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 Book Id: WPLBN0002097105 ► Abstract Description DetailsTeoria Analitics a Numerelor reprezents pentru mine 0 pasiune. Rezultatele expuse mai departe constituie rodul catorva ani buni de cercetsri si csutsri. Lucrarea de fass se compune din 9 articole, publicate toate prin reviste de matematics romanesti sau strsine, iar unele prezentate chiar la congrese si conferinse nasionale cat si internasionale [vezi "Lista publicasiilor autorului pe tema tezei"). Ea se structureazs in patru capitole: - in primele trei capi tole se introduc noi funsii in teoria numerelor, se studiazs proprietssile lor, probleme nerezol vate legate de ele, implicasii in lumea stiinsific! internasional! (ce alsi matematicieni au abordat nosiunile acestea), conexisi cu alte funcsii bine stiute, importansa rezultatelor obsinute: - in ul timul capitol se aduc contribusii la studierea unei- funsii cunoscute in teoria numerelor (totient sau phi a lui Euler), in principal referitoare la conjectura lui carmichael. [Exist! referinse particulare dup! fiecare paraqraf (articol), iar referinse generale in finalul tezei.)...
 Book Id: WPLBN0002097040 ► Abstract Description DetailsIn 1996 the author wrote reviews for "Zentralblatt fUr Mathematik" for books [11 and [21 and this was him first contact of with the Smarandache's problems. In [1] Florentin Smarandache formulated 105 unsolved problems, while in [21 C. Dumitrescu and V. Seleacu formulated 140 unsolved problems. The second book contains almost all problems from [11, but now everyone problem has unique number and by this reason the author will use the numeration of the problems from [2]. Also, in [2] there are some problems, which are not included in [1]. On the other hane, there are problems from [1], which are not included in [2]. One of them is Problem 62 from [1], which is included here under the same number. In the summer of 1998 the author found the books in his library and for a first time tried to solve a problem from them. After some attempts one of the problems was solved and this was a power impulse for the next research. In the present book are collected the 27 problems solved by the middle of February 1999.... Table of Contents DetailsPreface 5 -- 1. On The 4-Th Smarandache's Problem 7 -- 2. On The 16-Th Smarandache's Problem 12 -- 3. On The 22-Nd, The 23-Rd, And The 24th -- Smarandache's Problems 16 -- 4. On The 37-Th And The 38th -- Smarandache's Problems 22 -- 5. On The 39-Th, The 40-Th, The 41st, And -- The 42-Nd Smarandache's Problems 27 -- 6. On The 43-Rd And 44-Th Smarandache's -- Problems 33 -- 7. On The 61-St, The 62-Nd, And The 63red -- Smarandache's Problems 38 -- 8. On The 97-Th, The 98-Th, And The 99th -- Smarandache's Problems 50 -- 9. On The 100-Th, The 101-St, And The 102nd -- Smarandache's Problems 57 -- 10. On The Ll7-Th Smarandache's Problem 62 -- Ll. On The Ll8-Th Smarandache's Problem 64 -- 12. On The 125-Th Smarandache's Problem 66 -- 13. On The I26-Th Smarandache's Problem 68 -- 14. On The 62-Nd Smarandache's Problem 71 -- Is. Conclusion 74 -- 16. Appendix 76 -- References 83 -- Curriculum Vitae Of K. Atanassov 86 --...
 Book Id: WPLBN0002097087 ► Abstract Description DetailsThis book consists of a selection of papers most of which were produced during the period 1999-2002. They have been inspired by questions raised in recent articles in current Mathematics journals and in Florentin Smarandache’s wellknown publication Only Problems, Not Solutions. All topics are independent of one another and can be read separately. Findings are illustrated with diagrams and tables. The latter have been kept to a minimum as it is often not the numbers but the general behaviour and pattern of numbers that matters. One of the facinations with number problems is that they are often easy to formulate but hard to solve – if ever, and if one finds a solution, new questions present themselves and one may end up having more new questions than questions answered....
 Book Id: WPLBN0002097037 ► Abstract Description DetailsA Smarandache notion is an element of an ill-defined set, sometimes being almost an accident oflabeling. However, that takes nothing away from the interest and excitement that can be generated by exploring the consequences of such a problem It is a well-known cliche among writers that the best novels are those where the author does not know what is going to happen until that point in the story is actually reached. That statement also holds for some of these problems. In mathematics, one often does not know what the consequences of a statement are. Cnlike a novel however, there are no complete plot resolutions in mathematics as there are no villains to rub out. As the French emphatically say in another context, "Vive la difference'"...
 Book Id: WPLBN0002097100 ► Abstract Description Detailsintroduction of 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 study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use of graphs has become inevitable in fuzzy models. The neutrosophic models are fuzzy models that permit the factor of indeterminacy. It also plays a significant role, and utilizes the concept of neutrosophic graphs. Thus neutrosophic graphs and neutrosophic bipartite graphs plays the role of representing the neutrosophic models. Thus to construct the neutrosophic graphs one needs some of the neutrosophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and study these concepts. As our analysis in this book is application of neutrosophic algebraic structure we found it deem fit t...
 Book Id: WPLBN0002097106 ► Abstract Description DetailsThis book contains a collection of poems compiled by the author Florentin Smarandache.
 Book Id: WPLBN0002097099 ► Abstract Description DetailsThis book arose out of a collection of papers written by Amarnath Murthy. The papers deal with mathematical ideas derived from the work of Florentin Smarandache, a man who seems to have no end of ideas. Most of the papers were published in Smarandache Notions Journal and there was a great deal of overlap. My intent in transforming the papers into a coherent book was to remove the duplications, organize the material based on topic and clean up some of the most obvious errors. However, I made no attempt to verify every statement, so the mathematical work is almost exclusively that of Murthy....
 Book Id: WPLBN0002097092 ► Abstract Description DetailsA complete understanding of what something is must include an understanding of what it is not. In his paper, “Paradoxist Mathematics” [19], Florentin Smarandache proposed a number of ways in which we could explore “new math concepts and theories, especially if they run counter to the classical ones.” In a manner consistent with his unique point of view, he defined several types of geometry that are purposefully not Euclidean and that focus on structures that the rest of us can use to enhance our understanding of geometry in general....
 Book Id: WPLBN0002097045 ► Abstract Description DetailsGraphs 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 us help in the analysis of such real world problems and they happen to be mathematical tools which can give the hidden pattern of the problem under investigation. This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe some of its properties. These concepts are also extended neutrosophically in this book....
 Book Id: WPLBN0002097094 ► Abstract Description DetailsLast autumn I received a letter from a student at Arizona State University. He sent me a response to my letter to the editor in Mathematical Spectrum, including some pages of F. Smarandache's open problems. At first, I was not interested in the enclosure, for some of the problems are not so new and creative. But reading carefully, there are also some problems which stimulate the curiosity on arithmetic functions and number sequences. Then I needed almost no time to understand his talent in mathematics. I returned a letter to the student with a copy of my publication in The Mathematical Scientist and including a response where I stated that I was willing to write additional articles....
 Book Id: WPLBN0002097632 Subjects: Non-Fiction, Mathematics, Smarandache Collection ► Abstract Description DetailsThis paper is based on an article in Mathematical Spectrum, VoL 29, No 1. It concerns what happens when an operation applied to an n-digit integer results in an n digit integer. Since the number of ndigit integers is finite a repetition must occur after applying the operation a finite number of times. It was assumed in the above article that this would lead to a periodic sequence which is not always true because the process may lead to an invariant. The second problem with the initial article is that, say, 7 is considered as 07 or 007 as the case may be in order make its reverse to be 70 or 700. However, the reverse of 7 is 7. In order not to loose the beauty of these sequences the author has introduced stringent definitions to prevent the sequences from collapse when the reversal process is carried out....
 Book Id: WPLBN0002097089 ► Abstract Description DetailsSurfing on the Ocean of Numbers - why this title? Because this little book does not attempt to give theorems and rigorous proofs in the theory of numbers. Instead it will attempt to throw light on some properties of numbers, nota bene integers, through a study of the behaviour of large numbers of integers in order to draw some reasonably certain conclusions or support already made conjectures. But no matter how far we extend our search or increase our samples in these studies we are in fact, in spite of more and more powerful technologies, merely skimming the surface of the immense sea of numbers. - Hence the title....
 Book Id: WPLBN0002097084 Subjects: Non Fiction, Mathematics, Finances ► Abstract Description DetailsThis 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 notion of utility. Extrinsic utility is proposed as a cardinally measurable quantity; measurable in terms of the expected information content of a set of alternative choices. The entropic notion of utility is subsequently used to model the financial behavior of individual investors based on their governing risk-return preferences involving financial structured products manufactured out of complex, multi-asset options. Evolutionary superiority of the Black-Scholes function in dynamic hedging scenarios is computationally demonstrated using a haploid genetic algorithm model programmed in Borland C. The work explores, both theoretically and computationally, the psycho-cognitive factors governing the financial behavior of individual investors both in the presence as well as absence o...
 Book Id: WPLBN0002097633 ► Abstract Description DetailsA collection of papers concerning smarandache type functions, numbers, sequences, integer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc. is published this year....
 Book Id: WPLBN0002097095 ► Abstract Description DetailsA 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 combinatorial properties of maps. The main trend is the enumeration of maps, particularly the rooted maps, pioneered by W. Tutte, and today, this kind of papers are still appeared on the journals frequently today. All of those is surveyed in Liu’s book [33]. To determine the embedding of a graph on surfaces, including coloring a map on surfaces is another trend in map theory. Its object is combinatorialization of surfaces, see Gross and Tucker [22], Mohar and Thomassen [53] and White [70], especially the [53] for detail. The construction of regular maps on surfaces, related maps with groups and geometry is a glimmer of the map theory with other mathematics....
 Book Id: WPLBN0002097039 ► Abstract Description DetailsThe creation of a book is an act that requires several preconditions. I) An interesting and worthwhile subject; 2) A fair, yet demanding editor.; 3) Someone willing to put the words on paper. Given the existence of these three items, the leap to making the book a good one becomes the responsibility of the author. The Smarandache function is simultaneously a logical extension to earlier functions in number theory as well as a key to many future paths of exploration. As such, it is hoped that you get as much out of this book as the author did in writing it. While all books are a collective work, the responsibility for any errors ultimately falls to the author, and this is no exception.... Excerpt DetailsAs one of the oldest of mathematical disciplines, the roots of number theory extend back into antiquity. Problems are often easy to state, but extremely difficult to solve. Which is the origin of much of their charm. All mathematicians, amateurs and professionals alike, have a soft spot in their hearts for the "purity" of the integers. When "Fermat's Last Theorem" was finally proven after centuries of effort, the result was discussed on many major news shows in the US. Brief comments also appeared in the major weekly news magazines....
 Book Id: WPLBN0002097083 Subjects: Non Fiction, Education, Mathematics ► Abstract Description DetailsI have met the Smarandache's world for the first time about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research Press web site dedicated to the Smarandache notions and held by Dr. Perez (address: http://www.gallup.unm.edu/~smarandache/), the Smarandache Notions Journal always published by American Research Press, and several books on conjectures, functions, unsolved problems, notions and other proposed by Professor F. Smarandache in "The Florentin Smarandache papers" special collections at: the Arizona State University (Tempe, USA), Archives of American Mathematics (University of Texas at Austin, USA), University of Craiova Library (Romania), and Archives of State (Rm. Valcea, Romania). The Smarandache's universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this universe has a very simple structure from number theory standpoint, it doesn't cease to be deeply mysterious and interesting. This book, following the Smarandache spirit, presents new ...