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... neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and stu...

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...in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu ... ...SBN: 1-931233-87-X Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS P r e f a c e ... ... SUGGESTED PROBLEMS 127 BIBLIOGRAPHY 133 INDEX 141 ABOUT THE AUTHORS 149 5 Preface Study of neutrosophic alge... ...is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directe... ...ntly fought against Brahmin supremacy for the emancipation of the oppressed peoples of the downtrodden castes. This present book was a side-project ... ...c fields, neutrosophic spaces and neutrosophic matrices and illustrate them with examples. For these notions are used in the definition of neutrosop... ... Group Dynamics to another psychological interpretation of a graph in which people are represented by points and interpersonal relations by lines. S... ...alues. A square matrix is given preferable sparse and a directed graph is associated with it in the following ways. The points denote the index of... ...uppose R (XY) fuzzy membership relation. The related bipartite graph with associated edge weights. 57 The relational membership matrix y 1...

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...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 ...

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...y Press Vall 1996 © Cha.rles Ashbacher & Erhu.s U":n.i"V"ersity Press The graph on the first cover belongs to: M. Popescu, P. Popescu, V. Seleac... ...on the first cover belongs to: M. Popescu, P. Popescu, V. Seleacu, "About the behaviour of some new functions in the number theory" (to appear this ... ...ngs to: M. Popescu, P. Popescu, V. Seleacu, "About the behaviour of some new functions in the number theory" (to appear this year) . "Collection o... ...ndache Function, also by Erhus Cniversity Press, dealt almost exclusively with some "basic" consequences of the Smarandache function. In this one, t... ...e urge to comment, feel free to do so at the address given below or to the people at Erhus Cniversity Press. Any comments regarding future directions... ... truly believed in me and my abilities. It takes real effort to fail when people of his quality are teaching you. Finally, I would like to dedicate ... ...ion SCm) = n, where n is the smallest number such that m divides n'. and associated consequences has spawned many new branches of mathematics. A pre... ... indirectly involve the Smarandache function. In fact, most of those dealt with here do not. All of the problems presented in this book were either p... ... 1,3,5,9, 11, 13, 17,21,25,27,29,33,35,37,43, There were two conjectures associated with this sieve. a) There are an infinite number of primes in t...

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....ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu ... ... ISBN: 1-931233-86-1 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS D e d i c a t i o n ... ...ty relations and composition of fuzzy relations 22 1.4 Optimization Of FRE with Max-Product composition 32 1.5 Composite fuzzy relation ... ...edean triangular norms 40 1.6 Solving non-linear optimization problem with FRE constraints 48 1.7 Method of solution to fuzzy relation ... ...zy relational equations 70 1.12 FRE with defuzzification algorithm for the largest solution 75 1.13 Solvability and Unique solvability ... ...ock of this partition if and only if R (x, y) ≥ α. Each similarity relation is associated with the set π (R) = {π ( α R) ⏐α ∈ (0,1]} of partition of... ...y referred to as quasi equivalence relations. The notion of fuzzy equations is associated with the concept of compositions of binary relations. The... ... be broadly classified as college students, school going children, office going people, vendors etc. Each category will choose a different hour acco... ...llege students may prefer to travel from 8 a.m. to 9 a.m. and the office going people may prefer to travel from 9.00 a.m. to 10.00 a.m. and the ret...

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...In a lecture that Einstein gave to the Prussian Academy of Sciences in 1921, he said the following: "Geometry predicates nothing about relations of real things, but only geometry together with the purport of physical laws can do so... The idea of the measuring...

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...Preface. 5 -- About the cover 9 -- Welcome from Campus President, DrRaul Ramirez. 10 -- Registrants/Attendees. 11 -- Keynotes. 12 -- The light barrier: its construction and demolition. 14 -- Jim Malmberg. 17 -- DrDavid Iadevaia. 25 -- DrLarissa ...

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... TODAY'S TAKE ON EINSTEIN’S RELATIVITY PROCEEDINGS OF THE CONFERENCE OF 18 FEB 2005 Cover Montage by Bob Wise Models of X-1 R... ...Montage by Bob Wise Models of X-1 Rocket Plane & San Francisco Cable Car by the Danbury Mint Edited by Homer B. Tilton and Florentin Smarandache ... ...edicates nothing about relations of real things, but only geometry together with the purport of physical laws can do so... The idea of the measuring... ...do so... The idea of the measuring rod and the idea of the clock contained with it in the theory of relativity do not find their exact corresponden... ...itur. However, rather than admit he had changed his mind, he eased into his new view while saying the old one should be accepted a bit longer. ... ...at they not be used for destructive or selfish purposes. These ideas place people in their true context, and that context is not dominated by mater... ...rialism and selfish intentions that materialism implies. Namely controlling people by controlling material or by controlling what one thinks one kno... ...tinguished flows on the space-form. Each flow has a definite physical state associated to it. When considering metric states in Euclidean space it i... ...ve time, that is, time moving in two opposite directions. Positive time is associated with charge while negative time is associated with monopoles. ...

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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 ...

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...c.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@unm.edu K. ... ...my. Cover design by Meena Kandasamy. Many books can be downloaded from the following E-Library of Science: http://www.gallup.unm.edu/~smaran... ...tm ISBN: 1931233-98-5 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ...all the definition of bimatrices and neutrosophic bimatrices, illustrate them with examples. This chapter has two sections. In the first section we... ...two the new notion of neutrosophic bimatrices are introduced and illustrated with examples. 1.1 Definition and Basic Operations on Bimatrices ... ...as m rows and n columns. It is to be noted a bimatrix has no numerical value associated with it. It is only a convenient way of representing a pair... ...hs have an association with bimatrices. We can have three types of bimatrices associated with bigraphs. 1. Weighted bigraph’s bimatrices 2. Incid... ...e engineers. Using an expert's opinion we study the effect of such unemployed people on the society. An expert spells out the five major concepts r... .... Now when we held discussions with human right activists, NGOs and other people sensitive to child labour problem we could form 3 sets of disjo...

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...In this book for the first time we have ventured into the total analysis of migrant labourers in rural Tamil Nadu who are victims of HIV/AIDS using FCM, BAM and Neutrosophic Cognitive Maps. As in our study and analysis we felt several of the ...

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...Migration acquires great significance in the study of peoples and populations, for it not only involves the merely mathematical spatial redistribution of people, but also because it has enormous impact on livelihood, life-styles, employment, socioeconomic and politi...

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... SMARANDACHE ANALYSIS OF SOCIAL ASPECTS OF MIGRANT LABOURERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With ... ... Phoenix 2004 ANALYSIS OF SOCIAL ASPECTS OF MIGRANT LABOURERS LIVING WITH HIV/AIDS USING FUZZY THEORY AND NEUTROSOPHIC COGNITIVE MAPS With ... .../~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu ... ...lup, NM 87301, USA e-mail: smarand@gallup.unm.edu Translation of the Tamil interviews by Meena Kandasamy XIQUAN Phoenix 2004... ...amil interviews by Meena Kandasamy XIQUAN Phoenix 2004 The picture on the cover is a poster by Bronwyn Bancroft, an Australian Ab... ...M and Combined Overlap Block NRM 299 Chapter Six Interview of 60 People Living With HIV/AIDS 327 Chapter Seven Conclusions/Suggestions ... ... and who are HIV/AIDS infected. So this study cannot be extended to urban people or rich/ sophisticated/ educated populations of Tamil Nadu. We h... ...remise of the prevention programs: for, masculinity is predominantly (mis)associated with having multiple sex partners, and a complete void between ... ...y pick up habits like alcoholism, addiction to tobacco and drugs. Doctors associated with our study also linked this prevalence of high-risk behavio...

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...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...

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...In this section we give the definition of linear algebra and just state the few important theorems like Cayley Hamilton theorem, Cyclic Decomposition Theorem, Generalized Cayley Hamilton Theorem and give some properties about linear algebra....

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...n/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: smarand@gallup.unm.edu K. I... ... ISBN: 1931233-97-7 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ... SUGGESTED PROBLEMS 201 BIBLIOGRAPHY 223 INDEX 229 ABOUT THE AUTHORS 238 5 Preface The algebraic structure, lin... ...so a very powerful algebraic tool that can yield itself to applications. With the recent introduction of bimatrices (2005) we have ventured in thi... ...ve aimed to make this book engrossing and illustrative and supplemented it with nearly 150 examples. The final chapter gives 114 problems which will... ...stic value (S-characteristic value) of T if the characteristic vector of T associated with c generate a subspace, which is a linear algebra that is ... ...te a subspace, which is a linear algebra that is the characteristic space, associated with c is a linear algebra. So the eigen vector associated wit... ...roup Dynamics to another psychological interpretation of a graph in which people are represented by points and interpersonal relations by lines. Su... ...ces of any factor like demand or production is very much dependent on the people and the government policy and other external factors. 201 ...

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...g Progress in Physics template. This template can be downloaded from Progress in Physics home page http://www.geocities.com/ptep_online. Abstract and the necessary information about author(s) should be included into the papers. To submit a paper, mail the file(s) to Chief Editor. All submitted papers should be as brief as possible. Short articles are preferable. All that h...

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...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 10-20sec. Stable states of unmatter can be built on quarks and anti-quarks: applying the unmatter prin...

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...hematics PROGRESSINPHYSICS A quarterly issue scientifc journal, registered with the Library of Congress (DC). This journal is peer reviewed and includ... ...ics PROGRESSINPHYSICS A quarterly issue scientifc journal, registered with the Library of Congress (DC). This journal is peer reviewed and included in... ...he Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathSciN... ...n J. Crothers thenarmis@yahoo.com Department of Mathematics, University of New Mexico, 200 College Road, Gallup, NM 87301, USA Copyright c Progress ... ... into (M g ,g g ). Thus, r becomes a parameter for the spacetime manifold associated with the gravitational feld. If R p ∈(M g ,g g ) is the proper r... ... ,g g ). Thus, r becomes a parameter for the spacetime manifold associated with the gravitational feld. If R p ∈(M g ,g g ) is the proper radius, then... ...tigated nonsense. The correct form of the metric (18) is obtained from the associated Schwarzschild form (24): C(r)=r 2 , r 0 =α. Furthermore, the pro... ...ntainman.com.au/process_physics/ and http://www.scieng.finders.edu.au/cpes/people/cahill_r/processphysics.html lacks much of the experienced nature of... ...lso the neutralities. Why? Because when an idea is launched, a category of people will accept it, others will reject it, and a third one will ignore i...

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...As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a ...

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... Florentin Smarandache editor Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logi... ...c Probability and Statistics University of New Mexico - Gallup 1-3 December 2001 (second... ...second printed edition) FLORENTIN SMARANDACHE editor PROCEEDINGS OF THE FIRST INTERNATIONAL CONFERENCE ON NEUTROSOPHY, NEUTROSOPHIC LOG... ... > b. No order between – c + and c. Addition of non-standard finite numbers with themselves or with real numbers: - a + b = - (a + b) ... ...on, multiplication, division, roots, and powers of non-standard finite numbers with themselves or with real numbers. By extension let inf ] - 0, 1 ... ...robability that candidate C will win an election is say 25-30% true (percent of people voting for him), 35% false (percent of people voting against h... ...ercent of people voting against him), and 40% or 41% indeterminate (percent of people not coming to the ballot box, or giving a blank vote - not sel... ...vent (disjunction) of the frame of discernment. The DST starts by defining a map associated to a body of evidence (source of information), called basic... ...all proper subsets . G. Shafer has defined the belief (credibility) function Bel associated with bpa as Bel (18) Bel summarizes all our reasons to beli...

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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 ...

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... ISBN: 1-931233-85-3 Standard Address Number: 297-5092 Printed in the United States of America 3 Acknowledgements The author grate... ...f America 3 Acknowledgements The author gratefully acknowledges the continued support, guidance and inspiration from his supervisor Dr. Ku... ...n Technology and Business, Bond University for financially supporting him with a generous postgraduate fellowship, without which it would have been ... ...llowship, without which it would have been impossible for him to carry on with his doctoral study. 4 Table of Contents: ... ...th zero likelihood of loss. But there 9 will definitely be enterprising people who will happily set off in their cars without a thought! T... ... 10 Individuals often have very distorted perceptions of risk – people are prepared to pay extraordinarily high amounts for flight insuran... ...re was a 50% chance that a severe earthquake would occur on the notorious New Madrid fault during a two-day period around December 3, 1990. Professi... ...irresolvable risk which is primarily born out of the inherent imprecision associated with the information gleaned out of market data such as price, ... ... by considering a third, neutral state in between the high and low states associated with binary logic circuits. A plausible application of ...

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...For most of the 20th century, both relativity and star travel fascinated this writer. The reasons Albert Einstein concluded there is an absolute barrier at the speed of light seemed at first clear, then later not so clear upon closer ex...

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...One's reach should exceed one's grasp. Thus we reach for Alpha Centauri with a round-trip manned and womanned mission as the proposed overarching goal under a clear plan of exploration - a grand experiment described in later chapters. Whether or not we succeed in grasping the goal under this or ...

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...Prefaces. 6 -- Ch.1. Introduction . 11 -- Ch.2. The Human Barrier. 14 -- Ch.3. An Overview. 18 -- Ch.4. Acceleration Due to Light Pressure. 21 -- Ch.5. Light Sailing is Not All There Is. 27 -- Ch.6. Einstein's Light Barrier. 32 -- Ch.7. The Phase One Experiment: The First...

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...BEGIN the ADVENTURE How to Break the Light Barrier by A.D. 2070 Homer B. Tilton Florentin Smarandache ... ...rrier by A.D. 2070 Homer B. Tilton Florentin Smarandache 2 To the memory of Benjamin E. Tilton (1876-1955), a close contemporary of Alber... ...tin Smarandache Department of Mathematics and Sciences The University of New Mexico at Gallup, USA Pima... ...rons are spherical bubbles of information expanding at the speed of light with center at the position the particle had at the time of emission in th... ...particle had at the time of emission in the observer system in accordance with the second postulate of special relativity. 5 Contents... ... engineer and the radio amateur, the term "resonance" can lead to a whole new vista of mental images, a healthy vista in the present context. To rad... ...locity of light resulting in observed distortions of space, time, and mass associated with fast-moving objects. Scientists are coming more and more ... ...ck home to end civilization. Harley says it's because there are too many people too close together. You pray that efforts to find and reach new sho... ...nd reach new shores for Human settlement pay off in time. You wonder why people can't just get along as Rodney King asked, and get with the space p...

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...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 ...

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... ISBN: 1-931233-60-8 Standard Address Number: 297-5092 Printed in the United States of America 3 Foreword As someone who works ... ...meone 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 f... ...ively on the logic, as the primary purpose of this book is to contrast it with other forms of logic. There is a journal devoted to the publication of... ...t, Neutrosophic Probability and Statistics, was held at The University of New Mexico, Gallup, 1-3 December 2001; see the site: http://www.gallup.un... ...ination of an extension of the classical logic called three-valued logic. With values that can be interpreted as “yes”, “no”, and “something else” it... ...ed to each category several times over. I would also like to thank the people at American Research Press for their diligence in getting this book... ...ures. For example, in the first expression, there could be many different people considered to a friend of yours. To determine if this expression is... ...his three-valued logic is an extension of classical logic. In most cases, new mathematical structures are defined so that they are consistent with t... ...ose to a Boolean algebra, NL1 satisfies several other properties commonly associated with a Boolean algebra. NL2 is farther from a Boolean algebra, ...