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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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...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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... 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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...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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... & 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...........