[138] **viXra:1004.0140 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** Henry Ibstedt

**Comments:**
13 pages.

This article has been inspired by questions asked by Charles
Ashbacher in the Journal of Recreational Mathematics, vol. 29.2. It concerns the
Smarandache Deconstructive Sequence. This sequence is a special case of a more
general concatenation and sequencing procedure which is the subject of this
study. Answers are given to the above questions. The properties of this kind of
sequences are studied with particular emphasis on the divisibility of their terms by
primes.

**Category:** Number Theory

[137] **viXra:1004.0139 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache

**Comments:**
236 pages.

AIDS is not simply a physical malady, it is also an artifact
of social and sexual transgression, violated taboo, fractured
identity-political and personal projections. Its key words are
primarily the property of the powerful. AIDS: Keywords - is my
attempt to identify and contest some of the assumptions
underlying our current 'knowledge'. In this effort I am joined by
many AIDS activists including people living with
AIDS - Acquired Immuno Deficiency Syndrome.

**Category:** Artificial Intelligence

[136] **viXra:1004.0138 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** Arnaud Martin, Christophie Osswald, Jean Dezert, Florentin Smarandache

**Comments:**
23 pages.

Martin and Osswald [15] have recently proposed many generalizations
of combination rules on quantitative beliefs in order to
manage the conflict and to consider the specificity of the responses
of the experts. Since the experts express themselves usually in natural
language with linguistic labels, Smarandache and Dezert [13]
have introduced a mathematical framework for dealing directly also
with qualitative beliefs. In this paper we recall some element of our
previous works and propose the new combination rules, developed
for the fusion of both qualitative or quantitative beliefs.

**Category:** Artificial Intelligence

[135] **viXra:1004.0137 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** L. Kuciuk, M. Antholy

**Comments:**
23 pages.

In this paper we make a presentation of these exciting geometries and present a model for
a particular one.

**Category:** Geometry

[134] **viXra:1004.0136 [pdf]**
*submitted on 30 Apr 2010*

**Authors:** Fernando Loup

**Comments:** 91 Pages. This work was sent to arXiv.org as arXiv:0710.0924 in 4 October 2007 to celebrate the 50th Anniversary of the Space Race and the launch of the Sputnik I (4 October 1957).
It suffered major modifications in order to be accepted for publication. Versions #1 and #2 can be considered as a different paper from versions #3 and #4
It was published in the book Space Exploration Research Chapter IX from Nova Scientific Publishers ISBN 978-1-60692-264-4 2009.
It was also published in the Volume 14 Issue 3-4 (Journal of Magnetohydrodynamics, Plasma and Space Research) ISSN: 1083-4729
The published versions are the #3 and #4 from
arXiv.org - The versions #1 and #2 contains a mathematical description about how to solve the pathologies of the Einstein Field Equation known as the Superluminal Alcubierre Warp Drive.
It also contains a Memorial to Serguei Pavlovitch Korolev(the creator of the Sputnik I) and a Memorial to all the Cosmonauts and Astronauts that died in Outer Space in the spaceships Soyuz I,Soyuz XI,Apollo I,Challenger and Columbia…the first 50 years of the Space Race
We feel that this work in the unpublished version #1 and #2 deserves to be placed on viXra as a valid paper to overcome the limitations of the Superluminal Alcubierre Warp Drive Spacetime specially the part of the Horizons and the causally disconnected portions of the Spacetime inside the Warp Drive bubble.We use something that resembles the Apollo spacecrafts
This version is exactly equal without changes to the version #2 stored in arXiv.org
This paper was inspired in a TV series from the British Broadcasting Corporation called "The Space Race"

We use the 5D Extra Dimensional Force according to Basini-Capozziello-Ponce De Leon,
Overduin-Wesson and Mashoon-Wesson-Liu Formalisms to study the behaviour of the Chung-Freese Superluminal
BraneWorld compared to the Alcubierre Warp Drive and we arrive at some interesting results from the
point of view of the Alcubierre ansatz although we used two different Shape Functions one continuous
g(rs) as an alternative to the original Alcubierre f(rs) and a Piecewise Shape Function fpc(rs) with
a behaviour similar to the Natario Warp Drive. We introduce here the Casimir Warp Drive.We also
demonstrate that in flat 5D Minkowsky Spacetime or weak Gravitational Fields we cannot tell if we
live in a 5D or a 4D Universe according to Basini-Capozziello-Ponce De Leon,Overduin-Wesson and
Mashoon-Wesson-Liu Dimensional Reduction but in the extreme conditions of Strong Gravitational
Fields we demonstrate that the effects of the 5D Extra Dimension becomes visible and perhaps the
study of the extreme conditions in Black Holes can tell if we live in a Higher Dimensional Universe.We
use a 5D Maartens-Clarkson Schwarzschild Cosmic Black String centered in the Sun coupled to the
5D Extra Force from Ponce De Leon together with Mashoon-Wesson-Liu and the definitions of
Basini-Capozziello and Bertolami-Paramos for the Warp Fields in order to demonstrate that the Anomalous
Effect disturbing two American space probes known as the Pioneer Anomaly is a force of 5D Extra
Dimensional Nature.As a matter of fact the Pioneer Anomaly is the first experimental evidence of the
"Fifth Force" predicted years ago by Mashoon-Wesson-Liu and we also demonstrate that this Extra
Force is coming from the Sun.

**Category:** Relativity and Cosmology

[133] **viXra:1004.0135 [pdf]**
*submitted on 30 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that there are infinitely many primes P such that each of
jP^{3} + k - j is a prime.

**Category:** Number Theory

[132] **viXra:1004.0134 [pdf]**
*submitted on 30 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that there are infinitely many primes P such that each of
jP^{3} + 7 - j is a prime.

**Category:** Number Theory

[131] **viXra:1004.0133 [pdf]**
*submitted on 30 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that there are infinitely many primes P such that each of
jP^{3} + 5 - j is a prime.

**Category:** Number Theory

[130] **viXra:1004.0132 [pdf]**
*submitted on 30 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that there are infinitely many primes P such that 2P^{3} + 1 and
P^{3} + 2 are all prime.

**Category:** Number Theory

[129] **viXra:1004.0131 [pdf]**
*submitted on 30 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that if J_{2} (ω) ≠ 0 then there are infinitely many primes P such
that each of jP^{2} + k - j is a prime, if J_{2} (ω) = 0 then there are finitely many primes P such
that each of jP^{2} + k - j is a prime.

**Category:** Number Theory

[128] **viXra:1004.0130 [pdf]**
*submitted on 29 Apr 2010*

**Authors:** Alon Retter

**Comments:**
17 pages.

This paper presents a remarkable analogy between the human society and Astronomy. Please keep
an open mind as the resemblance is not only qualitative but also quantitative. We point out many
similarities between stars and people, such as properties of grouping - single stars vs. singles, binary
stars vs. couples, cities vs. clusters, countries vs. galaxies, etc. Men and women are linked with cool
and hot stars. We match planets with children and attribute the two genders to gas and solid planets.
Moons are related with pets or grandchildren, asteroids with germs / viruses, accretion disks with
bellies and jets with pukes. Suicide attempts in people are associated with supernovae in stars.
Inflation is connected with the rapid growth of the embryo, and the time the universe became
transparent to light is linked with the human birth. A simple analogue to the cosmic background
radiation is the bellybutton, and the universe acceleration is coupled with the pace increase in
modern life. The mean values of the distributions of star multiples and the number of US
households are almost identical (2.04 and 2.03). Moreover, an amazing resemblance between
the two curves is evident (Fig. 1). The distribution of gas (or solid) planets is similar to that of boys
(or girls) as well, and the fit could improve once selection effects are considered. Monte Carlo
simulations suggest that our results are significant at a confidence level higher of ~99.9%! The
surprising linkage between humanity and stars can lead to many predictions. It is proposed that
about a third of stars harbor planets. We predict that stars are equally divided between hot and cool
stars and planets between gas and solid planets. The presence of four gas and four solid planets in
the solar system supports our prediction. We also forecast that the mean number of planets around
host stars should be near two, larger around binaries than in single stars and higher in hot stars than
in cool stars. We vision the presence of twin planets that share the same orbit. The wealth of known
extra-solar planets should already contain a few such systems. We forecast the presence of a new
astronomical phenomenon, which we alias 'planova' - an eruption in a planet that may destroy it,
and speculate about the presence of planet jets. The ideas and results of this paper are clearly
unusual and unbelievable. A brief explanation to our findings is presented in the discussion and
further developed in forthcoming papers.

**Category:** Astrophysics

[127] **viXra:1004.0129 [pdf]**
*submitted on 29 Apr 2010*

**Authors:** Alon Retter

**Comments:**
7 pages.

We present a remarkable analogy between the human society and Astronomy. Please keep an open
mind as the resemblance is both qualitative and quantitative. We link stars and children with
persons and planets. The two genders are matched with cool and hot stars and with gas and solid
planets. The mean values of the distributions of star multiples and US households are almost
identical. Moreover, an amazing resemblance between the two curves is evident. In addition,
the distribution of gas / solid planets is similar to that of boys / girls as well, and the fit could
improve once selection effects are considered. Monte Carlo simulations suggest that our results
are significant at a confidence level of 99.9%! We thus predict that about a third of stars harbor
planets and that stars are equally divided between hot and cool stars and planets between gas and
solid planets. The presence of 4 gas and 4 solid planets in the solar system supports our prediction.
We forecast that the mean number of planets around host stars should be near two, and vision the
presence of twin planets that share the same orbit. The wealth of known extra-solar planets should
already contain a few such systems.

**Category:** Astrophysics

[126] **viXra:1004.0128 [pdf]**
*submitted on 29 Apr 2010*

**Authors:** Alon Retter

**Comments:**
6 pages.

We examine the basic term 'particle'. We start by exploring a universe that contains a single
particle. In such a universe there is no meaning for motion, energy, space and time. Only for a two
particles universe the physical quantities can be measured. However, the determination of the
physical quantities implies that the particles are not separated from each other! We thus propose that
all particles are interconnected. This novel perception naturally explains the two well known
paradoxes: the twin-electrons experiment and Schrödinger's cat. In fact, we argue that the twinelectrons
experiment is an actual proof for global non-detachment. We state that it cannot be shown
that a particle is elementary. If one is divided by two numerous times, zero is never reached. There
must be a jump into zero - the singularity. The sought Higgs particle is simply the singularity itself,
which cannot be found, having no properties.

**Category:** High Energy Particle Physics

[125] **viXra:1004.0127 [pdf]**
*submitted on 28 Apr 2010*

**Authors:** V. Torres-Zúñiga

**Comments:**
9 pages, figures in color. Manuscript to be submitted to Revista de la Sociedad Mexicana de Física E

In this article, a simple experiment is described for correcting the
misconception that acoustic pressure and levitation effects are hard to observe in
school laboratories. Analysis of the free fall velocity of a toy parachute within a
vertical tube, driven by sound in a range of frequencies around the resonant
condition, exhibits the resonance frequency, the node pressure zones, and the
optimal conditions to obtain acoustical levitation of a light body.

**Category:** Classical Physics

[124] **viXra:1004.0126 [pdf]**
*replaced on 4 May 2010*

**Authors:** Philip Gibbs

**Comments:** 4 pages

A Smarandache friendly prime pair (SFPP) is a pair of prime numbers (p,q), p < q, such that
the product pq is equal to the sum of all primes from p to q inclusive. Previously four such
pairs were known: (2,5), (3,13), (5,31) and (7,53). Now a fifth one is found by a brute force
computer search. A heuristic approximation can be to estimate the expected number of SFPPs in
a given interval. The result suggests that the probability of further pairs existing is about 0.07.

**Category:** Number Theory

[123] **viXra:1004.0125 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** Felice Russo

**Comments:**
3 pages.

In this paper a question posed in [1] and concerning the Smarandache
friendly prime pairs is analysed.

**Category:** Number Theory

[122] **viXra:1004.0124 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** Florentin Smarandache, Sukanto Bhattacharya, Mohammad Khoshnevisan

**Comments:**
109 pages.

Computational models pervade all branches of the exact sciences and have in recent
times also started to prove to be of immense utility in some of the traditionally 'soft'
sciences like ecology, sociology and politics. This volume is a collection of a few cuttingedge
research papers on the application of variety of computational models and tools in
the analysis, interpretation and solution of vexing real-world problems and issues in
economics, management, ecology and global politics by some prolific researchers in the
field.

**Category:** Economics and Finance

[121] **viXra:1004.0123 [pdf]**
*submitted on 27 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove x^{2} + y^{4} (J. Friedlander and H. Iwaniec, The polynomial
x^{2} + y^{4} Captures its primes, Ann. Math., 148(1998) 945-1040)

**Category:** Number Theory

[120] **viXra:1004.0122 [pdf]**
*submitted on 27 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove x^{3} + 2y^{3} (D. R. Heath-Brown, prime represented by x^{3} + 2y^{3}, Acta Math., 186(2001)1-84).

**Category:** Number Theory

[119] **viXra:1004.0121 [pdf]**
*submitted on 25 Apr 2010*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 17 pages, Also archived as arXiv:1004.1820 [physics.gen-ph].

It was pointed out in a previous paper that although neither the Klein-Gordon equation nor the Dirac
Hamiltonian produces sound solitary free-particle relativistic quantum mechanics, the natural square-root
relativistic Hamiltonian for a nonzero-mass free particle does achieve this. Failures of the Klein-Gordon
and Dirac theories are reviewed: the solitary Dirac free particle has, inter alia, an invariant speed well in
excess of c and staggering spontaneous Compton acceleration, but no pathologies whatsoever arise from the
square-root relativistic Hamiltonian. Dirac's key misapprehension of the underlying four-vector character
of the time-dependent, configuration-representation Schrödinger equation for a solitary particle is laid bare,
as is the invalidity of the standard "proof" that the nonrelativistic limit of the Dirac equation is the Pauli
equation. Lorentz boosts from the particle rest frame point uniquely to the square-root Hamiltonian,
but these don't exist for a massless particle. Instead, Maxwell's equations are dissected in spatial Fourier
transform to separate nondynamical longitudinal from dynamical transverse field degrees of freedom. Upon
their decoupling in the absence of sources, the transverse field components are seen to obey two identical
time-dependent Schrödinger equations (owing to two linear polarizations), which have the massless freeparticle
diagonalized square-root Hamiltonian. Those fields are readily modfied to conform to the attributes
of solitary-photon wave functions. The wave functions' relations to the potentials in radiation gauge are
also worked out. The exercise is then repeated without the considerable benefit of the spatial Fourier
transform.

**Category:** Quantum Physics

[118] **viXra:1004.0120 [pdf]**
*submitted on 24 Apr 2010*

**Authors:** Niels Vandamme

**Comments:** 7 pages

This paper propounds several hypotheses which offer an alternate
explanation to some of the real or purported effects encountered in quantum
mechanics and relativity, giving a mechanical explanation for the absolute speed
of light, the conversion of matter to energy, and the observed superluminal
expansion of the universe.

**Category:** Quantum Physics

[117] **viXra:1004.0119 [pdf]**
*submitted on 24 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove and P_{1} = P^{9} ± m and P_{1} = (2P)^{9} ± n

**Category:** Number Theory

[116] **viXra:1004.0118 [pdf]**
*submitted on 24 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove and P_{1} = P^{P0} ± m and P_{1} = (2P)^{p0} ± n

**Category:** Number Theory

[115] **viXra:1004.0117 [pdf]**
*submitted on 24 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove and P_{1} = P^{5} ± m and P_{1} = (2P)^{5} ± n

**Category:** Number Theory

[114] **viXra:1004.0116 [pdf]**
*submitted on 24 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that 1P = P ± m and 1 P = 2P ± n have infinitely many

**Category:** Number Theory

[113] **viXra:1004.0115 [pdf]**
*replaced on 14 Jun 2010*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 10 pages

We review the Wu-Sprung potential adding a correction involving a
fractional derivative of Riemann Zeta function, we study a global semiclassical analysis
in order to fit a Hamiltonian H=T+V fitting to the Riemann zeros and another new
Hamiltonian whose energy levels are precisely the prime numbers, through these paper
we use the notation log_{e} (x) = ln(x) = log(x) for the logarithm , also unles we specify
Σ_{γ} h(γ) means that we sum over ALL the imaginary parts of the nontrivial zero
on both the upper and lower complex plane.

**Category:** Number Theory

[112] **viXra:1004.0114 [pdf]**
*submitted on 22 Apr 2010*

**Authors:** Ron Bourgoin

**Comments:** 3 pages

Arxiv:1004.2901 exposes a chink in the armor.
It seems that joining general relativity with quantum
mechanics is like trying to fit a square peg in a
round hole. Obviously there's something terribly
wrong with one of the theories. Since quantum
mechanics has been far too successful in too many
areas, it is felt general relativity has to go.

**Category:** Relativity and Cosmology

[111] **viXra:1004.0113 [pdf]**
*submitted on 21 Apr 2010*

**Authors:** Florentin Smarandache

**Comments:** 802 pages.

The fourth volume, in my book series of "Collected Papers", includes 100 published and
unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated,
scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved
problems and conjectures, updated or alternative versions of previous papers, short or long
humanistic essays, letters to the editors - all collected in the previous three decades
(1980-2010) - but most of them are from the last decade (2000-2010), some of them being lost and found, yet
others are extended, diversified, improved versions.

**Category:** General Science and Philosophy

[110] **viXra:1004.0112 [pdf]**
*submitted on 21 Apr 2010*

**Authors:** V. Veeramani, Roque Batulan

**Comments:** 7 pages

This paper contains the Basic Definitions of an Intuitionstic Fuzzy Set theory and
operations on it. Mainly we discussed the basic concepts of α - cut with examples
and Characterisations.

**Category:** Set Theory and Logic

[109] **viXra:1004.0111 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture P: m^{2} +1 and m^{2} + 3 [4].

**Category:** Number Theory

[108] **viXra:1004.0110 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture N: x^{3} + y^{3} + z^{3} [4].

**Category:** Number Theory

[107] **viXra:1004.0109 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove Hardy-Littlewood conjecture M: x^{3} + y^{3} + k [4].

**Category:** Number Theory

[106] **viXra:1004.0108 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove Hardy-Littlewood conjecture K: x^{3} + k [4].

**Category:** Number Theory

[105] **viXra:1004.0107 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture F: am^{2} + bm+ c [4].

**Category:** Number Theory

[104] **viXra:1004.0106 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture B: P, P + k [4].

**Category:** Number Theory

[103] **viXra:1004.0105 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove binary Goldbach conjecture and N = P1 + ... + Pn [4]

**Category:** Number Theory

[102] **viXra:1004.0104 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that Jiang prime k -tuple theorem is true[1-3] and
Hardy-Littlewood prime k -tuple conjecture is false[4-8]. The tool of additive prime number
theory is basically the Hardy-Littlewood prime tuple conjecutre, but can not prove and count
any prime problems[6].

**Category:** Number Theory

[101] **viXra:1004.0103 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Andrew Beckwith

**Comments:**
4 pages, one figure. Actual ( minus the address ) submission for the following conference :
extended abstract of 4 pages for possibly being placed in C. Corda's section namely , "Second Big Challenge Symposium - The Big Challenge of
Cosmological Understanding: Gravitation, Dark Matter and Dark Energy.
Towards New Scenarios" during the 8th International Conference of
Numerical Analysis and Applied Mathematics, at Hotel Rodos Palace,
Rhodes, Greece, 19-25 September 2010.

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe in five
dimensions is stated, with particular emphasis upon if five dimensional geometries as given below give us new physical
insight as to cosmological evolution. We postulate that a calculated inflaton φ(t) may re-emerge after fading out in the
aftermath of inflation. The inflaton may be a contributing factor to, with non zero graviton mass, in re acceleration of the
universe a billion years ago. Many theorists assume that the inflaton is the source of entropy. The inflaton also may be
the source of re acceleration of the universe, especially if the effects of a re emergent inflaton are in tandem with the
appearance of macro effects of a small graviton mass, leading to a speed up of the rate of expansion of the universe one
billion years ago, at red shift value of Z ~ .423

**Category:** Relativity and Cosmology

[100] **viXra:1004.0102 [pdf]**
*submitted on 20 Apr 2010*

**Authors:** Andrew Beckwith

**Comments:**
4 pages, 1 figure. extended abstract of 3-4 pages for possibly being placed in C. Corda's
section namely , "Second Big Challenge Symposium - The Big Challenge of
Cosmological Understanding: Gravitation, Dark Matter and Dark Energy.
Towards New Scenarios" during the 8th International Conference of
Numerical Analysis and Applied Mathematics, at Hotel Rodos Palace,
Rhodes, Greece, 19-25 September 2010.

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe
in five dimensions is stated, with particular emphasis upon if five dimensional geometries as given
below give us new physical insight as to cosmological evolution. One noticeable datum, that a
calculated inflaton φ(t) re-emerged after fading out in the aftermath of inflation. The inflaton is
a contributing factor to, with non zero graviton mass, in re acceleration of the universe a billion years
ago. The inflaton also may be the source of re acceleration of the universe, especially if the effects
of a re emergent inflaton are in tandem with the appearance of macro effects of a small graviton
mass, leading to a speed up of the rate of expansion of the universe one billion years ago, at red shit
value of Z ~ .423

**Category:** Relativity and Cosmology

[99] **viXra:1004.0101 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Bernard Riley

**Comments:** 10 pages

Particles resulting from the breaking of symmetries are arranged symmetrically
about mass levels that descend in geometric progression from the Planck Mass
within three sequences, of common ratio 1/π, 2/π and 1/e. Particles arranged in
this way include the weak gauge bosons W^{±} and Z^{0}, the quark weak isospin
doublets u-d, s-c and b-t, and all hadronic isospin doublets. Many pairs of
hadrons with some common quark content also form symmetric partnerships.
Often, the mass difference characterising a partnership is precisely equal to the
mass of a level. The spin-0 partners of the quarks and charged leptons are
identified. The mass sequences may derive from the geometry of compact extra
spaces of Planck scale.

**Category:** High Energy Particle Physics

[98] **viXra:1004.0100 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Ron Bourgoin

**Comments:** 2 pages

Why run the race when there is no trophy?
The creative human being is often not
recognized, not rewarded. What to do?

**Category:** Mind Science

[97] **viXra:1004.0099 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Willi Penker

**Comments:** 2 pages

Following the basic rules of the uncertainty principle, gravitation itself becomes
uncertain and even massive black holes go into superposition without the
possibility of ending up in a real singularity.

**Category:** Quantum Gravity and String Theory

[96] **viXra:1004.0098 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Carlos Gershenson

**Comments:** 12 pages.

We develop on the idea that everything is related, inside, and therefore
determined by a context. This stance, which at first might seem obvious, has several
important consequences. This paper first presents ideas on Contextuality, for then
applying them to problems in philosophy of cognitive science. Because of space
limitations, for the second part we will assume that the reader is familiar with the
literature of philosophy of cognitive science, but if this is not the case, it would not
be a limitation for understanding the main ideas of this paper. We do not argue that
Contextuality is a panaceic answer for explaining everything, but we do argue that
everything is inside a context. And because this is always, we sometimes ignore it,
but we believe that many problems are dissolved with a contextual approach,
noticing things we ignore because of their obviousity. We first give a notion of
context. We present the idea that errors are just incongruencies inside a context. We
also present previous ideas of absolute being, relative being, and lessincompleteness.
We state that all logics, and also truth judgements, are contextdependant,
and we develop a "Context-dependant Logic". We apply ideas of
Contextuality to problems in semantics, the problem of "where is the mind", and the
study of consciousness.

**Category:** Mind Science

[95] **viXra:1004.0097 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Flavian Vasile

**Comments:** 9 pages.

This paper presents consciousness as the sum of describable processes, without limiting it
only to verbal understanding. Consciousness is presented as a buffer space of the unconscious,
accessed by any mental decision-taking processes. Consciousness is composed of sequential outputs
of non-conscious processes that form, as frames in a picture, the impression of our ego
continuity. The functional consequences of this point of view are then further discussed.

**Category:** Mind Science

[94] **viXra:1004.0096 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Cheng-Gui Huang

**Comments:** 1 pages.

I claim that Neutrosophy, by Professor Florentin Smarandache, is a deep thought in human culture.
That gives advantage to break the mechanical understanding of human culture. For example,
according to the mechanical theory: existence and non-existence could not be simultaneously.
Actually existence and non-existence are simultaneously. Everyone knows that human life is
like a way in the empty space of a bird flying. Everyone can not see himself a second ago,
everyone can not see himself for the time being and everyone can not see himself a second
future. Everyone could not know what is the existence of self. Everyone is also difficult to
say the non-existence of self. So the existence and non-existence of self are simultaneously.
And the existence and nonexistence of everything are simultaneously, where, the law of excluded
middle does not apply. These basic facts express the depth of Smarandache's Neutrosophy. He
has a lot of friends in ancient and in nowadays, in the West and in the East.

**Category:** Set Theory and Logic

[93] **viXra:1004.0095 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Sukanto Bhattacharya

**Comments:** 7 pages.

The efficient market hypothesis based primarily on the statistical principle of Bayesian
inference has been proved to be only a special-case scenario. The generalized financial
market, modeled as a binary, stochastic system capable of attaining one of two possible
states ...

**Category:** Economics and Finance

[92] **viXra:1004.0094 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Anne-Laure Jousselme, Patrick Maupin

**Comments:** 7 pages.

In situation analysis (SA), an agent observing a
scene receives information from heterogeneous sources of information
including for example remote sensing devices, human reports
and databases. The aim of this agent is to reach a certain
level of awareness of the situation in order to make decisions. For
the purpose of applications, this state of awareness can be conceived
as a state of knowledge in the classical epistemic logic
sense. Considering the logical connection between belief and
knowledge, the challenge for the designer is to transform the raw,
imprecise, conflictual and often paradoxical information received
from the different sources into statements understandable by both
man and machines. Hence, quantitative (i.e. measuring the world)
and qualitative (i.e. reasoning about the structure of the world)
information processing coexist in SA. A great challenge in SA
is the conciliation of both aspects in mathematical and logical
frameworks. As a consequence, SA applications need frameworks
general enough to take into account the different types of uncertainty
and information present in the SA context, doubled with a
semantics allowing meaningful reasoning on situations. The aim
of this paper is to evaluate the capacity of neutrosophic logic and
Dezert- Smarandache theory (DSmT) to cope with the ontological
and epistemological problems of SA.

**Category:** Artificial Intelligence

[91] **viXra:1004.0093 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Sukanto Bhattacharya, Florentin Smarandache, Mohammad Khoshnevisan

**Comments:** 10 pages.

In our present paper, we have explored the possibilities and developed arguments for an application
of principles of neutrosophic game theory as a generalization of the fuzzy game theory model to a
better understanding of the Israel-Palestine problem in terms of the goals and governing strategies
of either side. We build on an earlier attempted justification of a game theoretic explanation of
this problem by Yakir Plessner (2001) and go on to argue in favour of a neutrosophic adaptation of
the standard 2x2 zero-sum game theoretic model in order to identify an optimal outcome

**Category:** Economics and Finance

[90] **viXra:1004.0092 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Feng Liu

**Comments:** 8 pages.

Logic should have been defined as the unity of contradiction between logic director and logic
implementation. Chinese Daoism asserts that everything is defined in the unity of opposites,
namely yin and yang, accordingly yang conducts change and yin brings it up (I-Ching, also known
as Book of Changes). In this way logic is redefined in an indeterminate style to facilitate
"both A and Anti-A" etc. in neutrosophics of logic. The unity of opposites is also described
as neutrality in neutrosophy. An intermediate multi-referential model of excitation and inhibition
is developed to derive a multiagent architecture of logic, based on Chinese yin-yang philosophy.
This methodology of excitation/inhibition suggests a rhymed way of logic, leading to a dynamic
methodology of weight strategy that links logic with neural network approach. It also confirms
the crucial role of indeterminacy in logic as a fatal criticism to classical mathematics and
current basis of science.

**Category:** Set Theory and Logic

[89] **viXra:1004.0091 [pdf]**
*submitted on 19 Apr 2010*

**Authors:** Feng Liu

**Comments:** 12 pages.

As a philosophical analysis of some fatal paradoxes, the paper distinguishes the conceptual difference
between representation of truth and source of truth, and leads to the conclusion that in order to acquire
the genuine source of truth, independently of specific representations possibly belonging to different
worlds, one is necessary to ignore all the ideas, logics, conceptions, philosophies and representable
knowledge even himself belonging to those misleading worlds, returning to his infant nature, as a
preliminary step for his cultivation of unconstrained wisdom. It also carries out some coordinative
crucial issues as natural-doctrine, minded-unwitting, logic-infancy, conception-deconception,
determinacy-indeterminacy. The paper tries to verify the role of neutrosophy and neutrosophic logic in
religious issues and open a gateway toward the oriental classics, excavating the lost treasure.

**Category:** Set Theory and Logic

[88] **viXra:1004.0090 [pdf]**
*replaced on 2017-03-11 20:16:12*

**Authors:** Andrew Beckwith

**Comments:** 21 Pages. Will be a Poster in this version for Rencontres De Moriond. Also, accepted by JHEPGC, in this new version, with some alterations added.

If a non-zero graviton mass exists, the question arises if a release of gravitons, possibly as a ‘Graviton gas” at the onset of inflation could be an initial vacuum state. Pros and cons to this idea are raised, in part based upon Bose gasses. The analysis starts with Volovik’s condensed matter treatment of GR and ends with consequences, which the author sees if the supposition is true.

**Category:** Quantum Gravity and String Theory

[87] **viXra:1004.0089 [pdf]**
*replaced on 12 May 2010*

**Authors:** V.A.Induchoodan Menon

**Comments:** 21 pages

The author introduces the concept of a primary gas which is an abstract
gas where the microstates are occupied successively in time unlike in the case of
a real gas where the microstates are occupied simultaneously. He shows that a
single plane wave associated with a standing wave formed by the confinement
of a luminal wave could be treated as the microstate of the primary gas that
represents a particle. This approach makes it possible to understand the
dynamics of a particle in terms of the thermodynamics of the primary gas. In
this approach, time and space turn out to be the intrinsic properties of the
primary gas that represents a particle and the quantized nature of time and space
emerges from it in a natural manner. It is shown that the action (with a negative
sign) of a particle could be identified with the entropy of the primary gas and the
principle of least action is nothing but the second law of thermodynamics. The
author shows that the uncertainty relation of quantum mechanics can be derived
directly from the equation for fluctuations and he explains the statistical basis of
the virtual interactions.

**Category:** Quantum Physics

[86] **viXra:1004.0088 [pdf]**
*submitted on 18 Apr 2010*

**Authors:** Tong Xin Ping

**Comments:** 6 Pages, In Chinese

The implicit function in the Hardy-Littewood conjecture

**Category:** Number Theory

[85] **viXra:1004.0087 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:**
2 pages.

In this short note we study the existence and number of solutions in the
set of integers (Z) and in the set of natural numbers (N) of Diophantine equations of
second degree with two unknowns of the general form ax^{2} - by^{2} = c .

**Category:** Number Theory

[84] **viXra:1004.0086 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** Dmitri Rabounski

**Comments:**
2 pages.

This short letter manifests how Smarandache geometries can be employed in order to
extend the "classical" (Riemannian geometry) basis of the General Theory of Relativity
through joining the properties of two or more (different) geometries in the same single
space. Perspectives in this way seem much profitly: the basic space-time of General
Relativity can be extended to not only metric geometries, but even to non-metric ones
(where no distances can be measured), or to spaces of the mixed kind which possess
the properties of both metric and non-metric spaces (the latter should be referred to as
"semi-metric spaces"). If both metric and non-metric properties possessed at the same
(at least one) point of a space, it is one of Smarandache geometries, and should be referred
to as "Smarandache semi-metric space". Such spaces can be introduced according
to the mathematical apparatus of physically observable quantities (chronometric
invariants), if considering a breaking of the observable space metric on the continuous
background of the fundamental metric tensor.

**Category:** Relativity and Cosmology

[83] **viXra:1004.0084 [pdf]**
*submitted on 9 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral

**Comments:** 288 pages.

In this book we introduce mainly three new classes of linear
algebras; neutrosophic group linear algebras, neutrosophic
semigroup linear algebras and neutrosophic set linear algebras.
The authors also define the fuzzy analogue of these three
structures.

**Category:** Algebra

[82] **viXra:1004.0083 [pdf]**
*replaced on 17 Apr 2010*

**Authors:** M. D. Sheppeard

**Comments:**
8 pages. submitted to JPA

A unique matrix is easily assigned to each Bilson-Thompson braid
diagram. The quark and lepton matrices are then related to bosons via a twisted
quantum Fourier transform, for which fermion and boson multiplets fit the dimension
structure of heterotic strings.

**Category:** Quantum Gravity and String Theory

[81] **viXra:1004.0082 [pdf]**
*submitted on 16 Apr 2010*

**Authors:** V. Torres-Zúñiga, O.G. Morales-Saavedra, G. Hennrich, J.O. Flores-Flores, R. Ortega-Martínez

**Comments:**
15 pages. Manuscript submitted and accepted for publication as an article in Mol. Cryst. Liq. Cryst.

In this work, a liquid crystalline octopolar molecule 1,3,5-tris(ethynylphenyl)benzene-(1)
was successfully embedded as dopant chromophore within a SiO_{3}-symmetry structure, which is
constituted by an electron-rich core and electron-poor periphery groups. The sonogel method, induced
by energetic ultrasonic (US) waves applied at the TEOS/H_{2}O reactant mixture interface has proven to
be a suitable route in the manufacture of monolithic hybrid systems suitable for optical
characterizations. The octopolar-based hybrid samples were comprehensively studied in their
morphology, spectroscopic, linear and second-order nonlinear optical (NLO) properties, according to
several characterization techniques: epimicroscopy, AFM, UV-Vis- and fluorescence (PL)
spectroscopies, and the NLO-SHG-technique. Epimicroscopy, photoluminiscent and absorption
spectra evidence an optimal and homogeneous inclusion of the octopolar compounds within the glassy
sonogel network. Without necessity of molecular poling processes, the effective quadratic-NLO
susceptibility χ_{effS}^{(2)} of the hybrid was estimated to 13.6x10^{-3} pm/V at 1064 nm by SHG-transmission
experiments recorded far-off of the resonance regime.

**Category:** Condensed Matter

[80] **viXra:1004.0081 [pdf]**
*replaced on 2015-11-19 16:54:17*

**Authors:** Bruce Rout

**Comments:** 5 Pages.

A closed form analytic model has been presented and matched to the
morphology of spiral galaxies[9]. This model consists of an Archemedean
spiral which matches the physical attributes of spiral galaxies as a result
of relativistic effects due to great distances on a rotating rigid body. This
effect was first posed by Minkowski[5]. We present a derivation of this
analytical model though the application of Lortentz transformations.

**Category:** Relativity and Cosmology

[79] **viXra:1004.0080 [pdf]**
*replaced on 21 Apr 2010*

**Authors:** Xiangjun Feng

**Comments:**
3 pages and 3 figures. This paper has been published in the on-line journal of World Chinese Forum On Science of General Systems (WCFSGS), ISSN 1936-7260.
The paper has also been included in the NONEXTENSIVE STATISTICAL MECHANICS AND THERMODYNAMICS: BIBLIOGRAPHY edited by Prof. Constantino Tsallis . Â
Report Number: 300-P-10-04-01
Journal Reference: WCFSGS VOL 6, NO. S1 ( A SPECIAL EDITION ON NONEXTENSIVE MECHANICS ), APRIL 2010, ISSN 1936 - 7260.

It is demonstrated clearly that for the same
classical generalized system the Tsallis power-laws with
both the q > 1 and the q < 1 can be induced by the
constraint of the constant harmonic mean for the so-called
reciprocal energies E_{r} and at the same time the
Boltzmann distribution or the negative exponential
probability distribution can be generated with the
constraint of the constant arithmetic mean for the
generalized energies E . The author thus argues that there
might be no definite "extensive system" or "classical
system" and there are only "classical physical parameters"
and "classical constraints". For any physical system or
generalized system, it is the non-natural constraints which
determine both the forms of the entropies and the nonuniform
equilibrium distributions.

**Category:** Condensed Matter

[78] **viXra:1004.0079 [pdf]**
*submitted on 12 Apr 2010*

**Authors:** Andrew Beckwith

**Comments:**
30 pages, 5 figures. One of two subject areas submitted to the conference 11th annual international
meeting "Fundamental Frontiers of Physics" which will take place in the capital of France, Paris, from
the 6th to the 9th of July, 2010.

The following document is to prepare an analysis on if the cosmological constant is a vacuum field.
Candidates for how to analyze this issue come up in terms of brane theory, modified treatments of WdM
theory (pseudo time component added) and/ or how to look at squeezing of vacuum states, as initially
coherent semi classical constructions, or string theory versions of coherent states. The article presents a
thought experiment if there is a non zero graviton mass, and at the end, in the conclusion states
experimental modeling criteria which may indicate if a non zero graviton mass is measurable, which would
indicate the existence, de facto of a possible replacement for DE, based upon non zero mass gravitons, and
indications for a replacement for a cosmological constant.

**Category:** Relativity and Cosmology

[77] **viXra:1004.0078 [pdf]**
*submitted on 12 Apr 2010*

**Authors:** Amrit S. Sorli

**Comments:** 5 pages

Clocks are systems for measuring frequency, velocity, duration and numerical order
t_{0},t_{1},t_{2},...,t_{n} of physical events. Time t obtained with clocks is not a forth dimension X_{4} of
space, time t is only a component of X_{4} = i * c * t. This view of clock/time as a
measuring system sees physical phenomena running exclusively in space and not in time.
This view is supported with several experiments which confirm that time t of physical event
can be zero. Time is not part of space; time is run of clocks in space. Past, present and
future exist as a psychological time in the mind only not in the universe. We experience
motion i.e. change in the space through the frame of psychological time. We "project" linear
psychological time "past-present-future" into the space, however it is not there. Observer who
distinguishes between space-time, physical time and psychological time is aware that in
quantum measurement he only measures physical events in space and not in time.
Clock/time is merely a measuring device. With this understanding observer's observation,
measurement and experience of quantum phenomena are closer to their real nature. Stream
of numerical order of quantum phenomena t_{0},t_{1},t_{2},...,t_{n} runs in space only and not in time.
Stream of quantum phenomena has no duration on its own. Duration is result of
measurement.

**Category:** Quantum Physics

[76] **viXra:1004.0077 [pdf]**
*submitted on 9 Mar 2010*

**Authors:** V. Christianto, Florentin Smarandache

**Comments:** 17 pages

In this article, we will shortly review a few old thoughts and recent thoughts on the
relation between Mathematics and the Natural Sciences. Of course, the classic references
to this open problem will include Wigner's paper (1964); a more recent review article is
Darvas (2008). But it appears that this issue is partly on the domain of natural philosophy
and also philosophy of inquiry. Therefore we will begin with a review on some known
thoughts of Kant, Bacon, Popper, etc.

**Category:** General Science and Philosophy

[75] **viXra:1004.0076 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache

**Comments:** 8 pages

In this paper exponential ratio and exponential product type estimators using two
auxiliary variables are proposed for estimating unknown population variance S_{y}^{2}. Problem is
extended to the case of two-phase sampling. Theoretical results are supported by an empirical
study.

**Category:** Statistics

[74] **viXra:1004.0075 [pdf]**
*submitted on 11 Apr 2010*

**Authors:** Ervin Goldfain

**Comments:** 17 pages, This contribution is a sequel to EPL, 82 (2008), 11001. Its content has been updated and expanded with research findings
from 2008 up to the present.

Quantum field theories, regardless of their content, lead to a finite or infinite number of coupled nonlinear
field equations. In general, solving these equations in analytic form or managing them through lattice-based
computations has been met with limited success. We argue that the theory of nonlinear dynamical systems
offers a fresh approach to this challenge. Working from the universal route to chaos in coupled systems of
differential equations, we find that: a) particles acquire mass as plane wave solutions of the complex
Ginzburg-Landau equation (CGLE), without any reference to the hypothetical Higgs scalar; b) the
U(1) x SU(2) and SU(3) gauge groups, as well as leptons and quarks, are sequentially generated

**Category:** High Energy Particle Physics

[73] **viXra:1004.0074 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Roald C. Maximo

**Comments:** 2 pages

Many physicists still do not accept the obvious conclusion that (c + v) and (c - v) are valid solutions when applied to moving observers. There are
actually well known experimental proofs to validate those expressions. Besides the Sagnac effect, one experiment that has been hidden and given
no publicity was a measurement of the orbital periods of the Jovian satellite (Io) performed by Ole C. Römer that shows just such a velocity
composition as the Earth approaches the planet or recedes in its orbit. [1]
But, perhaps due to the pervading lato sensu interpretation of the second postulate of the Special Theory of Relativity in connection with the
currently generalized opinion that any physical theory, to be valid, must conform to the TR, many physicists are reluctant to accept it. Whenever
such a situation arises, they are eager to draw the Lorentz transformation from their pockets and apply it in some way to alleviate the discomfort.

**Category:** Relativity and Cosmology

[72] **viXra:1004.0073 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Michael Harney

**Comments:** 5 pages

Maxwell's equations describe the interactions of the electromagnetic field at
a macroscopic level. In the 1920s, Louis DeBroglie demonstrated that every
moving particle (including an electron) has a wave nature, and we know
from Einstein that every wave has a particle nature, which we call the
photon. Later in the 1930s, Paul Dirac's development of the famous Dirac
equation showed the quantum nature of the electron at relativistic speeds.
Then in 1948 Richard Feynman and Julian Schwinger extended these
concepts in the development of quantum electrodynamics which gives a full
accounting (although a very strange one) of how an electron can borrow
energy from the vacuum of space and return it legally as long it does so
within limits of the uncertainty principle.

**Category:** Quantum Physics

[71] **viXra:1004.0072 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Michael Harney, Michael Weber, Milo Wolff

**Comments:** 2 pages

The method described is designed to increase laser output power using a concept from Wheeler-Feynman
absorber theory [1,2] and the work of Tetrode [3], where photons are modeled as sources of energy that
must also have a sink (an electron) to be absorbed. According to Wheeler-Feynman and Tetrode, if an
electron is not present to absorb the photon, then the photon can never be emitted. In Wheeler-Feynman
absorber theory, advanced and retarded potentials resemble time-reversal equations because there must be
communication faster than light between the source-photon and the sink-electron, reasoned Feynman, so
that the source photon's atom would know whether to emit a photon. This enigma was resolved by Milo
Wolff in his work "Exploring the Physics of the Unknown Universe" [4], where he describes the use of
spherical scalar in-waves and out-waves that travel at c and whose local speed is based on local-mass
density. The in-out waves form electrons and also allows communication between them.

**Category:** Quantum Physics

[70] **viXra:1004.0071 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove that such that (see paper) has infinitely many prime
solutions.

**Category:** Number Theory

[69] **viXra:1004.0070 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture E : x^{2} + 1

**Category:** Number Theory

[68] **viXra:1004.0069 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove that such that P_{n} = 2 P_{1}P_{2} ... P_{n-1} has infinitely many prime
solutions.

**Category:** Number Theory

[67] **viXra:1004.0068 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove that there exist infinitely many primes P such that each of
(j)^{n} P + (k - j)^{n} is a prime.

**Category:** Number Theory

[66] **viXra:1004.0067 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove that there exist infinitely many primes P such that each of
(j)^{3} P + (k - j)^{3} is a prime.

**Category:** Number Theory

[65] **viXra:1004.0066 [pdf]**
*submitted on 10 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that there exist infinitely many primes P such that each of
(j)^{2} P + (k - j)^{2} is a prime.

**Category:** Number Theory

[64] **viXra:1004.0065 [pdf]**
*replaced on 17 Nov 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

In this paper we introduce the operators of validation and invalidation of a proposition,
and we extend the operator of S-denying a proposition, or an axiomatic system, from
the geometric space to respectively any theory in any domain of knowledge, and show
six examples in geometry, in mathematical analysis, and in topology.

**Category:** General Science and Philosophy

[63] **viXra:1004.0064 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache

**Comments:** 11 pages

This study proposes improved chain-ratio type estimator for
estimating population mean using some known values of population
parameter(s) of the second auxiliary character. The proposed estimators have
been compared with two-phase ratio estimator and some other chain type
estimators. The performances of the proposed estimators have been
supposed with a numerical illustration.

**Category:** Statistics

[62] **viXra:1004.0063 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 16 pages

Optimum Statistical Test Procedure

**Category:** Statistics

[61] **viXra:1004.0062 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache

**Comments:** 15 pages

In practice, the information regarding the population proportion possessing certain
attribute is easily available see Jhajj et.al. (2006). For estimating the population mean Y
of the study variable y, following Bahl and Tuteja (1991), a ratio-product type
exponential estimator has been proposed by using the known information of population
proportion possessing an attribute (highly correlated with y) in simple random sampling.
The expressions for the bias and the mean-squared error (MSE) of the estimator and its
minimum value have been obtained. The proposed estimator has an improvement over
mean per unit estimator, ratio and product type exponential estimators as well as Naik
and Gupta (1996) estimators. The results have also been extended to the case of two
phase sampling. The results obtained have been illustrated numerically by taking some
empirical populations considered in the literature.

**Category:** Statistics

[60] **viXra:1004.0061 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache

**Comments:** 12 pages

In this paper we have proposed an almost unbiased ratio and product type
exponential estimator for the finite population mean Y-bar. It has been shown that Bahl and
Tuteja (1991) ratio and product type exponential estimators are particular members of the
proposed estimator. Empirical study is carried to demonstrate the superiority of the
proposed estimator.

**Category:** Statistics

[59] **viXra:1004.0060 [pdf]**
*submitted on 8 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove that n x a^{n} ± 1 has infinitely many prime solutions
and n x 2^{n} ± 1 have finite prime solutions.

**Category:** Number Theory

[58] **viXra:1004.0059 [pdf]**
*submitted on 8 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 pages

Using Jiang function we prove that 3 x a^{3} ± 1 has infinitely many prime solutions

**Category:** Number Theory

[57] **viXra:1004.0058 [pdf]**
*submitted on 8 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 pages

Using Jiang function we prove that 2 x a^{2} ± 1 has infinitely many prime solutions

**Category:** Number Theory

[56] **viXra:1004.0057 [pdf]**
*submitted on 9 Apr 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 6 pages

We present in this paper some examples of how to compute by hand the PCR5 fusion rule for
three sources, so the reader will better understand its mechanism.
We also take into consideration the importance of sources, which is different from the classical
discounting of sources.

**Category:** Artificial Intelligence

[55] **viXra:1004.0056 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache

**Comments:** 11 pages

It is well recognized that the use of auxiliary information in sample survey design
results in efficient estimators of population parameters under some realistic conditions.
Out of many ratio, product and regression methods of estimation are good examples in
this context. Using the knowledge of kurtosis of an auxiliary variable Upadhyaya and
Singh (1999) has suggested an estimator for population variance. In this paper, following
the approach of Singh and Singh (1993), we have suggested almost unbiased ratio and
product-type estimators for population variance.

**Category:** Statistics

[54] **viXra:1004.0055 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Jayant Singh, Hansraj Yadav, Florentin Smarandache

**Comments:** 11 pages

Migration has various dimensions; urbanization due to migration is one of
them. In Rajasthan State, District level analysis of urbanization due to
migrants shows trend invariably for all the districts of the state though the
contribution in urbanization by the migrants varies from district to district.
In some districts the share of migrants moving to urban areas is very
impressive though in others it is not that much high. The migrants'
contribution in urbanization is on the rising over the decades. In this paper
district level migration in the Rajasthan state is examined in relation to
total urbanization and urbanization due to migration.

**Category:** Social Science

[53] **viXra:1004.0054 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 9 pages

This article presents several alternatives to Pearson's correlation coefficient
and many examples. In the samples where the rank in a discrete variable counts more
than the variable values, the mixture of Pearson's and Spearman's gives a better result.

**Category:** Statistics

[52] **viXra:1004.0053 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache, Mircea Eugen Șelariu

**Comments:** 10 pages

This article presents two methods, in parallel, of solving more complex integrals, among
which is the Poisson's integral, in order to emphasize the obvious advantages of a new method
of integration, which uses the supermathematics circular ex-centric functions.
We will specially analyze the possibilities of easy passing/changing of the supermathematics
circular ex-centric functions of a centric variable α to the same functions of ex-centric variable &theta.
The angle α is the angle at the center point O(0,0), which represents the centric variable and θ
is the angle at the ex-center E(k,ε), representing the ex-centric variable. These are the angles
from which the points W_{1} and W_{2} are visible on the unity circle - resulted from the intersection
of the unity/trigonometric circle with the revolving straight line d around the ex-centric
E(k,&epsilon) - from O and from E, respectively.

**Category:** Functions and Analysis

[51] **viXra:1004.0052 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 21 pages

One proposes a first alternative rule of combination to WAO (Weighted Average Operator) proposed recently by Josang,
Daniel and Vannoorenberghe, called Proportional Conflict Redistribution rule (denoted PCR1). PCR1 and WAO are particular cases of
WO (the Weighted Operator) because the conflicting mass is redistributed with respect to some weighting factors. In this first PCR rule,
the proportionalization is done for each non-empty set with respect to the non-zero sum of its corresponding mass matrix - instead of its
mass column average as in WAO, but the results are the same as Ph. Smets has pointed out. Also, we extend WAO (which herein gives
no solution) for the degenerate case when all column sums of all non-empty sets are zero, and then the conflicting mass is transferred
to the non-empty disjunctive form of all non-empty sets together; but if this disjunctive form happens to be empty, then one considers
an open world (i.e. the frame of discernment might contain new hypotheses) and thus all conflicting mass is transferred to the empty
set. In addition to WAO, we propose a general formula for PCR1 (WAO for non-degenerate cases). Several numerical examples and
comparisons with other rules for combination of evidence published in literature are presented too. Another distinction between these
alternative rules is that WAO is defined on the power set, while PCR1 is on the hyper-power set (Dedekind's lattice). A nice feature of
PCR1, is that it works not only on non-degenerate cases but also on degenerate cases as well appearing in dynamic fusion, while WAO
gives the sum of masses in this cases less than 1 (WAO does not work in these cases). Meanwhile we show that PCR1 and WAO do not
preserve unfortunately the neutrality property of the vacuous belief assignment though the fusion process. This severe drawback can
however be easily circumvented by new PCR rules presented in a companion paper.

**Category:** Artificial Intelligence

[50] **viXra:1004.0051 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Haibin Wang, Florentin Smarandache, Yan-Qing Zhang, Rajshekhar Sunderraman

**Comments:** 4 pages

Neutrosophic set is a part of neutrosophy which
studies the origin, nature, and scope of neutralities, as
well as their interactions with different ideational
spectra. Neutrosophic set is a powerful general formal
framework that has been recently proposed. However,
neutrosophic set needs to be specified from a technical
point of view. To this effect, we define the settheoretic
operators on an instance of neutrosophic set,
we call it single valued neutrosophic set (SVNS). We
provide various properties of SVNS, which are
connected to the operations and relations over SVNS.

**Category:** Set Theory and Logic

[49] **viXra:1004.0050 [pdf]**
*submitted on 8 Apr 2010*

**Authors:** Claudiu Coandă

**Comments:** 4 pages

In this article we prove the Smarandache-Pătrașcu's Theorem in relation to the inscribed
orthohomological triangles using the barycentric coordinates.

**Category:** Geometry

[48] **viXra:1004.0049 [pdf]**
*submitted on 8 Apr 2010*

**Authors:** Alex Ceapa

**Comments:** 80 pages

At the time factors of unknown origin and physical meaning (like β in the Lorentz
transformation, the Dirac matrices, etc.) are embedded in some underlying equations and,
by way of consequence, the physical significance of the terms of these equations rests
undisclosed, we validate the principle of the physical determination of equations in
special relativity theory and relativistic quantum theory, as first step toward an exciting
foundation of modern physics on this principle (yet all restraints of the principle are off in
modern physics).

**Category:** Relativity and Cosmology

[47] **viXra:1004.0048 [pdf]**
*submitted on 6 Apr 2010*

**Authors:** Ervin Goldfain

**Comments:** 16 pages, This contribution is a sequel to a paper published in Hadronic Journal, Vol. 31(6), p.179, 2008.

Despite its remarkable predictive power, the Standard Model for particle physics (SM) leaves out many
open questions. Two representative examples are the issue of CP violation and the anomalous magnetic
moment of leptons (AMM). Our work develops from the premise that the postulate of unitary evolution no
longer holds near or above the scale of electroweak interaction or near the "new physics" sector of SM.
Results suggest that CP violation in kaon physics and the AMM problem are manifestations of nonequilibrium
dynamics. Numerical predictions are found to be in close agreement with experimental data.

**Category:** High Energy Particle Physics

[46] **viXra:1004.0047 [pdf]**
*replaced on 6 Jun 2010*

**Authors:** Arman.V.zadeh

**Comments:** 33 pages

In this article we want to say about the Compton Effect and the Zeeman Effect.
(Both of them are almost one effect (in the fundament and with considering just the
refraction proposition of them). We know both of them are about the
electromagnetism waves (the waves) and some special properties of them. For
example the Zeeman effect is about the refraction of the magnetic fields (or the
other made fields by that) of the electromagnetism waves since we put the source
of that near the source of the magnetic or electrical field (we'll see the breaking or
refraction of the wave) and this proposition is possible that the wave refracts to
some part for example two or three part but we should remember that these effects
(Zeeman, Compton) aren't just for the light(the electromagnetism type) and of
course these proposition are less about the light (and some part of the light like the
x-ray or β-ray or γ-ray or ...) But it can't be impossible that these effects be
correct also about the light. Of course the Compton Effect is depending on the
angle θ with coefficient (1 - cosθ).
Now we want to justify that. We can say; if we want to consider the thing's (or
waves or the atoms or...) properties we can consider the moving of them and we
say that when an electron or another thing is turning around the nucleus quickly
we'll take a special force that caused it, and now during the moving or after the
moving we can get a special force and we can with this subject say the reason of
many effects and now we try to justify simply with this method. For the first time
this proposition is so easy but we can take this easy proposition as a principle of
our discussion.

**Category:** Classical Physics

[45] **viXra:1004.0046 [pdf]**
*submitted on 6 Apr 2010*

**Authors:** Ron Bourgoin

**Comments:** 4 pages

The authors of ArXiv:1003.5008 tell us they are searching
for the foundations of quantum mechanics, a theory they
say was born early in the twentieth century. As a matter
of fact, the theory was born in the eighteenth century.

**Category:** Quantum Physics

[44] **viXra:1004.0045 [pdf]**
*submitted on 6 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove the finite Mersenne primes and the finite repunits primes.

**Category:** Number Theory

[43] **viXra:1004.0044 [pdf]**
*submitted on 6 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove the finite fermat primes.

**Category:** Number Theory

[42] **viXra:1004.0043 [pdf]**
*submitted on 6 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 7 pages

Why we have five fingers. We suggest two principles: (1) the prime principle and (2)
the symmetric principle. We prove that 1, 3, 5, 7, 11, 23, 47, and 2, 4, 6, 10, 14, 22, 46,
94 are the most stable numbers, which are the basic building-blocks in clusters and
nanostructures. The prime principle is the mathematical foundations for clusters and
nanosciences. It is a theory of everything.

**Category:** Number Theory

[41] **viXra:1004.0042 [pdf]**
*submitted on 6 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove prime theorem: P_{2} = aP_{1} + b, Polignac
theorem and Goldbach theorem.

**Category:** Number Theory

[40] **viXra:1004.0041 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 1 pages

As a generalization of the factorial and double factorial one defines the kfactorial
of n as the below product of all possible strictly positive factors (see paper)

**Category:** Number Theory

[39] **viXra:1004.0040 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

Back and Forth Factorials

**Category:** Number Theory

[38] **viXra:1004.0039 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

According to the Brightsen Nucleon Cluster Model [1] all nuclides of beta stable isotopes can be
described by three fundamental nucleon clusters {NPN,PNP,NP), with halo clusters
(NN,PP,NNN) now experimentally observed. The Brightsen model builds on the early cluster
models of the Resonating Group Structure of John Wheeler [2] and the Linus Pauling
Close-Packed Spheron Model [3], which predict mathematically that the wave function of a composite
nucleus can be viewed quantum mechanically as a combination of partial wave functions that
correspond to the multiple ways nucleons (protons, neutrons) can be distributed into closepacked
clusters, thus rejecting the standard model Hartree-Fock formalism of average field
interactions between independent nucleons in nuclear shells. Presented in this section are a
number of unsolved problems, questions, and future experimental pathways based on the
Brightsen Nucleon Cluster Model formalism--many additional applications can be gleamed from
careful study of the literature cited in the references provided

**Category:** Nuclear and Atomic Physics

[37] **viXra:1004.0038 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 20 pages

Browsing through my fifth to twelfth grade years of preoccupation for creation I
discovered a notebook of Number Theory.
I liked to play with numbers as Tudor Arghezi (1880-1967) - our second national
Romanian poet {after the genial poet Mihai Eminescu (1850-1889)} - played with words.
I was so curious and amazed by the numbers' properties.
Interesting theorems, equations, and inequalities!
Such fascinating people who dedicated their research to numbers, just for the sake of
science!
I collected many results and tried to write a handbook of mathematicians and their
results.

**Category:** Number Theory

[36] **viXra:1004.0037 [pdf]**
*submitted on 3 Apr 2010*

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache, N. Suresh Babu, R.S. Selvaraj

**Comments:** 152 pages

In this book the authors introduce the new notion of
rank distance bicodes and generalize this concept to Rank
Distance n-codes (RD n-codes), n, greater than or equal to
three. This definition leads to several classes of new RD
bicodes like semi circulant rank bicodes of type I and II,
semicyclic circulant rank bicode, circulant rank bicodes,
bidivisible bicode and so on. It is important to mention that
these new classes of codes will not only multitask
simultaneously but also they will be best suited to the
present computerised era. Apart from this, these codes are
best suited in cryptography.

**Category:** Digital Signal Processing

[35] **viXra:1004.0036 [pdf]**
*submitted on 5 Apr 2010*

**Authors:** V.A.Induchoodan Menon

**Comments:** 12 pages

The author develops his idea of the standing electromagnetic half
wave structure of the electron and proposes that the confinement of the
wave is effected by the interactions with the Higgs field which can be
explained on the basis of the uncertainty principle. These interactions
allow vacuum to act like a thermal bath with the standing half wave in
equilibrium with it. It is shown that this equilibrium is not destroyed
even when it is in uniform translational motion. This invariance of the
equilibrium to the velocity transformation is another way of looking at
the theory of relativity.

**Category:** Quantum Physics

[34] **viXra:1004.0035 [pdf]**
*replaced on 8 Aug 2010*

**Authors:** Giuliano Bettini

**Comments:** v3 169 pages In Italian, v4 164 pages in English.

A book of semi qualitative ideas on electron, quarks and life. We intend to make us a
purely electromagnetic image of all interactions and elementary particles, in
particular electron, and quarks. This would force even the idea of a single universal
vibration, a single field.
The electron is interpreted as a small electric current carrying the elementary charge,
elementary mass and Planck quantum of action. With the aid of a few math we
identify the electron as an electromagnetic half wave closed on a Moebius strip. This
is equivalent to a full wavelength making two turns on the border. It is also probably
not totally irrelevant to note that this leads to interesting numerics on the fine
structure constant. We identify a quark with a confined electromagnetic wave which
is not sufficient in itself to complete a closed loop in space. So quarks are pictured as
1/3 and 2/3 of a full wavelength. A space model of their combination leads in a
unique way to the entire set of all and only the mesons and baryons. In a quite
spontaneous way also the color theory is interpreted. Finally the various helices of
quarks are interpreted as living organisms and similarities with a biological behaviour
are showed.
Arguments here are of course admittedly primitive and mainly qualitative, also if
supported with some math, but to my knowledge this overall conjecture has not been
discussed elsewhere, and therefore may be useful for further research.

**Category:** Quantum Physics

[33] **viXra:1004.0034 [pdf]**
*submitted on 4 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 page

Using Jiang function we prove that x^{6} + 1091 has no prime solutions.

**Category:** Number Theory

[32] **viXra:1004.0033 [pdf]**
*submitted on 4 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 15 - j is a prime.

**Category:** Number Theory

[31] **viXra:1004.0032 [pdf]**
*submitted on 4 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 9 - j is a prime.

**Category:** Number Theory

[30] **viXra:1004.0031 [pdf]**
*submitted on 4 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + k - j is a prime.

**Category:** Number Theory

[29] **viXra:1004.0030 [pdf]**
*submitted on 4 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 7 - j is a prime.

**Category:** Number Theory

[28] **viXra:1004.0029 [pdf]**
*submitted on 4 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 5 - j is a prime.

**Category:** Number Theory

[27] **viXra:1004.0028 [pdf]**
*submitted on 5 Apr 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 13 pages

As it is well known, the Riemann hypothesis on the zeros of the ζ(s)
function has been assumed to be true in various basic developments of
the 20-th century mathematics, although it has never been proved to
be correct. The need for a resolution of this open historical problem
has been voiced by several distinguished mathematicians. By using preceding
works, in this paper we present comprehensive disproofs of the
Riemann hypothesis. Moreover, in 1994 the author discovered the arithmetic
function J_{n}(ω) that can replace Riemann's ζ(s) function in view of
its proved features: if J_{n}(ω) ≠ 0, then the function has infinitely many
prime solutions; and if J_{n}(ω) = 0, then the function has finitely many
prime solutions. By using the Jiang J_{2}(ω) function we prove the twin
prime theorem, Goldbach's theorem and the prime theorem of the form
x^{2} + 1. Due to the importance of resolving the historical open nature
of the Riemann hypothesis, comments by interested colleagues are here
solicited.

**Category:** Number Theory

[26] **viXra:1004.0027 [pdf]**
*replaced on 9 Jul 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 413 pages

In my works (see the bibliography at the end of the Preface) I often expressed
the view that the protracted lack of resolution of fundamental problems in science
signals the needs of basically new mathematics. This is the case, for example, for:
quantitative representations of biological structures; resolution of the vexing
problem of grand-unification; invariant treatment of irreversibility at the classical and
operator levels; identification of hadronic constituents definable in our spacetime;
achievement of a classical representation of antimatter; and other basic open
problems.

**Category:** Number Theory

[25] **viXra:1004.0026 [pdf]**
*replaced on 22 Apr 2010*

**Authors:** Florentin Smarandache

**Comments:** 14 pages

These paradoxes are called "neutrosophic" since they are based on indeterminacy (or neutrality,
i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the
Venn Diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, illdefined
ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth
table and introduce two neutrosophic operators (neuterization and antonymization operators)
give many classes of neutrosophic paradoxes.

**Category:** Set Theory and Logic

[24] **viXra:1004.0025 [pdf]**
*submitted on 3 Apr 2010*

**Authors:** Ion Pătraşcu, Florentin Smarandache

**Comments:** 3 pages

In this note we prove a problem given at a Romanian student mathematical competition, and we
obtain an interesting result by using a Theorem of Orthohomological Triangles.

**Category:** Geometry

[23] **viXra:1004.0024 [pdf]**
*submitted on 3 Apr 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

Neutrosophic Logic (NL) is a Theory of Everything in logics, since it is the most general
so far. In the Neutrosophic Propositional Calculus a neutrosophic proposition has the
truth value (T, I, F), where T is the degree of truth, I is the degree of indeterminacy (or
neutral, i.e. neither truth nor falsehood), and F is the degree of falsehood, where T, I, F
standard or non-standard subsets of the non-standard unit interval ]-0, 1+[. In addition,
these values may vary over time, space, hidden parameters, etc.
Therefore, NL is a triple-infinite logic but, by splitting the Indeterminacy, we prove in
this article that NL is a n-infinite logic, with n = 1, 2, 3, 4, 5, 6, ... .
Also, we present a total order on Neutrosophic Logic.

**Category:** General Science and Philosophy

[22] **viXra:1004.0023 [pdf]**
*replaced on 7 Apr 2010*

**Authors:** Florentin Smarandache

**Comments:** 21 pages

The following blogs on applications of neutrosophics and multispace in sciences
include meditations / reflections on science, comments, hypotheses, proposals,
comparisons of ideas, possible projects, extensions or deviations or alternatives to
classical knowledge, etc. selected from e-mails, letters, drafts, conversations, impressions,
my diary, etc.

**Category:** General Science and Philosophy

[21] **viXra:1004.0021 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya

**Comments:** 12 pages

This short technical paper advocates a bootstrapping algorithm from which we can form a
statistically reliable opinion based on limited clinically observed data, regarding whether
an osteo-hyperplasia could actually be a case of Ewing's osteosarcoma. The basic
premise underlying our methodology is that a primary bone tumour, if it is indeed
Ewing's osteosarcoma, cannot increase in volume beyond some critical limit without
showing metastasis. We propose a statistical method to extrapolate such critical limit to
primary tumour volume. Our model does not involve any physiological variables but
rather is entirely based on time series observations of increase in primary tumour volume
from the point of initial detection to the actual detection of metastases.

**Category:** Quantitative Biology

[20] **viXra:1004.0020 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

Back and Forth Summands

**Category:** Number Theory

[19] **viXra:1004.0019 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Liu Feng, Florentin Smarandache

**Comments:** 6 pages

To deal with tough issues in knowledge management, the paper reexamines knowledge structure
and has proposed a novel knowledge communication model based on the oriental cultural foundation.
Knowledge discovery is not a simple addition or accumulation of information, but needs a feasible structural
description. As an oriental approach, the paper constructs the structure on the bases of unity of opposites and
their neutralities (as in neutrosophy; neutralities are the included middle of two opposites), which stresses
the individualized self knowledge pattern or self knowledge structure. It signifies the dynamics in
knowledge management - the principle of attraction between opposite natures and the neutralities in
between them. It implies an identity in the opposites which serves as the impartial knowledge (since the
opposites tend towards their neutralities), the completeness of knowledge, which is defined in the paper as
imaginary part of knowledge.

**Category:** General Science and Philosophy

[18] **viXra:1004.0018 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache, Sukanto Bhattacharya

**Comments:** 7 pages

We have posed a simple but interesting graph theoretic problem and posited a heuristic solution
procedure, which we have christened as Vectored Route-length Minimization Search (VeRMinS).
Basically, it constitutes of a re-casting of the classical "shortest route" problem within a strictly
Euclidean space. We have only presented a heuristic solution process with the hope that a formal
proof will eventually emerge as the problem receives wider exposure within mathematical circles.

**Category:** Combinatorics and Graph Theory

[17] **viXra:1004.0017 [pdf]**
*replaced on 19 Apr 2010*

**Authors:** Sukanto Bhattacharya, Kuldeep Kumar, Florentin Smarandache

**Comments:** 9 pages.

This study actually draws from and builds on an earlier paper (Kumar and
Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to
the problem of determining the conditional probability that a financial fraud has
been actually committed, given that no Type I error occurred while rejecting the
null hypothesis H_{0}: The observed first-digit frequencies approximate a Benford
distribution; and accepting the alternative hypothesis H_{1}: The observed first-digit
frequencies do not approximate a Benford distribution. We have also suggested
a conceptual model to implement such a neutrosophic fraud detection system.

**Category:** Economics and Finance

[16] **viXra:1004.0016 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 11 pages

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of
T-norms/T-conorms in fuzzy logic and set.
Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic
Topologies.

**Category:** Set Theory and Logic

[15] **viXra:1004.0015 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Haibin Wang, Rajshekhar Sunderraman, Florentin Smarandache, André Rogatko

**Comments:** 25 pages

In this paper, we present a generalization of the relational data model based on interval
neutrosophic set [1]. Our data model is capable of manipulating incomplete as well as
inconsistent information. Fuzzy relation or intuitionistic fuzzy relation can only handle
incomplete information. Associated with each relation are two membership functions one is
called truth-membership function T which keeps track of the extent to which we believe the
tuple is in the relation, another is called falsity-membership function F which keeps track of the
extent to which we believe that it is not in the relation. A neutrosophic relation is inconsistent if
there exists one tuple a such that T(α) + F(α) > 1. In order to handle inconsistent situation, we
propose an operator called "split" to transform inconsistent neutrosophic relations into
pseudo-consistent neutrosophic relations and do the set-theoretic and relation-theoretic
operations on them and finally use another operator called "combine" to transform the result
back to neutrosophic relation. For this data model, we define algebraic operators that are
generalizations of the usual operators such as intersection, union, selection, join on fuzzy
relations. Our data model can underlie any database and knowledge-base management system
that deals with incomplete and inconsistent information.

**Category:** Data Structures and Algorithms

[14] **viXra:1004.0014 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

As a consequence of the Integral Test we find a triple inequality which bounds up and
down both a series with respect to its corresponding improper integral, and reciprocally
an improper integral with respect to its corresponding series.

**Category:** Functions and Analysis

[13] **viXra:1004.0013 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache, V. Christianto

**Comments:** 15 pages

We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic
logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic
operators using the smarandache codification of the Venn diagram and a defined vector
neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.

**Category:** Set Theory and Logic

[12] **viXra:1004.0012 [pdf]**
*submitted on 2 Apr 2010*

**Authors:** Arman.V.zadeh

**Comments:** 10 pages

In this article we want to say about the gravity between the atoms to the new and
special way. We know that the atom and the gravity between them are stable by
moving the electron on the circuits around the nucleus(from the past articles) and
know in this article we want to point to some interesting and new methods (at the
new theory) to explain the events happened between the atoms and some materials
in the gravity system. For this calculate some equation about the gravity.

**Category:** Classical Physics

[11] **viXra:1004.0011 [pdf]**
*submitted on 2 Apr 2010*

**Authors:** Emil D. Gigov

**Comments:** 4 pages

Wave theory of light was tested by the Michelson's interferometer, whereas Newtonian corpuscular
theory can be tested with the new interferometer, which can show whether the speed of light in
empty space is variable during Doppler effect. Such measurement is possible due to the effect of
Fizeau.

**Category:** Classical Physics

[10] **viXra:1004.0010 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 6 pages

The paper presents an initial explorations on T, I, F operations based on genetic concept
hierarchy and genetic referential hierarchy, as a novel proposal to the indeterminacy issue in
neutrosophic logic, in contrast to the T, I, F values inherited from conventional logics in which
those values would fail to demonstrate the genetic aspect of a concept and accordingly loose the
connection between generality and practicality. Based on the novel definition of logic and on the
relativity of T, F concept, it illustrates that T, F are hierarchical operations which inter-consist and
inter-complement each other, that "I" relates to a learning behavior profiled by an inspiration from
I-ching, and that the neutralization operation, as the means to solve contradictions, will eventually
come to the unification of opposites, leading to the fundamental issues in Buddhism and such alike.
It also implies that Buddhism and Daoism are not religions.

**Category:** Set Theory and Logic

[9] **viXra:1004.0009 [pdf]**
*replaced on 31 Aug 2010*

**Authors:** Florentin Smarandache

**Comments:** 7 pages

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and
intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between
NS and IFS are underlined.

**Category:** Artificial Intelligence

[8] **viXra:1004.0008 [pdf]**
*replaced on 31 Aug 2010*

**Authors:** Florentin Smarandache

**Comments:** 7 pages

In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic
logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set
and neutrosophic set) are pointed out.

**Category:** Artificial Intelligence

[7] **viXra:1004.0007 [pdf]**
*replaced on 12 Apr 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

It is easy to deal with a Venn Diagram for 1 ≤ n ≤ 3 sets. When n gets larger, the picture
becomes more complicated, that's why we thought at the following codification. That's
why we propose an easy and systematic algebraic way of dealing with the representation
of intersections and unions of many sets.

**Category:** Data Structures and Algorithms

[6] **viXra:1004.0006 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 10 pages

Based on the authors intensive investigation on the oriental dialectics, the paper presents a novel
theoretical frame of matter element in the world leading science, extenics dealing with inconsistency or
incompatibility, covering the widest range of application area from informatics, system engineering to
management and finance. The dialectic matter-element is defined as the integral of all existing and prospecting
ones based on all the infinite possible cognitive models. The novel model serves as the origin of constraint
matter elements, the unity of both state description and cognitive action (cognition force with respect to neural
science), a latent part of extenics, and possibly as essence of matter element. It explains, in a novel perspective,
the origin of a name, and uncovers the source of contradiction and even the impetus of cognition.

**Category:** Set Theory and Logic

[5] **viXra:1004.0005 [pdf]**
*replaced on 21 Jul 2011*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 4 pages

This short paper introduces two new fusion rules for combining quantitative basic belief
assignments. These rules although very simple have not been proposed in literature so far and could serve as
useful alternatives because of their low computation cost with respect to the recent advanced Proportional
Conflict Redistribution rules developed in the DSmT framework.

**Category:** Artificial Intelligence

[4] **viXra:1004.0004 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Haibin Wang, Yan-Qing Zhang, Rajshekhar Sunderraman, Florentin Smarandache

**Comments:** 15 pages

In this paper we propose a framework called Semanic Web Services (see paper for full abstract)

**Category:** Artificial Intelligence

[3] **viXra:1004.0003 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Mircea Eugen Șelariu

**Comments:** 14 pages, translated from Romanian by Marian Nitu and Florentin Smarandache

In this paper we talk about the so-called Super-Mathematics Functions (SMF), which often
constitute the base for generating technical, neo-geometrical, therefore less artistic objects.
These functions are the results of 38 years of research, which began at University of Stuttgart
in 1969. Since then, 42 related works have been published, written by over 19 authors, as shown in
the References.

**Category:** Geometry

[2] **viXra:1004.0002 [pdf]**
*submitted on 1 Apr 2010*

**Authors:** Arman.V.zadeh

**Comments:** 9 pages

In this article we want to consider the polarization for matters
and atoms. We know that if a special ray go down to the surface
of a transparent matter and if it was not polarized when it beats
to the transparent matter like glass and water it will reflex to
polarized way (of course it be in a special angle from water to
the ray or from ray to perpendicular line to the water. Now we
want to say the reason of that which why effect this event. We
know that the special angle is different for different matters like
glass or water or... and that's because which the (n) or
refracture index for different matters is different and we easily
can get the special number for different matters but to this way
that we should get the angle between the refracted ray and
reflected way to 90^{o} and this subject that why we should take
the angle to 90^{o} is a experiment number. So we can get the angle
with the Snell law and Brewster law. And in this article we want
to consider that why the angle should be 90^{o} (to theory way).

**Category:** Classical Physics

[1] **viXra:1004.0001 [pdf]**
*submitted on 1 Apr 2010*

**Authors:** Arman.V.zadeh

**Comments:** 7 pages

This article is about the magnetism particular's of matters and
here we try to say easily the magnetism effects of matters in the
small system like atom also we try to say the magnetism field
with the electrical field.

**Category:** Classical Physics