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...Lecture delivered before the International Congress of Mathematicians at Paris in 1900 and subsequently published in the Bulletin of the American Mathematical Society Vol. 8 (1902), 479-481....

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...Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these pro...

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Preface 5 Definitions, Problems, Theorems 7 References 76

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...7 years. 'A tangled tale' merges his two talents as storyteller and mathematician. It consists of 10 short humorous stories which present one or more mathematical problems. The 10 'knots' as they are called, were first published in 'The Monthly Packet' magazine between April 1880 and March 1885, where readers were invited to solve the problems, and the solution was discuss...

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...In the beginning, this international avant-garde was a mutism: to make literature by not writing literature at all!! (any mathematical/chemical/physical etc. abstract sign, any drawing, draft, picture, graffito (having no words, no letters) could mean a poem; the non-literature created became, paradoxically, a new kind of literature; later the p...

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...tician............................ 6 Political reason to leave his native country............. 10 Smarandache Function......................... 20 Mathematical poems........................... 22 What is the paradoxism?........................ 23 Funny stories.............................. 25 Scientific activity Affiliations............................... 27 Mathema...

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...This issue of the journal is devoted to the proceedings of the third International Conference on Number Theory and Smarandache Problems. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache problems in particular. In this volume we assemble not only those papers which were pre...

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...ula 33 A. Muktibodh, etc. : Sequences of pyramidal numbers 39 R. Zhang 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®erenc...

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...e that often the subsutras are not used under the main sutra for which it is the subsutra or the corollary. This is the main deviation from the usual mathematical principles of theorem (sutra) and corollaries (subsutra). (2) It cannot be easily compromised that a single sutra (a Sanskrit word) can be mathematically interpreted in this manner even by a stalwart in Sanskrit...

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...ve Maps with Examples 78 3.5 Description of Neutrosophic Relational Maps 87 3.6 Description of the new Fuzzy Neutrosophic model 92 Chapter Four MATHEMATICAL ANALYSIS OF THE VIEWS ABOUT VEDIC MATHEMATICS USING FUZZY MODELS 95 4.1 Views of students about the use of Vedic Mathematics in their curriculum 97 4.2 Teachers views on Vedic Mathematics and its overall influe...

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...Fuzzy Relational Maps 14 2.2 Use of FRMs to analyze the socio economic problems of HIV / AIDS infected women patients 24 Chapter Three ... ....2 Suggestions given by the HIV/AIDS patients 239 6.3 Conclusions from our mathematical analysis 241 APPENDIX 1. Linguistic Questionnair... ...ic model. Neutrosophic models are used in the analysis of the socio-economic problems of HIV/AIDS infected women patients living in rural Tamil Nad... ...t of these women talked very openly and that in spite of their sufferings and problems they did not suffer depression. These interviews taken as a p... ...ause all the readers may not be from rural Tamil Nadu, so only by knowing the problems faced by these women and their culture it would be easy for t... ...he verbatim opinion of the expert. The final chapter is based not only on our mathematical analysis but also on the interviews, views of experts and... ...V/AIDS only through their infected husbands so it is pertinent to use only a mathematical model, which is interdependent. So we choose to use Fuzzy... ...they are aware of it and so on. Now we give a brief description of the fuzzy mathematical tools. 2.1 Introduction to Fuzzy Relational Maps (FR... ...DS affected women, which is an unsupervised data, we present more of the non-mathematical description of how our model works to make this book read...

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...pes of loops 102 4.5 Smarandache hyperloops 103 5. Research problems 107 R e f e r e n c e s 113 I n d e x ... ...s in general and loops in particular. The final section gives 52 research problems for the researchers in order to make them involved in the study o... ...rder to make them involved in the study of Smarandache loops. The list of problems provided at the end of each section is a main feature of this boo... ...ent edges have the same colour in the graph G. For more about colouring problems and graphs please refer [3]. 1.3 Lattices and its properties ... ... {e} with x ≠ y. This is left as an exercise for the reader to verify. PROBLEMS 1. Does there exist a loop of order 4? 2. Give an example of a... ... Conf., 33-37 (1995). 76. Vasantha.W.B, Loop algebras of Moufang loops, Mathematical Forum, Vol. XI, 21-25 (1997). 77. Vasantha.W.B, On Quasi l...

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... E-mail: steve_gd@hotmail.com Keywords: G-dimensional theory, mathematical physics, relativity, Smarandache hypothesis, gravity, quant... ...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... ...andache, Florentin "Sorites Paradoxes", in "Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry", Xiqu...

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...rmetic verse; - intelligible unintelligible language; - unsolved and open problems of mathematics like very nise poems of the spirit – we must scie... ...viste nuîncape îndoial ă (formulele sunt în limbaj LaTeX): <Starting from mathematical logic and its class of paradoxes: “All is ${\cal C}$, then n... ...ophy, Neutrosophic Probability, Set, an Logic, în “Notices of the American Mathematical Society”, March 2001. [9 ] Smarandache, Florentin, Linguist... ...n ă. Poeme cu ... probleme!” (Laws of internal composition. Poems with ... problems!, Morocco, 1982) as a PRE- PARADOXIST volume. Returning to Craio... ...he wind. 2. EXTENSIVE REPORT IS BEING PREPARED ON A FRESH APPROACH TO THE PROBLEMS – We just hired three kids fresh out of college. 3. CLOSE PROJEC... ... is about hopeless. 10. WE WILL LOOK INTO IT – Forget it! We have enough problems for now. 11. PLEASE NOT AND INITIAL – Let’s spread the responsib... ...d now hear this Indian tale, more than 25 years old joke, that ends in a … mathematical formula! Once upon a time, somewhere in North America, an In... ...e la care am colaborat, unele – de circula ţie interna ţional ă (“American Mathematical Monthly!, “Nieuw Archief voor Wiskunde”, “Zentralblatt fur M... ...uiesc s ă se duc ă la bibliotec ă şi s ă cerceteze “Notices of the American Mathematical Society” (octombrie 1987, nr. 34, p. 924-925), unde este ins...

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...rmetic verse; - intelligible unintelligible language; - unsolved and open problems of mathematics like very nise poems of the spirit – we must scie... ...viste nuîncape îndoial ă (formulele sunt în limbaj LaTeX): <Starting from mathematical logic and its class of paradoxes: “All is ${\cal C}$, then n... ...ophy, Neutrosophic Probability, Set, an Logic, în “Notices of the American Mathematical Society”, March 2001. [9 ] Smarandache, Florentin, Linguist... ...n ă. Poeme cu ... probleme!” (Laws of internal composition. Poems with ... problems!, Morocco, 1982) as a PRE- PARADOXIST volume. Returning to Craio... ...he wind. 2. EXTENSIVE REPORT IS BEING PREPARED ON A FRESH APPROACH TO THE PROBLEMS – We just hired three kids fresh out of college. 3. CLOSE PROJEC... ... is about hopeless. 10. WE WILL LOOK INTO IT – Forget it! We have enough problems for now. 11. PLEASE NOT AND INITIAL – Let’s spread the responsib... ...d now hear this Indian tale, more than 25 years old joke, that ends in a … mathematical formula! Once upon a time, somewhere in North America, an In... ...e la care am colaborat, unele – de circula ţie interna ţional ă (“American Mathematical Monthly!, “Nieuw Archief voor Wiskunde”, “Zentralblatt fur M... ...uiesc s ă se duc ă la bibliotec ă şi s ă cerceteze “Notices of the American Mathematical Society” (octombrie 1987, nr. 34, p. 924-925), unde este ins...

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...ng the company was all about me and never realized that I could be part of the problems that befell it. Now I subscribe to the TEAM adage, that Tog... ...0 years, a horizontal figure eight as a never-ending ribbon has symbolized the mathematical and philosophical concept of infinity. Imagine yourself...

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... nature. A technical analysis program is useless without a stock exchange or if its mathematically erroneous. Yet, the two concepts are often conf... ...appears to be unaware of the work of an important, though eccentric, Czech-Austrian mathematical logician, Kurt Gödel (1906-1978). A passing acquain... ...versa. Needless to say that Hempel's approach did not get us nearer to solving the problems of causal priority and of indeterministic causation. ... ...ir complexity makes it impossible. This article deals with some commonsense, basic problems raised by the Laws. The next article in this series ana... ...Note - Godel's Theorems The work of an important, though eccentric, Czech- Austrian mathematical logician, Kurt Gödel (1906-1978) dealt with the com... ...mb to numbers. To complicate things further, different nations weigh environmental problems disparately. Despite recent attempts, such as the Envir... ...ing the human body adapt and cope; and global plans to cope with energy production problems, poverty, and disease triggered by global warming. For... ... act directionally to achieve their goals. These literary devices pose two related problems: (a) we cannot be sure that the actions of alien beings... ...cs and geometry. Reality can be successfully described and captured by alternative mathematical systems and geometries. Additionally, we often conf...

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... out? A: We have to keep thinking about our contact with the Creator. All our problems in this world indicate that we do not have contact with Him. ... ... will begin to search for the reason despite ourselves. The solution for our problems is in, “Taste and see that the Lord is good.” There is no oth... ...ay that it would be impossible for anyone else to see the soul behind the dry mathematical facts. Here too, it all depends on which words we use to ... ...rt to make it to the top. But most people are busy with their little everyday problems and their small affairs. The ordinary T H E K A B B A L A H ... ... of my life?” Did he have to write more than two thousand pages of completely mathematical text to answer it? Without understanding what happens in ... ...esires, too, but they are neither the most important nor the biggest of man’s problems; they are not the ones he should wrestle with. If you want to ... ...nd only then be able to see what kind of mood he was in. I think there are two problems here: The first is that in his new situation, he will have to... ...” of his own situation, photocopy it, and express it in a form of an accurate mathematical formula, mean- ing Gimatria, and convey it to the student.... ...rs. This way he goes through the same situation as his teacher. Gimatria is a mathematical formula that expresses the sum total of our spiritual exp...

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...hat God hides things in plain view, as is the case here. Kabbalah utilizes many mathematical concepts such as matrices, geometry, numbers, graphs, c... ...lains what spiritual load a man must take out of his life. Not how to solve our problems, but how to find a solution to the very problem for which a... ...lems, but how to find a solution to the very problem for which all our everyday problems are sent to us. Suffering is just put in our way to bring u... ... to do when something befalls us – where to run, who to call? Solving our daily problems straightforwardly, trying to escape them as we are used to ... ...ear any situation that may occur. When one commences to study Kabbalah, suddenly problems, previously unknown, begin to crop up. Without the learning...

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...changing our perspective, we might be able to better cope with our day-to-day problems. This perspec- tive determines our reactions, our feelings, an... ... the relationship in our world between mother and child. We can solve all the problems that arise in physical relationships by understanding the roo... ...he answers to those questions come in the form of knowledge and strength. The problems of this world disappear once a person attains the first spiri... ... things are, in fact, a kind of drug that people try in order to escape their problems. Drug addicts are normally very quiet people, but the entire ... ...? There is another question: why do we have the ability to rid our- selves of problems through ordinary medicine, instead of resolving our problems ... ...h itself, which uses drawings, formulas, and matrices. Kabbalah utilizes pure mathematical rules in order to express spiritual phenomena. There are ... ...actical science of all; it explains how we can all “live well.” Q: What is the mathematical structure of the wisdom of Kab- balah? A: The mathematical...

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...y matter will not cancel out when you apply this semi-philisophical, semi-mathematical theory to them". For example: People think that their job defi... ...ole? But that's silly anyway, you say. Maybe we do need to beware of these problems, but we're not even close to it being an issue. No one has robot ... ...s himself as "a 28 year old fun-loving person. I have a variety of health problems, but I do try my best to live each day as best I can, although it...

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...gh war, and through postwar turbulence. But I see my generation, being full of problems and suffering, unable to establish itself, and unable to find ... ...quences of our actions and His response to them; be able to discuss all of our problems in a dialogue withHim;askfor Hishelp;seekHisprotection and adv... ...ND places before us in a hidden fashion, it will not assist us in solving our problems. Insteadwewillremainafloatwithoutsupportandwithout logical ans... ...reator to save us from egoism. This forces us to strive to overcome all of our problems, which brings us further suffering. For this reason, Rabbi Ash... ...rectfeelings,asisdonein thispartofthebook,orinthelanguageofSefirot,thephysics- mathematical description of spiritual objects. This language is univers... ...weasktheCreatorforspiritualperceptions,but do not ask Him to solve the various problems in our daily lives,indicateshowweakisourfaithintheomnipotencea...

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...t understood. School began to become enjoyable and I could not learn fast enough and even spent my spare time reading books and working on difficult mathematical problems. Mum and Dad were happy that I was doing well at school and encouraged me to learn all I could and become a success in life. Glad that I was making them happy I worked harder and stayed top of my class a...