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...The author's motivating interest the past few years has been the development and dissemination of G-dimensional theory (GDT). K. Toshihara, from Japan, proposed the concept of a paper defining G-Dimensional theory in relation to the Smarandache quantum paradoxes. After reviewing a draft, Dr. M. L. Perez, Editor of the SNJ, ...

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... L. Stephen Young G-DIMENSIONAL THEORY & THE SMARANDACHE QUANTUM PARADOXES: Comparative L... ... American Research Press Rehoboth 2001 2 L. Stephen Young G-DIMENSIONAL THEORY & THE SMARANDACHE QUANTUM PARADOXES: Comparative L... ...ess Number 297-5092 Printed in the United States of America 4 G-DIMENSIONAL THEORY & THE SMARANDACHE QUANTUM PARADOXES: Comparative L... ...itute theoretical artifacts or can be considered true physical paradoxes, G Dimensional Theory, a unique, logical and physically congruent system of... ...th modern and classical theory, is presented in Sections 3-4. A comparative analysis of the Smarandache quantum paradoxes within context of the two ... ... 72205, USA E-mail: steve_gd@hotmail.com Keywords: G-dimensional theory, mathematical physics, relativity, Smarandache hypothe... ...nitive answer, an alternative solution method is to use comparative paradox analysis, i.e.: Given two otherwise equivalent physical system theories... ...ality is a desired trait in a scientific value system, and that comparative analysis offers a possible solution to the Smarandache quantum paradoxes.... ...of physics, G-Dimensional Theory (GDT), becomes especially relevant to this analysis. The physical models of GDT are shown to have significant vari...

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...ODELS TO ANALYZE HIV/AIDS WOMEN PATIENTS' PROBLEM 4.1 Use of NRM in the Analysis of the Problem 65 4.2 NAM model to study the Problem 77 ... ...iven by the HIV/AIDS patients 239 6.3 Conclusions from our mathematical analysis 241 APPENDIX 1. Linguistic Questionnaire 255 2. Table ... ... indeterminacy is the neutrosophic model. Neutrosophic models are used in the analysis of the socio-economic problems of HIV/AIDS infected women pa... ... introduction about HIV/AIDS among rural women in Tamil Nadu. Chapter 2 is an analysis of the situation using fuzzy theory in general and Fuzzy Rela... ...e hard to visualize. Fuzzy theorist often picture membership functions as two-dimensional graphs with the domain X represented as a one-dimensional ... ...k is numerical and multidimensional. The AI framework is symbolic and is one dimensional with usually only bivalent expert rules or propositions al... ...o fuzzy sets. Thus a fuzzy system S is a transformation S: I n → I P . The n-dimensional unit hyper cube I n houses all the fuzzy subsets of the d... ... FAM encodes the FAM rule or association (A i , B i ), which associates the p-dimensional fuzzy set B i with the n-dimensional fuzzy set A i . Thes... ...). The simplest NAM encodes the NAM rule or association which associates a p dimensional neutrosophic set B i with the n – dimensional neutrosophi...

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..."Socrates’ haunting cave scenario, immortalized by Plato, exposes reality issues that still bewitch us today: duality, dimensionality, experiential vs agreement reality, free will and our quest for purpose"............ "Now, 2,500 yr later, billions of humans chained to reality TV are de facto agreement reality prisoners like the hapless so...

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...ia I.4: Freeze, Flee or Fight ~ innate responses to existential threats Synopsis II: Saving Experiential Reality (by preserving intrinsic dimensionality) II.1: Perspective II.2: Brain Activity Patterns ~ our (3+1)D link with experiential reality II.3: Multichannel Spectroscopy ~ n-dimensional detection & processing II.4: Multivariate Data Analysis ~ navi...

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...good in a world without aeroplanes or if it ignores the laws of nature. A technical analysis program is useless without a stock exchange or if its m... ... is infinite). Despite its hardware appearance (a read/write head which scans a two-dimensional tape inscribed with ones and zeroes, etc.) – it is r... ...on: its gathering, its accumulation, classification, inter-relation, association, analysis, synthesis, integration, and all other modes of process... ...mmodities in the Group's Headquarters in Switzerland – Manager of the Research and Analysis Division – Manager of the Data Processing Division – P...

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...and doze off, drooling thick saliva diagrams over sheets and crumpled pillow, like the two-dimensional rendition of a layered archeological excavati... ...dible Commodities in the Group's Headquarters in Switzerland – Manager of the Research and Analysis Division – Manager of the Data Processing Divi...

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...CHABILITY: PERIYAR’S VIEW AND PRESENT DAY SITUATION A FUZZY AND NEUTROSOPHIC ANALYSIS 2.1 Analysis of untouchability due to Hindu religion usi... ...Analysis of untouchability due to Hindu religion using FCMs and NCMs 43 2.2 Analysis of discrimination faced by Dalits/ Sudras in the field of ed... ...Social inequality faced by Dalits and some of the most backward classes - an analysis using FCM and NCM 66 5 2.4 Problems faced by Dalits in th... ...ced by Dalits in the political arena due to discrimination – a FCM and NCM analysis 75 2.5 Study of Economic Status of Dalits due to untouchabi... ...conomic Status of Dalits due to untouchability using fuzzy and neutrosophic analysis 83 2.6 Analysis of the social problem of untouchability us... ...ffect on the nation’s progress. That is why, in order to understand the multi-dimensional facets of untouchability and its consequences, we have giv...

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Critical analysis of the foundations and tenets of capitalism and of the dismal science - economics.

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... to yield results only decades hence. There is no effective method of cost/benefit analysis applicable to such time horizons. How are consumer cho... ...isual exposure to advertising - regardless of its content. Humans may be too multi-dimensional and hyper- complex to be usefully captured by econome... ...of a paper published by NBER on March 2000 and titled "The Foundations of Technical Analysis" - Andrew Lo, Harry Mamaysky, and Jiang Wang - claim t... ...al Analysis" - Andrew Lo, Harry Mamaysky, and Jiang Wang - claim that: "Technical analysis, also known as 'charting', has been part of financial p... ...cademic scrutiny and acceptance as more traditional approaches such as fundamental analysis. One of the main obstacles is the highly subjective nat... ...was highly formal and the formalism was highly mathematical. Computers were a three-dimensional extension of formal logic which is the set of RULES ... ... is infinite). Despite its hardware appearance (a read/write head which scans a two-dimensional tape inscribed with ones and zeroes, etc.) – it is r... ... met. This issue can be further radicalized. What is the difference between a two dimensional representation of Kant (portrait), a three dimension... ...ree dimensional representation of the philosopher (a statute) and yet another three dimensional representation of him (Kant himself as perceived by ...

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...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 u...

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... 5 Preface Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are ba... ...vented by Kosko and neutrosophic cognitive maps introduced by us help in the analysis of such real world problems and they happen to be mathematica... ...y study several models that are at times time dependent or when a comparative analysis is needed can use these models. On a personal note, we th... ...FCM and overlap FCM when some of the attributes overlap i.e. in the study or analysis of a model when we have some common attributes given by exper... ...f some fuzzy event, perhaps the strength of a political statement, in medical analysis or so on. The edge values p ij e takes values in the fuzzy c... ...the public has a good standing and rapport. So the problem involved is multi dimensional. So if we wish to divide this into two sets of problems ... ...ational Conference on Fuzzy Systems, 795- 801, 1992. 50. Halmos, P.R. Finite dimensional vector spaces, D Van Nostrand Co, Princeton, 1958. 51. H...

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... The forth chapter introduces the concept of interval dual numbers, we also extend it to the concept of neutrosophic and 8 fuzzy dual numbers. Higher dimensional dual numbers are defined, described and developed in chapter three. Chapter two gives means and methods to construct the new element g such that g2 = 0. The authors feel Zn (n a composite positive integer) is a ri...

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...Dedication 5 Preface 7 Chapter One INTRODUCTION 9 Chapter Two DUAL NUMBERS 11 Chapter Three HIGHER DIMENSIONAL DUAL NUMBERS 55 Chapter Four DUAL INTERVAL NUMBERS AND INTERVAL DUAL NUMBERS 89 Chapter Five APPLICATION OF THESE NEW TYPES OF DUAL NUMBERS 129 Chapter Six SUGGESTED PROBLEMS 131 FURTHER READING 153 IN...

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...erful and an advanced tool which can handle over one linear model at a time. Bimatrices will be useful when time bound comparisons are needed in the analysis of the model....

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...se operations. In fact this property will be nice in a way, for, in all our analysis we would not in general get a solution from a set we have start... ...e. Bimatrices will be useful when time bound comparisons are needed in the analysis of the model. Thus for the first time the notion of bimatrices ... ...inear bioperator is introduced in section four. Section Five introduces and analysis the notions of bieigen values and bieigen vectors. In section s... ... the capacity to generate V = V 1 ∪ V 2 . The important fact is that same dimensional bivector spaces are in general not isomorphic. Example 2... ... = {Polynomials of degree less than or equal to 4}. Clearly V is a finite dimensional bivector space of dimension 9. In order to avoid confusion w... ...ciated with matrices. We assume throughout V = V 1 ∪ V 2 is only a finite dimensional bivector space. Now we proceed on to define linear Bitransf... ... , α 2 ) = T 1 ( α 1 ) ∪ T 2 ( α 2 ) = (0, 0). If V is a finite dimensional the birank of T is the dimension of the range of T and the b... ...resent the bitransformation by bimatrices. Let V = V 1 ∪ V 2 be a (n, p) dimensional bivector space over the field F and let W = W 1 ∪ W 2 be a...

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...ogical graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applicat...

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...of FRM models and the attributes taken for the study related with the PWDs and the caretakers, the FRM model formed using these attributes and their analysis. The third section gives the suggestions and conclusions derived from the survey as well as the FRM model. Key Words: FRM model, fixed point, hidden pattern, relational matrix, limit cycle. AMS(2000): 04A72....

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... has. THEOREM (CAYLEY HAMILTON): Let T be a linear operator on a finite dimensional vector space V. If f is the characteristic polynomial for T, ... ...EM: (CYCLIC DECOMPOSITION THEOREM): Let T be a linear operator on a finite dimensional vector space V and let W 0 be a proper T-admissible subspace... ...ERALIZED CAYLEY HAMILTON THEOREM): Let T be a linear operator on a finite dimensional vector space V. Let p and f be the minimal and characteristic... ...α ≠ 0. v. 〈α | c β + γ〉 = c〈α | β〉 + 〈α | γ〉. Let Q n or F n be a n dimensional vector space over Q or F respectively for α, β ∈ Q n or F ... ...tor space together with a specified inner product in that space. A finite dimensional real inner product space is often called a Euclidean space. ... ...ce of type III. So this definition will help in practical problems where analysis is to take place in such set up. Now we can define Smarandache l... ...repel but remain without action or not able to predict the action for such analysis we can certainly adopt the concept of neutrosophic graphs. In ...

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... Part 2 Electrical engineering 2 Example problems that illustrate electrical analysis using behavior methodology ... ...rt 3 Heat transfer engineering 7 Example problems that illustrate heat transfer analysis using behavior methodology ... ...t 4 Stress/strain engineering 11 Example problems that illustrate stress/strain analysis using behavior methodology 149 12 The modulus ... ... factor 184 16 Fluid flow behavior methodology 192 Part 6 Dimensional homogeneity 17 A critical appraisal of the convent... ... Dimensional homogeneity 17 A critical appraisal of the conventional view of dimensional homogeneity 203 18 Dimensional homogeneity ... ...that Engineering phenomena are rigorously described only by equations that are dimensionally homogeneous. Based on data obtained by Ohm, Fo... ...problems are generally much easier to solve if the variables are separated. Dimensional homogeneity My view of homogeneity differs considera... ... in specified dimensions rather than the parameters themselves. • Equations are dimensionally homogeneous, but no significance is attached to hom... ...he ratio of primary parameters is variable. If this variable ratio is used in the analysis of a problem, the analysis usually must be indirect. If...

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... thenarmis@yahoo.com The black hole, which arises solely from an incorrect analysis of the Hilbert solution, is based upon a misunderstanding of the s... ...tion The variabler has given rise to much confusion. In the con- ventional analysis, based upon the Hilbert metric, which is almost invariably and inc... ...matter and charge requires the determination of the mappingψ. The orthodox analysis has completely failed to understand this and has consequently fail... ...nd this and has consequently failed to solve the problem. The conventional analysis simply looks at the Hilbert metric and makes the following unjusti... ...ory — all the postulates are naturally contained in the geometry of a four-dimensional pseudo- Riemannian space with the sign-alternating signature (−... ...e theory. Verifcation of the theory by experiments has shown that the four-dimensional pseudo-Riemannian space satisfes our observable world in most c... ...al coordinates are imaginary, because the observable projection of a four- dimensional impulse on the spatial section of any given observer is positiv... ...n to displace a free mass-bearing particle of rest-mass m 0 through a four-dimensional interval of length ds. What happens to matter during this actio... ...metric tensorg αβ to the energy-momentum tensor of matter through the four-dimensional curvature of space-time. This implies that the gravitational fe...

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...T OF MODERN CHEMISTRY 90 ANTOINE L. LAVOISIER (1743-1794) French Chemist 92 The Father of Modern Chemistry. Founder of the quantitative chemical analysis. Proposed The Law Of Conservation Of Matter. JOHN DALTON (1766-1844) English Chemist 98 Proponent of the Modern Atomic Theory. Created the atomic symbols and a table of atomic weights. JONS J. BERZELIUS (17...

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... and spatial coordinates are imag- inary, because the projection of a four-dimensional impulse on the spatial section of any given observer is positiv... ... observable quantities (chronometric invariants) are pro- jections of four-dimensional quantities on his time line and the spatial section, made by pr... ... usual symbols Γ α μν = =g ασ Γ μν,σ , usingh ik instead ofg αβ . The four-dimensional generalization of the chr.inv.-quan- tities F i , A ik , and D ... ...e time, as Synge’s well-known book [12] shows, in a space of constant four-dimensional curvature, K= const, we haveR αβγδ =K(g αγ g βδ −g αδ g βγ ),R ... ... in an arbitrary curvature space, we obtain a correlation between the four-dimensional curvature K and the observable three- dimensional curvature in ... ... a ν =γ μ γ ν D μ a ν (57) where D μ is the covariant derivative of tensor analysis. Decomposing the Clifford product γ μ γ ν into its sym- metric and... ...nopoles in Maxwell’s theory was investigated by [89] and a recent critical analysis of “unifed” theories of gravity with electromagnetism has been pre... ...the notion of fractal “manifolds”. A scale- fractal calculus and a fractal-analysis construction that are esential in building the notion of a fractal... ...lgebras and physics. Edited by R. Ablam- owicz, B. Fauser. Vol 2: Clifford analysis. Edited by J. Ryan, W. Sprosig. Birkhauser, Boston, 2000. 7. Loune...

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...near transformation, linear operator etc. We say a vector space is finite dimensional if there exists a finite set of linearly independent elements ... ...nts (v 1 , v 2 , …, v n ) in V which generate V, otherwise it is infinite dimensional that is there does not exist a finite set of linearly independe... ...ache basis is really a new concept. DEFINITION 1.2.2: Let V be a finite dimensional vector space over a field K. Let B = {v 1 , v 2 , …, v n } be ... ... very definition of these concepts. DEFINITION 1.2.3: Let V be a finite dimensional vector space over a field K. Let B = {v 1 , v 2 , …, v n } b... ... L be any vector space over the field K. We say L is a Smarandache finite dimensional vector space (S-finite dimensional vector space) of K if every... ...o introduce Smarandache non- associative algebras we don't give a complete analysis of Jordan algebras. Further we are mainly interested in the algeb... ...Smarandache P-algebras using P- identities in groupoid rings. 120 4. Analysis of alternative algebras and Smarandache alternative algebras using... ... to these algebras. Further these algebras became little difficult for analysis as x 2 = 0 for all elements x in a Lie algebra. Yet we have intr...

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...complete systematic introduction of all concepts together with a sequential analysis of these concepts. Examples are provided abundantly to make the... ...t set of vectors in V, which spans the space V. The space V is finite 24 dimensional if it has a finite basis which spans V, otherwise we say V is... ...onal if it has a finite basis which spans V, otherwise we say V is infinite dimensional. Example 1.4.5: Let V = F × F × F = {(x 1 , x 2 , x 3 ) / ... ...morphic with L(V, V) = {set of all linear operators from V to V}. (V is a n-dimensional vector space over Q). 6. Prove we can always get a matrix ... ...e can always get a matrix associated with any linear operator from a finite dimensional vector space V to V. 7. Let T be the linear operator on R ... ...in the basis of V to be the dimension of V. A semivector space is finite dimensional if the space has a unique basis and the number of elements i... ... researchers. Except for Smarandache notions such rich type of mathematical analysis would be completely absent in the realm of mathematics. 1. D...

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...ersity of New Mexico Gallup, NM 87301, USA 0.1 Introduction to Non-Standard Analysis. In 1960s Abraham Robinson has developed the non-stan... ...s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines t... ...“ - a” one signifies a monad, i.e. a set of hyper-real numbers in non-standard analysis: .( - a)= {a-x: x %‘ * , x is infinitesimal}, and sim... ...e appurtenances (t [ 1, and f [ 1 or I [ 1). 5 NEUTROSOPHIC STATISTICS: Analysis of events, described by the neutrosophic probability, means n... ...nge in error element (dt) and the resulting control action growth in the three dimensional implication function ( A x B---->E). The first step is t... ...f which were necessary for survival or reproduction and all ignored in the one-dimensional biological practice of 'population genetics'. These form a... ...ll the dimensions - system wide (intrinsic value). In highly complex (high dimensional) systems however there will be multiple attractors presen... ...the lower systemic type in many aspects of our daily lives, as seen in our one-dimensional prejudices and our behaviours of conflict and competition.... ...on values, we can see that this relates to forcing a 1 bit systemic value (one dimensional) onto a multi-bit extrinsic value (two dimensional) to wh...

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...ting the laws of physics and in performing measurements). His space-time is a four dimensional continuum. What commenced as a matter of mathematica... ...D-branes are the probability fields of all possible vibrations. The Universe A 12 dimensional universe is postulated, with 9 space dimensions and ... ...es", the worlds in the Many Worlds interpretation of Quantum Mechanics. Such a 12 dimensional Universe is reducible to an 11 dimensional M Theory ... ...nsional Universe is reducible to an 11 dimensional M Theory and, from there, to 10 dimensional string theories. In the Appendix we study an alterna... ... multiple universes may be merely an artefact, enumerating all the ways that a four-dimensional surface can be folded, using supersymmetric formal... ...h the processing of the incoming stimuli and their analyses. These processing and analysis are mostly unconscious, but they exert influence over t... ...tion into Parapsychology of scientific methods of observation, experimentation, and analysis (e.g., the use of statistics and probability in the stu... ...ertainty that we possess all the conceivable tools for the detection, description, analysis and utilization of relations between entities. Put diff... ...cannot prove that such a God is impossible because perfections are not amenable to analysis. But that hardly amounts to any kind of proof! Read No...