smarandache...

**Category:** General Mathematics

[61] **viXra:1403.0086 [pdf]**
*submitted on 2014-03-12 14:20:19*

**Authors:** Solomon I. Khmelnik

**Comments:** 22 Pages.

First of all, the author solemnly declares that he recognizes the energy conservation law (understanding, however, that it will not help). Next we shall show that this law does not contradict the possibility of building a perpetual motion machine that uses the force of gravity. This, of course, reduces the kinetic energy of the Earth, but the author ignores this problem (in the same way as it is ignored by the designers of hydropower plants).

**Category:** Classical Physics

[60] **viXra:1403.0085 [pdf]**
*replaced on 2014-11-26 08:04:04*

**Authors:** Aleksandr V. Bukalov

**Comments:** 5 Pages. Physics of consciousness and life, Cosmology and Astrophysics. — 2011. — № 4. — P. 49–53.

It is shown that 160-minute oscillations of luminosity of the Sun and some quasars, found out by a series of researchers, could be explained within the bounds of superconducting cosmology (SCC) as the oscillations of the primary Higgs vacuum, which remained in the present Universe. The anthropic consequences of existence of such oscillations are discussed.
Key words: vacuum, superconducting cosmology, Higgs field, Anthropic Principle.

**Category:** Relativity and Cosmology

[59] **viXra:1403.0084 [pdf]**
*submitted on 2014-03-12 14:35:25*

**Authors:** Solomon I. Khmelnik

**Comments:** 23 Pages. in Russian

First of all, the author solemnly declares that he recognizes the energy conservation law (understanding, however, that it will not help). Next we shall show that this law does not contradict the possibility of building a perpetual motion machine that uses the force of gravity. This, of course, reduces the kinetic energy of the Earth, but the author ignores this problem (in the same way as it is ignored by the designers of hydropower plants). // Прежде всего автор торжественно заявляет, что признает закон сохранения энергии (понимая, однако, что это ему не поможет). Далее показывается, что этот закон не противоречит возможности построения вечного двигателя, использующего силы земного притяжения. При этом, естественно, уменьшается кинетическая энергия Земли, но эту проблему автор игнорирует (точно так же, как ее игнорируют конструкторы гидростанций).

**Category:** Classical Physics

[58] **viXra:1403.0083 [pdf]**
*replaced on 2017-02-08 08:52:53*

**Authors:** Ralf Wüsthofen

**Comments:** 10 Pages. First submission to the Annals of Mathematics on March 24, 2013, LATEST VERSION ON http://vixra.org/abs/1702.0300

This paper presents an elementary and short proof of the strong Goldbach conjecture. Whereas the traditional approaches focus on the control over the distribution of the primes by means of circle method and sieve theory, the proof is based on the constructive properties of the prime numbers, reflecting their multiplicative character within the natural numbers. With an equivalent but more convenient form of the conjecture in mind, we create a structure on the natural numbers. That structure leads to arithmetic identities which immediately imply the conjecture, more precisely, an even strengthened form of it. Moreover, we can achieve further results by generalizing the structuring. Thus, it turns out that the statement of the strong Goldbach conjecture is the special case of a general principle.

**Category:** Number Theory

[57] **viXra:1403.0079 [pdf]**
*replaced on 2014-09-19 12:34:56*

**Authors:** Yuri Heymann

**Comments:** 10 Pages.

We tested alternative cosmologies using Monte Carlo simulations based on the sampling method of the zCosmos galactic survey. The survey encompasses a collection of observable galaxies with respective redshifts that have been obtained for a given spectroscopic area of the sky. Using a cosmological model, we can convert the redshifts into light-travel times and, by slicing the survey into small redshift buckets, compute a curve of galactic density over time. Because foreground galaxies obstruct the images of more distant galaxies, we simulated the theoretical galactic density curve using an average galactic radius. By comparing the galactic density curves of the simulations with that of the survey, we could assess the cosmologies. We applied the test to the expanding-universe cosmology of de Sitter and to a dichotomous cosmology.

**Category:** Astrophysics

[56] **viXra:1403.0078 [pdf]**
*submitted on 2014-03-11 17:04:04*

**Authors:** Ray Fleming

**Comments:** 5 Pages.

Ernest Sternglass determined that a neutral meson, the π0 could be modeled as a relativistic electron-positron pair, and later determined that the muon could be modeled as an electron rotating around a similar electron-positron pair. The author noticed that there is a second higher-energy orbital solution not previously published by Sternglass where the electron-positron pair orbits around the electron’s center. A simple computation shows that the mass-energy of this second solution is consistent with the tau particle. Based on these models the mu and tau leptons are not fundamental particles as described in currently popular theories but are instead two excited meta-stable states of an electron and an electron-positron pair.

**Category:** High Energy Particle Physics

[55] **viXra:1403.0077 [pdf]**
*replaced on 2014-11-25 17:59:18*

**Authors:** Aleksandr V. Bukalov

**Comments:** 3 Pages. Physics of consciousness and life, Cosmology and Astrophysics. — 2013. — № 4. — P. 5–7

From the cosmological model of superconductivity (CCM) are obtained the formulas of the baryons and neutrinos numbers in the Universe. The connection between the number of baryons and leptons with the holographic principle is discussed. It is proposed to consider the number of generations of particles in the standard model as a quantum number.
Key words: baryons, neutrinos, cosmology, baryon charge, CMBR.

**Category:** Astrophysics

[54] **viXra:1403.0076 [pdf]**
*replaced on 2014-11-26 08:15:17*

**Authors:** Aleksandr V. Bukalov

**Comments:** 2 Pages. Physics of consciousness and life, Cosmology and Astrophysics. — 2013. — № 3. — P. 10–11.

The problem of coincidence of cosmic values is discussed. It is shown that in the modern era, at z = 0, on the basis of collaboration PLANCK data, the ratio between the density of the cosmic microwave background radiation and the critical density of the universe holds with high accuracy. Such ratio, as well as other unexplained in the standard Friedmann cosmology, is well explained in the cosmological model with superconductivity (CMS), previously proposed by the author.
Keywords: cosmology, microwave radiation, coincidence problem.

**Category:** Relativity and Cosmology

[53] **viXra:1403.0075 [pdf]**
*replaced on 2015-07-08 07:59:15*

**Authors:** Yuri Heymann

**Comments:** 11 Pages.

This paper aims to offer a testing framework for the structural properties of the Brownian motion of the underlying stochastic process of a time series. In particular, the test can be applied to financial time-series data and discriminate among the lognormal random walk used in the Black-Scholes-Merton model, the Gaussian random walk used in the Ornstein-Uhlenbeck stochastic process, and the square-root random walk used in the Cox, Ingersoll and Ross process. Alpha-level hypothesis testing is provided. This testing framework is helpful for selecting the best stochastic processes for pricing contingent claims and risk management.

**Category:** Statistics

[52] **viXra:1403.0074 [pdf]**
*replaced on 2014-03-12 05:57:42*

**Authors:** Yuri Heymann

**Comments:** 6 Pages.

The present study is an investigation of the thermal history of the earth using heat transfer modeling. Assuming that the earth was a hot ball at a homogeneous temperature upon its formation, the model makes the following two predictions about conditions 4.5 Ga later (the earth's approximate present age): (i) there will be
a geothermal gradient within a range of 1.5-5.0C per 100 meters in the rst km of the earth crust; and (ii) the earth's crust will be about 45 km thick, which is in agreement with average continental crust thickness.
The fact that oceanic crust is much thinner (around 5-10 km thick) is explained by convective heat transfer and plate tectonics. The strong agreement between he predicted thickness of earth's crust with the average actual continental crust thickness, helps confirm the accuracy of the current inner core model of the earth indicating a solid inner core made of iron based
on seismological studies.

**Category:** Geophysics

[51] **viXra:1403.0073 [pdf]**
*submitted on 2014-03-10 18:38:18*

**Authors:** Roger N. Weller

**Comments:** 13 Pages.

The concepts of a proposed Modified Standard Model are applied to explain the charged pion and muon decays along with an analysis of the nuclear reactions involved in major neutrino detection experiments.

**Category:** High Energy Particle Physics

[50] **viXra:1403.0072 [pdf]**
*replaced on 2014-03-15 08:53:33*

**Authors:** Vitaly Kuyukov Petrovich

**Comments:** 4 Pages.

In this article reviews the evolution of the future of the Universe with a cosmological constant. When restricting the event horizon of the Universe, there exists a nonzero temperature of the Hawking. This effect leads to the reduction of the cosmological event horizon after a stage of expansion of the Universe with constant density of dark energy. Time compression in this Universe is determined only cosmological constant.

**Category:** Quantum Gravity and String Theory

[49] **viXra:1403.0069 [pdf]**
*replaced on 2015-01-19 12:53:16*

**Authors:** Branko Zivlak, Dragoslav Stoiljkovich

**Comments:** 10 Pages. 8 formulas

Starting from "A Theory of Natural Philosophy" by Roger Boscovich (1711−1787), we are showing that some significant masses in the micro and macro world, mi, (the Planck mass, fundamental mass, background mass, hypothetical mass quantum mq, as well as the masses of vacuum, infinite universe and our universe) can be calculated by a simple equation mi=mqN1/i, where N is a large non-dimensional number (6.3870772•10^+121) and i=-1, 0, 1, 2, 3, 4, infinite. Knowing these significant masses is useful for the calculation of other real masses. We are also showing the examples of calculating the masses of proton, electron and up quark.

**Category:** Classical Physics

[48] **viXra:1403.0068 [pdf]**
*submitted on 2014-03-10 08:20:29*

**Authors:** Richard S. Morse

**Comments:** 18 Pages.

Lines of Particle Transport (LOPT) are proposed as the means by which energy is transferred between objects. Particles of energy move through connected Lines of Particles (LOP) of various energy states (or perceived energy states) with more open particle patterns (low frequency of particle generation) allowing higher energy compressed particles (high frequency of particle generation) to transfer through their respective interconnected LOP, thus forming Lines of Particle Transport (LOPT). This allows the lower energy object to receive energy and thereby increase the object’s energy level until both objects are of the same energy level or state. When both objects are of the same energy level, they have identical particle patterns, and at that point transfer stabilizes along the interconnected LOPT.
The proposed LOPT theory is supported by current observation and resolves the conundrum of the duality of light by eliminating the issue of wave interference, therefore eliminating support for wave theory. The constancy of the speed of light is resolved through LOPT regardless of the speed of the source relative to the observer. This solution opens areas for revised thinking on a number of energy transfer and force issues and thus places particle movement and LOPT theory in a position to solve and resolve numerous physics issues, leading to a quantum explanation for gravity.

**Category:** Quantum Gravity and String Theory

[47] **viXra:1403.0066 [pdf]**
*submitted on 2014-03-09 20:55:03*

**Authors:** Jeffrey Joseph Wolynski

**Comments:** 3 Pages. 3 diagrams, 3 references

In the star sciences astronomers and astrophysicists have ignored basic understanding of what life needs to survive as well as what is needed for water to exist in liquid form. The life hypothesis as covered in the General Theory of Stellar Metamorphosis is contrasted with the Habitable Zone Hypothesis of establishment scientism.

**Category:** Astrophysics

[46] **viXra:1403.0065 [pdf]**
*submitted on 2014-03-10 04:42:23*

**Authors:** Miroslaw J. Kubiak

**Comments:** 5 Pages.

In the papers [1, 2] we presented the concept of the effective mass tensor (EMT) in General Relativity (GR). According to this concept under the influence of the gravitational field the bare mass tensor becomes the EMT. The concept of the EMT is a new physical interpretation of GR, where the curvature of space-time has been replaced by the EMT. In this paper we consider again the concept of the EMT in the GR but in the aspect of Newton’s bucket argument.

**Category:** Relativity and Cosmology

[45] **viXra:1403.0061 [pdf]**
*submitted on 2014-03-09 10:53:12*

**Authors:** Solomon I. Khmelnik

**Comments:** 164 Pages. Book.

This book describes various versions of processors, designed for affine transformations of many-dimensional figures – planar and spatial. This processors is oriented to affine transformation of unstructured geometrical figures with arbitrary points distribution. The type of data presentation used in this book is non-conventional, based on a not well-known theory of vectors and geometrical figures coding. The problems of affine transformation are used widely in science and engineering. The examples of their application are computer tomography and data compression for telecommunication systems. The book covers the figures coding theory – the codes structure, algorithms of coding and decoding for planar and spatial figures, arithmetical operations with planar and spatial figures. The theory is supplemented by numerous examples. The arrangement of several versions of geometrical processor is considered – data representation, operating blocks, hardwares realization of coding, decoding and arithmetic operations algorithms. The processor’s internal performance is appraised. The book is designed for students, engineers and developers, who intend to use the computer arithmetic of geometrical figures in their own research and development in the field of specialized processors. // В книге рассматриваются различные варианты процессоров, предназначенных для аффинных преобразований многомерных фигур - плоских и пространственных. Эти процессоры ориентированы на аффинное преобразование неструктурированных геометрических фигур с произвольным характером распределения точек. При этом ипользуется нетрадиционная форма представления данных, основанная на малоизвестной теории кодирования векторов и геометрических фигур. Задачи аффинного преобразования пространства широко используются в науке и технике. В книге описывается теория кодирования фигур – структура кодов, алгоритмы кодирования, декодирования плоских и пространственных фигур, арифметические операции с плоскими и пространственными фигурами. Теория дополняется многочисленными примерами. Рассматривается несколько вариантов геометрического процессора – представление данных, операционные блоки, техническая реализация алгоритмов кодирования, декодирования и арифметических операций. Оценивается быстродействие этих процессоров.

**Category:** Digital Signal Processing

[44] **viXra:1403.0059 [pdf]**
*replaced on 2018-04-28 15:30:19*

**Authors:** Solomon I. Khmelnik

**Comments:** 128 Pages.

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence. Then we consider the so-called closed systems. We prove that for them the necessary and sufficient conditions of global extremum for the named functional always exist. Accordingly, the search for global extremum is always successful, and so the unique solution of Naviet-Stokes is found. We contend that the systems described by Navier-Stokes equations with determined boundary solutions (pressure or speed) on all the boundaries, are closed systems. We show that such type of systems include systems bounded by impermeable walls, by free space under a known pressure, by movable walls under known pressure, by the so-called generating surfaces, through which the fluid flow passes with a known speed. The book is supplemented by open code programs in the MATLAB system – functions realizing the calculation method and test programs. Links on test programs are given in the text of the book when the examples are described. // Формулируется и доказывается вариационный принцип экстремума для вязкой несжимаемой и сжимаемой жидкости, из которого следует, что уравнения Навье-Стокса являются условиями экстремума некоторого функционала. Описывается метод поиска решения этих уравнений, который состоит в движении по градиенту к экстремуму этого функционала. Формулируются условия достижения этого экстремума, которые являются одновременно необходимыми и достаточными условиями существования глобального экстремума этого функционала. Книга дополняется открытыми кодами программам в системе MATLAB – функциями, реализующими расчетный метод, и тестовыми программами.

**Category:** Mathematical Physics

[43] **viXra:1403.0057 [pdf]**
*submitted on 2014-03-09 03:52:37*

**Authors:** Hasmukh K. Tank

**Comments:** Two-page letter

In a recent paper, titled “Explanation for the observed wave-particle-duality of Light” (Tank, H.K. http://vixra.org/abs/1402.0153, 2014) it was explained that: “Since at very high frequencies, narrowband filtering and generation of purely monochromatic light of one Hertz bandwidth is not yet technically possible, there has been quite a wide bandwidth of waves involved, in the double slit experiments and photoelectric experiments performed so far. And since this wide ‘band’ of waves coherently add only at discrete points in space and time, we get ‘particles’ at the detectors.” Now, to further confirm the validity of this explanation, a new kind of experiment is proposed here, in which protons and electrons are accelerated at appropriate velocities vp ve , such that their de Broglie wavelengths are equal; i.e. ( h / mp vp )= ( h / me ve ) and let them pass through closely spaced slits so that they can interfere with each other. Similarly, in another experiment, their wave-functions: A exp i ( kp X - ωp t ) = A exp i ( ke X - ωe t ) , and let them pass through closely spaced slits, and see how the two matter-waves interfere.

**Category:** Quantum Physics

[42] **viXra:1403.0056 [pdf]**
*submitted on 2014-03-08 07:27:04*

**Authors:** Xu Feng

**Comments:** 2 Pages.

Proof of the Brich and swinnerton-Dyer conjecture

**Category:** Number Theory

[41] **viXra:1403.0055 [pdf]**
*submitted on 2014-03-08 09:29:36*

**Authors:** Ray Fleming

**Comments:** 4 Pages.

After the author determined that the mass of a proton and electron are equal to the vacuum energy excluded by a shell the size of their charge radii, it became important to find a particle model that forms a shell, since there is no commonly accepted shell-like model. A survey of all common geometric solids was undertaken and only the rhombic tricontahedron was identified as a likely candidate that would allow for a stable quasi-spherical form made of an unequal number of point charges, 12 outer and 20 inner. The electrostatic forces were then computed and it was found that the inward and outward forces cancelled to a large extent. The remaining inward directed force necessary for stability would have to be due to magnetic interactions, which should be possible given a modest amount of rotation. Consequently the rhombic triacontahedron is thought to be a promising semi-classical model for the electron and proton.

**Category:** Nuclear and Atomic Physics

[40] **viXra:1403.0054 [pdf]**
*submitted on 2014-03-08 04:54:38*

**Authors:** Xu Feng

**Comments:** 1 Page.

it is on the other mathematical formulas of the prime numbers.

**Category:** Number Theory

[39] **viXra:1403.0053 [pdf]**
*submitted on 2014-03-07 22:15:22*

**Authors:** Francis. M. Sanchez, Valéry A. Kotov

**Comments:** 12 Pages. Rejected by Nature (8 March 2014) without serious analysis (no refferee consulted)

A Coherence Principle (CP) is proposed, a generalization and idealization of the virial
theorem, stating that each well-defined phenomenon should be mono-frequency. When
applied to the steady-state critical cosmology, characterized by the scale factor exp(t/T), this
principle leads to three independent expressions for T compatible with the so-called Universe
age TU ≈ 13.80(4) Gyr, as estimated by the recent Planck mission for the spatially-flat six parameters Λ-CDM model. The most precise formula is given by a c-free analysis of the
“incredible” non-Doppler cosmic oscillation, implying tachyonic physics. This refutes (a) the
primordial Big Bang model, (b) the cosmological anthropic principle and (c) the Multiverse
theory, – in favor of the reconstructing Universe model with frequency about 10^103 Hz and
pseudo-period T. This corresponds to critical condition Ω = 1, Hubble parameter H0 ≈ 70.8
km s^-1 Mpc^-1, matter density Ωm = 3/10, and baryonic one Ωb ≈ Ωm^2/2 = 0.045, with detailed
predictions for astrophysics. The CP is connected with practical holography, which formalism
is shown to be consistent with the basic quantum one, and holographic conservations are
either demonstrated or observed, opening the way for further study. The CP is shown to apply
also in atomic and stellar physics, together with biology, predicting the DNA chain to be a linear
hologram.

**Category:** General Science and Philosophy

[38] **viXra:1403.0052 [pdf]**
*submitted on 2014-03-08 01:53:57*

**Authors:** A.Garcés Doz

**Comments:** 35 Pages.

This paper presents a proof of the fundamental connection between the zeros of the Riemann function and quantum mechanics. Two results that unify gravity and electromagnetism, by exact calculation, both the elementary electric charge and mass of the electron. These two results depend directly on the sum of the imaginary parts of the zeros of the Riemann function, exactly following the Hilbert-Polya conjecture. This summatory, is the exponential sums of all the negative values of the imaginary part of all zeros of the Riemann function.The main consequences are: scales of the Planck length gravity becomes repulsive, through the interaction of the gravitinos. Special relativity is a special case of a generalization, in which the geometry of a wormhole (hyperbolic geometry) implies that the energy of the tachyon states is zero, only if the velocity at the outer surface of the wormhole is infinite, or what is the same: an observer at rest can not distinguish an infinite speed of zero velocity, both are equivalent. There is not mere speculation; since only under this assumption the mass of the electron as a function of the non-trivial zeros of the Riemann zeta function is calculated. Time ceases to exist, takes the value zero. These wormholes would explain the quantum entanglement, as well as resolve the paradox of information loss in black holes. Fundamental constants used in this calculation are: elementary charge, gravitational Newton constant, Planck mass, mass of the electron, and fine structure constant for zero momentum.

**Category:** Quantum Gravity and String Theory

[37] **viXra:1403.0051 [pdf]**
*submitted on 2014-03-08 03:06:59*

**Authors:** Xu Feng

**Comments:** 1 Page.

Proof of the Riemann Hypothesis

**Category:** Number Theory

[36] **viXra:1403.0047 [pdf]**
*submitted on 2014-03-07 05:13:42*

**Authors:** Chetan Waghela

**Comments:** 17 Pages. submitted as poster for QIPA 2013 at HRI.

Hamiltonian Mechanics works for conserved systems. Quantum Mechanics is given in Hamiltonian language. In papers by Dekker and recently by A. Sergi, this problem was circumvented by complexifying the energy and interpreting the dissipative part as Imaginary part. Based on the Dekker model, a following interpretation is presented in Density-Operator language for Pseudo-Hermiticity. Proper forms of Quantum measures are provided, as there is need in this new formalism, namely correcting Pati and Zielinski, Wang.

**Category:** Quantum Physics

[35] **viXra:1403.0043 [pdf]**
*replaced on 2014-03-10 02:25:14*

**Authors:** Carlos Castro

**Comments:** 16 Pages. Submitted to Modern Physics Letters A

Recently, novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) were explored and which provided a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. An elegant $nonlinear$ momentum-addition law was derived that tackled the ``soccer-ball'' problem in DSR. Generalized photon dispersion relations allowed also for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, but breaking the $extended$ Lorentz symmetry in $C$-spaces. This does $not$ occur in DSR nor in other approaches, like the presence of quantum spacetime foam. In this work we show why a $minimal$ length (say the Planck scale) follows naturally from the Extended Relativity principle in Clifford Spaces. Our argument relies entirely on the Physics behind the extended notion of Lorentz transformations in $ C$-space, and $does ~not$ invoke quantum gravity arguments, nor quantum group deformations of Lorentz/Poincare algebras, nor other prior arguments displayed in the Physics literature. The Extended Relativity Theory in Clifford $Phase$ Spaces requires also the introduction of a $maximal$ scale which can be identified with the Hubble scale. It is found also that $ C$-space physics favors a choice of signature $ ( -, +, +, .... , + ) $.

**Category:** Quantum Gravity and String Theory

[34] **viXra:1403.0041 [pdf]**
*submitted on 2014-03-06 12:37:41*

**Authors:** A.M. Ilyanok

**Comments:** Pages 23, Figures 6, Table 1

The present chapter investigates electron. It is shown that electron has an intricate internal structure which determines both static and dynamic properties of the electron itself and important parameters of te condensed matter.
Stationary “cold” electron (≤0.1eV) is modeled by a thin elastic ring called ector having diameter which is 137,036 times larger Bohr’s radius of hydrogen which consists of specific form of magnetic field. On the basis of the ector model the size, mass, charge, electromagnetic mass, spin and magnetic moment of electron are described. The model of “cold” ring electron in a condensed matter explains from new perspective critical parameters of phase transitions “metal-semiconductor” (Winner’s crystallization) and low temperature and high temperature superconductivity.
Ring electron spirals into a void torus as compared to steady moving “hot” electrons (>>0.1эВ). The size of the torus depends on its kinetic energy which makes it possible to describe changes of the cross-section of the interaction with gas – Ramsauer effect. The model of ring electron transforming onto the torus also makes it possible to construct a hydrogen atom and describe energy states of the atom including its spectrum, process of emission/absorption, size of the atom and its stability.
The model of the toroid electron explains correlation of the change of the interacting cross-section of relativistic electron with accelerating electro-magnetic wave up to complete disappearance of the interaction called disruption in the energy spectrum of cosmic electrons.
Very high coincidence degree with the experimental data and simplicity of formulas testify to the adequacy of the employed model.

**Category:** Quantum Physics

[33] **viXra:1403.0036 [pdf]**
*replaced on 2018-10-04 06:44:16*

**Authors:** Robert A. Herrmann

**Comments:** 27 Pages.

The General Grand Unification (GGU) Model predicts physical and physical-like behavior. The premises can be considered as descriptions for directly observable physical events. Descriptions for physical events or objects are composed of elements taken from a general language and, as customary, are representations for the actual physical events or objects, respectively. The predictions yield all observable and describable physical events. Further, higher-forms of descriptions are predicted. These yield physical-like events, where the differences in linguistic behavior and descriptions for the terms
employed signify differences in the behavior between the physical-like ultranatural events or objects being described and the original physical events or objects, respectively. After introducing the necessary terminology and concepts, Section 5 of this paper presents a Biblical
interpretation. The corporeal physical-systems and events that correspond to the, generally described, human being are identified. Then
closely associated and predicted incorporeal physical-like systems and events are interpreted. Of significance is the choice predicted existence
of non-physical but physical-like “invisible” universes that have various applications including the modeling of statements that appear in
Revelations.

**Category:** Religion and Spiritualism

[32] **viXra:1403.0035 [pdf]**
*submitted on 2014-03-06 06:29:46*

**Authors:** Frank Dodd Tony Smith Jr

**Comments:** 5 Pages.

What is the Deep State of the USA/UK and how will it deal with a Hedge Fund Casino Financial Crisis on the scale of Hundreds of Trillions of Dollars ?

**Category:** Social Science

[31] **viXra:1403.0034 [pdf]**
*submitted on 2014-03-05 21:05:47*

**Authors:** Blazej Kot

**Comments:** 10 Pages. Previously published in Prespacetime Journal, January 2014, Volume 5, Issue 1, pp. 8-18

I suggest we treat causality, not matter, as the fundamental constituent of reality. I introduce a unit of causality named toma and outline how the resulting framework leads naturally to general relativity, quantum electrodynamics and quantum chromodynamics. This novel framework is the first to show how to derive GR, QED and QCD from first principles and as such holds promise for being a Grand Unified Theory.

**Category:** Quantum Gravity and String Theory

[30] **viXra:1403.0033 [pdf]**
*submitted on 2014-03-05 12:44:53*

**Authors:** E.Koorambas

**Comments:** 4 Pages.

We introduce the permutation group of arithmetic operations symbols by getting the permutations of all the common arithmetic operations symbols, with keeping the brackets out of ordering. We find 6 ways of doing the arithmetic operations. Therefore the output of any mathematical formulas depends on which one element of the arithmetical permutation group we work on. We find invariants by the reordering of the arithmetic operation x+y, xy. Working with the irreducible representation of the permutation arithmetic symbols group we define new arithmetic structures called arithmetic particles symbols.

**Category:** General Mathematics

[29] **viXra:1403.0032 [pdf]**
*replaced on 2015-06-02 07:54:01*

**Authors:** sangwha Yi

**Comments:** 16 Pages. Thank you for reading

In the general relativity theory, we define the accelerated frame that moves in -axis in the curved space-time. And we calculate the curvature tensor of the stationary accelerated frame in the gravity field. In this time, the curvature tensor divide the observational curvature tensor of the people and the curvature tensor of the people’s self on the planet in the gravity field

**Category:** Relativity and Cosmology

[28] **viXra:1403.0030 [pdf]**
*submitted on 2014-03-05 11:29:08*

**Authors:** Ramzi Suleiman

**Comments:** 17 Pages.

The present article proposes a theory of relativity which disentangles Einstein's relativistic approach from Lorentz's invariance principle, the latter being basically an Ether theory. This modification, termed Complete Relativity (CR) is justified both theoretically and experimentally. On the theoretical side it is argued, as done half a century ago by Herbert Dingle, that the inconsistency in Special Relativity theory (SR) is a result of Einstein's attempt to reconcile the theory with the Lorentz's electrodynamics. On the empirical side, questioning the adequacy of the Lorentz invariance principle is supported by numerous experimental results, attesting to symmetry-breaking at high enough energy, and by Quantum Gravity and other theories which allow for such breaking.
In part I of the theory, presented here, I focus is on relativistic time and space under conditions of uniform motion. Relaxing the constraint of SR's second axiom yields time and distance transformations in which the direction of relative movement with respect to an observer has dramatic effects. The derived time and distance expressions are tested using three different types of experiments: The seminal Michelson-Morley null experiment, the famous Frisch and Smith muon decay experiment, and recent quasi-luminal neutrino experiments. Tests of the theory, using the above mentioned experiments, shows that it succeeds in predicting all the reported results. In comparison, SR, which is known to predict the results of the first two types of experiments, fails completely in predicting the results of the quasi-luminal neutrino experiments. Because in the quasi-luminal neutrino experiment the neutrinos depart from a source laboratory and approach a detector laboratory, their results qualify as a crucial test for comparison between SR and CR.

**Category:** Relativity and Cosmology

[27] **viXra:1403.0029 [pdf]**
*submitted on 2014-03-05 11:33:45*

**Authors:** Ramzi Suleiman

**Comments:** 36 Pages.

Cooperation and fairness in encounters with strangers are puzzling behaviors, since they contradict the law of natural selection. Compelling evidence shows that direct and indirect reciprocity and altruistic punishment are important mechanisms for the evolution of cooperation in the long-term. For short-interaction, cooperation and fairness are explained by theories which assume that individuals have other-regarding sentiments, or that they base their decisions on perceptions of others' intentions. The present paper proposes a new theory of decisions in interactive situations. The theory retains the assumption that individuals are solely self-interested, but assumes that individuals value their outcomes relative to their aspiration levels. The proposed theory is used to derive predictions of mutual cooperation in the prisoner's dilemma game, of proposers' offers in ultimatum bargaining games, and in the sequential common-pool-resource dilemma game. These predictions are tested using experimental data. Strikingly, for the standard ultimatum game the predicted mean relative offer is the famous Golden Ratio.
Keywords: Cooperation, Fairness, Aspiration Level, Prisoner's Dilemma, Ultimatum Game, Resource Dilemma, Golden Ratio.

**Category:** Economics and Finance

[26] **viXra:1403.0028 [pdf]**
*submitted on 2014-03-05 08:39:17*

**Authors:** Nainan K. Varghese

**Comments:** 3 Pages. Published in General Science Journal

Reversals of earth’s direction of motion in its orbital path around sun is an essential requirement for contemporary explanations on stellar aberration. Earth’s orbital path around sun is an apparent concept. Reversal of direction of motion of a macro body of the size of earth and moving at real linear speed of earth, in three months period without affecting its integrity is irrational. However, considering corpuscles of light as 3D matter-particles can provide logical explanation for this phenomenon.

**Category:** Astrophysics

[25] **viXra:1403.0027 [pdf]**
*submitted on 2014-03-04 18:28:28*

**Authors:** Victor Christianto

**Comments:** 5 Pages. This file is not yet submitted to any journal. Your comments are welcome.

Quantum non-locality belongs to one puzzling feature of quantum mechanics, which some people think as unexplained using classical theories. But there seems a possibility to explain quantum non-locality using Maxwell equations or complex Minkowski metric. Therefore it seems worth to discuss this issue.

**Category:** Quantum Physics

[24] **viXra:1403.0026 [pdf]**
*submitted on 2014-03-05 02:09:31*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I present a property of a set of primes, interesting not because it has a value for distinguish primes from odd composites, because there are such numbers which also have this property, but because it seems to split the set of primes into two classes – the primes that have this property and the primes that have not this property – containing primes in surprisingly equal proportion.

**Category:** Number Theory

[23] **viXra:1403.0025 [pdf]**
*submitted on 2014-03-05 02:29:58*

**Authors:** Zhang Tianshu

**Comments:** 15 Pages.

If every positive integer is able to be operated into 1 by set operational rule of the Collatz conjecture, then begin with 1, we can get all positive integers by another operational rule on quite the contrary to the set operational rule after pass infinite many operations. Thereby, we try to substitute such a proof of equal value for directly proving the Collatz conjecture by mathematical induction, and achieved our anticipated goal.

**Category:** Number Theory

[22] **viXra:1403.0024 [pdf]**
*submitted on 2014-03-05 02:39:35*

**Authors:** Daniele Sasso

**Comments:** 12 Pages.

We consider physics of reference frames moving with any speed, starting from the inertial field. We point out the different physical behavior of electrodynamic systems with respect to other systems, due to the different physical meaning of mass. These considerations allow to define a generalized concept of field that materializes in the domain Space-Time-Mass where new equations of trasformations for reference frames are used. We define at last physical properties of differential forces of reaction in fields of force.

**Category:** Relativity and Cosmology

[21] **viXra:1403.0023 [pdf]**
*replaced on 2016-08-27 03:17:14*

**Authors:** Sergey G. Fedosin

**Comments:** 36 pages. Jordan Journal of Physics. Vol. 9 (No. 1), pp. 1-30, (2016).

Based on the condition of relativistic energy uniqueness the calibration of the cosmological constant was performed. This allowed us to obtain the corresponding equation for the metric, to determine the generalized momentum, the relativistic energy, momentum and the mass of the system, as well as the expressions for the kinetic and potential energies. The scalar curvature at an arbitrary point of the system equaled zero, if the matter is absent at this point; the presence of a gravitational or electromagnetic field is enough for the space-time curvature. Four-potentials of the acceleration field and pressure field, as well as tensor invariants determining the energy density of these fields, were introduced into the Lagrangian in order to describe the system’s motion more precisely. The structure of the Lagrangian used is completely symmetrical in form with respect to the four-potentials of gravitational and electromagnetic fields and acceleration and pressure fields. The stress-energy tensors of the gravitational, acceleration and pressure fields are obtained in explicit form, each of them can be expressed through the corresponding field vector and additional solenoidal vector. A description of the equations of acceleration and pressure fields is provided.

**Category:** Relativity and Cosmology

[20] **viXra:1403.0022 [pdf]**
*submitted on 2014-03-05 03:38:21*

**Authors:** Sosale Chandrasekhar

**Comments:** 25 Pages.

It is argued that the chemiosmotic theory, in positing the egress and ingress of protons across a membrane via different routes, violates the principle of microscopic reversibility (PMR). The theory was proposed as a mechanism for coupling the exergonic oxidation of NADH to the endergonic synthesis of ATP, believed to be a ready-to-use form of biochemical energy. The key proton-pump mechanism, however, should also operate in reverse by the PMR, hence is unlikely to be valid. Generally, the transfer of free energy via coupled equilibria is problematical, as neither of the coupled processes would go to completion. (However, it may be feasible in the case of entropy-driven reactions, as happens in the reactions of the Krebs cycle that lead to the formation of NADH.) Furthermore, reported thermodynamic data do not support the idea of ATP as a ‘high energy’ molecule, but rather indicate that ATP hydrolysis is driven by release of phosphate. In fact, many of the reactions believed to be thermodynamically driven by ATP hydrolysis are likely exergonic per se. ATP possibly provides part of the activation energy for the reaction in many cases. An alternative (non-equilibrium) mechanism for ATP synthesis is proposed based on the increase in pH that would accompany the oxidation of NADH. This would generate ADP3- and HPO42- which could form ATP4- in a thermodynamically favoured process within hydrophobic pockets.

**Category:** Chemistry

[19] **viXra:1403.0021 [pdf]**
*submitted on 2014-03-04 10:50:18*

**Authors:** Mende F. F.

**Comments:** 2 Pages.

In order to understand advantages and deficiencies in the special theory of relativity (STR) we they must describe as it is built and what basic condition lie at its basis. Within the framework the conversions of Galileo with the description of physical phenomena they are used four independent variables (three coordinates and time). In STR variables they are not already independent variables, since is accepted the postulate about the independence of the speed of light upon transfer of one inertial system (ISR) into another.

**Category:** Classical Physics

[18] **viXra:1403.0020 [pdf]**
*submitted on 2014-03-04 07:06:43*

**Authors:** Mende F. F.

**Comments:** 6 Pages.

Faradey established the law of induction, carrying out experiments on the solenoids, including turning off in them current, or moving with respect to the solenoids the turns of the wire, to which was connected the galvanometer.

**Category:** History and Philosophy of Physics

[17] **viXra:1403.0018 [pdf]**
*submitted on 2014-03-04 08:34:38*

**Authors:** Valentino Giudice

**Comments:** 13 Pages.

In this article I describe the five-dimensional model, a model having five dimensions: three space dimensions and two time dimensions.

**Category:** Relativity and Cosmology

[16] **viXra:1403.0017 [pdf]**
*replaced on 2014-04-06 10:28:27*

**Authors:** George Rajna

**Comments:** 11 Pages.

The resolution of the Proton Radius Puzzle is the diffraction pattern, giving another wavelength in case of muonic hydrogen oscillation for the proton than it is in case of normal hydrogen because of the different mass rate.
Taking into account the Planck Distribution Law of the electromagnetic oscillators, we can explain the electron/proton mass rate and the Weak and Strong Interactions. Lattice QCD gives the same results as the diffraction patterns of the electromagnetic oscillators, explaining the color confinement and the asymptotic freedom of the Strong Interactions.

**Category:** Nuclear and Atomic Physics

[15] **viXra:1403.0016 [pdf]**
*replaced on 2017-01-03 01:15:18*

**Authors:** Luke Kenneth Casson Leighton

**Comments:** 15 Pages.

We introduce an expansion of the Rishon Model to cover quark generations,
(including a previously unnoticed one), provide an explanation for T and V
as a topologically convenient moniker representing aspects of phase and
polarity within knots (of for example String Theory), and explain particle
decay in terms of simple ``phase transform" rules. We identify all current
particles (with the exception of ``Top") including the gluon, the Bosons and
the Higgs, purely in terms of the underlying mechanism which topologically
can be considered to be Rishons. All this is predicated on the simple
assumption that all particles in effect photons phase-locked in a
repeating pattern inherently obeying Maxwell's equations, in symbiotic support
of their own outwardly-propagating electro-magnetic synchotronic radiation, and that Rishons represent a phase ``measurement" (real or
imaginary) at key strategic points on the photon's path.

**Category:** High Energy Particle Physics

[14] **viXra:1403.0015 [pdf]**
*submitted on 2014-03-03 15:53:20*

**Authors:** LIU Changli, GE Fengjun

**Comments:** 4 Pages.

Why massless particles, for example photons, can only have two helicity one-particle states is the main subject of this work. As we know, the little group which describes massive particle one-particle states' transformations under the Lorentz transformation is SO(3), while the little group describing massless states is ISO(2). In this paper, a new method is proposed to contract SO(3) group to ISO(2) group. We use this contraction method to prove that the particle can only have two helicity one-particle states from the perspective of \emph{kinematics}, when the particle mass trends to zero. Our proof is different from the dynamic explanation in the existing theories.

**Category:** High Energy Particle Physics

[13] **viXra:1403.0014 [pdf]**
*submitted on 2014-03-03 20:04:31*

**Authors:** S. J. Nettleton

**Comments:** 25 Pages.

Presentation to the University of Technology Sydney Food-Water-Energy Security Conference 13 July 2013 on the role of Generation IV integrated fast reactors in food, water, energy and environmental security

**Category:** Nuclear and Atomic Physics

[12] **viXra:1403.0013 [pdf]**
*replaced on 2014-03-04 11:32:13*

**Authors:** Friedwardt Winterberg

**Comments:** 9 Pages.

It is shown that the hypothesis of an inflationary universe to solve the horizon and flatness problem can be avoided by Lorentzian relativity assuming the existence of a preferred reference system at rest with the zero point vacuum energy cut off at the Planck energy. Under this assumption there will be a “firewall” at the event horizon of an expanding universe where all matter disintegrates into radiation having everywhere the Unruh black body radiation temperature. The replacement of the Einsteinian relativity by the Lorentzian relativity to solve the problem of quantum gravity was suggested to the author by Heisenberg.

**Category:** High Energy Particle Physics

[11] **viXra:1403.0012 [pdf]**
*submitted on 2014-03-03 07:07:50*

**Authors:** Vyacheslav Telnin

**Comments:** 1 Page.

At the beginning the vector space A is constructed from infinite number
of tensor cofactors. With the help of (viXra.org 1402.0167) these tensor
cofactors are constructed from rational powers of vector space W. Then
these powers are summed and the sum is denoted as N. And it turns out
that A is W raised to the power N. The N turned out to be any real number
( rational or irrational).

**Category:** General Mathematics

[10] **viXra:1403.0011 [pdf]**
*submitted on 2014-03-03 07:33:31*

**Authors:** Mende F. F.

**Comments:** 11 Pages.

The important task of electrodynamics is the presence of laws governing the appearance of electrical pour on, and, therefore, also the forces of those acting on the charge, at the particular point spaces, since only electric fields, generated other one or method or another, exert power influences on the charge.

**Category:** Classical Physics

[9] **viXra:1403.0010 [pdf]**
*submitted on 2014-03-03 08:59:38*

**Authors:** Jeffrey Joseph Wolynski

**Comments:** 2 Pages. 3 references, 1 diagram

It is explained what shape an object needs to be in order to experience gravitational collapse. Diagrams are provided and the alternative to the nebular hypothesis, stellar metamorphosis is presented, to explain what happens to young stars after they are formed.

**Category:** Astrophysics

[8] **viXra:1403.0008 [pdf]**
*replaced on 2014-03-05 06:57:09*

**Authors:** Yibing Qiu

**Comments:** 2 Pages.

On the basis of concentric spherical layer-type model and multi-quantum
energy level distribution, propose a new mechanism of atomic energy absorption and
emission.

**Category:** Quantum Physics

[7] **viXra:1403.0007 [pdf]**
*submitted on 2014-03-02 11:40:33*

**Authors:** Kelly Loum

**Comments:** 2 Pages.

A simple thought experiment that can easily be performed in the laboratory that gives results that do not have an explanation.

**Category:** Quantum Physics

[6] **viXra:1403.0006 [pdf]**
*submitted on 2014-03-02 09:08:35*

**Authors:** Ray Fleming

**Comments:** 6 Pages.

The purpose of this paper is to investigate the possibility that the Casimir effect, normally very weak, is strong enough to be significant on the scale of nuclear forces around 1 femtometer (fm = 10-15m). Computations were performed for the Casimir effect between two spheres using a proximity force approximation. It was found that at 2.6 fm the computed Casimir force is strong enough to overcome Coulomb repulsion and at 0.8 fm it is 20 times stronger than Coulomb repulsion. These values indicate that this strong Casimir force is important on scales of distance consistent with the nuclear force. With refinement it appears likely that the strong Casimir force can account for the nuclear force in its entirety allowing unification of the nuclear force with quantum electrodynamic theory.

**Category:** Nuclear and Atomic Physics

[5] **viXra:1403.0005 [pdf]**
*submitted on 2014-03-02 05:01:31*

**Authors:** Hasmukh K. Tank

**Comments:** Fourteen page paper

The currently popular ‘Big Bang Theory’ is based on ‘Doppler Shift Interpretation’ of the ‘cosmological-red-shift’. But it is shown here that the value of Hubble-constant matches so perfectly with the strength-ratio of gravitational and electric forces, that such a coincidence is very un-likely. Secondly, if the expansion of the universe is accelerating, as the recent observations suggest, e.g.( Paal, G. et al. 1992, Adam G. Riess et al.1998, and Perlmutter, S. et al.1999)[1,2,3], then very large amount of dark-energy may be needed which is still not found. Therefore, it is proposed here that extra galactic photons may be loosing some of their energy through ‘vacuum polarization’, as described by Levine, I. (1997)[4] and Brown et al (1996)[5]. It is proposed here that: when an extra galactic photon is absorbed by either electron or positron of the virtual electron positron pair, then not only the ‘electrostatic potential energy’ of the pair is increased, but also its ‘gravitational potential energy’ as well; but when these ‘potential energies’ are released, then not only a photon, but also a graviton is emitted; so the input energy gets branched out. And we find here that the energy lost by the ‘cosmologically red shifted photons’ is strikingly proportional to the ‘strength ratio’ of gravitational and electric forces. Since, according to this new interpretation for the ‘cosmological red shift, the red-shift is a function of distance traveled by the photon, rather than relative velocity of the galaxies; so this study will also do away with the need for ‘dark energy’. In addition to this, six more alternative possibilities for the red shift are also indicated.

**Category:** Astrophysics

[4] **viXra:1403.0004 [pdf]**
*submitted on 2014-03-01 09:50:38*

**Authors:** Gary D. Simpson

**Comments:** 11 Pages.

A possibly novel mathematical structure is presented. The structure is a matrix whose elements are quaternions. The structure is distinct from a tensor.

**Category:** Mathematical Physics

[3] **viXra:1403.0003 [pdf]**
*submitted on 2014-03-01 03:35:45*

**Authors:** Yakov Gershman

**Comments:** 4 Pages.

One of the important requirements of the market to peanuts in shell is the lack of incompletely filled with fruit. Traditional mechanical sorting methods cannot solve the problem completely. In this work experimentally proved the possibility of the complete removal of immature fruits ("singles") by using image processing of x-ray and infrared.

**Category:** Quantitative Biology

[2] **viXra:1403.0002 [pdf]**
*submitted on 2014-03-01 01:01:17*

**Authors:** Vyacheslav Telnin

**Comments:** 7 Pages.

viXra.org 1402.0167 gives general description of raising vector space W in the power M/L. The
result is the new vector space V. In this paper we take W - the 8 – dimensional generalization of
our 4 – dimensional vector space. Then we raise W in the power 1/3. The result is the 2 –
dimensional vector space V. The metric and algebraic tensors for V are the same as in viXra.org
1402.0176.
After that we take some vector from V and use it for construction of Lagrangian. And for
simplicity we restrict us by only first 4 dimensions of W. Then, from the principle of minimal
action, we get the equations for our vector. And we derive that vector from these equations.
Then we define the tensor and vector of energy – momentum for this Lagrangian. And also we
find the density of spin tensor and (with the help of the algebraic tensor) the density of spin
vector. The numerical cofactor in them is 1/3. So we consider that spin of this vector is 1/3. It
coincides with the power of W for V (vector space we took our vector from).

**Category:** Mathematical Physics

[1] **viXra:1403.0001 [pdf]**
*submitted on 2014-03-01 01:27:01*

**Authors:** Hasmukh K. Tank

**Comments:** Seven page letter

It is well known, that in some experiments, light exhibits ‘wave’ property; like interference and diffraction; whereas in other experiments, like photoelectric effect, it shows ‘particle’ nature. So, the physicists currently think in terms of ‘wave-particle-duality’ of light, their mutual exclusiveness, and complementarily. Here, in this paper, this ‘wave-particle-duality’ is explained; that at the frequencies of light, very narrow-band filtering, and generation of purely monochromatic light, of one Hz bandwidth, are not technically possible; so there is always some bandwidth and ‘line-width’, due to which the waves form wave-packets, localized in space, as ‘particles’. Then this familiarity with waves is applied to understand the observations of ‘cosmological red shift’.

**Category:** Relativity and Cosmology