[264] **viXra:1003.0275 [pdf]**
*replaced on 30 May 2010*

**Authors:** S. Halayka

**Comments:** 7 Pages. Added reference McDonald JR, Miller WA. Coupling
Non-Gravitational Fields with Simplicial Spacetimes

Using a numerical method, the external directed edges of a complete
graph are tested for their level of fitness in terms of how well they form
a radially symmetric field at long distance (e.g., a test for the inverse
square law in 3D space). It is found that the external directed edges of
a complete graph can very nearly form a radially symmetric field at long
distance if the number of graph vertices is great enough.

**Category:** Quantum Gravity and String Theory

[263] **viXra:1003.0274 [pdf]**
*submitted on 31 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 pages

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

**Category:** Number Theory

[262] **viXra:1003.0273 [pdf]**
*submitted on 31 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jiang function we prove that there exist infinitely many primes P_{1} such that
a P_{1} + b is prime.

**Category:** Number Theory

[261] **viXra:1003.0272 [pdf]**
*replaced on 3 Apr 2010*

**Authors:** Florentin Smarandache

**Comments:** 12 pages

In this paper we review nine previous proposed and solved problems of elementary 2D
geometry [4] and [6], and we extend them either from triangles to polygons or polyhedrons,or
from circles to spheres (from 2D-space to 3D-space), and make some comments about them.

**Category:** Geometry

[260] **viXra:1003.0271 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

On a Problem with Primes.

**Category:** Number Theory

[259] **viXra:1003.0270 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

In this paper one uses a mathematical modeling of psychological processes and one
improves the Weber's Law and Fechner's Law on sensations and stimuli.

**Category:** Mind Science

[258] **viXra:1003.0269 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** C. Le

**Comments:** 4 pages, edited by C. Le, and translated into German by Bernd Hutschenreuther

The Smarandache's Class of Paradoxes are semantic paradoxes of the form "All is <A>, the
<nonA> too!", where <nonA> is what is not <A>. As a particular case, replacing <A> but an
attribute (or, in general, by an idea) it is well know the Smarandache semantic paradox:
"All is possible, the impossible too!" which is the motto of the Paradoxism movement in arts,
letters, and sciences.

**Category:** Set Theory and Logic

[257] **viXra:1003.0268 [pdf]**
*replaced on 12 Apr 2010*

**Authors:** Stephen P. Smith

**Comments:** 15 pages

The proclivities of particularity and generality describe a polarity, held together by a
naked emotionality that signifies a felt middle-term. This polarity indicates a type of circular
reasoning, and can endlessly oscillate due to an equivocation that confuses particularity with
generality that may block emotional energies and prevent resolution. Deduction and induction
represent the same polarity, as does the frequentist and Bayesian interpretations of statistics.
Reintroducing emotion back into logic returns an intuitionist logic and grammar, and this permits
the resolution of felt tension. This intuitionism is tied to a time-sense that oscillates between
foresight (to particularity) and hindsight (to generality). Emotionality is found relating to
causation, agreeing with A.N. Whitehead. It is hypothesized that the intuitionist logic provides a
universal grammar, or a vitalistic organizing principle, that has impacted on biological evolution.
This agrees with panpsychism and panentheism.

**Category:** Linguistics

[256] **viXra:1003.0267 [pdf]**
*submitted on 30 Mar 2010*

**Authors:** Victor Porton

**Comments:** 4 pages

Considered convergence and limit for funcoids (a generalization of proximity spaces).
I also have defined (generalized) limit for arbitrary (not necessarily continuous)
functions under certain conditions.
This article is a part of my Algebraic General Topology research.

**Category:** Topology

[255] **viXra:1003.0265 [pdf]**
*submitted on 30 Mar 2010*

**Authors:** Arman.V.zadeh

**Comments:** 14 pages

This article is about atoms and their particulars in equations.
There are lots of equations from this subject that they have
given by different scientists. For example one of those
equations is the Planck equation that is for calculating the
electron's momentum in the atom and we can add mechanic's
statistic for some or all place's of electron in the atom.

**Category:** Classical Physics

[254] **viXra:1003.0264 [pdf]**
*submitted on 30 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 pages

Using Jiang function we prove that for every positive integer k there exist infinitely
many primes P such that each of P + 4^{n} is prime.

**Category:** Number Theory

[253] **viXra:1003.0263 [pdf]**
*submitted on 30 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 pages

Using Jiang function we prove that for every positive integer k there exist infinitely
many primes P_{1} and P_{2} such that each of 1 2 jP_{1} + (j + 1)P_{2} is prime.

**Category:** Number Theory

[252] **viXra:1003.0262 [pdf]**
*submitted on 30 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 pages

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

**Category:** Number Theory

[251] **viXra:1003.0261 [pdf]**
*submitted on 30 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 1 pages

Using Jiang function we prove that for every positive integer k there exist infinitely
many primes P such that each of jP + j +1 is prime.

**Category:** Number Theory

[250] **viXra:1003.0260 [pdf]**
*submitted on 30 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 3 pages

Using Jiang function we prove that for every positive integer k there exist infinitely
many primes P such that each of P + j(j + 1) is prime

**Category:** Number Theory

[249] **viXra:1003.0259 [pdf]**
*submitted on 28 Mar 2010*

**Authors:** Nigel B. Cook

**Comments:** 3 pages, see paper for equations in abstract

British mathematician Sir Geoffrey I. Taylor in secret work for British civil defence in 1941 (declassified in
1950 and published in the Proceedings of the Royal Society, vol. 201A, pp. 159-186), derived the strong
shock solution equation, namely distance, (equation) , where (equation) is the ambient (pre-shock)
atmospheric density, t is time after explosion, E is the energy released and Sg is Taylor's calculated
function of g, requiring a complex step-wise numerical integration. We present a proof of the equation (equation),
implying that Taylor's so-called constant (equation), not requiring any
complex integration. This is useful for close-in shock waves from nuclear explosions and supernovae
explosions. We further obtain the general arrival time of the shock wave (equation), by noting two
asymptotic solutions; namely, at very great distances, the blast
decays into a sound wave so the arrival time t approaches the ratio of distance to sound velocity (equation),
while at very close-in distances the strong shock equation previously derived becomes accurate, and
there is also an easily included effect at intermediate distances due to the expansion of the hot air in
reducing shock front arrival times. The errors of method made by Taylor for nuclear test explosions in air
were also made by Russian mathematician Leonid I. Sedov who applied similar cumbersome numerical
integrations in a 1946 paper (published in the Journal of Applied Mathematics and Mechanics, vol. 10,
pp. 241-50).

**Category:** Classical Physics

[248] **viXra:1003.0258 [pdf]**
*submitted on 28 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 2 pages

Using Jinag funciton we prove that there exist infinitely many primes P_{1} and P_{2} such
that each of P_{1} + jP_{2} + j is prime and there exist infinitely many primes P_{1} and P_{2}
such that each of P_{1} + jP_{2} + j is prime.

**Category:** Number Theory

[247] **viXra:1003.0257 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 26 pages

In this paper we introduce a new procedure called α-Discounting Method for
Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of
Saaty's Analytical Hierarchy Process (AHP). It works for any set of preferences that can
be transformed into a system of homogeneous linear equations. A degree of consistency
(and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D
MCDM is generalized to a set of preferences that can be transformed into a system of
linear and/or non-linear homogeneous and/or non-homogeneous equations and/or
inequalities.
Many consistent, weak inconsistent, and strong inconsistent examples are given.

**Category:** Artificial Intelligence

[246] **viXra:1003.0256 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

In this article we present the two classical negations of Euclid's Fifth Postulate
(done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of
these we propose a partial negation (or a degree of negation) of an axiom in geometry.
The most important contribution of this article is the introduction of the degree of
negation (or partial negation) of an axiom and, more general, of a scientific or humanistic
proposition (theorem, lemma, etc.) in any field - which works somehow like the negation
in fuzzy logic (with a degree of truth, and a degree of falsehood) or like the negation in
neutrosophic logic [with a degree of truth, a degree of falsehood, and a degree of
neutrality (i.e. neither truth nor falsehood, but unknown, ambiguous, indeterminate)].

**Category:** Geometry

[245] **viXra:1003.0255 [pdf]**
*submitted on 26 Mar 2010*

**Authors:** Giuliano Bettini

**Comments:** 48 pages

As a continuation of a preceding paper "The trapped light" a preliminary attempt of
how to construct a spinor theory of radar scattering or radar signal-target interaction
with the gauge theories of quantum mechanics is presented. This way radar signals
and radar targets may become visible macroscopic objects to be put in analogy with
Standard Model particles and interactions. The basic idea is that particles and forces
are all of electromagnetic nature, light, and appear different due to the size and shape
of interacting objects.
For the purpose that we propose here, you must first deal with a generic radar signal
in spinor form (note: it is TEM, TE, TM or evanescent. I mean "radar signal" in a
wide sense, ie for ex. also into a waveguide).
This is done by deriving a spinor representation of the TE TM through the Dirac
equation for plane wave, starting rigorously from Maxwell's equations without any
use of equivalent V, I as in previous papers.
As a byproduct the representation is extended to the TEM.
Then I introduce a tentative procedure to express the deflection of the field in a
different direction, and its variation in frequency, and rest mass. This is accomplished
through the interaction with SU(2)xU(1) gauge fields ie electroweak interactions.
Some simple but illustrative examples are given.
The ideas set out here need of course further research.

**Category:** Quantum Physics

[244] **viXra:1003.0254 [pdf]**
*submitted on 26 Mar 2010*

**Authors:** Cătălin Barbu

**Comments:** 4 pages

In this note, we present a proof of Smarandache's cevian triangle
hyperbolic theorem in the Einstein relativistic velocity model of hyperbolic geometry.

**Category:** Geometry

[243] **viXra:1003.0253 [pdf]**
*submitted on 26 Mar 2010*

**Authors:** Dainis Zeps

**Comments:** 12 pages

We consider idea of hierarchical multitime notion and of the cone of creation. Following
this idea, the time used in traditional sense is only a single projection of time in the
multitime. Multitime must have inner dimension upwards turning it into hierarchical
structure which acts as what we call global cone of creation. On our time projection,
evolution of species and BB, both global and local, in SM are examples of local cones
of creation. Higgs field as symmetry breaking accounts for complementary worlds on other
projections of time in multitime. We argue that time is form of referencing within
matter and doesn't have any sense without matter. These are the hypothetical assumptions
which may be tested, when LHC experiment shall go on.

**Category:** History and Philosophy of Physics

[242] **viXra:1003.0252 [pdf]**
*replaced on 2013-04-22 14:06:13*

**Authors:** Modris Tenisons, Dainis Zeps

**Comments:** 19 Pages. Corrected version

We consider an ornamental sign language of first order where principles of sieve displacement, of asymmetric building blocks as a base of ornament symmetry, color exchangeability and side equivalence principles work. Generic aspects of sieve and a genesis of ornamental pattern and ornament signs in it are discussed. Hemiolia principle for ornamental genesis is introduced. The discoverer of most of these principles were artist Modris Tenisons [4, 5, 6, 7 (refs. 23, 24), 8 (ref. 65)]. Here we apply a systematical research using simplest mathematical arguments.
We come to conclusions that mathematical argument in arising ornament is of much more significance than simply symmetries in it as in an image. We are after to inquire how ornament arises from global aspects intertwined with these local. We raise an argument of sign’s origin from code rather from image, and its eventual impact on research of ornamental patterns, and on research of human prehension of sign and its connection with consciousness.

**Category:** Artificial Intelligence

[241] **viXra:1003.0251 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 11 pages

We propose the poly-emporium theory. A search done in
Google on May 3rd, 2008, for the term "poly-emporium"
returned no entry, so we introduce it for the first time.

**Category:** Economics and Finance

[240] **viXra:1003.0250 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 3 pages

Mu-bit is defined here as 'multi-space bit'. It is different from standard meaning of bit in
conventional computation, because in Smarandache's multi-space theory, the bit is created
simultaneously at multi-spaces.
This new 'bit' term is different from multi-valued-bit already known in computer technology,
for example as MVLong [8][9].
This new concept is also different from qu-bit from quantum computation terminology [10]. We
know that using quantum mechanics logic we could introduce new way of computation with
'qubit' (quantum bit), but the logic remains Neumann. Now from the viewpoint of m-valued
multi-space logic, we introduce a new term: 'mu-bit' (from ' multi-space bit').

**Category:** Digital Signal Processing

[239] **viXra:1003.0249 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 5 pages

In the context of some recent papers suggesting CT-symmetric QM in order to
generalize PT-symmetric QM, in this paper we present an idea that there is quite
compelling reasoning to argue in favour of supersymmetric extension of Klein-Gordon
equation. Its numerical solutions in some simplest conditions are presented.
Since the potential corresponding to this supersymmetric KGE is neither Coulomb,
Yukawa, nor Hulthen potential [2a], then one can expect to observe a new type of
matter, which may be called 'supersymmetric-meson'. Its presence may be expected
in particular in the process of breaking of Coulomb barrier in low energy schemes.
Further observation is of course recommended in order to refute or verify this proposition.

**Category:** Quantum Physics

[238] **viXra:1003.0248 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 4 pages

In recent years, there has been a rapid increase in the literature which discusses new phenomenon
associated to social network. One of the well-known phenomenon in this regards is known as 'six
degrees of separation' [1], which implies that one can always keep a communication with each other
anywhere within a six-step. A number of experiments has verified this hypothesis, either in the
context of offline communication (postal mail), or online communication (email, etc.).
In this article, we argue that by introducing this known 'six degrees of separation' into the context of
group instability problem, one can find a new type of wisdom in organization. Therefore, we offer a
new conjecture, which may be called 'Group stability conjectures based on Graph/Network
distance."
To our knowledge this conjecture has not been discussed elsewhere, and therefore may be useful for
further research, in particular in the area of organization development and group stability studies.
The purpose of this article was of course not to draw a conclusive theory, but to suggest further
study of this proposed conjecture.

**Category:** Social Science

[237] **viXra:1003.0247 [pdf]**
*replaced on 30 Mar 2010*

**Authors:** Andrew Beckwith

**Comments:** 5 pages, 1 figure. Re done to make equivalence of Beckwith DM/DE and brane world
conditions shown as the same as Yurov.s 2002 conditions. Actual conference submission for the
Beyond the Standard Model 2010, by Dr. Andrew Beckwith. Heavily referenced by Dr. Beckwith in
PIERS 2010, XIAN, on March 22, at 11 a.m. in room D with two other presenters, Dr. Cruise of
Birmingham University, and Dr. Li of Chongquing University, as given by
http://piers.mit.edu/piers2010xian/files/FinalProgram.pdf. Note that Dr. Grishkuk, of Cardiff
University did not attend. Conference entry for proceedings as edited by
Dr. H. V. Klaptor-Kleingross, as given for http://www.phy.uct.ac.za/beyond2010/

The case for a four-dimensional graviton mass (non zero) influencing reacceleration of
the universe in both four and five dimensions is stated, with particular emphasis on the
question whether 4D and 5D geometries as given here yield new physical insight as to
cosmological evolution. Both cases give equivalent reacceleration one billion years ago,
which leads to the question whether other criteria can determine the relative benefits of
adding additional dimensions to cosmology models.

**Category:** Relativity and Cosmology

[236] **viXra:1003.0246 [pdf]**
*submitted on 25 Mar 2010*

**Authors:** Willi Penker

**Comments:** 3 pages

The effects of forces are well known; however, the basic
mechanisms of how forces work and are transmitted remain
unexplained. This essay is meant to determine these basic
mechanisms.

**Category:** Quantum Gravity and String Theory

[235] **viXra:1003.0245 [pdf]**
*submitted on 25 Mar 2010*

**Authors:** Cătălin Barbu

**Comments:** 4 pages

In this note, we present a proof of the hyperbolic a Smarandache's
pedal polygon theorem in the Poincaré disc model of hyperbolic geometry.

**Category:** Geometry

[234] **viXra:1003.0244 [pdf]**
*submitted on 3 Mar 2010*

**Authors:** Ron Bourgoin

**Comments:** 2 pages

The authors of Archiv:1003.4288 study a student named "Jim".
"Jim" displays a propensity for believing his mathematical
solutions rather than what his common sense tells him. He is
a student taking an introductory physics class. The authors
wonder why mathematical solutions take precedence over
common sense. In this brief note we cite as the root cause
of the problem the fact that we tell our students to distrust
their common sense. When we arrive at relativity theory,
for example, we inform our students that common sense
is useless in relativity theory. We tell them that common
sense is useless in quantum mechanics. Is it any wonder
our students believe whatever the math tells them?

**Category:** Mind Science

[233] **viXra:1003.0243 [pdf]**
*replaced on 2012-03-20 18:35:37*

**Authors:** John A. Gowan

**Comments:** 11 Pages.

Our sense of individual immortality is a consequence of the self-awareness of the Universe caught knowingly in the act of looking at itself through human eyes. I am how the Universe becomes self-aware and experiences itself. The immortality of the Universe is therefore quite naturally intuited to be my own. The Universe is a conservation domain: all parts of the Universe are immortal or otherwise conserved. Our true immortality is the eternal nature of the Universe itself - including its capacity to continuously evolve and create information, life, and self-knowledge.
Human life oscillates between a generalized (genomic) and a specific (individual) expression. The creation of a new human being is remarkably analogous to the creation of a new elementary particle: both processes require a symmetric energy state which recapitulates the original environmental conditions of its specialized domain.

**Category:** General Science and Philosophy

[232] **viXra:1003.0242 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 4 pages

In the preceding article we argue that biquaternionic extension
of Klein-Gordon equation has solution containing imaginary
part, which differs appreciably from known solution of
KGE. In the present article we discuss some possible interpretation
of this imaginary part of the solution of biquaternionic
KGE (BQKGE). Further observation is of course recommended
in order to refute or verify this proposition.

**Category:** Quantum Physics

[231] **viXra:1003.0240 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 8 pages

It is known that quaternion number has wide application in theoretical physics and engineering fields alike,
in particular to describe Maxwell electrodynamics. In the meantime, recently this quaternion number has
also been used to draw fractal graph. The present note is intended as an introduction to this very interesting
study, i.e. to find linkage between quaternion/biquaternion number, quantum mechanical equation
(Schrödinger equation) and fractal graph. Hopefully this note will be found useful for subsequent study.

**Category:** Quantum Physics

[230] **viXra:1003.0239 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 11 pages

A heuristic argument was presented in favor of hypothesis that
scientific communication corresponds to a process known as
scale-free network. As a result, it is argued that scientific
referencing through citation follows the same process,
therefore it could be expected that this shall also exhibit
fractality as observed in various phenomena associated with
scale-free networks. This argument appears conceivable
because the process of citation involves a decision-making,
coined here as 'citation game.' In this regard, it is
recommended to conduct citation analysis to measure the
fractality of this process. While at present this heuristic
argument cannot be considered as conclusive, further research
is recommended to verify or refute this hypothesis.

**Category:** General Science and Philosophy

[229] **viXra:1003.0237 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 6 pages

In the last few decades, the flexible exchange rate has become the predominating policy
implemented by most countries in the World, except only a few countries who can keep their
exchange rates fixed. The predominating position can be attributed mainly to Milton Friedman's
strong support. What is less known, nonetheless, is a hidden premise that the flexible exchange
rate policy will help fiscal policy in the sense that only governments who do not manage the
fiscal policy properly will get 'punished' by exchange rate decreases. But as the US-Japan
experience showed [1], this widely-held assumption is often not realistic. The same experience
has been observed in other countries too, i.e. that financial liberalization including flexible
exchange rate often became precursor of financial instability [2].
While in the past year, in Indonesia for particular, the exchange rate remains stable, it does not
mean that it would be free from troubles in the future. Therefore it is worthwhile to explore some
other choices for better exchange rate policy.
In the present paper will discuss, albeit in somewhat 'crude' manner, some long-term approaches
which have been discussed in the literature, and also not-so conventional approaches which may
be suitable for short term purposes.
The basic proposition in the present paper is that we argue in favor of returning to fixed (or
pegging) exchange rate, but of course it is not realistic to promote this policy for the short-term
future. Therefore we explore some unconventional alternatives for short-term. It is our hope that
the proposition would be useful to explore further by the economics policy makers.

**Category:** Economics and Finance

[228] **viXra:1003.0235 [pdf]**
*replaced on 26 May 2010*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 15 pages

In this paper we review and try to justify some results we gave before
concerning the zeta regularization of integrals ∫x^{m-s}dx
via the zeta regularization of the divergent series
Σx^{m-s}dx and the zeta function ζ(m - s)

**Category:** Number Theory

[227] **viXra:1003.0234 [pdf]**
*replaced on 26 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 7 pages

Using Jiang function we prove Jiang prime -tuple theorem. We prove that the Hardy-Littlewood
prime-tuple conjecture is false. Jiang prime -tuple theorem can replace the Hardy-Littlewood
prime-tuple conjecture.

**Category:** Number Theory

[226] **viXra:1003.0233 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 141 pages

Over 300 sequences and many unsolved problems and conjectures
related to them are presented herein.

**Category:** Number Theory

[225] **viXra:1003.0232 [pdf]**
*submitted on 7 Mar 2010*

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

**Comments:** 213 pages

In a world of chaotic alignments, traditional logic with its strict boundaries of truth
and falsity has not imbued itself with the capability of reflecting the reality. Despite
various attempts to reorient logic, there has remained an essential need for an
alternative system that could infuse into itself a representation of the real world. Out
of this need arose the system of Neutrosophy, and its connected logic, Neutrosophic
Logic. Neutrosophy is a new branch of philosophy that studies the origin, nature and
scope of neutralities, as well as their interactions with different ideational spectra.
This was introduced by one of the authors, Florentin Smarandache. A few of the
mentionable characteristics of this mode of thinking are [90-94]: It proposes new
philosophical theses, principles, laws, methods, formulas and movements; it reveals
that the world is full of indeterminacy; it interprets the uninterpretable; regards, from
many different angles, old concepts, systems and proves that an idea which is true in
a given referential system, may be false in another, and vice versa; attempts to make
peace in the war of ideas, and to make war in the peaceful ideas! The main principle
of neutrosophy is: Between an idea and its opposite

**Category:**

[224] **viXra:1003.0231 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 141 pages

In this book we introduce the notion of Smarandache special
definite algebraic structures. We can also call them equivalently
as Smarandache definite special algebraic structures. These new
structures are defined as those strong algebraic structures which
have in them a proper subset which is a weak algebraic
structure. For instance, the existence of a semigroup in a group
or a semifield in a field or a semiring in a ring. It is interesting
to note that these concepts cannot be defined when the algebraic
structure has finite cardinality i.e., when the algebraic structure
has finite number of elements in it.

**Category:** Algebra

[223] **viXra:1003.0230 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Sebastián Martín Ruiz

**Comments:** 25 pages

The Smarandache function is defined as follows:
S(n)= the smallest positive integer such that S(n)! is divisible by n. [1]
In this article we are going to see that the value this function takes when n
is a perfect number of the form n = 2^{k - 1}.(2^{k} - 1) , p = 2^{k} - 1 being a prime
number.

**Category:** Number Theory

[222] **viXra:1003.0229 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Linfan Mao

**Comments:** 275 pages

A Smarandache multi-space is a union of n different spaces equipped with some
different structures for an integer n ≥ 2, which can be used both for discrete or
connected spaces, particularly for geometries and spacetimes in theoretical physics.

**Category:** Combinatorics and Graph Theory

[221] **viXra:1003.0228 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Amarnath Murthy, Charles Ashbacher

**Comments:** 219 pages

This book arose out of a collection of papers written by Amarnath Murthy. The papers
deal with mathematical ideas derived from the work of Florentin Smarandache, a man
who seems to have no end of ideas. Most of the papers were published in Smarandache
Notions Journal and there was a great deal of overlap. My intent in transforming the
papers into a coherent book was to remove the duplications, organize the material based
on topic and clean up some of the most obvious errors. However, I made no attempt to
verify every statement, so the mathematical work is almost exclusively that of Murthy.

**Category:** Number Theory

[220] **viXra:1003.0227 [pdf]**
*replaced on 26 Jun 2011*

**Authors:** Linfan Mao

**Comments:** 399 pages.

Automorphism groups survey similarities on mathematical systems, which appear nearly
in all mathematical branches, such as those of algebra, combinatorics, geometry, ... and
theoretical physics, theoretical chemistry, etc. In geometry, configurations with high
symmetry born symmetrical patterns, a kind of beautiful pictures in aesthetics. Naturally,
automorphism groups enable one to distinguish systems by similarity. More automorphisms
imply more symmetries of that system. This fact has established the fundamental
role of automorphism groups in modern sciences. So it is important for graduate students
knowing automorphism groups with applications.

**Category:** Combinatorics and Graph Theory

[219] **viXra:1003.0225 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** József Sándor

**Comments:** 302 pages

This book contains short notes or articles, as well as studies on several topics of
Geometry and Number theory. The material is divided into five chapters: Geometric theorems;
Diophantine equations; Arithmetic functions; Divisibility properties of numbers
and functions; and Some irrationality results. Chapter 1 deals essentially with geometric
inequalities for the remarkable elements of triangles or tetrahedrons. Other themes have
an arithmetic character (as 9-12) on number theoretic problems in Geometry

**Category:** Number Theory

[218] **viXra:1003.0224 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Charles Ashbacher

**Comments:** 145 pages

As someone who works heavily in both math and computers, I can truly appreciate the
role that logic plays in our modern world. One cannot understand the foundations of
mathematics while lacking knowledge of the basics of logic and how proofs are
constructed. Two of the first classes I took as a graduate student in mathematics were in
the foundations of mathematics, and hardly a day goes by where I do not use some topic
from those courses.

**Category:** Set Theory and Logic

[217] **viXra:1003.0223 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Linfan Mao

**Comments:** 215 pages

SMARANDACHE GEOMETRIES
&
MAP THEORY WITH APPLICATIONS

**Category:** Combinatorics and Graph Theory

[216] **viXra:1003.0222 [pdf]**
*submitted on 21 Mar 2010*

**Authors:** John Hunter

**Comments:** 6 pages

It is proposed that there has been a longstanding misunderstanding of the relationship
between scale factor of the universe and redshift. It is shown how value of
omega(matter) of one quarter of the true value, (hence the apparent dark energy
phenomenon) can result from such a misconception. Predictions for the magnitudes
of supernovae against redshift are made and found to be in good agreement with
supernovae data, without dark energy.

**Category:** Relativity and Cosmology

[215] **viXra:1003.0221 [pdf]**
*replaced on 27 Jun 2011*

**Authors:** Linfan Mao

**Comments:** 502 pages.

Accompanied with humanity into the 21st century, a highlight trend for developing
a science is its overlap and hybrid, and harmoniously with other sciences, which
enables one to handle complex systems in the WORLD. This is also for developing
mathematics. As a powerful tool for dealing with relations among objectives,
combinatorics, including combinatorial theory and graph theory mushroomed in last
century. Its related with algebra, probability theory and geometry has made it to an
important subject in mathematics and interesting results emerged in large number
without metrics. Today, the time is come for applying combinatorial technique to
other mathematics and other sciences besides just to find combinatorial behavior
for objectives. That is the motivation of this book, i.e., to survey mathematics and
fields by combinatorial principle.

**Category:** Combinatorics and Graph Theory

[214] **viXra:1003.0220 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Charles Ashbacher

**Comments:** 80 pages

In writing a book, one encounters and overcomes many obstacles. Not the least of which is
the occasional case of writer's block. This is especially true in mathematics where
sometimes the answer is currently and may for all time be unknown. There is nothing
worse than writing yourself into a corner where your only exit is to build a door by
solving unsolved problems. In any case, it is my hope that you will read this volume
and come away thinking that I have overcome enough of those obstacles to make the book
worthwhile. As always, your comments and criticisms are welcome. Feel free to contact
me using any of the addresses listed below, although e-mail is the preferred method.

**Category:** Number Theory

[213] **viXra:1003.0219 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Charles Ashbacher

**Comments:** 135 pages

This is the fifth book that I have written that expands on the ideas of Florentin
Smarandache. In addition, I have edited two others that also deal with the areas of
mathematics under the Smarandache Notions umbrella. All of this is a credit to the
breadth and depth of his mathematical achievement. Therefore, I once again must
commend and thank him for providing so much material to work with. I also would like
to thank J. McGray for her encouragement and patience as I struggled to make this book
a reality. The material cited in this book can be found at the website
http://www.gallup.unm.edu/~smarandache/.
The deepest thanks go to my mother Paula Ashbacher, who encouraged me to play sports,
but in the off chance that I would never learn to hit the curve ball, also insisted that I read
books. This proved to be a wise career strategy.
Finally, I would like to express my deep love for Kathy Brogla, my partner/soul
mate/best friend. So pretty and vivacious, she makes life fun, exciting and a joy to
experience every single day. She is a remarkable woman and I am so blessed to have her
in my life. Kathy is also the creator of the image on the front cover.

**Category:** Number Theory

[212] **viXra:1003.0218 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** L. Stephen Young

**Comments:** 44 pages

The Smarandache Quantum Paradoxes ["Nature", Vol. 413, No. 6854] and Smarandache
Hypothesis (FTL) are defined as a formal set of (anti-logic) statements inclusive in modern
quantum theory. To determine whether they constitute theoretical artifacts or can be considered
true physical paradoxes, G Dimensional Theory, a unique, logical and physically congruent
system of physics, at significant variance with modern and classical theory, is presented in
Sections 3-4. A comparative analysis of the Smarandache quantum paradoxes within context of
the two theories follows in Section 5.

**Category:** Quantum Physics

[211] **viXra:1003.0217 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** Henry Ibstedt

**Comments:** 97 pages

This book consists of a selection of papers most of which were produced
during the period 1999-2002. They have been inspired by questions raised in
recent articles in current Mathematics journals and in Florentin Smarandache's
wellknown publication Only Problems, Not Solutions.

**Category:** Number Theory

[210] **viXra:1003.0216 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** C. Dumitrescu, V. Seleacu

**Comments:** 137 pages

The function named in the title of this book is originated from the
exiled Romanian mathematician Florentin Smarandache.

**Category:** Number Theory

[209] **viXra:1003.0215 [pdf]**
*replaced on 6 Mar 2010*

**Authors:** Titu Popescu

**Comments:** 100 pages, v1 in Romainian, V2 in English Translated by P. Georgelin, F. Smarandache, and L. Popescu

In the history of thought and creation, the decisive events, the great and significant
moments, the strongly affirmative stages - then the imposition of the optimizing novelties - have
depended on the name and prestige of a personality. Referring to those, we personalize further on.
The examples are extremely numerous, even in our nearest past. When we mention a creation - in
the largest sense of the term - with the name of the personality who illustrates it most extensively
at a given time, we state precisely the specific importance of it; we give it, with other words, the
identity to which we can refer continuously with full knowledge and without causing any
confusion among the receivers. The facts are called with the name of the man who produced
them, and in this way we can compose a parallel onomastic dictionary, in which the work is
included in the person's space, keeping its content. The consecrated proper names evolve through
quickly imposed habits, a large range of increments that announce the essential outline of their
peak production. No space for ambiguity remains when we address to readers or listeners who are
somewhat acquainted with the subject and we use such terms as Aristotelianism, Platonism,
Kantianism, Hegelianism, Proustianism, Eminescianism, Barbianism, etc. We have even the
advantage of a centered communication when we suggest with a sole notion the work as well as
its dominant features, linked with the renown of the concerned author.

**Category:** History and Philosophy of Physics

[208] **viXra:1003.0214 [pdf]**
*submitted on 18 Mar 2010*

**Authors:** N. Mebarki, M. Boussahel

**Comments:** 38 pages

A classical gauge model based on the Lie group SU(3)_{L} X U(1)_{N}
with exotic quarks is reformulated within the formalism of non-associative
geometry associated to an L-cycle. The N charges of the fermionic
particles and the related parameters constraints are uniquely
determinedalgebraic consequences. Moreover, the number of scalar particles are dictated
by the non-associativity of the geometry. As a byproduct of this
formalism, the scalar, charged and neutral gauge bosons masses as well as the
mixing angles are derived. Furthermore, various expressions of the
vector and axial couplings of the quarks and leptons with the neutral gauge
bosons and lower bounds of the very heavy gauge bosons are also obtained.

**Category:** High Energy Particle Physics

[207] **viXra:1003.0213 [pdf]**
*submitted on 18 Mar 2010*

**Authors:** Zhang Wenpeng

**Comments:** 1 page

Fermat's and Euler's theorem on congruencies are generalized to the case when the integers a
and m are not necessarily co-prime.

**Category:** Relativity and Cosmology

[206] **viXra:1003.0212 [pdf]**
*submitted on 18 Mar 2010*

**Authors:** Golden Gadzirayi Nyambuya

**Comments:** 12 pages, 2 figures, submitted to MNRAS-MJ.

In this reading, a new theoreticalmodel of star and cluster formation is posited. Thismodel seeks
to set a mathematical framework to understand the origins of the stellar Initial Mass Function
and within this framework, explain star and cluster formation from a unified perspective by tieing
together into a single garment three important observational facts: (1) that the most massive
stars of most observed clusters of stars are preferentially found in their centers; (2) Larson's
1982 empirical observation that the maximum stellar mass is related to the total mass of the
parent cloud; (3) that clump masses in giant molecular clouds exhibit a power mass spectrum
law akin to that found in star clusters and this behavior is also true for molecular clouds as well.
Key to this model is the way the cloud fragments to form cores from which the new stars are
born. We show that the recently proposed azimuthally symmetric theory of gravitation has two
scale of fragmentation where one is the scale that leads to cloud collapse and the other is the
scale on which the cloud fragments. The collapse and fragmentation takes place simultaneously.
If the proposed model is anything to go by, then, one can safely posit that the slope of the IMF
can be explained from two things: the star formation rate of the cores from which these stars
form and the density index describing the density profile. Additionally and more importantly,
if the present is anything to by, then, fragmentation of molecular clouds is posited as being a
result of them possessing some spin angular momentum.

**Category:** Relativity and Cosmology

[205] **viXra:1003.0211 [pdf]**
*submitted on 18 Mar 2010*

**Authors:** Tong Xin Ping

**Comments:** 4 Pages, In Chinese

We have sieve method formula of π(N) and sieve method formula of r^{2}(N). By these
sieve method formula, we can obtain (see paper for equation)

**Category:** Number Theory

[204] **viXra:1003.0210 [pdf]**
*submitted on 18 Mar 2010*

**Authors:** Roald C. Maximo

**Comments:** 3 pages

In this short essay, I am starting from very basic concepts to try, step by step, to establish a valid
physical relation between speed, energy and time. My intention, just from the start, is to by pass the Theory of
Relativity and also avoid the application of the Lorentz transformation as canned good. If it has to be part of
the solution it shall also arise spontaneously during the formulations as it ended up being the case.

**Category:** Relativity and Cosmology

[203] **viXra:1003.0209 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 461 pages

This second book devoted on advances and applications of Dezert-Smarandache Theory
(DSmT) for information fusion collects recent papers from different researchers working in
engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical
investigations while, Part 2 presents several applications of this new theory. Some ideas
in this book are still under current development or improvements, but we think it is important
to propose them in order to share ideas and motivate new debates with people interested in
new reasoning methods and information fusion. So, we hope that this second volume on DSmT
will continue to stir up some interests to researchers and engineers working in data fusion and
in artificial intelligence.

**Category:** Artificial Intelligence

[202] **viXra:1003.0208 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 438 pages

This book is devoted to an emerging branch of Information Fusion based on new approach for modelling
the fusion problematic when the information provided by the sources is both uncertain and
(highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache
Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT
from the beginning to the latest development. Part 1 of this book presents the current state-of-the-art on
theoretical investigations while Part 2 presents several applications of this new theory. We hope that this
first book on DSmT will stir up some interests to researchers and engineers working in data fusion and in
artificial intelligence. Many simple but didactic examples are proposed throughout the book. As a young
emerging theory, DSmT is probably not exempt from improvements and its development will continue to
evolve over the years. We just want through this book to propose a new look at the Information Fusion
problematic and open a new track to attack the combination of information.

**Category:** Artificial Intelligence

[201] **viXra:1003.0205 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 8 pages

In a number of preceding papers we introduced a new PT-symmetric periodic potential, derived
from biquaternion radial Klein-Gordon equation. In the present paper we will review our
preceding result, and continue with numerical solution of Gamow integral for that periodic
potential. And then we also compare with other periodic potentials which are already known,
such as Posch-Teller or Rosen-Morse potential. We also discuss a number of recent development
in the context of condensed matter nuclear science, in particular those experiments which are
carried out by Prof. A. Takahashi and his team from Kobe University. There is hint to describe
his team's experiment as 'mesofusion' (or mesoscopic fusion). We then analyze possibility to
enhance the performance of Takahashi's mesofusion experiment under external pulse field.
Further experiments are of course recommended in order to verify or refute the propositions
outlined herein.

**Category:** Quantum Physics

[200] **viXra:1003.0204 [pdf]**
*replaced on 2014-03-13 04:08:55*

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

**Comments:** 3 Pages.

A new type of potential for nucleus, which is different from Coulomb potential or Yukawa potential. This new potential may have effect for radius range within r = 5 - 10 fm.

**Category:** General Mathematics

[199] **viXra:1003.0203 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 6 pages

In recent years there are new interests on special symmetry
in physical systems, called PT-symmetry with various ramifications.
Along with the isodual symmetry popularized by RM
Santilli, these ideas form one of cornerstone in hadron physics.
In the present article, we argue that it is plausible to generalise
both ideas to become iso-PT symmetry which indicate there
should be new potential obeying this symmetry. We also discuss
some possible interpretation of the imaginary solution of
the solution of biquaternionic KGE (BQKGE); which indicate
the plausible existence of the propose iso-PT symmetry. Further
observation is of course recommended in order to refute or verify
this proposition.

**Category:** Quantum Physics

[198] **viXra:1003.0202 [pdf]**
*submitted on 17 Mar 2010*

**Authors:** James R. Bogan

**Comments:** 7 pages

We suggest discovery targets for the Higgs boson and a Tev mass scale for quantum gravity,
in terms of the cosmological constant, and ultimately, the electron.

**Category:** High Energy Particle Physics

[197] **viXra:1003.0201 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 96 pages

Nowadays, plenty of factories from Europe and other developed countries have been relocated
to this country, considering its tremendous economic scale and rapid growth rate during the
past three decades.
But most of what happens inside the China nowadays is deeply hidden from the outside world
("the foreigners" as China people would call). This fact is partly because most reports on
China were written by the so-called fly-high experts who are busy completing their reports
despite a busy schedule. Very few books or reports were written by people inside, or at least
"foreigners" who spent a few years in China. Therefore in this book, we took a different approach,
by inviting local scientists and other writers to describe what happens surround them.

**Category:** Economics and Finance

[196] **viXra:1003.0200 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 63 pages

After more than a decade Michael Porter's book Competitive
Advantage of Nations stays ahead of the other books, in
particular as alternative framework from the comparative
advantage idea inspired by Adam Smith.
This small book is merely an alternative proposition, a
postscript perhaps, to Porter's book, with basic idea that one
cannot rely merely on industrial processes alone to keep
stay ahead of market changes. Hence, for cities in
developing countries the municipal shall find out their city's
best resources, and develop their city starting from there,
instead of striving blindly in the conventional industrial path.

**Category:** Economics and Finance

[195] **viXra:1003.0199 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 206 pages

Historically a code refers to a cryptosystem that deals with
linguistic units: words, phrases etc. We do not discuss such
codes in this book. Here codes are message carriers or
information storages or information transmitters which in time
of need should not be decoded or read by an enemy or an
intruder. When we use very abstract mathematics in using a
specific code, it is difficult for non-mathematicians to make use
of it. At the same time, one cannot compromise with the
capacity of the codes. So the authors in this book have
introduced several classes of codes which are explained very
non-technically so that a strong foundation in higher
mathematics is not needed. The authors also give an easy
method to detect and correct errors that occur during
transmission. Further some of the codes are so constructed to
mislead the intruder. False n-codes, whole n-codes can serve
this purpose.

**Category:** Number Theory

[194] **viXra:1003.0198 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

TSix conjectures on pairs of consecutive primes are listed below together with
examples in each case.

**Category:** Number Theory

[193] **viXra:1003.0197 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Aloïs Kirchnera, Frédéric Dambrevilleb, Francis Celeste, Florentin Smarandache, Jean Dezert

**Comments:** 9 pages

This paper defines and implements a non-Bayesian
fusion rule for combining densities of probabilities estimated
by local (non-linear) filters for tracking a moving target by
passive sensors. This rule is the restriction to a strict probabilistic
paradigm of the recent and efficient Proportional Conflict Redistribution
rule no 5 (PCR5) developed in the DSmT framework
for fusing basic belief assignments. A sampling method for
probabilistic PCR5 (p-PCR5) is defined. It is shown that
p-PCR5 is more robust to an erroneous modeling and allows to
keep the modes of local densities and preserve as much as
possible the whole information inherent to each densities to
combine. In particular, p-PCR5 is able of maintaining multiple
hypotheses/modes after fusion, when the hypotheses are too
distant in regards to their deviations. This new p-PCR5 rule has
been tested on a simple example of distributed non-linear filtering
application to show the interest of such approach for future
developments. The non-linear distributed filter is implemented
through a basic particles filtering technique. The results obtained
in our simulations show the ability of this p-PCR5-based filter
to track the target even when the models are not well consistent
in regards to the initialization and real cinematic.
Keywords: Filtering, Robust estimation, non-Bayesian fusion
rule, PCR5, Particle filtering.

**Category:** Artificial Intelligence

[192] **viXra:1003.0196 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 13 pages

In this paper we extend the new family of (quantitative) Belief Conditioning Rules (BCR) recently
developed in the Dezert-Smarandache Theory (DSmT) to their qualitative counterpart for belief revision. Since
the revision of quantitative as well as qualitative belief assignment given the occurrence of a new event (the
conditioning constraint) can be done in many possible ways, we present here only what we consider as the most
appealing Qualitative Belief Conditioning Rules (QBCR) which allow to revise the belief directly with words and
linguistic labels and thus avoids the introduction of ad-hoc translations of quantitative beliefs into quantitative
ones for solving the problem.

**Category:** Artificial Intelligence

[191] **viXra:1003.0195 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Xin-De Li, Xinhan Huang, Florentin Smarandache, Jean Dezert

**Comments:** 12 pages

This paper deals with enriched qualitative belief functions for reasoning under uncertainty and for
combining information expressed in natural language through linguistic labels. In this work, two possible enrichments
(quantitative and/or qualitative) of linguistic labels are considered and operators (addition, multiplication,
division, etc) for dealing with them are proposed and explained. We denote them qe-operators, qe standing for
"qualitative-enriched" operators. These operators can be seen as a direct extension of the classical qualitative
operators (q-operators) proposed recently in the Dezert-Smarandache Theory of plausible and paradoxist reasoning
(DSmT). q-operators are also justified in details in this paper. The quantitative enrichment of linguistic label
is a numerical supporting degree in [0,∞), while the qualitative enrichment takes its values in a finite ordered
set of linguistic values. Quantitative enrichment is less precise than qualitative enrichment, but it is expected
more close with what human experts can easily provide when expressing linguistic labels with supporting degrees.
Two simple examples are given to show how the fusion of qualitative-enriched belief assignments can be done.

**Category:** Artificial Intelligence

[190] **viXra:1003.0194 [pdf]**
*submitted on 16 Mar 2010*

**Authors:** Andrew Beckwith

**Comments:** A. Yurov; arXiv : hep-th/028129 v1, 19 Aug, 2002
material added to the analysis presented in S.A. at Beyond the Standard Model. 50 pages

presentation of 7 new pages with respect to linkage between 1st and 2nd inflation, 1st 10^{-35} seconds
after big bang, and 2nd one billion years ago

**Category:** Relativity and Cosmology

[189] **viXra:1003.0193 [pdf]**
*replaced on 29 Mar 2010*

**Authors:** Andrew Beckwith

**Comments:** 16 pages, four figures. Re statement of prior submission, with specific
commentary as given in Appendix B, and also the radius of the Universe question , as
can be ascertained via modeling included. This material added, to make presentation
conform more closely to the Xian, PRC PIERS presentation given in 2010, March 22, at
11 a.m. which did emphasize, at the end the importance of material in Appendix B, as
well as the given conclusion, and the radius of the Universe question, as of Eq. (38),
as very important to applications of GW/ graviton based astronomy/ astro physics.
Appendix B in particular delves into how massless graviton Field equations, and their
small mass graviton versions do not connect, in the limit of mass of a graviton
approaching zero.

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe
in five dimensions is stated; with emphasis upon if five dimensional geometries as given below give
us new physical insight as to cosmological evolution. A calculated inflaton φ(t) may partly reemerge
after fading out in the aftermath of inflation. The inflaton 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 at red shit value of Z ~ .423. A final statement as to how and why the radius of the
universe question may be affected by these deliberations is presented , in terms of if the graviton is
either purely a field theoretic , or semi classical object, as via t'Hoofts deterministic QM is presented
in the end, as an open question.

**Category:** Relativity and Cosmology

[188] **viXra:1003.0192 [pdf]**
*replaced on 19 Aug 2011*

**Authors:** Victor Porton

**Comments:** 53 pages

It is a part of my Algebraic General Topology research.
In this article, I introduce the concepts of funcoids, which generalize proximity spaces
and reloids, which generalize uniform spaces. The concept of funcoid is generalized concept
of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of
uniformity. Also funcoids generalize pretopologies and preclosures. Also funcoids and reloids
are generalizations of binary relations whose domains and ranges are filters (instead of sets).
Also funcoids and reloids can be considered as a generalization of (oriented) graphs, this
provides us with a common generalization of analysis and discrete mathematics. The concept of continuity is defined by an algebraic formula (instead of old messy epsilondelta notation) for arbitrarymorphisms (including funcoids and reloids) of a partially ordered category. In one formula are generalized continuity, proximity continuity, and uniform continuity.

**Category:** Topology

[187] **viXra:1003.0191 [pdf]**
*submitted on 16 Mar 2010*

**Authors:** Leonid I. Filippov

**Comments:** In Russian, 33 pages, 12 figures

Determination to make the Einstein's treatment of simultaneity and relativistic notions of
length and time interval measurement more intuitive and illustrative led to creation of a
model in which light impulses are substituted with sound signals. The model uncovers the
substance of Einstein's mathematical constructs and the mechanisms that give rise to relativistic
effects. Consistent application of the model resulted in new constructions.
The paper examines known mechanical and electromagnetic phenomena that can be clarified by
this model. The use of such an approach leads to the notion of a distinguished frame of
reference. In particular, the theory calls for the existence of electromagnetic interaction
that contradicts the principle of relativity. The paper contains a description of an
experimental apparatus built to test this prediction, as well as the results of the experiments.

**Category:** Relativity and Cosmology

[186] **viXra:1003.0190 [pdf]**
*submitted on 16 Mar 2010*

**Authors:** Ervin Goldfain

**Comments:** 1 page, Published in "Progress in Physics" vol. 3 (2008).

The possibility of a hidden sector of particle physics that lies beyond the energy range of
the Standard Model has been recently advocated by many authors. A bizarre implication
of this conjecture is the emergence of a continuous spectrum of massless fields with
non-integral scaling dimensions called "un-particles". The purpose of this Letter is to
show that the idea of "un-particles" was considered in at least two previous independent
publications, prior to its first claimed disclosure.

**Category:** High Energy Particle Physics

[185] **viXra:1003.0189 [pdf]**
*submitted on 16 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 13 pages

Santilli's prime chains: (see paper for equations) There exist infinitely many primes such that are
primes for arbitrary length .
It is the Book proof. This is a generalization of Euclid-Euler proof for the existence of
infinitely many primes. Therefore Euclid-Euler-Jiang theorem in the distribution of primes is
advanced. It is the Book theorem.

**Category:** Number Theory

[184] **viXra:1003.0188 [pdf]**
*submitted on 16 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 5 pages

Using Jiang's function we prove that there are infinitely many primes such that 3P-2 and 3P+2 are primes.

**Category:** Number Theory

[183] **viXra:1003.0187 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Mihály Bencze, Florin Popovici, Florentin Smarandache

**Comments:** 5 pages

In this article we present a generalization of a Leibniz's theorem in geometry and
an application of this.

**Category:** Geometry

[182] **viXra:1003.0186 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Mihály Bencze, Florentin Smarandache

**Comments:** 8 pages

In this paper we present some new inequalities relative to
integer and functional parts.

**Category:** Number Theory

[181] **viXra:1003.0185 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 8 pages

The present note revised the preceding article discussing new
discovery of a new planetoid in the solar system. Some recent
discoveries have been included, and its implications in the
context of quantization of celestial system are discussed, in
particular from the viewpoint of superfluid dynamics. In
effect, it seems that there are reasons to argue in favor of
gravitation-related phenomena from boson condensation.

**Category:** Astrophysics

[180] **viXra:1003.0184 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 11 pages

Despite the economics jargon on 'rational choice', nowadays the entire world has nothing else to choose except to
succumb under the spell of magic words of modern economics, i.e. 'neoliberalism', 'financial liberalization', 'free
market' (laissez-faire), and 'globalization'. All of these can be shown to be part of a preconception, i.e. far beyond
the 'neutral' idea of natural sciences.
In Fritjof Capra's book 'Turning Point' (Bantam Books, 1982) these phenomena are summarized as follows:
economics thinking have started by assuming that in economics sciences one can achieve the same generality and
universality that physicists enjoy in doing Natural Sciences. In other words, economists try to become through their
work 'hard science' rather than recognizing that in economics the subject of their study is human/people which is
far from being predictable, either as individual or as society.
In our humble opinion, economics is a mixture of both, hard and soft sciences. In order to show this, we introduce
a new study, called Poly-Emporium Theory, where we show that phenomena from hard science and soft science
co-exist and interact in economics. Poly-Emporium Theory is the study of interactions among many (big and small)
firms in the market, and it is different from oligopoly since poly-emporium takes into consideration the small firms
too (not only the big firms that dominate the market as in oligopoly).
The above logic of thinking is the starting point to submit a new idea, under the heading of 'Cultural Advantage.'
The first book in the series has title: Cultural Advantage for Cities: An alternative for Developing Countries. This
presentation summarizes its basic ideas, with a hope that these ideas may be found interesting to develop further.
For clarity the readers are referred to the book.

**Category:** Economics and Finance

[179] **viXra:1003.0183 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

In this paper problem of testing of hypothesis is discussed when the samples
have been drawn from normal distribution. The study of hypothesis testing
is also extended to Baye's set up.

**Category:** Statistics

[178] **viXra:1003.0182 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 22 pages

Jaipur urban area has grown tremendously in last three decades. Composition
of People migrating due to various reasons has display a meticulous trend.
Dominance of people moving due to marriages is getting sturdy whereas
Jaipur city is losing its luster in attracting persons for education and business.
Short duration migration from Jaipur district to urban area has gone down to a
very low level. Flow of migrants from Rural areas to Jaipur outpaced the
migrants from urban areas and its composition from various in terms long and
short distances migration has substantially changed over two consecutive
decades. Movements of males and females were differ on many criterion as
male moving faster than females for employment & education and females
move faster than male for marriages and moving along family was found
evident in short, medium and long distances migration. Gender gap in people
migration from different reasons was observed and a gender specific trend
was seen favour. Short duration migration and migration due to education &
employment is not as prominence as it was two decade back

**Category:** Social Science

[177] **viXra:1003.0181 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 41 pages

In this paper we propose five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together
with several examples. From PCR1 to PCR2, PCR3, PCR4, PCR5 one increases the complexity of the rules and also the exactitude
of the redistribution of conflicting masses. PCR1 restricted from the hyper-power set to the power set and without degenerate cases
gives the same result as the Weighted Average Operator (WAO) proposed recently by Jøsang, Daniel and Vannoorenberghe but does
not satisfy the neutrality property of vacuous belief assignment. That's why improved PCR rules are proposed in this paper. PCR4 is
an improvement of minC and Dempster's rules. The PCR rules redistribute the conflicting mass, after the conjunctive rule has been
applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix.
There are infinitely many ways these functions (weighting factors) can be chosen depending on the complexity one wants to deal with
in specific applications and fusion systems. Any fusion combination rule is at some degree ad-hoc.

**Category:** Artificial Intelligence

[176] **viXra:1003.0180 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** C. Dumitrescu, N. Vîrlan, Şt. Zamfir, E. Rădescu, N. Rădescu, Florentin Smarandache

**Comments:** 15 pages

In this paper we extended the Smarandache function from the set N* of
positive integers to the set Q of rational numbers.
Using the inversion formula, this function is also regarded as a generating
function. We put in evidence a procedure to construct a (numerical) function starting
from a given function in two particular cases. Also connections between the
Smarandache function and Euler's totient function as with Riemann's zeta function are
established.

**Category:** Number Theory

[175] **viXra:1003.0179 [pdf]**
*replaced on 16 Jul 2010*

**Authors:** Jongsoo Park

**Comments:** 76 pages

Ben Green and Terence Tao showed that for any positive integer k, there exist infinitely many
arithmetic progressions of length k consisting only of prime numbers. [14] Four parallel proofs of Szemer'edi's
theorem have been achieved; one by direct combinatorics, one by ergodic theory, one by hypergraph theory, and
one by Fourier analysis and additive combinatorics. Even with so many proofs, Professor T. Tao points out that
with this problem, there remains a sense that our understanding of this result is incomplete; for instance, none of
the approaches were powerful enough to detect progressions in the primes, mainly due to the sparsity of the
prime sequence. [22] Oliver Lonsdale Atkin introduced a prime sieve using irreducible binary quadratic forms
and modular arithmetic; the algorithm enumerates representations of integers by certain binary quadratic forms.
A way that uses modular arithmetic is widely known: 6n+δ, 12n+δ, 30n+δ, 60n+δ.[31] In this paper,
we assert that the composite number of the 12n+1, 5, 7, 11 series as selected by a Modular Arithmetic and
Multiplication Table are not random but consist of very structural and regular arithmetic progression groups.

**Category:** Number Theory

[174] **viXra:1003.0178 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

The utility of this article is that it establishes if the number of the natural solutions
of a general linear equation is limited or not. We will show also a method of solving,
using integer numbers, the equation ax - by = c (which represents a generalization of
lemmas 1 and 2 of [4]), an example of solving a linear equation with 3 unknowns in N,
and some considerations on solving, using natural numbers, equations with n unknowns.

**Category:** Number Theory

[173] **viXra:1003.0177 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

In this article we present four necessary and sufficient conditions for a
natural number to be prime.

**Category:** Number Theory

[172] **viXra:1003.0176 [pdf]**
*submitted on 15 Mar 2010*

**Authors:** Willi Penker

**Comments:** 3 pages

The theory of black holes states that without the energy set
free by nuclear fusion, the gravity of a big star will always be
stronger than all other forces, causing it to collapse and
ending in a singularity. During such a collapse, however,
gravity itself should free enough binding energy to ultimately
prevent the star from collapsing to a state where its escape
velocity reaches the speed of light.

**Category:** Relativity and Cosmology

[171] **viXra:1003.0175 [pdf]**
*submitted on 15 Mar 2010*

**Authors:** Jonathan J. Dickau

**Comments:** 6 pages, The author notes that revisions are needed for this paper to be rigorously
accurate, but wishes to foster conversation on this topic.

Both researchers and educators have expressed displeasure with the definition of entropy as a
measure of disorder. Instead, it is argued by Leff, Lambert, and others that the increase of
entropy can be far more accurately described using terms such as 'dispersal of energy,' 'spreading
and sharing of energy,' and 'spatial and temporal spreading.' In decoherence theory, a similar
metaphor is used to describe the phenomena involved with quantum non-locality, superposition,
and entanglement. Specifically the wavefunction of a quantum entity, such as a sub-atomic particle
or photon is not seen to collapse but rather is transferred through interactions to a system and/or
its environment. This suggests there may be a common basis for entropy and non-locality. I explore
the idea that energy is motive and extensive by nature, and that all its forms of expression
involve motion, action, and propagation, which clearly leads to its being spread and shared when
unconstrained, among the available microstates of its local system and the larger environment. Thus
a single description, focusing on this universal quality of energy, explains both 2nd Law entropy
and quantum non-locality.

**Category:** Quantum Physics

[170] **viXra:1003.0174 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jose L. Salmeron, Florentin Smarandache

**Comments:** 12 pages

For academics and practitioners concerned with computers, business and
mathematics, one central issue is supporting decision makers. In this paper, we
propose a generalization of Decision Matrix Method (DMM), using Neutrosophic
logic. It emerges as an alternative to the existing logics and it represents a
mathematical model of uncertainty and indeterminacy. This paper proposes the
Neutrosophic Decision Matrix Method as a more realistic tool for decision
making. In addition, a de-neutrosophication process is included.

**Category:** Artificial Intelligence

[169] **viXra:1003.0173 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 44 pages

This is a collection of linguistic-mathematical approaches to Romanian rebus, poetical
and juridical texts, and proposes fancies, recreational math problems, and paradoxes. We
study the frequencies of letters, syllables, vowels in various poetry, grill definitions in
rebus, and rebus rules. We also compare the scientific language, lyrical language, and
puzzles' language, and compute the Shannon entropy and Onicescu informational energy.

**Category:** Linguistics

[168] **viXra:1003.0172 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 11 pages

A general family of estimators for estimating the population mean of the variable
under study, which make use of known value of certain population parameter(s), is proposed.
Under Simple Random Sampling Without Replacement (SRSWOR) scheme, the expressions of
bias and mean-squared error (MSE) up to first order of approximation are derived. Some well
known estimators have been shown as particular member of this family. An empirical study is
carried out to illustrate the performance of the constructed estimator over others.

**Category:** Statistics

[167] **viXra:1003.0171 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

In this paper we give two theorems from the Propositional Calculus of the
Boolean Logic with their consequences and applications and we prove them
axiomatically.

**Category:** Set Theory and Logic

[166] **viXra:1003.0170 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 18 pages

By using the arithmetic function J_{2n+1}(ω) we prove that Diophantine equation
(see paper) has infinitely many prime solutions.It is the Book proof. The J_{2n+1}(ω) ushers in a new
era in the prime numbers theory.

**Category:** Number Theory

[165] **viXra:1003.0169 [pdf]**
*submitted on 14 Mar 2010*

**Authors:** A.G. Kyriakos

**Comments:** 12 Pages.

Two possibilities of the quantum theory construction, indicated by Feynman, are examined.
The special features of the structure of the Standard Model (SM) are enumerated, which attest to
the fact that SM is not an axiomatic, but an algorithmic theory. Deficiencies of SM and
possibilities of overcoming these deficiencies are indicated. The structure of the nonlinear
quantum field theory (NQFT) as an axiomatic theory, which makes it possible to overcome
deficiencies in the Standard Model, is presented.

**Category:** High Energy Particle Physics

[164] **viXra:1003.0168 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

In this article we will widen the concepts of "binomial coefficients" and
"trinomial coefficients" to the concept of "k-nomial coefficients", and one
obtains some general properties of these. As an application, we will
generalize the" triangle of Pascal".

**Category:** Algebra

[163] **viXra:1003.0167 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 7 pages

In this article one builds a class of recursive sets, one establishes
properties of these sets and one proposes applications. This article widens
some results of [1].

**Category:** Set Theory and Logic

[162] **viXra:1003.0166 [pdf]**
*replaced on 20 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 7 pages

A great number of articles widen known scientific results (theorems, inequalities,
math/physics/chemical etc. propositions, formulas), and this is due to a simple procedure,
of which it is good to say a few words:
Let suppose that we want to generalizes a known mathematical proposition P(a) ,
where a is a constant, to the proposition P(n) , where n is a variable which belongs to
subset of N .
To prove that P is true for n by recurrence means the following: the first step is
trivial, since it is about the known result P(a) (and thus it was already verified before by
other mathematicians!). To pass from P(n) to P(n + 1) , one uses too P(a) : therefore one
widens a proposition by using the proposition itself, in other words the found
generalization will be paradoxically proved with the help of the particular case from
which one started!
We present below the generalizations of Hölder, Minkovski, and respectively
Tchebychev inequalities.

**Category:** Functions and Analysis

[161] **viXra:1003.0165 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 19 pages

Description Logics (DLs) are appropriate, widely used, logics for managing structured
knowledge. They allow reasoning about individuals and concepts, i.e. set of individuals
with common properties. Typically, DLs are limited to dealing with crisp, well defined
concepts. That is, concepts for which the problem whether an individual is an instance of
it is a yes/no question. More often than not, the concepts encountered in the real world do
not have a precisely defined criteria of membership: we may say that an individual is an
instance of a concept only to a certain degree, depending on the individual's properties.
The DLs that deal with such fuzzy concepts are called fuzzy DLs. In order to deal
with fuzzy, incomplete, indeterminate and inconsistent concepts, we need to extend the
capabilities of fuzzy DLs further.
In this paper we will present an extension of fuzzy ALC, combining Smarandache's
neutrosophic logic with a classical DL. In particular, concepts become neutrosophic (here
neutrosophic means fuzzy, incomplete, indeterminate and inconsistent), thus, reasoning
about such neutrosophic concepts is supported. We will define its syntax, its semantics,
describe its properties and present a constraint propagation calculus for reasoning in it.

**Category:** Artificial Intelligence

[160] **viXra:1003.0164 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 7 pages

In these paragraphs one presents three generalizations of the famous theorem of
Ceva

**Category:** Geometry

[159] **viXra:1003.0163 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 7 pages

In the paragraphs which follow we will prove a result which replaces the theorem
of Euler: "If (a,m) = 1, then a^{φ(m)} = 1 (mod m)",
for the case when a and m are not relatively primes.

**Category:** Number Theory

[158] **viXra:1003.0162 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

In this short note we will prove a generalization of Joung's theorem in space.

**Category:** Geometry

[157] **viXra:1003.0161 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 11 pages

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of
information has always been and still remains of primal importance for the development of reliable information fusion systems.
In this short survey paper, we present the theory of plausible and paradoxical reasoning, known as DSmT (Dezert-Smarandache
Theory) in literature, developed for dealing with imprecise, uncertain and potentially highly conflicting sources of information.
DSmT is a new paradigm shift for information fusion and recent publications have shown the interest and the potential ability
of DSmT to solve fusion problems where Dempster's rule used in Dempster-Shafer Theory (DST) provides counter-intuitive
results or fails to provide useful result at all. This paper is focused on the foundations of DSmT and on its main rules of combination
(classic, hybrid and Proportional Conflict Redistribution rules). Shafer's model on which is based DST appears as a
particular and specific case of DSm hybrid model which can be easily handled by DSmT as well. Several simple but illustrative
examples are given throughout this paper to show the interest and the generality of this new theory.

**Category:** Artificial Intelligence

[156] **viXra:1003.0159 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 21 pages

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of
information has always been, and still remains today, of primal importance for the development of reliable modern information systems
involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning,
known as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and paradoxical
sources of information. We focus our presentation here rather on the foundations of DSmT, and on the two important new rules of
combination, than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the
presentation to show the efficiency and the generality of this new approach.

**Category:** Artificial Intelligence

[155] **viXra:1003.0158 [pdf]**
*replaced on 2 Apr 2010*

**Authors:** Giuliano Bettini

**Comments:** 17 pages, slightly amended

Examines the possibility of a purely electromagnetic formation of the physical world,
and in particular electron.
For this purpose presents a number of parallels between elementary particles and
radar signals and radar target.

**Category:** Quantum Physics

[154] **viXra:1003.0157 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 13 pages

This paper introduces the notion of qualitative belief assignment to model beliefs of human experts
expressed in natural language (with linguistic labels). We show how qualitative beliefs can be efficiently combined
using an extension of Dezert-Smarandache Theory (DSmT) of plausible and paradoxical quantitative reasoning
to qualitative reasoning. We propose a new arithmetic on linguistic labels which allows a direct extension of
classical DSm fusion rule or DSm Hybrid rules. An approximate qualitative PCR5 rule is also proposed jointly
with a Qualitative Average Operator. We also show how crisp or interval mappings can be used to deal indirectly
with linguistic labels. A very simple example is provided to illustrate our qualitative fusion rules.

**Category:** Artificial Intelligence

[153] **viXra:1003.0156 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Albena Tchamova, Florentin Smarandache, Pavlina Konstantinova

**Comments:** 10 pages

In this paper we consider and analyze the behavior of two combinational rules for temporal (sequential)
attribute data fusion for target type estimation. Our comparative analysis is based on Dempster's
fusion rule proposed in Dempster-Shafer Theory (DST) and on the Proportional Conflict Redistribution rule no.
5 (PCR5) recently proposed in Dezert-Smarandache Theory (DSmT). We show through very simple scenario
and Monte-Carlo simulation, how PCR5 allows a very efficient Target Type Tracking and reduces drastically the
latency delay for correct Target Type decision with respect to Demspter's rule. For cases presenting some short
Target Type switches, Demspter's rule is proved to be unable to detect the switches and thus to track correctly
the Target Type changes. The approach proposed here is totally new, efficient and promising to be incorporated
in real-time Generalized Data Association - Multi Target Tracking systems (GDA-MTT) and provides an important
result on the behavior of PCR5 with respect to Dempster's rule. The MatLab source code is provided in
[5].

**Category:** Artificial Intelligence

[152] **viXra:1003.0155 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jose L. Salmeron, Florentin Smarandache

**Comments:** 13 pages

IS projects success is a complex concept, and its evaluation is complicated, unstructured
and not readily quantifiable. Numerous scientific publications address the issue of
success in the IS field as well as in other fields. But, little efforts have been done for
processing indeterminacy and uncertainty in success research. This paper shows a
formal method for mapping success using Neutrosophic Success Map. This is an
emerging tool for processing indeterminacy and uncertainty in success research. EIS
success have been analyzed using this tool.

**Category:** Artificial Intelligence

[151] **viXra:1003.0154 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 20 pages

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of
information has always been, and still remains today, of primal importance for the development of reliable modern information systems
involving artificial reasoning. In this chapter, we present a survey of our recent theory of plausible and paradoxical reasoning, known
as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and paradoxical sources of
information. We focus our presentation here rather on the foundations of DSmT, and on the two important new rules of combination,
than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the presentation
to show the efficiency and the generality of this new approach. The last part of this chapter concerns the presentation of the neutrosophic
logic, the neutro-fuzzy inference and its connection with DSmT. Fuzzy logic and neutrosophic logic are useful tools in decision making
after fusioning the information using the DSm hybrid rule of combination of masses.

**Category:** Artificial Intelligence

[150] **viXra:1003.0153 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

In this short note many conjectures on partitions of integers as summations of prime
numbers are presented, which are extension of Goldbach conjecture.

**Category:** Number Theory

[149] **viXra:1003.0152 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache, Milan Daniel

**Comments:** 11 pages

This paper presents in detail the generalized pignistic transformation (GPT) succinctly developed in the Dezert-Smarandache
Theory (DSmT) framework as a tool for decision process. The GPT allows to provide a subjective probability measure from any generalized
basic belief assignment given by any corpus of evidence. We mainly focus our presentation on the 3D case and provide the
complete result obtained by the GPT and its validation drawn from the probability theory.

**Category:** Artificial Intelligence

[148] **viXra:1003.0151 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 11 pages

A METHOD OF SOLVING A DIOPHANTINE EQUATION
OF SECOND DEGREE WITH N VARIABLES

**Category:** Number Theory

[147] **viXra:1003.0150 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 17 pages

In this paper, one studies the famous well-known and challenging Tweety Penguin Triangle Problem (TPTP or TP2)
pointed out by Judea Pearl in one of his books. We first present the solution of the TP2 based on the fallacious Bayesian reasoning and
prove that reasoning cannot be used to conclude on the ability of the penguin-bird Tweety to fly or not to fly. Then we present in details
the counter-intuitive solution obtained from the Dempster-Shafer Theory (DST). Finally, we show how the solution can be obtained
with our new theory of plausible and paradoxical reasoning (DSmT)

**Category:** Artificial Intelligence

[146] **viXra:1003.0149 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 13 pages

This paper presents several classes of fusion problems which cannot be directly attacked by the classical mathematical
theory of evidence, also known as the Dempster-Shafer Theory (DST) either because the Shafer's model for the frame of discernment
is impossible to obtain or just because the Dempster's rule of combination fails to provide coherent results (or no result at all). We
present and discuss the potentiality of the DSmT combined with its classical (or hybrid) rule of combination to attack these infinite
classes of fusion problems.

**Category:** Artificial Intelligence

[145] **viXra:1003.0148 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 33 pages

This paper presents a general method for combining uncertain and paradoxical source of evidences
for a wide class of fusion problems. From the foundations of the Dezert-Smarandache Theory (DSmT) we show
how the DSm rule of combination can be adapted to take into account all possible integrity constraints (if any)
of the problem under consideration due to the true nature of elements/concepts involved into it. We show how
the Shafer's model can be considered as a specific DSm hybrid model and be easily handled by our approach and
a new efficient rule of combination different from the Dempster's rule is obtained. Several simple examples are
also provided to show the efficiency and the generality of the approach proposed in this work.

**Category:** Artificial Intelligence

[144] **viXra:1003.0147 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 11 pages

The recent theory of plausible and paradoxical reasoning (DSmT) developed by the authors appears
to be a nice promising theoretical tools to solve many information fusion problems where the Shafer's model
cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where
a strong internal conflict between sources arises. The main idea of DSmT is to work on the hyper-powerset of
the frame of discernment of the problem under consideration. Although the definition of hyper-powerset is well
established, the major difficulty in practice is to generate such hyper-powersets in order to implement DSmT
fusion rule on computers. We present in this paper a simple algorithm for generating hyper-powersets and
discuss the limitations of our actual computers to generate such hyper-powersets when the dimension of the
problem increases.

**Category:** Artificial Intelligence

[143] **viXra:1003.0146 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache

**Comments:** 13 pages

In this paper, we examine several issues for ordering or partially ordering elements of hyperpowertsets
involved in the recent theory of plausible, uncertain and paradoxical reasoning (DSmT) developed by
the authors. We will show the benefit of some of these issues to obtain a nice and useful matrix representation
of belief functions.

**Category:** Artificial Intelligence

[142] **viXra:1003.0145 [pdf]**
*replaced on 16 Oct 2010*

**Authors:** Ervin Goldfain

**Comments:** 16 pages, Paper published in Electronic Journal of Theoretical Physics. EJTP 7, No. 24 (2010) 219–234

Understanding the origin of certain symmetry breaking scenarios in high-energy physics remains an open
challenge. Here we argue that, at least in some cases, symmetry violation is an effect of non-equilibrium
dynamics that is likely to develop somewhere above the energy scale of electroweak interaction. We also
find that, imposing Poincare symmetry in non-equilibrium field theory, leads to fractalization of space-time
continuum via period-doubling transition to chaos.

**Category:** High Energy Particle Physics

[141] **viXra:1003.0144 [pdf]**
*submitted on 12 Mar 2010*

**Authors:** Ioannis Iraklis Haranas

**Comments:** 3 pages, Published Journal of Theoretics

The idea of a possible variable light cosmology was recently investigated by certain authors.
In our brief note an estimate for a possible
variation in the speed of light can be calculated if fundamental relations of cosmology are
used along with a plausible definition of the speed of light.

**Category:** Relativity and Cosmology

[140] **viXra:1003.0143 [pdf]**
*submitted on 12 Mar 2010*

**Authors:** Alex Ceapa

**Comments:** 4 pages, Published:Journal of Theoretics Oct/Nov 2002 Vol.4, No.5

Inertial observers can not only measure their absolute velocities but that of light as well, thereby
being able to shed insight into the principle of the constancy of light velocity. The light
speeds c±v, though considered to conflict with this principle, are shown herein to not be true
physical entities.

**Category:** Relativity and Cosmology

[139] **viXra:1003.0142 [pdf]**
*submitted on 12 Mar 2010*

**Authors:** N. Mebarki

**Comments:** 10 pages, Presented at Invisible Universe International Conference, 29 June-10 July 2009, Paris, France

Anisotropic cosmological models with a generalized Chaplygin gas in a Finsler space-time geometry are considered
and a class of exact solutions as well as cosmological parameters behaviors are studied. Moreover, the viability and stability
criteria for a general solution are also discussed.

**Category:** Relativity and Cosmology

[138] **viXra:1003.0141 [pdf]**
*submitted on 12 Mar 2010*

**Authors:** N. Mebarki, M. Y. Boudjada

**Comments:** 3 pages, Presented in the 12th Marcel Grossmann Meeting 12-18 July 2009, Paris, France

In Finslerian space-time, a higher order curvature cosmological model of gravity is proposed and a
class of cosmological solutions is obtained. Moreover, the viability and stability near critical points are
also discussed.

**Category:** Relativity and Cosmology

[137] **viXra:1003.0140 [pdf]**
*submitted on 12 Mar 2010*

**Authors:** N. Mebarki, F. Khelili, O. Benabbes

**Comments:** 20 pages, Published in EJTP No22 (2009)5-28

A unified description of a symmetrized and anti-symmetrized Moyal star product of the
non-commutative infinitesimal gauge transformations is presented and the corresponding Seiberg-Witten
maps are derived. Moreover, the noncommutative covariant derivative, field strenght tensor as well
as gauge transformations are shown to be consistently constructed not on the enveloping but on the
Lie and/or Poisson algebra. As an application, a pure geometric extension of the standard model is
shown explicitly.

**Category:** High Energy Particle Physics

[136] **viXra:1003.0139 [pdf]**
*submitted on 12 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 9 pages

Using Jiang function J_{2}(ω) we prove gaps among products of m prime:
d(x) = d(x + 1) = d(x + 5 - 3) = d(x + 7 - 3) = ... = d(x + P_{n} - 3) = m > 1 infinitely-often,
where P_{n} denotes the n - th prime.

**Category:** Number Theory

[135] **viXra:1003.0138 [pdf]**
*submitted on 12 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 14 pages

In this paper we explain the behavior of the entire universe from the smallest to the largest
scales. We found the only tachyonic string theory (other string theories all are guesses),
find an equation that changed the universe: F-bar = -mc^{2}/R, establish the expansion theory
of the universe without dark matter and dark energy, and prove that the principle of
equivalence is nonexistent. We demonstrate that gravity is action-at-a-distance and that a
gravitational wave is unobservable.We suggest a new universe model.

**Category:** Quantum Gravity and String Theory

[134] **viXra:1003.0137 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** M. Khoshnevisan, F. Kaymram, Housila P. Singh, Rajesh Singh, Florentin Smarandache

**Comments:** 10 pages

This paper proposes a class of estimators for population correlation coefficient
when information about the population mean and population variance of one of the
variables is not avaliable but information about these parameters of another variable
(auxiliary) is avaliable, in two phase sampling and analyzes its properties. Optimum
estimator in the class is identified with its variance formula. The estimators of the class
involve unknown constants whose optimum values depend on unknown population
parameters.Following Singh (1982) and Srivastava and Jhajj (1983), it has been shown
that when these population parameters are replaced by their consistent estimates the
resulting class of estimators has the same asymptotic variance as that of optimum
estimator. An empirical study is carried out to demonstrate the performance of the
constructed estimators.

**Category:** Statistics

[133] **viXra:1003.0136 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** M. Khoshnevisan, F. Kaymram, Housila P. Singh, Rajesh Singh, Florentin Smarandache

**Comments:** 11 pages

This paper investigates the efficiency of an alternative to ratio estimator
under the super population model with uncorrelated errors and a gammadistributed
auxiliary variable. Comparisons with usual ratio and unbiased
estimators are also made.

**Category:** Statistics

[132] **viXra:1003.0135 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** M. Khoshnevisan, Sukanto Bhattacharya, Florentin Smarandache

**Comments:** 13 pages

In this paper we have proposed a semi-heuristic optimization algorithm for designing
optimal plant layouts in process-focused manufacturing/service facilities. Our proposed
algorithm marries the well-known CRAFT (Computerized Relative Allocation of
Facilities Technique) with the Hungarian assignment algorithm. Being a semi-heuristic
search, our algorithm is likely to be more efficient in terms of computer CPU engagement
time as it tends to converge on the global optimum faster than the traditional CRAFT
algorithm - a pure heuristic. We also present a numerical illustration of our algorithm.

**Category:** Data Structures and Algorithms

[131] **viXra:1003.0134 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 15 pages

Thirty-three new definitions are presented, derived from
neutrosophic set, neutrosophic probability, neutrosophic statistics, and
neutrosophic logic.
Each one is independent, short, with references and cross references
like in a dictionary style.

**Category:** Data Structures and Algorithms

[130] **viXra:1003.0133 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** M. Khoshnevisan, Florentin Smarandache, Sukanto Bhattacharya

**Comments:** 18 pages

In this paper we have devised an alternative methodological approach for
quantifying utility in terms of expected information content of the decisionmaker's
choice set. We have proposed an extension to the concept of utility by
incorporating extrinsic utility; which we have defined as the utility derived from
the element of choice afforded to the decision-maker by the availability of an
object within his or her object set. We have subsequently applied this extended
utility concept to the case of investor utility derived from a structured, financial
product - an custom-made investment portfolio incorporating an endogenous
capital-guarantee through inclusion of cash as a risk-free asset, based on the
Black-Scholes derivative-pricing formulation. We have also provided instances
of potential application of information and coding theory in the realms of financial
decision-making with such structured portfolios, in terms of transmission of
product information.

**Category:** Economics and Finance

[129] **viXra:1003.0132 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** M. Khoshnevisan, Sukanto Bhattacharya, Florentin Smarandache

**Comments:** 14 pages

In this paper we propose a classification scheme to isolate truly benign tumors from those
that initially start off as benign but subsequently show metastases. A non-parametric
artificial neural network methodology has been chosen because of the analytical
difficulties associated with extraction of closed-form stochastic-likelihood parameters
given the extremely complicated and possibly non-linear behavior of the state variables.
This is intended as the first of a three-part research output. In this paper, we have
proposed and justified the computational schema. In the second part we shall set up a
working model of our schema and pilot-test it with clinical data while in the concluding
part we shall give an in-depth analysis of the numerical output and model findings and
compare it to existing methods of tumor growth modeling and malignancy prediction.

**Category:** Quantitative Biology

[128] **viXra:1003.0131 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** M. Khoshnevisan, Florentin Smarandache, Sukanto Bhattacharya

**Comments:** 24 pages

In this paper we take a look at a simple portfolio insurance strategy using a protective put
and computationally derive the investor's governing utility structures underlying such a
strategy under alternative market scenarios. Investor utility is deemed to increase with an
increase in the excess equity generated by the portfolio insurance strategy over a simple
investment strategy without any insurance. Three alternative market scenarios
(probability spaces) have been explored - "Down", "Neutral" and "Up", categorized
according to whether the price of the underlying security is most likely to go down, stay
unchanged or go up. The methodology used is computational, primarily based on
simulation and numerical extrapolation. The Arrow-Pratt measure of risk aversion has
been used to determine how the investors react towards risk under the different scenarios.

**Category:** Economics and Finance

[127] **viXra:1003.0130 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jack Allen, Housila P. Singh, Florentin Smarandache

**Comments:** 16 pages

This paper proposes a family of estimators of population mean using information on several auxiliary variables
and analyzes its properties in the presence of measurement errors.

**Category:** Statistics

[126] **viXra:1003.0129 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jack Allen, Sukanto Bhattacharya, Florentin Smarandache

**Comments:** 21 pages

Each individual investor is different, with different financial goals, different levels of
risk tolerance and different personal preferences. From the point of view of investment
management, these characteristics are often defined as objectives and constraints.
Objectives can be the type of return being sought, while constraints include factors such
as time horizon, how liquid the investor is, any personal tax situation and how risk is
handled. It's really a balancing act between risk and return with each investor having
unique requirements, as well as a unique financial outlook - essentially a constrained
utility maximization objective. To analyze how well a customer fits into a particular
investor class, one investment house has even designed a structured questionnaire with
about two-dozen questions that each has to be answered with values from 1 to 5. The
questions range from personal background (age, marital state, number of children, job
type, education type, etc.) to what the customer expects from an investment (capital
protection, tax shelter, liquid assets, etc.). A fuzzy logic system has been designed for the
evaluation of the answers to the above questions. We have investigated the notion of
fuzziness with respect to funds allocation.

**Category:** Economics and Finance

[125] **viXra:1003.0128 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Housila P. Singh, Sharad Saxena, Jack Allen, Sarjinder Singh, Florentin Smarandache

**Comments:** 20 pages

This paper is speculated to propose a class of shrinkage estimators for shape parameter β in
failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed
interval containing the parameter β is available in addition to sample information and analyses their
properties. Some estimators are generated from the proposed class and compared with the minimum
mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency
and absolute relative bias indicate that certain of these estimators substantially improve the MMSE
estimator in some guessed interval of the parameter space of β, especially for censored samples with
small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties.

**Category:** Statistics

[124] **viXra:1003.0127 [pdf]**
*submitted on 11 Mar 2010*

**Authors:** Ervin Goldfain

**Comments:** 9 pages, This paper is a condensed version of an article published in a nonlinear dynamics journal in 2009

Both theory and experiment strongly suggest that new phenomena await discovery above the
energy range of the standard model for particle physics (SM). We argue that a correct description of
physics in the Terascale sector needs to account for the unquenched randomness induced by short-distance
fluctuations. The existence of unparticles, alleged to emerge at the next-generation colliders, is motivated
by a dynamic setting that is far-of-equilibrium and able to sustain a rich spectrum of complex phenomena.

**Category:** High Energy Particle Physics

[123] **viXra:1003.0126 [pdf]**
*submitted on 11 Mar 2010*

**Authors:** Alex Ceapa

**Comments:** 2 pages, Published in Journal of Theoretics, vol.6-3, June/July 2004

Der Waerden obtained the spinorial transcription of the Dirac equation from the relativistic
energy-momentum relationship. The recent validation of the principle of the physical determination
of equations in the special relativity theory enables us to deduce the meaning of mass from his
results.

**Category:** Relativity and Cosmology

[122] **viXra:1003.0125 [pdf]**
*replaced on 2013-04-22 14:03:34*

**Authors:** Dainis Zeps

**Comments:** 9 Pages. Corrected version

Problems around teaching ancient languages are discussed. It is suggested to assume that learning and teaching of languages require some superhuman effort. Author’s experience of teaching ancient languages and producing electronic educational tools both for text version and for Internet in Faculty of Theology in University of Latvia is described. Problems around cognitive models of reasoning and place of languages there are discussed.

**Category:** Linguistics

[121] **viXra:1003.0123 [pdf]**
*replaced on 11 Mar 2010*

**Authors:** Ervin Goldfain

**Comments:** 2 pages, Letters submitted to the Editors of Classical and Quantum Gravity (v1) and Physics Review Letters (v2).

This memo is in regards to the recently published contribution by Ambjorn J. et al.
"Planckian Birth of Quantum de Sitter Universe" PRL 100, 091304 (2008).
The article claims that "causal dynamical triangulation" enables a consistent
regularization of quantum gravity. A "quantum universe" emerging from a nonperturbative
sum over geometries is alleged to recover "with high accuracy a fourdimensional
de Sitter space-time". On closer examination, the approach is built on many
objectionable premises

**Category:** Quantum Gravity and String Theory

[120] **viXra:1003.0122 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 6 pages

A Generalized Numeration Base is defined in this
paper, and then particular cases are presented, such as Prime
Base, Square Base, m-Power Base, Factorial Base, and
operations in these bases.

**Category:** Number Theory

[119] **viXra:1003.0121 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 14 pages

Other new sequences are introduced in number theory, and for each
one a general question: how many primes each sequence has.

**Category:** Number Theory

[118] **viXra:1003.0120 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 42 pages

New sequences in number theory are showed below with
definitions, examples, solved or open questions and references for
each case.

**Category:** Number Theory

[117] **viXra:1003.0119 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 6 pages

Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are
explained in this paper, taught by the author to the elementary and high school teachers at the
University of New Mexico - Gallup in 1997-8 and afterwards. They have a more educational
interest because make the students think different!

**Category:** Set Theory and Logic

[116] **viXra:1003.0118 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 16 pages

A collection of original sequences, open questions, and problems are mentioned below.

**Category:** Number Theory

[115] **viXra:1003.0117 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 12 pages

Classes of linguistic paradoxes are introduced with examples and
explanations. They are part of the author's work on the Paradoxist
Philosophy based on mathematical logic.
The general cases exposed below are modeled on the English
language structure in a rigid way. In order to find nice
particular examples of such paradoxes one grammatically adjusts the
sentences.

**Category:** Set Theory and Logic

[114] **viXra:1003.0116 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 23 pages

The goal of this paper is to experiment new math concepts
and theories, especially if they run counter to the classical
ones. To prove that contradiction is not a catastrophe, and
to learn to handle it in an (un)usual way.
To transform the apparently unscientific ideas into scientific
ones, and to develop their study (The Theory of Imperfections).
And finally, to interconnect opposite (and not only) human
fields of knowledge into as-heterogeneous-as-possible
another fields.

**Category:** Geometry

[113] **viXra:1003.0115 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

New notions are introduced in algebra in order to better study the congruences in number theory.
For example, the <special semigroups> make an important such contribution.

**Category:** Algebra

[112] **viXra:1003.0114 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 30 pages

In this article one investigates Rugina's Orientation Table and one gives particular examples for
several of its seven models.
Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in
Rugina's Orientation Table in systems which are s% stable and 100-s% unstable, where s may be 100, 95, 65,
50, 35, 5, and 0.
The Classical Logic and Modern Logic are united in Rugina's Integrated Logic, and then generalized in the
Neutrosophic Logic.

**Category:** Artificial Intelligence

[111] **viXra:1003.0113 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 6 pages

This study proposes some exponential ratio-type estimators for estimating the population
mean of the variable under study ... (see paper for full abstract)

**Category:** Statistics

[110] **viXra:1003.0112 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

In this article we will construct a family of expressions ε(n). For each element
E(n) from ε(n), the convergence of the series Σ E(n)
can be determined in accordance to the theorems of this article.

**Category:** Number Theory

[109] **viXra:1003.0111 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 8 pages

In this paper we define a function L which
will allow us to (separately or simultaneously) generalize
many theorems from Number Theory obtained by Wilson, Fermat,
Euler, Gauss, Lagrange, Leibniz, Moser, and Sierpinski.

**Category:** Number Theory

[108] **viXra:1003.0110 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

Comments on "A new combination of evidence based on compromise"

**Category:** Artificial Intelligence

[107] **viXra:1003.0109 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jack Allen, Housila P. Singh, Sarjinder Singh, Florentin Smarandache

**Comments:** 21 pages

In this paper we have suggested two classes of estimators for population median MY of the study
character Y using information on two auxiliary characters X and Z in double sampling. It has
been shown that the suggested classes of estimators are more efficient than the one suggested by
Singh et al (2001). Estimators based on estimated optimum values have been also considered
with their properties. The optimum values of the first phase and second phase sample sizes are
also obtained for the fixed cost of survey.

**Category:** Statistics

[106] **viXra:1003.0108 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Mark Alford

**Comments:** 9 pages

In this paper we introduce two new DSm fusion conditioning rules with example, and as
a generalization of them a class of DSm fusion conditioning rules, and then extend them
to a class of DSm conditioning rules.

**Category:** Artificial Intelligence

[105] **viXra:1003.0107 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 9 pages

This article presents a necessary and
sufficient theorem for N numbers, coprime two by two, to
be prime simultaneously.
It generalizes V. Popa's theorem [3], as well as
I. Cucurezeanu's theorem ([1], p. 165), Clement's theorem,
S. Patrizio's theorems [2], etc.
Particularly, this General Theorem offers different
characterizations for twin primes, for quadruple primes,
etc.

**Category:** Number Theory

[104] **viXra:1003.0106 [pdf]**
*submitted on 10 Mar 2010*

**Authors:** Ioannis Iraklis Haranas

**Comments:** 6 pages, Publisher Journal of Theoretics, vol. 4, no. 1, 2001.

Recent observations confirm quantized galactic redshifts and hint a possible new form of
quantum mechanics, which could probably explain these observed properties of the
galaxies. This brief contribution investigates a possible relation between the new cosmic
Planck constant h_{g} and other fundamental constants of physics.

**Category:** Astrophysics

[103] **viXra:1003.0104 [pdf]**
*replaced on 12 Mar 2010*

**Authors:** John R. McWhinnie

**Comments:** 13 pages

This article is an attempt to expose the role played by messenger
particles in physics. The concept of the "messenger particle" has long been
considered in physics. The latest research shows evidence that the four fundamental
forces of nature ,Gravitation, Electromagnetic and the Weak and
Strong Nuclear forces are all created by messenger particles. This hypotheses
is leading to a new way of thinking about the fundamental sub-atomic
wave/particles that are the building blocks of our universe. Some of the latest
evidence actually shows that in order to understand what is happening with
these messenger particles it is necessary to perceive them as information carriers.
The four messenger particles that are thought to exist are the Graviton
(not yet discovered) , Photon, Weak Guage Boson and the Gluon. This paper
shall be concerned with the Photon as an information carrier.

**Category:** Relativity and Cosmology

[102] **viXra:1003.0103 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Mihály Bencze, Florentin Smarandache

**Comments:** 11 pages

In this paper we give a method, based on the characteristic function of a set, to
solve some difficult problems of set theory found in undergraduate studies.

**Category:** Number Theory

[101] **viXra:1003.0102 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

On Carmichaël's conjecture

**Category:** Number Theory

[100] **viXra:1003.0101 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Albena Tchamova, Jean Dezert, Florentin Smarandache

**Comments:** 6 pages

This paper presents a new approach for solving
the paradoxical Blackman's Association Problem. It utilizes
the recently defined new class fusion rule based on fuzzy Tconorm/
T-norm operators together with Dezert-Smarandache theory
based, relative variations of generalized
pignistic probabilities measure of correct associations,
defined from a partial ordering function of hyper-power set.
The ability of this approach to solve the problem against the
classical Dempster-Shafer's method, proposed in the
literature is proven. It is shown that the approach improves
the separation power of the decision process for this
association problem.

**Category:** Artificial Intelligence

[99] **viXra:1003.0100 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Jean Dezert, Florentin Smarandache, Albena Tchamova

**Comments:** 11 pages

Modern multitarget-multisensor tracking systems involve the development of reliable methods for
the data association and the fusion of multiple sensor information, and more specifically the partioning of
observations into tracks. This paper discusses and compares the application of Dempster-Shafer Theory (DST)
and the Dezert-Smarandache Theory (DSmT) methods to the fusion of multiple sensor attributes for target
identification purpose. We focus our attention on the paradoxical Blackman's association problem and propose
several approaches to outperfom Blackman's solution. We clarify some preconceived ideas about the use of degree
of conflict between sources as potential criterion for partitioning evidences.

**Category:** Artificial Intelligence

[98] **viXra:1003.0099 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 126 pages

Industrial Biotechnology is an interdisciplinary topic to which
tools of modern biotechnology are applied for finding proper
proportion of raw mix of chemicals, determination of set points,
finding the flow rates etc., This study is significant as it results
in better economy, quality product and control of pollution. The
authors in this book have given only methods of industrial
biotechnology mainly to help researchers, students and chemical
engineers. Since biotechnology concerns practical and diverse
applications including production of new drugs, clearing up
pollution etc. we have in this book given methods to control
pollution in chemical industries as it has become a great health
threat in India. In some cases, the damage due to environmental
pollution outweighs the benefits of the product.

**Category:** Chemistry

[97] **viXra:1003.0098 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 273 pages

Graphs and matrices play a vital role in the analysis
and study of several of the real world problems which
are based only on unsupervised data. The fuzzy and
neutrosophic tools like fuzzy cognitive maps invented
by Kosko and neutrosophic cognitive maps introduced
by us help in the analysis of such real world problems
and they happen to be mathematical tools which can
give the hidden pattern of the problem under
investigation. This book, in order to generalize the two
models, has systematically invented mathematical
tools like bimatrices, trimatrices, n-matrices, bigraphs,
trigraphs and n-graphs and describe some of its
properties. These concepts are also extended
neutrosophically in this book.

**Category:** Algebra

[96] **viXra:1003.0097 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 181 pages

Matrix theory has been one of the most utilised concepts in
fuzzy models and neutrosophic models. From solving
equations to characterising linear transformations or linear
operators, matrices are used. Matrices find their applications
in several real models. In fact it is not an exaggeration if
one says that matrix theory and linear algebra (i.e. vector
spaces) form an inseparable component of each other.

**Category:** Algebra

[95] **viXra:1003.0096 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 238 pages

The algebraic structure, linear algebra happens to be one of
the subjects which yields itself to applications to several
fields like coding or communication theory, Markov chains,
representation of groups and graphs, Leontief economic
models and so on. This book has for the first time,
introduced a new algebraic structure called linear bialgebra,
which is also a very powerful algebraic tool that can yield
itself to applications.

**Category:** Algebra

[94] **viXra:1003.0095 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Mihály Bencze, Florentin Smarandache

**Comments:** 3 pages

Many methods to compute the sum of the first n natural numbers of the same
powers (see [4]) are well known.
In this article we present a simple proof of the method from [3].

**Category:** Number Theory

[93] **viXra:1003.0094 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Jean Dezert

**Comments:** 27 pages

In this paper we propose a new family of Belief Conditioning Rules (BCR) for belief revision.
These rules are not directly related with the fusion of several sources of evidence but with the revision of a belief
assignment available at a given time according to the new truth (i.e. conditioning constraint) one has about the
space of solutions of the problem.

**Category:** Artificial Intelligence

[92] **viXra:1003.0093 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 5 pages

In this article we establish some properties regarding the solutions of a linear
congruence, bases of solutions of a linear congruence, and the finding of other solutions
starting from these bases.
This article is a continuation of my article "On linear congruences".

**Category:** Number Theory

[91] **viXra:1003.0092 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 75 pages

This volume is a collection of six papers on the use of auxiliary
information and a priori values in construction of improved estimators. The
work included here will be of immense application for researchers and
students who employ auxiliary information in any form.

**Category:** Statistics

[90] **viXra:1003.0091 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 7 pages

Some ratio estimators for estimating the population mean of the variable under study, which
make use of information regarding the population proportion possessing certain attribute, are
proposed. Under simple random sampling without replacement (SRSWOR) scheme, the
expressions of bias and mean-squared error (MSE) up to the first order of approximation are
derived. The results obtained have been illustrated numerically by taking some empirical
population considered in the literature.

**Category:** Statistics

[89] **viXra:1003.0090 [pdf]**
*submitted on 8 Mar 2010*

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

**Comments:** 9 pages

In this paper, we describe a very simple experiment with distilled water which
could exhibit anomalous potential electrical energy with very minimum preparation
energy. While this observed excess energy here is less impressive than [1][2]
and the material used is also far less exotic than common LENR-CANR experiments,
from the viewpoint of minimum preparation requirement - and therefore
less barrier for rapid implementation--, it seems that further experiments could be
recommended in order to verify and also to explore various implications of this
new proposition.

**Category:** Chemistry

[88] **viXra:1003.0089 [pdf]**
*replaced on 12 May 2010*

**Authors:** Stein E. Johansen

**Comments:** 41 pages, Submitted to Journal of Calcutta Mathematical Society, Nov 18, 2009.

We present a certain *geometrical* interpretation of the natural numbers, where these numbers appear as *joint
products of 5- and 3-multiples* located at specified *positions* in a *revolving chamber*. Numbers without
factors 2, 3 or 5 appear at *eight* such positions, and any prime number larger than 7 manifests at one of
these eight positions after a specified amount of rotations of the chamber. Our approach determines the
sets of rotations constituting primes at the respective eight positions, as the *complements* of the sets
of rotations constituting *non-primes* at the respective eight positions. These sets of rotations constituting
non-primes are exhibited from a *basic 8x8-matrix* of the *mutual products* originating from the eight prime numbers located
at the eight positions in the *original* chamber. This 8x8-matrix is proven to generate *all* non-primes
located at the eight positions in *strict rotation regularities* of the chamber. These regularities are
expressed in relation to the multiple 11^{2} as an anchoring *reference point* and by means of convenient
*translations* between certain classes of multiples. We find the expressions of rotations generating *all*
non-primes located at *same* position in the chamber as a set of *eight related series*. The *total* set of
non-primes located at the eight positions is exposed as *eight* such sets of eight series, and with each
of the series *completely* characterized by *four simple variables* when compared to a reference series
anchored in 11^{2}. This represents a *complete* exposition of non-primes generated by a quite simple mathematical
structure. *Ad negativo* this also represents a *complete* exposition of all *prime numbers* as the union of the
eight complement sets for these eight non-prime sets of eight series.

**Category:** Number Theory

[87] **viXra:1003.0088 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Ioannis Iraklis Haranas

**Comments:** 5 pages, Publisher Journal of Theoretics, vol. 4, no. 1, 2001.

In a study by F. Calogero [1] entitled "Cosmic origin of quantization" an expression was derived for
the variability of h with time, and its consequences if any, of such an idea in cosmology were examined.
In this paper we will offer a different derivation of the Calogero conjecture based on a postulate
concerning a variable speed of light, [2] in conjuction with Weinberg's relationship for the mass of
an elementary particle.

**Category:** Astrophysics

[86] **viXra:1003.0087 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 7 pages, Dedicated to the 30-th anniversary of China reform and opening

We establish the Santilli's isomathematics based on the generalization of the
modern mathematics. (more see paper)

**Category:** Number Theory

[85] **viXra:1003.0086 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 5 pages

In this paper we prove that it is sufficient to prove S_{1}^{3} + S_{2}^{3} = 1
for Fermat's last theorem
using the complex hyperbolic functions in the hypercomplex variable theory. More than 200 years
ago Euler gave a proof of S_{1}^{3} + S_{2}^{3} = 1. Fermat's last theorem has been proved.

**Category:** Number Theory

[84] **viXra:1003.0084 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 4 pages

We find Blasius function to satisfy the boundary condition f'(∞) = 1 and obtain the
approximate solutions of Blasius equation.

**Category:** Number Theory

[83] **viXra:1003.0083 [pdf]**
*submitted on 5 Mar 2010*

**Authors:** M. Khoshnevisan, Sukanto Bhattacharya, Florentin Smarandache

**Comments:** 87 pages

The purpose of this book is to apply the Artificial Intelligence and control systems to
different real models.

**Category:** Artificial Intelligence

[82] **viXra:1003.0082 [pdf]**
*replaced on 6 Mar 2010*

**Authors:** Florentin Smarandache, Salah Osman

**Comments:** 293 pages, v1 in Arabic, v2 in English

Neutrosophy is ascribed to Dr. Florentin Smarandache,
professor of mathematics and sciences, and head of its
department at the University of New Mexico - Gallup (USA).
The main aim of this book is to provide the reader with the
philosophy of neutrosophy and its application to the
Arabic-Islamic thought. So the book is divided into two parts; the first
belongs to prof. Smarandache, in which he exposes his
philosophy of neutrosophy. The second belongs to Dr. Salah
Osman, assistant professor of logic and the philosophy of
science in Minufiya university - in which he applies the
philosophy of neutrosophy to the Arabic-Islamic thought.

**Category:** General Science and Philosophy

[81] **viXra:1003.0081 [pdf]**
*submitted on 8 Mar 2010*

**Authors:** Ervin Goldfain

**Comments:** 13 pages, This paper was published in IJNSNS 6(3), pp. 223-234, 2005

The standard model embodies our current knowledge of elementary particle physics
and represents a well-tested framework for the study of non-gravitational phenomena
at low energies. It is built on the foundations of relativistic quantum field
theory (QFT), which provides the correct description of electroweak and strong
interactions involving leptons and quarks. It is generally believed that, extending
the validity of QFT to energies on or beyond the TeV range must include the
unavoidable signature of vacuum fluctuations and strong-field gravity. We argue
that an effective approach to the high-energy regime of QFT demands the tools of
complex dynamics and fractal operators. The unexpected consequences of using fractal
operators to model complexity beyond the current range of QFT are outlined and discussed.

**Category:** High Energy Particle Physics

[80] **viXra:1003.0080 [pdf]**
*replaced on 11 Apr 2010*

**Authors:** Carlos Castro

**Comments:** 18 pages, has been submitted to Foundations of Physics

A novel (to our knowledge) Generalized Nonlinear Schrödinger equation
based on the modifications of Nottale-Cresson's fractal-scale calculus
and resulting from the noncommutativity of the phase space coordinates
is explicitly derived. The modifications to the ground state energy of a
harmonic oscillator yields the observed value of the vacuum energy density.
In the concluding remarks we discuss how nonlinear and nonlocal
QM wave equations arise naturally from this fractal-scale calculus formalism
which may have a key role in the final formulation of Quantum
Gravity.

**Category:** Quantum Gravity and String Theory

[79] **viXra:1003.0079 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 175 pages

While I began researching for this book on linear algebra, I was a little startled.
Though, it is an accepted phenomenon, that mathematicians are rarely the ones to
react surprised, this serious search left me that way for a variety of reasons. First,
several of the linear algebra books that my institute library stocked (and it is a really
good library) were old and crumbly and dated as far back as 1913 with the most 'new'
books only being the ones published in the 1960s.

**Category:** Algebra

[78] **viXra:1003.0078 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 455 pages

In 1965, Lofti A. Zadeh introduced the notion of a fuzzy subset of a set as
a method for representing uncertainty. It provoked, at first (and as
expected), a strong negative reaction from some influential scientists and
mathematicians - many of whom turned openly hostile. However, despite
the controversy, the subject also attracted the attention of other
mathematicians and in the following years, the field grew enormously,
finding applications in areas as diverse as washing machines to
handwriting recognition. In its trajectory of stupendous growth, it has also
come to include the theory of fuzzy algebra and for the past five decades,
several researchers have been working on concepts like fuzzy semigroup,
fuzzy groups, fuzzy rings, fuzzy ideals, fuzzy semirings, fuzzy near-rings
and so on.

**Category:** Algebra

[77] **viXra:1003.0077 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 272 pages

The study of bialgebraic structures started very recently. Till date there are no books
solely dealing with bistructures. The study of bigroups was carried out in 1994-1996.
Further research on bigroups and fuzzy bigroups was published in 1998. In the year
1999, bivector spaces was introduced. In 2001, concept of free De Morgan
bisemigroups and bisemilattices was studied. It is said by Zoltan Esik that these
bialgebraic structures like bigroupoids, bisemigroups, binear rings help in the
construction of finite machines or finite automaton and semi automaton. The notion of
non-associative bialgebraic structures was first introduced in the year 2002. The
concept of bialgebraic structures which we define and study are slightly different from
the bistructures using category theory of Girard's classical linear logic. We do not
approach the bialgebraic structures using category theory or linear logic.

**Category:** Algebra

[76] **viXra:1003.0076 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 201 pages

An associative ring is just realized or built using reals or complex; finite or infinite
by defining two binary operations on it. But on the contrary when we want to define
or study or even introduce a non-associative ring we need two separate algebraic
structures say a commutative ring with 1 (or a field) together with a loop or a
groupoid or a vector space or a linear algebra. The two non-associative well-known
algebras viz. Lie algebras and Jordan algebras are mainly built using a vector space
over a field satisfying special identities called the Jacobi identity and Jordan identity
respectively. Study of these algebras started as early as 1940s. Hence the study of
non-associative algebras or even non-associative rings boils down to the study of
properties of vector spaces or linear algebras over fields.

**Category:** Algebra

[75] **viXra:1003.0075 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 201 pages

Near-rings are one of the generalized structures of rings. The study and research on
near-rings is very systematic and continuous. Near-ring newsletters containing
complete and updated bibliography on the subject are published periodically by a
team of mathematicians (Editors: Yuen Fong, Alan Oswald, Gunter Pilz and K. C.
Smith) with financial assistance from the National Cheng Kung University, Taiwan.
These newsletters give an overall picture of the research carried out and the recent
advancements and new concepts in the field. Conferences devoted solely to near-rings
are held once every two years. There are about half a dozen books on near-rings apart
from the conference proceedings. Above all there is a online searchable database and
bibliography on near-rings. As a result the author feels it is very essential to have a
book on Smarandache near-rings where the Smarandache analogues of the near-ring
concepts are developed. The reader is expected to have a good background both in
algebra and in near-rings; for, several results are to be proved by the reader as an
exercise.

**Category:** Algebra

[74] **viXra:1003.0074 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 222 pages

Over the past 25 years, I have been immersed in research in Algebra and more
particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings)
specially to motivate both ring theorists and Smarandache algebraists to
develop and study several important and innovative properties about S-rings.

**Category:** Algebra

[73] **viXra:1003.0073 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 129 pages

The theory of loops (groups without associativity), though researched by several
mathematicians has not found a sound expression, for books, be it research level or
otherwise, solely dealing with the properties of loops are absent. This is in marked
contrast with group theory where books are abundantly available for all levels: as
graduate texts and as advanced research books.

**Category:** Algebra

[72] **viXra:1003.0072 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 122 pages

Smarandache notions, which can be undoubtedly characterized as interesting
mathematics, has the capacity of being utilized to analyse, study and introduce,
naturally, the concepts of several structures by means of extension or identification as
a substructure. Several researchers around the world working on Smarandache notions
have systematically carried out this study. This is the first book on the Smarandache
algebraic structures that have two binary operations.

**Category:** Algebra

[71] **viXra:1003.0071 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 115 pages

The study of Smarandache Algebraic Structure was initiated in the year 1998 by Raul
Padilla following a paper written by Florentin Smarandache called "Special Algebraic
Structures". In his research, Padilla treated the Smarandache algebraic structures mainly with
associative binary operation. Since then the subject has been pursued by a growing number of
researchers and now it would be better if one gets a coherent account of the basic and main
results in these algebraic structures. This book aims to give a systematic development of the
basic non-associative algebraic structures viz. Smarandache groupoids. Smarandache
groupoids exhibits simultaneously the properties of a semigroup and a groupoid. Such a
combined study of an associative and a non associative structure has not been so far carried
out. Except for the introduction of smarandacheian notions by Prof. Florentin Smarandache
such types of studies would have been completely absent in the mathematical world.

**Category:** Algebra

[70] **viXra:1003.0070 [pdf]**
*submitted on 7 Mar 2010*

**Authors:** W. B. Vasantha Kandasamy

**Comments:** 95 pages

The main motivation and desire for writing this book, is the direct appreciation
and attraction towards the Smarandache notions in general and Smarandache
algebraic structures in particular. The Smarandache semigroups exhibit properties of
both a group and a semigroup simultaneously. This book is a piece of work on
Smarandache semigroups and assumes the reader to have a good background on
group theory; we give some recollection about groups and some of its properties just
for quick reference.

**Category:** Algebra

[69] **viXra:1003.0069 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Mihály Bencze, Florentin Smarandache

**Comments:** 2 pages

In this paper we present theorems and applications of Wallis theorem
related to trigonometric integrals.

**Category:** Number Theory

[68] **viXra:1003.0068 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

In this note we present a method of solving this Diophantine
equation, method which is different from Ljunggren's, Mordell's, and R.K.Guy's.

**Category:** Number Theory

[67] **viXra:1003.0067 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 9 pages

In this article we determine several theorems and methods for solving linear
congruences and systems of linear congruences and we find the number of distinct
solutions. Many examples of solving congruences are given.

**Category:** Number Theory

[66] **viXra:1003.0066 [pdf]**
*replaced on 6 Mar 2010*

**Authors:** Ion Goian, Raisa Grigor, Vasile Marin, Florentin Smarandache

**Comments:** 119 pages, v1 in Romanian language, v2 in Russian language.

Theory and problems on algebraic structures.

**Category:** Algebra

[65] **viXra:1003.0065 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Feng Liu, Florentin Smarandache

**Comments:** 10 pages

The paper presents a fresh new comprehensive ideology on Neutrosophic Logic based
on contradiction study in a broad sense: general critics on conventional logic by examining the essence of
logic, fresh insights on logic definition based on Chinese philosophical survey, and a novel and genetic
logic model as the elementary cell against Von Neumann oriented ones based on this novel definition. As
for the logic definition, the paper illustrates that logic is rather a tradeoff between different factors than
truth and false abstraction. It is stressed that the kernel of any intelligent system is exactly a contradiction
model. The paper aims to solve the chaos of logic and exhibit the potential power of neutrosophy: a new
branch of scientific philosophy.

**Category:** Set Theory and Logic

[64] **viXra:1003.0064 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** M. C. Florea, J. Dezert, P. Valin, Florentin Smarandache, Anne-Laure Jousselme

**Comments:** 8 pages

This paper presents two new promising combination
rules for the fusion of uncertain and potentially highly
conflicting sources of evidences in the theory of belief functions
established first in Dempster-Shafer Theory (DST) and
then recently extended in Dezert-Smarandache Theory
(DSmT). Our work is to provide here new issues to palliate
the well-known limitations of Dempster's rule and to work
beyond its limits of applicability. Since the famous Zadeh's
criticism of Dempster's rule in 1979, many researchers have
proposed new interesting alternative rules of combination to
palliate the weakness of Dempster's rule in order to provide
acceptable results specially in highly conflicting situations.
In this work, we present two new combination rules: the
class of Adaptive Combination Rules (ACR) and a new efficient
Proportional Conflict Redistribution (PCR) rule. Both
rules allow to deal with highly conflicting sources for static
and dynamic fusion applications. We present some interesting
properties for ACR and PCR rules and discuss some
simulation results obtained with both rules for Zadeh's problem
and for a target identification problem.

**Category:** Artificial Intelligence

[63] **viXra:1003.0063 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Mihály Bencze, Florentin Smarandache

**Comments:** 3 pages

In this paper, we present some new inequalities for factorial sum.

**Category:** Number Theory

[62] **viXra:1003.0062 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Feng Liu, Florentin Smarandache

**Comments:** 7 pages

The paper presents a fresh new start on the neutrality of neutrosophy in
that "both A and Non-A" as an alternative to describe Neuter-A in that we conceptualize
things in both intentional and unintentional background. This unity of opposites
constitutes both objective world and subjective world. The whole induction of such
argument is based on the intensive study on Buddhism and Daoism including I-ching. In
addition, a framework of contradiction oriented learning philosophy inspired from the
Later Trigrams of King Wen in I-ching is meanwhile presented. It is shown that although
A and Non-A are logically inconsistent, but they are philosophically consistent in the
sense that Non-A can be the unintentionally instead of negation that leads to confusion. It
is also shown that Buddhism and Daoism play an important role in neutrosophy, and
should be extended in the way of neutrosophy to all sciences according to the original
intention of neutrosophy.

**Category:** Set Theory and Logic

[61] **viXra:1003.0061 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 38 pages

Partially or totally unsolved questions in number
theory and geometry especially, such as coloration
problems, elementary geometric conjectures,
partitions, generalized periods of a number,
length of a generalized period, arithmetic and
geometric progressions are exposed.

**Category:** Number Theory

[60] **viXra:1003.0060 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Xin-De Li, Xian-Zhong Dai, Jean Dezert, Florentin Smarandache

**Comments:** 6 pages

Most of modern systems for information retrieval, fusion
and management have to deal more and more with information
expressed quatitatively (by linguistic labels) since
human reports are better and easier expressed in natural
language than with numbers. In this paper, we propose
to use Herrera-Martínez' 2-Tuple linguistic representation
model (i.e. equidistant linguistic labels with a numeric
value assessment) for reasoning with uncertain and qualitative
information in Dezert-Smarandache Theory (DSmT)
framework to preserve the precision and the efficiency of
the fusion of linguistic information expressing the expert's
qualitative beliefs. We present operators to deal with the
2-Tuples and show from a simple example how qualitative
DSmT-based fusion rules can be used for qualitative reasoning
and fusioning under uncertainty.

**Category:** Artificial Intelligence

[59] **viXra:1003.0059 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Xin-De Li, Florentin Smarandache, Xian-Zhong Dai

**Comments:** 12 pages

Modern systems for information retrieval, fusion and management need to deal more and more with information
coming from human experts usually expressed qualitatively in natural language with linguistic labels. In this paper, we
propose and use two new 2-Tuple linguistic representation models (i.e., a distribution function model (DFM) and an improved
Herrera-Martínez's model) jointly with the fusion rules developed in Dezert-Smarandache Theory (DSmT), in order to
combine efficiently qualitative information expressed in term of qualitative belief functions. The two models both preserve
the precision and improve the efficiency of the fusion of linguistic information expressing the global expert's opinion. However,
DFM is more general and efficient than the latter, especially for unbalanced linguistic labels. Some simple examples are also
provided to show how the 2-Tuple qualitative fusion rules are performed and their advantages.

**Category:** Artificial Intelligence

[58] **viXra:1003.0058 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Ion Pătraşcu

**Comments:** 5 pages, Translated by Prof. Florentin Smarandache

In this article we prove the theorems of the orthopole and we obtain, through
duality, its dual, and then some interesting specific examples of the dual of the theorem
of the orthopole.

**Category:** Geometry

[57] **viXra:1003.0057 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Ion Pătraşcu

**Comments:** 7 pages, Translated by Prof. Florentin Smarandache

The purpose of this article is to familiarize the reader with these notions, emphasizing on
connections between them.

**Category:** Geometry

[56] **viXra:1003.0056 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Ion Pătraşcu

**Comments:** 5 pages, Translated by Prof. Florentin Smarandache

In this article we elementarily prove some theorems on the poles and polars
theory, we present the transformation using duality and we apply this transformation to
obtain the dual theorem relative to the Samson's line.

**Category:** Geometry

[55] **viXra:1003.0055 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 3 pages

As we know, it has been quite common nowadays for particle physicists to think of
six impossible things before breakfast, just like what their cosmology fellows used to
do. In the present paper, we discuss a number of those impossible things, including
PT-symmetric periodic potential, its link with condensed matter nuclear science, and
possible neat link with Quark confinement theory. In recent years, the PT-symmetry
and its related periodic potential have gained considerable interests among physicists.
We begin with a review of some results from a preceding paper discussing derivation of
PT-symmetric periodic potential from biquaternion Klein-Gordon equation and proceed
further with the remaining issues. Further observation is of course recommended in
order to refute or verify this proposition.

**Category:** High Energy Particle Physics

[54] **viXra:1003.0054 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 4 pages

It has been known for quite long time that the electrodynamics of Maxwell equations
can be extended and generalized further into Proca equations. The implications of introducing
Proca equations include an alternative description of superconductivity, via
extending London equations. In the light of another paper suggesting that Maxwell
equations can be written using quaternion numbers, then we discuss a plausible extension
of Proca equation using biquaternion number. Further implications and experiments
are recommended.

**Category:** Condensed Matter

[53] **viXra:1003.0053 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Ervin Goldfain, Florentin Smarandache

**Comments:** 6 pages

Emergent physics refers to the formation and evolution of collective patterns in systems
that are nonlinear and out-of-equilibrium. This type of large-scale behavior often develops
as a result of simple interactions at the component level and involves a dynamic
interplay between order and randomness. On account of its universality, there are credible
hints that emergence may play a leading role in the Tera-ElectronVolt (TeV) sector of
particle physics. Following this path, we examine the possibility of hypothetical highenergy
states that have fractional number of quanta per state and consist of arbitrary
mixtures of particles and antiparticles. These states are similar to "un-particles", massless
fields of non-integral scaling dimensions that were recently conjectured to emerge
in the TeV sector of particle physics. They are also linked to "unmatter", exotic clusters
of matter and antimatter introduced few years ago in the context of Neutrosophy.
The connection between 'unmatter' and 'unparticle' is explained in details in this paper.
Unparticles have very odd properties which result from the fact that they represent fractional
field quanta. Unparticles are manifested as mixed states that contain arbitrary mixtures of
particles and antiparticles (therefore they simultaneously evolve "forward" and "backward" in time).
From this, the connection with unmatter. Using the fractal operators of differentiation and
integration we get the connection between unparticle and unmatter. 'Unmatter' was coined by
F. Smarandache in 2004 who published three papers on the subject.

**Category:** Condensed Matter

[52] **viXra:1003.0052 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

In the scientific research, it is important to keep our freedom of thinking and not being
yoked by others' theories without checking them, no matter where they come from.
Cogito, ergo sum (I think, therefore I am), said Descartes (1596-1650), and this Latin
aphorism became his first principle in philosophy.

**Category:** History and Philosophy of Physics

[51] **viXra:1003.0051 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

The present article discusses Neutrosophic logic view to Schrödinger's cat paradox.
We argue that this paradox involves some degree of indeterminacy (unknown) which
Neutrosophic logic can take into consideration, whereas other methods including Fuzzy
logic cannot. To make this proposition clear, we revisit our previous paper by offering
an illustration using modified coin tossing problem, known as Parrondo's game.

**Category:** Quantum Physics

[50] **viXra:1003.0050 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 7 pages

It was known for quite long time that a quaternion space can be generalized to a Clifford
space, and vice versa; but how to find its neat link with more convenient metric form
in the General Relativity theory, has not been explored extensively. We begin with a
representation of group with non-zero quaternions to derive closed FLRW metric [1],
and from there obtains Carmeli metric, which can be extended further to become 5D
and 6D metric (which we propose to call Kaluza-Klein-Carmeli metric). Thereafter
we discuss some plausible implications of this metric, beyond describing a galaxy's
spiraling motion and redshift data as these have been done by Carmeli and Hartnett
[4, 5, 6]. In subsequent section we explain Podkletnov's rotating disc experiment. We
also note possible implications to quantum gravity. Further observations are of course
recommended in order to refute or verify this proposition.

**Category:** Quantum Physics

[49] **viXra:1003.0049 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 2 pages

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation
has solution containing imaginary part, which differs appreciably from known solution
of KGE. In the present article we present numerical /computer solution of radial
biquaternionic KGE (radialBQKGE); which differs appreciably from conventional
Yukawa potential. Further observation is of course recommended in order to refute or
verify this proposition.

**Category:** Quantum Physics

[48] **viXra:1003.0048 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 3 pages

Unlike what some physicists and graduate students used to think, that physics science
has come to the point that the only improvement needed is merely like adding more
numbers in decimal place for the masses of elementary particles or gravitational constant,
there is a number of unsolved problems in this field that may require that the
whole theory shall be reassessed. In the present article we discuss thirty of those unsolved
problems and their likely implications. In the first section we will discuss some
well-known problems in cosmology and particle physics, and then other unsolved problems
will be discussed in next section.

**Category:** High Energy Particle Physics

[47] **viXra:1003.0047 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 9 pages

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed
using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion
multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM)
field principle characteristics. In particular, it is shown that Q-connexion (with
quaternion non-metricity) and related curvature of 4 dimensional (4D) space-times
with 3D Q-space sections are formally equivalent to respectively YM-field potential
and strength, traditionally emerging from the minimal action assumption. Plausible
links between YM field equation and Klein-Gordon equation, in particular via its
known isomorphism with Duffin-Kemmer equation, are also discussed.

**Category:** Quantum Physics

[46] **viXra:1003.0046 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 3 pages

In the present article we would like to make a few comments on a recent paper
by A. Yefremov in this journal [1]. It is interesting to note here that he concludes his
analysis by pointing out that using full machinery of Quaternion Relativity it is possible
to explain Pioneer XI anomaly with excellent agreement compared with observed data,
and explain around 45% of Pioneer X anomalous acceleration. We argue that perhaps
it will be necessary to consider extension of Lorentz transformation to Finsler-Berwald
metric, as discussed by a number of authors in the past few years. In this regard, it
would be interesting to see if the use of extended Lorentz transformation could also
elucidate the long-lasting problem known as Ehrenfest paradox. Further observation is
of course recommended in order to refute or verify this proposition.

**Category:** Astrophysics

[45] **viXra:1003.0045 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** V. Christianto, Diego L. Rapoport, Florentin Smarandache

**Comments:** 5 pages

In recent years, there are attempts to describe quantization of planetary distance
based on time-independent gravitational Schrödinger equation, including Rubcic &
Rubcic's method and also Nottale's Scale Relativity method. Nonetheless, there is
no solution yet for time-dependent gravitational Schrödinger equation (TDGSE). In
the present paper, a numerical solution of time-dependent gravitational Schrödinger
equation is presented, apparently for the first time. This numerical solution leads
to gravitational Bohr-radius, as expected. In the subsequent section, we also discuss
plausible extension of this gravitational Schrödinger equation to include the effect
of phion condensate via Gross-Pitaevskii equation, as described recently by Moffat.
Alternatively one can consider this condensate from the viewpoint of Bogoliubov-deGennes
theory, which can be approximated with coupled time-independent
gravitational Schrödinger equation. Further observation is of course recommended
in order to refute or verify this proposition.

**Category:** Astrophysics

[44] **viXra:1003.0044 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 4 pages

There have been various explanations of Pioneer blueshift anomaly in the past few
years; nonetheless no explanation has been offered from the viewpoint of Q-relativity
physics. In the present paper it is argued that Pioneer anomalous blueshift may
be caused by Pioneer spacecraft experiencing angular shift induced by similar Qrelativity
effect which may also affect Jupiter satellites. By taking into consideration
"aether drift" effect, the proposed method as described herein could explain Pioneer
blueshift anomaly within ~ 0.26% error range, which speaks for itself. Another new
proposition of redshift quantization is also proposed from gravitational Bohr-radius
which is consistent with Bohr-Sommerfeld quantization. Further observation is of
course recommended in order to refute or verify this proposition.

**Category:** Astrophysics

[43] **viXra:1003.0043 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 4 pages

Using phion condensate model as described by Moffat [1], we consider a plausible
explanation of (Tifft) intrinsic redshift quantization as described by Bell [6] as result
of Hall effect in rotating frame. We also discuss another alternative to explain redshift
quantization from the viewpoint of Weyl quantization, which could yield Bohr-Sommerfeld quantization.

**Category:** Quantum Physics

[42] **viXra:1003.0042 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

In this paper we present four possible extensions of Bell's Theorem: Bayesian and
Fuzzy Bayesian intrepretation, Information Fusion interpretation, Geometric interpretation,
and the viewpoint of photon fluid as medium for quantum interaction.

**Category:** Quantum Physics

[41] **viXra:1003.0041 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

In the present article, we argue that it is possible to generalize Schrödinger equation
to describe quantization of celestial systems. While this hypothesis has been described
by some authors, including Nottale, here we argue that such a macroquantization was
formed by topological superfluid vortice. We also provide derivation of Schrödinger
equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid
dynamics interpretation.

**Category:** Quantum Physics

[40] **viXra:1003.0040 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

This article discusses Neutrosophic Logic interpretation of the Schrodinger's cat
paradox. We argue that this paradox involves some degree of indeterminacy (unknown)
which Neutrosophic Logic could take into consideration, whereas other methods
including Fuzzy Logic could not. For a balanced discussion, other interpretations
have also been discussed.

**Category:** Quantum Physics

[39] **viXra:1003.0039 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, Dmitri Rabounski

**Comments:** 5 pages

Applying the R. A. Brightsen Nucleon Cluster Model of the atomic nucleus we discuss
how unmatter entities (the conjugations of matter and antimatter) may be formed as
clusters inside a nucleus. The model supports a hypothesis that antimatter nucleon
clusters are present as a parton (sensu Feynman) superposition within the spatial
confinement of the proton (^{1}H_{1}), the neutron,
and the deuteron (^{1}H_{2}). If model
predictions can be confirmed both mathematically and experimentally, a new physics
is suggested. A proposed experiment is connected to othopositronium annihilation
anomalies, which, being related to one of known unmatter entity, orthopositronium
(built on electron and positron), opens a way to expand the Standard Model.

**Category:** Nuclear and Atomic Physics

[38] **viXra:1003.0038 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 4 pages

As shown, experiments registered unmatter: a new kind of matter whose atoms include
both nucleons and anti-nucleons, while their life span was very short, no more than
10^{-20}sec. Stable states of unmatter can be built on quarks and anti-quarks: applying
the unmatter principle here it is obtained a quantum chromodynamics formula that
gives many combinations of unmatter built on quarks and anti-quarks.

**Category:** High Energy Particle Physics

[37] **viXra:1003.0037 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Dmitri Rabounski, Larissa Borissova, Florentin Smarandache

**Comments:** 7 pages

This article shows, Synge-Weber's classical problem statement about two particles
interacting by a signal can be reduced to the case where the same particle is located
in two different points A and B of the basic space-time in the same moment of time,
so the states A and B are entangled. This particle, being actual two particles in the
entangled states A and B, can interact with itself radiating a photon (signal) in the
point A and absorbing it in the point B. That is our goal, to introduce entangled states
into General Relativity. Under specific physical conditions the entangled particles in
General Relativity can reach a state where neither particle A nor particle B can be the
cause of future events. We call this specific state Quantum Causality Threshold.

**Category:** Quantum Physics

[36] **viXra:1003.0036 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

In this short paper, as an extension and consequence of Einstein-Podolski-Rosen
paradox and Bell's inequality, one promotes the hypothesis (it has been called the
Smarandache Hypothesis [1, 2, 3]) that: There is no speed barrier in the Universe
and one can construct arbitrary speeds, and also one asks if it is possible to have an
infinite speed (instantaneous transmission)? Future research: to study the composition
of faster-than-light velocities and what happens with the laws of physics at faster-thanlight
velocities?

**Category:** Quantum Physics

[35] **viXra:1003.0035 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 3 pages

Besides matter and antimatter there must exist unmatter (as a new form of matter) in
accordance with the neutrosophy theory that between an entity <A> and its opposite
<AntiA> there exist intermediate entities <NeutA>. Unmatter is neither matter nor
antimatter, but something in between. An atom of unmatter is formed either by (1):
electrons, protons, and antineutrons, or by (2): antielectrons, antiprotons, and neutrons.
At CERN it will be possible to test the production of unmatter. The existence of
unmatter in the universe has a similar chance to that of the antimatter, and its production
also difficult for present technologies.

**Category:** Condensed Matter

[34] **viXra:1003.0034 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

There can be generated many paradoxes or quasi-paradoxes that may occur from
the combination of quantum and non-quantum worlds in physics. Even the passage
from the micro-cosmos to the macro-cosmos, and reciprocally, can generate unsolved
questions or counter-intuitive ideas. We define a quasi-paradox as a statement which
has a prima facie self-contradictory support or an explicit contradiction, but which
is not completely proven as a paradox. We present herein four elementary quantum
quasi-paradoxes and their corresponding quantum Sorites paradoxes, which form a
class of quantum quasi-paradoxes.

**Category:** Quantum Physics

[33] **viXra:1003.0033 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 34 pages, In Russian language

Essence Neutrosophy

**Category:** Quantum Physics

[32] **viXra:1003.0032 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Dmitri Rabounski, Florentin Smarandache, Larissa Borissova

**Comments:** 107 pages, In Russian language

METHODS IN THE GENERAL THEORY OF RELATIVITY

**Category:** Relativity and Cosmology

[31] **viXra:1003.0031 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 109 pages

This book was intended to discuss some paradoxes in Quantum Mechanics
from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a
recent concept Neutrosophic Logic. Essentially, this new concept offers new
insights on the idea of 'identity', which too often it has been accepted as
given.
Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic
introduced by L. Zadeh. While some aspects of theoretical foundations of
logic are discussed, this book is not intended solely for pure mathematicians,
but instead for physicists in the hope that some of ideas presented herein will
be found useful.
The book is motivated by observation that despite almost eight decades,
there is indication that some of those paradoxes known in Quantum Physics
are not yet solved. In our knowledge, this is because the solution of those
paradoxes requires re-examination of the foundations of logic itself, in particular
on the notion of identity and multi-valuedness of entity.
The book is also intended for young physicist fellows who think that somewhere
there should be a 'complete' explanation of these paradoxes in Quantum
Mechanics. If this book doesn't answer all of their questions, it is our
hope that at least it offers a new alternative viewpoint for these old questions.

**Category:** Quantum Physics

[30] **viXra:1003.0030 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Homer B. Tilton, Florentin Smarandache

**Comments:** 109 pages, PROCEEDINGS OF THE CONFERENCE OF 18 FEB 2005

Einstein originally declared that the distortions of special relativity
reflect real changes to the objects being remotely observed, then
reconsidered. The first non sequitur is quoted here from Sachs

**Category:** Relativity and Cosmology

[29] **viXra:1003.0029 [pdf]**
*replaced on 6 Mar 2010*

**Authors:** Dmitri Rabounski

**Comments:** 4 pages, translated by Florentin Smarandache, v1 in French, v2 in Romanian

The author pledge for the freedom of scientists to expose and publish their papers.

**Category:** General Science and Philosophy

[28] **viXra:1003.0028 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 15 pages

In this paper we consider two entangled particles and study all the possibilities:
when both are immobile, or one of them is immobile, or both are moving in
different directions, or one of them is moving in a different direction. Then we
study the causality between them and the paradoxes, which are generated. We
define the Causality Threshold of a particle A with respect to another particle B.

**Category:** Quantum Physics

[27] **viXra:1003.0027 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, V. Christianto, Fu Yuhua, Radi I. Khrapko, J. Hutchison

**Comments:** 147 pages

The reader will find herein a collection of unsolved problems in mathematics
and the physical sciences. Theoretical and experimental domains have each
been given consideration. The authors have taken a liberal approach in their
selection of problems and questions, and have not shied away from what
might otherwise be called speculative, in order to enhance the opportunities
for scientific discovery.
Progress and development in our knowledge of the structure, form and function
of the Universe, in the true sense of the word, its beauty and power, and
its timeless presence and mystery, before which even the greatest intellect is
awed and humbled, can spring forth only from an unshackled mind combined
with a willingness to imagine beyond the boundaries imposed by that
ossified authority by which science inevitably becomes, as history teaches
us, barren and decrepit.
Revealing the secrets of Nature, so that we truly see 'the sunlit plains extended,
and at night the wondrous glory of the everlasting stars', requires
far more than mere technical ability and mechanical dexterity learnt form
books and consensus. The dustbin of scientific history is replete with discredited
consensus and the grand reputations of erudite reactionaries. Only
by boldly asking questions, fearlessly, despite opposition, and searching for
answers where most have not looked for want of courage and independence
of thought, can one hope to discover for one's self. From nothing else can
creativity blossom and grow, and without which the garden of science can
only aspire to an overpopulation of weeds.

**Category:** Mathematical Physics

[26] **viXra:1003.0026 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Homer B. Tilton, Florentin Smarandache

**Comments:** 147 pages

Because of the almost universal failure to recognize the distinction
between physical (reality-based, dynamical) and visual (appearance-based,
kinematical) variables, a tremendous volume of mythology arose over the
past 100 years centered around Einstein's reality view of the distortions of
special relativity.

**Category:** Relativity and Cosmology

[25] **viXra:1003.0025 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 516 pages

The present book discusses, among other things, various quantization phenomena found in
Astrophysics and some related issues including Brownian Motion. With recent discoveries of
exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted
numerous discussions in the past few years.
Most chapters in this book come from published papers in various peer-reviewed journals,
and they cover different methods to describe quantization, including Weyl geometry,
Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters
Navier-Stokes equations are also discussed, because it is likely that this theory will remain
relevant in Astrophysics and Cosmology
While much of the arguments presented in this book are theoretical, nonetheless we
recommend further observation in order to verify or refute the propositions described herein.
It is of our hope that this volume could open a new chapter in our knowledge on the
formation and structure of Astrophysical systems.
The present book is also intended for young physicist and math fellows who perhaps will
find the arguments described here are at least worth pondering.

**Category:** Quantum Physics

[24] **viXra:1003.0024 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 476 pages

The present book covers a wide-range of issues from alternative hadron models to their
likely implications in New Energy research, including alternative interpretation of lowenergy
reaction (coldfusion) phenomena.

**Category:** Condensed Matter

[23] **viXra:1003.0023 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Dmitri Rabounski, Florentin Smarandache, Larissa Borissova

**Comments:** 80 pages

In this work the authors apply concepts of Neutrosophic Logic to the
General Theory of Relativity to obtain a generalisation of Einstein's fourdimensional
pseudo-Riemannian differentiable manifold in terms of Smarandache
Geometry (Smarandache manifolds), by which new classes of
relativistic particles and non-quantum teleportation are developed.
Fundamental features of Neutrosophic Logic are its denial of the Law
of Excluded Middle, and open (or estimated) levels of truth, falsity and
indeterminancy.
Both Neutrosophic Logic and Smarandache Geometry were invented
some years ago by one of the authors (F. Smarandache). The application of
these purely mathematical theories to General Relativity reveals hitherto
unknown possibilities for Einstein's theory.
The issue of how closely the new theoretical possibilities account for
physical phenomena, and indeed the viability of the concept of a fourdimensional
space-time continuum itself as a fundamental model of Nature,
must of course be explored by experiment.

**Category:** Relativity and Cosmology

[22] **viXra:1003.0022 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

One of the most reported problem related to the CMNS (condensed matter nuclear science, or
LENR), is the low probability of Coulomb barrier tunneling. It is supposed by standard physics
that tunneling is only possible at high enough energy (by solving Gamow function).
However, a recent study by A. Takahashi (2008, 2009) and experiment by Arata etc. (2008)
seem to suggest that it is not impossible to achieve a working experiment to create the CMNS
process.
In accordance with Takahashi's EQPET/TSC model [1][2][3], the proposed study will find out
some analytical and numerical solutions to the problem of barrier tunneling for cluster
deuterium, in particular using Langevin method to solve the time-independent Schrödinger
equation. It is hoped that the result can answer some of these mysteries.

**Category:** Condensed Matter

[21] **viXra:1003.0021 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Dmitri Rabounski, Florentin Smarandache, Larissa Borissova

**Comments:** 7 pages

We apply the S-denying procedure to signature conditions in a four-dimensional
pseudo-Riemannian space - i. e. we change one (or even all) of the conditions to
be partially true and partially false. We obtain five kinds of expanded space-time for
General Relativity. Kind I permits the space-time to be in collapse. Kind II permits
the space-time to change its own signature. Kind III has peculiarities, linked to the
third signature condition. Kind IV permits regions where the metric fully degenerates:
there may be non-quantum teleportation, and a home for virtual photons. Kind V is
common for kinds I, II, III, and IV.

**Category:** Relativity and Cosmology

[20] **viXra:1003.0020 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Larissa Borissova, Florentin Smarandache

**Comments:** 4 pages

As shown, any four-dimensional proper vector has two observable projections onto
time line, attributed to our world and the mirror world (for a mass-bearing particle, the
projections posses are attributed to positive and negative mass-charges). As predicted,
there should be a class of neutrally mass-charged particles that inhabit neither our
world nor the mirror world. Inside the space-time area (membrane) the space rotates
at the light speed, and all particles move at as well the light speed. So, the predicted
particles of the neutrally mass-charged class should seem as light-like vortices.

**Category:** Relativity and Cosmology

[19] **viXra:1003.0019 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 4 pages

In the light of some recent hypotheses suggesting plausible unification of thermostatistics
where Fermi-Dirac, Bose-Einstein and Tsallis statistics become its special
subsets, we consider further plausible extension to include non-integer Hausdorff
dimension, which becomes realization of fractal entropy concept. In the subsequent
section, we also discuss plausible extension of this unified statistics to include
anisotropic effect by using quaternion oscillator, which may be observed in the
context of Cosmic Microwave Background Radiation. Further observation is of course
recommended in order to refute or verify this proposition.

**Category:** Quantum Physics

[18] **viXra:1003.0018 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 3 pages

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation
has solution containing imaginary part, which differs appreciably from known solution
of KGE. In the present article we discuss some possible interpretation of this
imaginary part of the solution of biquaternionic KGE (BQKGE); thereafter we offer a
new derivation of biquaternion Schrödinger equation using this method. Further observation
is of course recommended in order to refute or verify this proposition.

**Category:** Quantum Physics

[17] **viXra:1003.0017 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 2 pages

In the present article we argue that it is possible to write down Schrödinger representation
of Navier-Stokes equation via Riccati equation. The proposed approach, while
differs appreciably from other method such as what is proposed by R. M. Kiehn, has an
advantage, i.e. it enables us extend further to quaternionic and biquaternionic version
of Navier-Stokes equation, for instance via Kravchenko's and Gibbon's route. Further
observation is of course recommended in order to refute or verify this proposition.

**Category:** Classical Physics

[16] **viXra:1003.0016 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

In the present article we argue that it is possible to find numerical solution of coupled
magnetic resonance equation for describing wireless energy transmit, as discussed recently
by Karalis (2006) and Kurs et al. (2007). The proposed approach may be found
useful in order to understand the phenomena of magnetic resonance. Further observation
is of course recommended in order to refute or verify this proposition.

**Category:** Classical Physics

[15] **viXra:1003.0015 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 5 pages

It is well-known, that when it comes to discussions among physicists concerning the
meaning and nature of gravitation, the room temperature can be so hot. Therefore,
for the sake of clarity, it seems worth that all choices were put on a table, and we
consider each choice's features and problems. The present article describes a nonexhaustive
list of such gravitation theories for the purpose of inviting further and more
clear discussions.

**Category:** Relativity and Cosmology

[14] **viXra:1003.0014 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 2 pages

An interesting hypothesis concerning the varying length of day has been formulated in
this edition, proposed by A.I. Arbab, based on a proposition of varying gravitational
constant, G. The main ideas are pointed out, and alternative frameworks are also discussed
in particular with respect to the present common beliefs in astrophysics. Further
observation is of course recommended in order to refute or verify this proposition.

**Category:** Relativity and Cosmology

[13] **viXra:1003.0013 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 2 pages

A numerical solution of Wheeler-De Witt equation for a quantum cosmological model
simulating boson and fermion creation in the early Universe evolution is presented. This
solution is based on a Wheeler-DeWitt equation obtained by Krechet, Fil'chenkov, and
Shikin, in the framework of quantum geometrodynamics for a Bianchi-I metric.

**Category:** Quantum Gravity and String Theory

[12] **viXra:1003.0012 [pdf]**
*submitted on 6 Mar 2010*

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

**Comments:** 3 pages

We shortly review a series of novel ideas on the physics of hadrons and nuclear matter.
Despite being vastly different in scope and content, these models share a common
attribute, in that they offer unconventional viewpoints on infrared QCD and nuclear phenomena.
In a sense, they are reminiscent of the plethora of formulations that have been
developed over the years on classical gravitation: many seemingly disparate approaches
can be effectively used to describe and explore the same physics.

**Category:** High Energy Particle Physics

[11] **viXra:1003.0011 [pdf]**
*replaced on 6 Mar 2010*

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

**Comments:** 4 pages

As a continuation of the preceding section, we shortly review a series of novel ideas
on the physics of hadrons. In the present paper, emphasis is given on some different
approaches to the hadron physics, which may be called as 'programs' in the sense of
Lakatos. For clarity, we only discuss geometrization program, symmetries/ unification
program, and phenomenology of inter-quark potential program.

**Category:** High Energy Particle Physics

[10] **viXra:1003.0010 [pdf]**
*replaced on 6 Mar 2010*

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

**Comments:** 6 pages

Quaternion space and its respective Quaternion Relativity (it also may be called as Rotational
Relativity) has been defined in a number of papers including [1], and it can
be shown that this new theory is capable to describe relativistic motion in elegant and
straightforward way. Nonetheless there are subsequent theoretical developments which
remains an open question, for instance to derive Maxwell equations in Q-space. Therefore
the purpose of the present paper is to derive a consistent description of Maxwell
equations in Q-space. First we consider a simplified method similar to the Feynman's
derivation of Maxwell equations from Lorentz force. And then we present another
derivation method using Dirac decomposition, introduced by Gersten (1999). Further
observation is of course recommended in order to refute or verify some implication of
this proposition.

**Category:** Classical Physics

[9] **viXra:1003.0009 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache

**Comments:** 2 pages

In this note we propose the extension of the Big Bang Theory of the origin of the
Universe to the model that there are cycles of beginning and ending.

**Category:** Quantum Physics

[8] **viXra:1003.0008 [pdf]**
*submitted on 5 Mar 2010*

**Authors:** Dainis Zeps

**Comments:** 11 pages, submitted to JCER

Impact of quantum mechanics on physical science epistemology and science at all is
considered.
We consider methodolically idea that science doesn't research its assumed objects but the
ability to research, thus making itself not distinguishable from the cognitive science in the
most general sense. Next idea is that what we discover firstly are the methods and the
technologies understanding about which may come (if at all) much much later after we have
learned to use these technologies in our life up to incredible level.
Instrumentality rather than objectivity should be researched in science. In this sense quantum
mechanical impact on sciences should be assessed. Using this approach, quantum
consciousness should be quested for.

**Category:** History and Philosophy of Physics

[7] **viXra:1003.0007 [pdf]**
*replaced on 15 Mar 2010*

**Authors:** Z.Y. Wang

**Comments:** 6 pages.

The waveguide can be regarded as a potential barrier to microwaves and we apply
quantum mechanics to study the coefficient of reflection R and transmission T . An initial
experimental result is also presented in this paper that the transverse momentum of the
electromagnetic field in a waveguide is zero which is no longer in proportion to the transverse wave
vector. We're preparing to detect under other conditions and will report as soon as possible.

**Category:** Quantum Physics

[6] **viXra:1003.0006 [pdf]**
*submitted on 4 Mar 2010*

**Authors:** Andrew Beckwith

**Comments:** Essay written for the Gravity Research Foundation 2010 Awards for Essays on Gravitation,
Submitted March 4th, 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. A calculated inflaton φ(t) may
partly re-emerge after fading out in the aftermath of inflation. The inflaton may contribute 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 at red shit value of Z ~ .423

**Category:** Relativity and Cosmology

[5] **viXra:1003.0005 [pdf]**
*replaced on 25 Mar 2010*

**Authors:** Constantinos Ragazas

**Comments:** 7 pages

In this paper we un-henge the mystery of Stonehenge and propose a simple and consistent explanation to
all its puzzling enigmas. How the stones got there? How was it built? Why was it built? Why is it aligned
with the summer solstice sunrise? When was it built? Who built it? We argue that Nature built Stonehenge
while men directed its construction. Its original function was neither an astronomical observatory nor a
healing religious center. Stonehenge acquired such attributes thousands of years later as people, even
now, felt its grandeur and wonder. Though the method of its construction can be easily explained, loosening
its magical hold on people's imagination may be a more difficult task.

**Category:** Archaeology

[4] **viXra:1003.0004 [pdf]**
*replaced on 8 Mar 2010*

**Authors:** Young-Mook Kang

**Comments:** 6 pages, Submitted to annals of mathematics

A study of growth of M(x) as x → ∞ is one of the most useful
approach to the Riemann hypophotesis(RH). It is very known that the RH is
equivalent to which M(x) = O(x^{1/2+ε}) for ε > 0. Also Littlewood proved that
"the RH is equivalent to the statement that
lim_{x → ∞} M(x)x^{-1/2-ε} = 0, for
every ε > 0".[1] To use growth of M(x) approaches zero as x → ∞, I simply
prove that the Riemann hypothesis is valid. Now Riemann hypothesis is not
hypothesis any longer.

**Category:** Number Theory

[3] **viXra:1003.0003 [pdf]**
*submitted on 3 Mar 2010*

**Authors:** Ron Bourgoin

**Comments:** 2 pages

The authors of [arxiv:1003.0247] neglect to consider
that the source of radiation is an accelerated electron,
that an emitted photon reacts, or pushes back, on the
electron that releases it. This is a linear process, therefore
a nonlinear Schrödinger equation is not applicable.

**Category:** Quantum Physics

[2] **viXra:1003.0002 [pdf]**
*submitted on 3 Mar 2010*

**Authors:** Ioannis Iraklis Haranas, Michael Harney

**Comments:** 6 pages, Submitted to the Journal of Gravitational Physics, p.6

We study the effects of a non-singular gravitational potential on satellite orbits by calculating the
corresponding changes of its orbital elements, using Gauss' planetary equations. We derive two
non-zero expressions for the changes of the argument of the perigee and the mean anomaly, and
we compare them to those of the general relativity. Using the GRACE satellite system, we obtain
numerical results from which we conclude that the effect of such a potential, on the perigee
cannot be separated from that of general relativity. Furthermore, we conclude that the effect on
the mean anomaly can probably be observed by today's technology.

**Category:** Relativity and Cosmology

[1] **viXra:1003.0001 [pdf]**
*submitted on 1 Mar 2010*

**Authors:** Andrew Beckwith

**Comments:** 10 pages, two figures. Source document for presentation to be made in Xian, PRC, March 23,
at PIERS http://piers.mit.edu/piers2010xian/. Main
contribution is reconciliation of re appearance of
inllaton as generator of entropy with graviton count, a la. Y. Ng's 2008 result, with increase in q(z)
increase in rate of acceleration of the universe one billion years ago.

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) may partly 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