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...s degree 1 or 4. Jordan in 1869 independently discovered trees as a purely mathematical discipline and Sylvester 1882 wrote that Jordan did so with... ... by psychologists L. Festinger and D. Cartwright. The world of Theoretical physics discovered graph theory for its own purposes more than once. In ... ...wo points are adjacent whenever both spaces are occupied. Another aspect of physics employs graph theory rather as pictorial device. Feynmann propos... ...e reader. 3.8 Neutrosophic Models versus Fuzzy models We know in all mathematical analysis of the unsupervised data, not only uncertainty is ... ...s predominant but also the concept of indeterminacy is in abundance. But in mathematical logic no one used the concept of indeterminacy till the yea... ...sophic logic. So whenever we introduce the notion of indeterminacy in our mathematical analysis we name the structure as Neutrosophic structure. V... ...bility). He contributed with proposed problems and solutions to the Student Mathematical Competitions. His latest interest is in information fusion ...

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...their properties It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary re... ...ominated criterion vectors is called the non-dominated set. In the absence of a mathematical specification of the decision maker’s utility function,... ...ity to determine outputs for a given set of inputs without using conventional, mathematical models. FLC follows the general strategy of control wor... ... with sup-t composition nor adjoint equation. Therefore, simple control is not “mathematically correct”. However, solutions of fuzzy relational equa... ...terminacy, and falsity may overlap, and n_sup = 30+51+28 > 100 in this case. Physics Examples a) For example the Schrodinger’s Theory says that ... ...one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosophic set. After... ...of the fluid under study their by changing the flow rates while analyzing as a mathematical model. So in the study of flow rates in chemical plants...

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...e F i e l d s 2 0 - 3 2 5. The SQP Set in MT & GDT Comparative Physics 32-41 Bibliography 4 2 - 4 3 ... ...2, USA E-mail: M_L_Perez@yahoo.com http://www.gallup.unm.edu/~smarandache/physics.htm ISBN: 1-931233-46-2 Standard Address Number 297-5092 ... ... G Dimensional Theory, a unique, logical and physically congruent system of physics, at significant variance with modern and classical theory, is pre... ... E-mail: steve_gd@hotmail.com Keywords: G-dimensional theory, mathematical physics, relativity, Smarandache hypothesis, gravity, quant... ...mail: steve_gd@hotmail.com Keywords: G-dimensional theory, mathematical physics, relativity, Smarandache hypothesis, gravity, quantum theory, Sm... ...usion principle, we see a fourth spatial dimension in GDT has evolved from a mathematical convenience to a logical necessity. Let Universal Space be ... ...is non-zero in another." [44] Again, GRT fails to meet the criteria of the mathematically non-trivial "strict VSE". In Section four the local regi... ...onditions for strict Very Strong Equivalence. In this context, GDT has clear mathematical superiority and raises a comparative paradox in SRT/GRT. 3... ...ollowing corollary theorems and hypotheses, some of which are logically and mathematically proven. From the intrusion principle, spatial curvature r...

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...nitive 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-matric...

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... 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 un... ...This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs,... ...t will be easy for an expert to work with. He need not be a person with good mathematical background. For an expert may be a doctor or a lay man wh... ...roughout this book will be denoted by dotted lines. The world of theoretical physics discovered graph theory for its own purposes. In the study of ... ... of the NRM model we will proceed on to describe the concepts of it in a more mathematical way. DESCRIPTION OF A NRM: Neutrosophic Cognitive Ma... .... 58. Jacobson, N. Structure of Rings, Colloquium Publications, 37, American Mathematical Society, 1956. 59. Jang, S.R., C.T. Sun and E. Mizutani. ... ...n USA. He published over 75 books and 100 articles and notes in mathematics, physics, philosophy, psychology, literature, rebus. In mathematics hi... ...nd imprecise probability). Also, small contributions to nuclear and particle physics, information fusion, neutrosophy (a generalization of dialecti...

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...since f( )<f( 0 ) = l a m a . Bibliography 1. M. Bencze, OQ.591, Octogon Mathematical Magazine, vol.9, no.1, April 2001, p.670. 2. J. S andor, Geom... ... c and D. Milo sevi c, Two inequalities for any right triangle, Octogon Mathematical Magazine, vol.9, no.1, 402-406. 2. J. S andor, On Emmerich’s ... .... Dacia, 1988. 3. M. Dinc a, About Erd os-Mordell’s inequality , Octogon Mathematical Magazine, vol.8, no.2, 2000, 481-482. 4. M. Dinc a, M. Bencze... ... 1 x 2 + 1 y 2 = 1 z 2 in integers, these Selected papers. 5. Ch.W. Trigg, Mathematical Quickies, New York, 1968. 58 2 On the equation 1 x 2 + 1 y 2 ... ...nd important particular case a = b = c = 1 (with applications in geometry, physics, nomo- grams, etc.). We shall use the Euler-Bell-Kalm ar lemma. Al... ...uation is very important, since occurs in geometry, number-theory, optics, physics, etc. For three distinct solutions, see [1]. Let now,n 3. Let us n... ...i surprize ^ n matematic a , Ed. Enc. Rom^ an a, 1975; English edition: Mathematical Quickies, New York, 1968. 4. B. Margit, Problem E:11248, Mat. ...

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...of the convergent property of . Especially, when , from the knowledge of mathematical analysis (see [2]), we have This completes the proof of the t... ... solutions, XiQuan Publishing House, Chicago, 1993, pp36. [2] T.M.Apostol. Mathematical analysis, 2nd ed., Addison Wesley Publish- ing Co., Reading, M... ... ON THE GENERALIZED CONSTRUCTIVE SET Gou su Department of Mathematics and Physics, Xi’an Institute of Posts and Telecoms, Xi’an, Shaanxi, P .R.China ... ...n Publ. House, 1993. [2] Heath Brown D R. Ibid. III. Journal of the London Mathematical Soci- ety, 1979, 20: 177-178. IDENTITIES ON THE -POWER COM...

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...o the geometry of general relativity, and it is currently a very active area of mathematical research (see [21, 16, 4, 8]). Riemannian manifolds c... ... collection of all s-segments with endpoints A and B. The “q” refers to quantum physics, which inspires this definition, although fuzzy logic would b... ...Intrinsic Geometry of Surfaces (J.M. Danskin, Trans.). Providence, RI: American Mathematical Society. 2. Antholy, M. (2001). Smarandache Geometry ... ...1996). All the way with Gauss-Bonnet and the sociology of mathematics. American Mathematical Monthly, 103 (6), 457-469. 12. Greenberg, M.J. (1980)... ...aightest geodesics on polyhedral surfaces. In H.C. Hege and K. Polthier (Eds.), Mathematical Visualizations. Berlin: Springer- Verlag. 19. Smarand...

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...their properties It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from X to Y, binary re... ...ominated criterion vectors is called the non-dominated set. In the absence of a mathematical specification of the decision maker’s utility function,... ...ity to determine outputs for a given set of inputs without using conventional, mathematical models. FLC follows the general strategy of control wor... ... with sup-t composition nor adjoint equation. Therefore, simple control is not “mathematically correct”. However, solutions of fuzzy relational equa... ...terminacy, and falsity may overlap, and n_sup = 30+51+28 > 100 in this case. Physics Examples a) For example the Schrodinger’s Theory says that ... ...one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosophic set. After... ...of the fluid under study their by changing the flow rates while analyzing as a mathematical model. So in the study of flow rates in chemical plants...

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... India. The fourth and concluding chapter gives observations drawn from our mathematical results based on the Fuzzy and Neutrosophic analysis. A... ... A study of this kind is being carried out for the first time. We have used mathematical tools to study this sociological problem because we wante... ... of the NRM model we will proceed on to describe the concepts of it in a more mathematical way. DESCRIPTION OF A NRM: Neutrosophic Cognitive Ma... ...ps (FCMs) and Neutrosophic Cognitive Maps (NCMs). For the first time, we use mathematical models to analyze untouchability. We specifically use Fuz... ...ave refrained from giving our views since the sole purpose of this study is a mathematical analysis of untouchability. 43 2.1 Analysis of un... ...n USA. He published over 75 books and 100 articles and notes in mathematics, physics, philosophy, psychology, literature, rebus. In mathematics hi... ...nd imprecise probability). Also, small contributions to nuclear and particle physics, information fusion, neutrosophy (a generalization of dialecti...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...n this paper the symmetric primitive matrices of order n with exponent n − 2 are completely characterized by applying a combinatorial approach, i.e., mathematical combinatorics ([7]). Key words: primitive matrix, primitive exponent, graph....

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...Aims and Scope: The International J.Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original ...

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...d YUN BAI. . . . . . . . . . . . . . . . . . . . . . . . . . . .06 Curvature Equations on Combinatorial Manifolds with Applications to Theoretical Physics BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . ....

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...NG written by Lao Zi, an ancient philosopher of China. Then how it works to mathematics, not suspended in thought? This paper explains this action by mathematical logic on mathematical systems generalized to Smarandache systems, or such systems with combinatorial structures, i.e., combinatorial systems, and shows how to extend the homomorphism theorem in abstract algebra t...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...iscussed in this paper, particularly, the CC conjecture presented by myself six years ago, which enables one to construct more symmetrical systems in mathematical sciences. Key Words: Smarandache sequence, labeling, Smarandache beauty, graph, group, Smarandache system, combinatorial system, CC conjecture...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all a...

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...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a brie...

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...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics PROGRESSINPHYSICS A quar... ...is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathSciNet (AMS, USA), DOAJ of Lund University (Sw... ... Mexico, 200 College Road, Gallup, NM 87301, USA Copyright c Progress in Physics, 2005 All rights reserved. Any part of Progress in Physics howsoeve... ...ate citation of this journal. Authors of articles published in Progress in Physics retain their rights to use their own articles in any other publicat... .... . . . . . . . . 113 Information for Authors and Subscribers Progress in Physics has been created for publications on advanced studies in theoretica... ...ard assumptions are incorrect, which I shall demonstrate with the required mathematical rigour. Contrary to the usual practise, one cannot talk about ... ... 0 =0 in (18) purely and simply by its invalid initial assumptions, not by mathematical imperative. It incor- rectly assumes p C n (r)≡R p (r)≡r, then... ...ly, the Kruskal-Szekeres formulation is meanin- gless, both physically and mathematically. In addition, the so-called “Schwarzschild radius” (not due ... ...as long ago as 1917, by T. Levi-Civita [20], on the grounds that, from the mathematical standpoint, it lacks the invariant character actually required...

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...e probability of complete financial ruin for the trader but no meaningful mathematical expression can model this case under the assumption of logari... ...so been theoretical advances in the esoteric area of econophysics whereby mathematical analogs have been proposed and substantiated between utility ... ...amics in so far as that both neoclassical economics and classical thermal physics seek to model natural systems in terms of solutions to constrained... ... logic based on behavioral reasoning, supported in most parts by rigorous mathematical exposition or numerical simulation and sensitivity analysis. T... ...isk classification is proposed – neutrosophic logic being a new branch of mathematical logic which allows for a three-way generalization of binary f... ...ogue – options-based portfolio insurance. In this chapter we propose and mathematically prove a theorem which we have named the “theorem of consiste... ...Entropy and Bayesian Methods in Inverse Problems: Fundamental Theories of Physics, D. Reidel Publishing Company, Holland, 1985. Hull, J. C. Optio...

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...and Élan Vitale is misplaced: Natural Selection IS the vital power itself. Modern Physics is converging with Philosophy (possibly with the philoso... ...ble. We have a corporeal body. It is a physical entity, subject to all the laws of physics. Yet, we experience ourselves, our internal lives, exter... ...n not know the "true nature" of anything. This is the realm of metaphysics, not of physics. Take Quantum Mechanics. It provides an astonishingly a... ...ro-processes and of the Universe without saying much about their "essence". Modern physics strives to provide correct predictions - rather than to ... ...xample of which is the spreadsheet). Data items were related to each other through mathematical formulas. This is the equivalent of the increasing ... ... or end and what, precisely, does it include? A fractal curve (boundary) is an apt mathematical treatment of this question. Indeterminacy can be de... ...ts). His space-time is a four dimensional continuum. What commenced as a matter of mathematical convenience was transformed into a hallowed doctrin... ...al systems (better known as "Chaos Theory") has also violated long held notions of mathematical continuity. The sets of solutions of many mathemati... ...gers. This set has a boundary and will react in the same way, simultaneously, to a mathematical action (say, to a multiplication by a constant). Bu...

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...c logic grew as an alternative to the existing logics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undef... ...eural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Prof. Bart Kosko, the guru... ...ct us almost as much as the determined factors. It is a major handicap in mathematical modeling that we are only able to give weightages for known c... ...ng issues are naturally solved, since Time is explicitly expressed in the mathematical equations used to describe the relations between concepts. Ho... ...Only the modifier is used. However, its meaning can be represented in the mathematical expression as (Q i ∪ ~ Q i ) ∩ M i which contains the qua... ...h we will be defining as neutrosophic graphs. The world of theoretical physics discovered graph theory for its own purposes. In the study of stat...

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... j. Prescriptive Powers – The theory must yield policy prescriptions, much like physics yields technology. Economists must develop "economic tec... ...verwhelming empirical evidence to the contrary - simply because it is aesthetic and mathematically convenient. So, what are economic "theories" goo... ...thal falsified all apocalyptic Malthusian scenarios hitherto. Operations research, mathematical modeling, transparent decision making, free trade, ... ...rlying asset at a handsome profit. Without delving too deeply into the model, this mathematical expression works well during trends and fails miser... ...ir value of a security or a market can be derived from available information using mathematical models - but is rarely reflected in prices. This is... ...ected in prices. This is the weak version of the market efficiency hypothesis. The mathematically convenient idealization of the efficient market, ... ...irth to metallurgy, computers to computer science and the transistor to solid state physics. The discoveries of science also lead, though usually c... ...orous requirement which cannot be formalized). Quantum mechanics is the branch of physics which describes the microcosm. It is governed by the Sc... ...hotomy. So, Death, as opposed to inertia or entropy, is not something that modern physics is fully equipped to deal with. Physics, by definition, ...

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...omic models. 1.3.1 Smarandache Markov chains Suppose a physical or a mathematical system is such that at any moment it can occupy one of a fin... ...ers of a set introduced, we have studied the theory of directed graphs to mathematically model the types of sets and relation. On similar lines we ... ... and relation. On similar lines we can introduce the directed bigraphs to mathematically model the types of sets and relation. Example 3.5.1: The... ...ich can be attached to some or all of the entities of a system of study. A mathematical bicode is a bicode with some mathematical structure. In many... ...de with some mathematical structure. In many cases as in case of codes the mathematical structure of a bicodes refers to the fact that it forms a bi... ...hich we will be defining as neutrosophic graphs. The world of theoretical physics discovered graph theory for its own purposes. In the study of sta...

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...neral manifolds, we know that Riemann surfaces have become a source of the mathematical creative power. Many good ideas for the manifolds with higher ... ..., in fact, any solution for one of these problems needs to establish a new mathematical system first. But as soon as the system has been established, t... ...ann geometry, Smarandache ge- ometries, ··· and the mechanics, theoretical physics, ···. For doing this, the most possible way is, perhaps by the comb... ...K.Polthier and M.Schmies, Straightest geodesics on polyhedral surfaces, in Mathematical Visualization(ed. byH.C.HegeandK.Polthier),Springer-Verlag, Be...

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...Research papers presented in this collection manifest only a few of many possible applications of neutrosophic logics to theoretical physics. Most of these applications target the theory of relativity and quantum physics, but other sections of physics are also possible to be considered....

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... S-Denying of the Signature Conditions Expands General Relativity’s Space, by Dmitri Rabounski, Florentin Smarandache, Larissa Borissova, Progress in Physics, 13-19, Vol. 3, 2006.......7 Positive, Neutral, and Negative Mass-Charges in General Relativity, by Larissa Borissova and Florentin Smarandache, Progress in Physics, 51-54, Vol. 3, 2006. .............14 Extensio...

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...Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 172...

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...te Johanne Fjamfle- die, A. R. in Obfervatorio Regio Grenovicenfi, 1725. Mathematical Elements of Natural Philofophy, confirm’d by Experiments, or a...

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...which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems or other mathematical problems. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will g...

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...g and S. Ma : An e±cient hybrid genetic algorithm for continuous optimization problems 46 L. Mao : An introduction to Smarandache multi-spaces and mathematical combinatorics 54 M. Selariu : Smarandache stepped functions 81 X. Zhang and Y. Zhang : Sequences of numbers with alternate common di®erences 93 Y. Zhang : On the near pseudo Smarandache function 98 A. Muktib...

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...In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinatorialization, implicated in the foreword of Chapter 5 of my book Automorphism groups of Maps, Sur...

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...mbinatorial principle . . . . . . . . . . . . . . . . . . . . . . 37 1.6.1 Proposition in lgic. . . . . . . . . . . . . . . . . . . . . . .37 1.6.2 Mathematical system. . . . . . . . . . . . . . . . . . . .39 1.6.3 Combinatorial system . . . . . . . . . . . . . . . . . . . 41 1.7 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Chapter 2. Algebra...

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...Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

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...54321 has 55 inversions, and 1342 has two inversions. So our interest will be of the numbers in Smarandache reverse sequence i.e. (1), because it has mathematical patterns and interesting properties....

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...troduced by Smarandache in under his idea of hybrid mathematics: combining different fields into a unifying field, which can be formally defined with mathematical words by the next definition. ...

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... & F. Smarandache..............................................571 71. About Factorial Sums, by Mihály Bencze and Florentin Smarandache, in Octogon Mathematical Magazine, Bra_ov, Romania, Vol. 15, No. 2, 810-812, 2007.......574 72. Inequalities for Integer and Fractional Parts, by Mihály Bencze, Florentin Smarandache, in “Octogon", Vol. 14, No. 1, 206-211, 2006...........

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... & F. Smarandache..............................................571 71. About Factorial Sums, by Mihály Bencze and Florentin Smarandache, in Octogon Mathematical Magazine, Bra_ov, Romania, Vol. 15, No. 2, 810-812, 2007.......574 72. Inequalities for Integer and Fractional Parts, by Mihály Bencze, Florentin Smarandache, in “Octogon", Vol. 14, No. 1, 206-211, 2006...........