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...ed 5 July 1687. Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The Principia is "justly regarded as one of the most important ...

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... it is not a complete truth. Why is that? Because in the meantime quantum mechanics was developed and there is no agreement between quantum physics... ...e expression of his or her own artistic creativity. The two examples from classical literature we have of this are the Iliad and the Odyssey, writt...

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...ically congruent system of physics, at significant variance with modern and classical theory, is presented in Sections 3-4. A comparative analysis o... ...on ill-defined and paradoxical boundary conditions in the axioms of quantum mechanics and the standard particle model. The boundaries define behavior... ...nens). These rules of inference are endorsed by both Stoic logic and modern classical logic…[Yet,] we arrive at an apparently false conclusion." [40... ... between the physical and the theory; which is logically favorable, to one (classical relativity), where incongruity between theory and physical mea... ...measurements. Using this methodology, predictive equivalence is found with classical relativity, i.e. equivalent congruity in predicted values with... ...(25) indicate nuclear singularities, a necessary property variance with the classically derived singularity is immediately obvious ―atoms are not bla... ...ive paradox in MT. An obvious inference is that the basis for quantum wave mechanics, the Bohr-deBroglie equations for hydrogen spectra, [10] can b... ...tes all relevant and predictively significant relationships in quantum wave mechanics, the standard model, quantum gravity and string theory can be i... ...uli (1925) - Schrödinger (1926) - Heisenberg (1927), progression of quantum mechanics. Atomic electron loci came to be defined as probability distrib...

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...at he falls asleep and misses the party). Are these actions and intentions in their classical senses? There is room for doubt. Davidson narrows down... ... a decade. Some argue against this and say that robots need not be automata in the classical, Church-Turing, sense. That they could act according t... ...of propositions). If the transition from input to output is deterministic we have a classical automaton – if it is determined by a table of probabil... ...ly acknowledged. Modern physics - notably the Copenhagen interpretation of quantum mechanics - has abandoned the classic split between (typically h... ...ywhere, vitiating the need for communication and interaction. Yet, modern Quantum Mechanics provides us with exactly this insight: that time and s... ...supposedly superior races to the travails of physical, galaxy-hopping missions? The classical answer is: in order to manipulate the environment and ... ... the intelligences contained are functional determinants of the container. Quantum Mechanics (rather, its Copenhagen interpretation) implies that t...

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...onate nature, Helen had no experience of intimate love. Oh, she was a doctor and was aware of the mechanics of mating, but the veiled references to ... ...Beedi Meaning rolled tabacco leaf cigarette Word Bharata Natyam Meaning temple dancing in the classical mode. Word Bhisti Meaning Water Carri...

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...tantly being made to how the rules of logic are incorporated into the fundamental circuits of a computer. The logic used in these classes is known as classical or Boolean logic. Neutrosophic logic is an extension of classical logic, but as you will see in the book, there are two intermediate steps between them. Neutrosophic logic is yet another idea generated by Florentin ...

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...ental circuits of a computer. The logic used in these classes is known as classical or Boolean logic. Neutrosophic logic is an extension of classic... ... by Florentin Smarandache, who seems to be a perpetual idea machine. Like classical logic, it can be used in many ways, everywhere from statistics to... ...logic, it can be used in many ways, everywhere from statistics to quantum mechanics. Neutrosophy is more than just a form of logic however. There ... ...hapter 1 of this book is devoted to an introduction to the fundamentals of classical logic, the behavior of the connectives as well as the principles... ...rmal reasoning. The next chapter is an examination of an extension of the classical logic called three-valued logic. With values that can be interpr... ... 5 Table of Contents Preface 3 Table of Contents 5 Chapter 1 Classical Logic 7 Section 1 Propositions Section 2 The Law of t... ...hat uses the I has applications in the branch of physics known as quantum mechanics. Quantum mechanics is the physics of the very small, where even... ...of poison to be broken, which will kill the cat. According to quantum mechanics, the probability that the atom will decay during the interval of... ...live after the interval is ½. However, in the weird world of quantum mechanics, the atom can decay, but until the box is opened and examined, t...

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...al model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about...

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...dache/NeutrosophicSet.PDF • 4. Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics: ... ...nknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision... ...g to a set; - the fuzzy set (for n = 1 and i = 0, and 0 [ t, i, f [ 1); - the classical set (for n = 1 and i = 0, with t, f either 0 or 1); - the p... ... = t_inf+i_inf+f_inf. The neutrosophic probability is a generalization of the classical probability and imprecise probability in which the chance t... ...space, etc. (some of them are hidden parameters, i.e. unknown parameters). In classical probability n_sup [ 1, while in neutrosophic probability n_s... ...veloped since the 17 th century completely and bodily. Also, from Aristotle’s mechanics to Einstein’s special theory of relativity and from classica... ...cial theory of relativity and from classical electrodynamics to modern quantum mechanics, the book has generalized the thoughts of unified field theo... ...s of temperature field, of existence and evolution of whirl vortex body), wave mechanics, electrodynamics, motion medium electrodynamics, trajectory ...

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...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 ac...

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... not to be.” In the same way all computer hardwares from early sixties up to this year are built upon the same binary logic. It is known that the Classical Logic, also called Bivalent Logic for taking only two values {0, 1}, or Boolean Logic from British mathematician George Boole (1815-64), was named by the philosopher Quine (1981) “sweet simplicity.” [57] But this ty...

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...iewicz and Multi-Valued Logic 12 2.3. Introduction to Multi-Valued Algebra, Chang’s Notation 15 2.4. Linkage between Multi-Valued Logic and Quantum Mechanics 15 2.5. Exercise 17 3 Neutrosophy 25 3.1. Introduction to Neutrosophy 25 3.2. Introduction to Non-Standard Analysis 26 3.3. Definition of Neutrosophic Components 27 3.4. Formalization 28 3.5. Evolution of an ...

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...A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the combina...

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...embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interest... ...n as the system has been established, the contribution of combinatorics to classical mathematics, such as, the Riemann geometry and Smarandache geomet... ...le. 1.1.2 Definition of a Smarandache geometry By the history, we know that classical geometries include the Euclid geom- etry, the hyperbolical geomet... ...s proposed by Smarandache in 1969 ([61]), which is a generalization of the classical geometries, i.e., the Euclid, Lobachevshy-Bolyai-Gauss and Rieman... ... 1,x,y ∈R} if we remove from S all the curves used to partiteS. There is a classical result for the partition of a surface gotten by T.Rad´ o in 1925.... ...erential geometry, Riemann geometry, Smarandache ge- ometries, ··· and the mechanics, theoretical physics, ···. For doing this, the most possible way ...

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...This work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. It reviews some of the classical notions of Benthamite utility and the normative utility paradigm offered by the von Neumann-Morgenstern expected utility theory; exploring its major pitfalls before moving into what is postulated as an entropic noti...

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...ty theory as applied to financial decision-making. It reviews some of the classical notions of Benthamite utility and the normative utility paradigm... ...ein et. al., 1978). There is reasonably well-established theory of classical utility maximization in the case of deductible general insurance... ...l preferences exhibit risk aversion (Meyer and Ormiston, 1999). Under the classical utility maximization appoach, the wealth function at the end of ... ...in, 1988). We have already witnessed some possible pitfalls of the classical expected utility maximization approach which governs the risk-re... ...plement such a utility measure. Staying within the confines of the classical normative utility theory (von Neumann and Morgenstern, 1947), on... ...rentice- Hall, 1997. Jaynes, E.T. Information theory and statistical mechanics. Physical Review 106, 1957: 620-630. Johnson, H. Options on...

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...uch larger than the diameter of the “annihilation area”, they can be kept from annihilation (see fig. 3). But because the orbit, according to Quantum Mechanics, is an actual cloud spreading far around the average radius, at any radius between the proton and the anti-proton there is a probability that they can meet one another at the annihilation distance. Therefore the nuc...

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...iophantine equation 33 2.13. Multispaces and applications in physics 34 3 Unsolved Problems in Astrophysics 35 3.1. Unsolved problems in Celestial Mechanics 35 3.2. Unsolved problems in Astrophysics 37 4 Unsolved Problems in Geophysics 45 4.1. Introduction 45 4.2. Some new questions 45 5 Unsolved Problems in Sorites Quantum Paradox and Smarandache Class of Paradoxe...

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... and in the context of scientific research as well (for example, Newtonian mechanics is true on one level of reality and it is false on another leve... ...lity and it is false on another level, as has been demonstrated by quantum mechanics). 198 The existential lie, which is what we are focusing on...

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...Harokopos Power as the Cause of Motion and a New Foundation of Clas- sical Mechanics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ...eld of a point particle. Phys. Rev., 1958, v. 110, 965. 20. Levi-Civita T. Mechanics. — On the analytical expression that must be given to the gravita... ...nies his reference body, Alternatively, Landau and Lifshitz in their The Classical Theory of Fields [1] use the space signature (−+++), which gives ... ...s compressed. 8 Action of the feld without sources According to §27 of The Classical Theory of Fields [1], an elementary action for a whole system con... ...em a is a dimensionless quantity equal to 1 16π ”. According to §27 of The Classical Theory of Fields we havedS f =aF αβ F αβ dVdt= 1 16πc F αβ F αβ d... ...arily ”large” negative values, which cannot have a minimum. Because in The Classical Theory of Fields Landau and Lifshitz take a pseudo-Riemannian spa... ...sverse waves. Following the arguments of Landau and Lifshitz in §47 of The Classical Theory of Fields [1], we defne the wave pressure of a feld as the... ... July, 2005 Power as the Cause of Motion and a New Foundation of Classical Mechanics Efthimios Harokopos P.O. Box 77034, Paleo Faliro, 17510 Athens, G... ...occasionalism for the purpose of establishing an alternative foundation of mechanics. The laws of motion derived in this paper along with the metaphys...

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...ence V. The Decoherence of Measurement VI. The Quantum of Continuity VII. Quantum Mechanics and Superstring Theories SPE C U L A T I ... ... - distant echoes of the new versions of the Many Worlds Interpretation of Quantum Mechanics). Still, why do we, intelligent conscious observers, s... ...y. These intuitive assertions can be easily converted into a formalism. In Quantum Mechanics, the State Vector can be constrained to collapse to th... ...ed to an increase in entropy (thermodynamic laws are the offspring of statistical mechanics). But this simply does not happen. And it is wrong to... .... Space is a yarn. Einstein was the last classicist (relativity just means that no classical observer has any preference over another in formulatin... ...eriously erode the tranquil continuity of yore. But the first serious crack in the classical (intuitive) weltanschauung was opened long ago with th... ...he five string theories, on the one hand, and M Theory on the other hand constitute classical LIMITS. Perturbation theory was used to derive their ... ... Relativity Theory (GRT) formalism and add to it specific matter fields. Thus, many classical black hole solutions satisfy string equations of motio... ...and has profound physical impacts and effects. It has quantum aspects combined with classical determinism. We propose that what we call the Subcons...

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...ying field in sets: 112 4. Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics: 116 ... ...aradoxes to paradoxism was documentarily described by Titu Popescu in his classical book concerning the movement: "Paradoxism's Aesthetics" (1994). ... ....3. Neutrosophic Set: <logic> A generalization of the intuitionistic set, classical set, fuzzy set, paraconsistent set, dialetheist set, paradoxist ... ...,f<=100); - the fuzzy set (for n=100 and i=0, and 0<=t,i,f<=100); - the classical set (for n=100 and i=0, with t,f either 0 or 100); - the paracon... ...eutrosphic probability and neutrosophic statistics, which generalize the classical and imprecise probability and statistics respectively. Keywords... ...orks, evolutionary programming, neutrosophic dynamic systems, and quantum mechanics. Especially in quantum theory there is an uncertainty abou... ... 100% unstable) He gives Orientation Tables for Physical Sciences and Mechanics (Rugina 1989), for the Theory of Probability, for what he called... ...the mysterious world of the atom, where the determinism fails; in quantum mechanics we are dealing with systems having an infinite number of degrees ... ...e real-world systems for designing control logic, and may work in quantum mechanics. # The candidate C, who runs for election in a metropolis M of p...

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... At first sight, this would seem to form a link with the views of quantum mechanics, with its associated wave-particle duality. In fact, de Brogli... ... Kaluza’s initial suggestion with ideas from the emerging field of quantum mechanics, and came up with a suggestion that the additional circular di... ..., String Theory entered the fray. cists have been ld suggestion, quantum mechanics and quan field theory burst onto the scene, and the extra dimen... ...ly stated, physi searching for decades for a theory which wou unite quantum mechanics and general relativity, bringing into the same fold the strong ... ... undulations of the “quantum foam” are encountered. This is where quantum mechanics tends to take over, from the smooth geometrical space-time swe... ... third concept is introduced, that of phase space. Phase space is the classical physics equivalent of the quantum mechanical Hilbert space. Phy... ...chanical Hilbert space. Physics is at the moment divided into two realms, classical physics, which involves Newtonian mechanics and the more recent... ...s dimensionality, each point of which represents the physical state of a (classical) system, the position and momentum information of each individu...

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... exp. edition, GTTI, Moscow, 1934). 2. Landau L. D. and Lifshitz E. M. The classical theory of felds. GITTL, Moscow, 1939 (ref. with the 4th fnal exp.... ...sts the fractal and nondifferentiable geometry. 2 Non relativistic quantum mechanics 2.1 Quantum potential In the scale relativity approach, one decom... ...d on the geodesics bundle of a nondifferentiable space- time in terms of a classical, differentiable part, V, and of a fractal, divergent, nondifferen... ...oth velocity felds are complex due to a fundamental two- valuedness of the classical (differentiable) velocity issued from the nondifferentiability [1... ... ∂ ∂t +V.∇−iDΔ. (1) The constant2D=<dξ 2 >/dt (= /m in standard quan- tum mechanics) measures the amplitude of the fractal fuc- tuations. Note that i... ...i. e., S R /2mD is the phase of the wave function). 3 Relativistic quantum mechanics 3.1 Quantum potential All the above description can be directly g... ...he quantum potential, whose origin remained mysterious in standard quantum mechanics, is a manifestation of the nondifferen- tiability and fractality ... ...d revised ed.: CERN, EXT-2003-025). 5. Landau L. D. and Lifshitz E. M. The classical theory of felds. GITTL, Moscow, 1939 (ref. with the 4th fnal exp.... ...rimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen Channels. Phys. Rev. Lett., 1998, v. ...

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...efined by our actions and output, physical and mental. Thus, one must question the classical differentiation between "internal" and "external". Som... ...rly childhood abuse, for instance, or malnutrition - are "external" and so are the "classical" pathogens (germs and viruses) and accidents. But thi... ...ature" of anything. This is the realm of metaphysics, not of physics. Take Quantum Mechanics. It provides an astonishingly accurate description of ... ... Where interpretations are offered (e.g., the Copenhagen interpretation of Quantum Mechanics) they invariably run into philosophical snags. Modern ... ...Bleuler before him – came with a theory regarding the structure of the mind and its mechanics: (suppressed) energies and (reactive) forces. Flow cha... ....D., Josef Breuer – put forth a theory regarding the structure of the mind and its mechanics: (suppressed) energies and (reactive) forces. Flow cha... ...efined by our actions and output, physical and mental. Thus, one must question the classical differentiation between "internal" and "external". Som... ...rly childhood abuse, for instance, or malnutrition - are "external" and so are the "classical" pathogens (germs and viruses) and accidents. But thi... ... input from the outside. Because they have no Self of their own (even less so than "classical" narcissists) – the "appropriators" tend to over-rate ...

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...d the speed of light is best resolved by applying the rules of relativistic mechanics to the problem, determining the equations of motion of the roc... ...Theory of Relativity is incomplete, since it is not compatible with Quantum Mechanics. At some future time relativity will be replaced by a more co... ...me relativity will be replaced by a more complete theory, just as Newtonian mechanics was replaced by relativity, but whatever replaces relativity m... ...2nd revised ed.: CERN, EXT–2003–025). 5. Landau L.D. and Lifshitz E.M. The classical theory of fields. GITTL, Moscow, 1939 (ref. with the 4th final... ...e, their polarizations are opposite of each other; 37 - in quantum mechanics, objects such as subatomic particles do not have specific, fix... ...never realized. The ranking of physical theories by me: 1. Newtonian mechanics and Hamiltonian mechanics, good theories and essentially Galil...

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...gg and sperm can be compared to the famous wave function (state vector) in quantum mechanics – the represent millions of potential final states (=m... ... Yet, globalization, technology, (and capitalism) are as much in opposition to the classical, hermetic nation-state as is philosophical anarchism. ... ... superfluous and superficial. Sociobiology is already blurring these lines. Quantum Mechanics has taught us that we can say nothing about what the w... ... - distant echoes of the new versions of the Many Worlds Interpretation of Quantum Mechanics). Still, why do we, intelligent conscious observers, ... ...y. These intuitive assertions can be easily converted into a formalism. In Quantum Mechanics, the State Vector can be constrained to collapse to th... .... Space is a yarn. Einstein was the last classicist (relativity just means that no classical observer has any preference over another in formulatin... ...riously erode the tranquil continuity of yore. But the first serious crack in the classical (intuitive) weltanschauung was opened long ago with th... ...it is imbued with much less energy, commitment, passion, and conviction. This is a classical case of quantity turned into quality. The creative per... ...nsic and which does not depend on space and time. Death What exactly is death? A classical point of departure in defining death, seems to be life...