Generalized Partitions And New Ideas On Number Theory And Smarandache Sequences

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Generalized Partitions and New Ideas on Number Theory and Smarandache Sequences

Author : Amarnath Murthy
Publisher : Infinite Study
ISBN 13 : 1931233349
Total Pages : 219 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Generalized Partitions and New Ideas on Number Theory and Smarandache Sequences by : Amarnath Murthy

Download or read book Generalized Partitions and New Ideas on Number Theory and Smarandache Sequences written by Amarnath Murthy and published by Infinite Study. This book was released on 2005-01-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Florentin Smarandache is an incredible source of ideas, only some of which are mathematical in nature. Amarnath Murthy has published a large number of papers in the broad area of Smarandache Notions, which are math problems whose origin can be traced to Smarandache. This book is an edited version of many of those papers, most of which appeared in Smarandache Notions Journal, and more information about SNJ is available at http://www.gallup.unm.edu/~smarandache/ . The topics covered are very broad, although there are two main themes under which most of the material can be classified. A Smarandache Partition Function is an operation where a set or number is split into pieces and together they make up the original object. For example, a Smarandache Repeatable Reciprocal partition of unity is a set of natural numbers where the sum of the reciprocals is one. The first chapter of the book deals with various types of partitions and their properties and partitions also appear in some of the later sections.The second main theme is a set of sequences defined using various properties. For example, the Smarandache n2n sequence is formed by concatenating a natural number and its double in that order. Once a sequence is defined, then some properties of the sequence are examined. A common exploration is to ask how many primes are in the sequence or a slight modification of the sequence. The final chapter is a collection of problems that did not seem to be a precise fit in either of the previous two categories. For example, for any number d, is it possible to find a perfect square that has digit sum d? While many results are proven, a large number of problems are left open, leaving a great deal of room for further exploration.

The Math Encyclopedia of Smarandache type Notions

Author : Marius Coman
Publisher : Infinite Study
ISBN 13 : 1599732521
Total Pages : 136 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis The Math Encyclopedia of Smarandache type Notions by : Marius Coman

Download or read book The Math Encyclopedia of Smarandache type Notions written by Marius Coman and published by Infinite Study. This book was released on with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.

SMARANDACHE NUMBERS REVISITED

Author : A.A.K. MAJUMDAR
Publisher : Infinite Study
ISBN 13 : 1599735733
Total Pages : 135 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis SMARANDACHE NUMBERS REVISITED by : A.A.K. MAJUMDAR

Download or read book SMARANDACHE NUMBERS REVISITED written by A.A.K. MAJUMDAR and published by Infinite Study. This book was released on 2018 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than seven years ago, my first book on some of the Smarandache notions was published. The book consisted of five chapters, and the topics covered were as follows : (1) some recursive type Smarandache sequences, (2) Smarandache determinant sequences, (3) the Smarandache function, (4) the pseudo Smarandache function, and (5) the Smarandache function related and the pseudo Smarandache function related triangles. Since then, new and diversified results have been published by different researchers. The aim of this book to update some of the contents of my previous book, and add some new results.

Smarandache Unsolved problems and New Progress (in Chinese language)

Author : Editors: Liu Yanni, Li Ling, Liu Baoli
Publisher : Infinite Study
ISBN 13 : 1599730634
Total Pages : 148 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Smarandache Unsolved problems and New Progress (in Chinese language) by : Editors: Liu Yanni, Li Ling, Liu Baoli

Download or read book Smarandache Unsolved problems and New Progress (in Chinese language) written by Editors: Liu Yanni, Li Ling, Liu Baoli and published by Infinite Study. This book was released on 2008 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: New improved results of the research in Chinese language on Smarandache¿s codification used in computer programming, smarandacheials, totient and congruence functions, sequences, irrational constants in number theory, multi-space and geometries.

The "Vertical" Generalization of Goldbach’s Conjecture – An Infinite Class of Conjectures Stronger than Goldbach’s

Author : Andrei-Lucian Drăgoi
Publisher : Dr. Andrei-Lucian Drăgoi
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4./5 ( download)

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Book Synopsis The "Vertical" Generalization of Goldbach’s Conjecture – An Infinite Class of Conjectures Stronger than Goldbach’s by : Andrei-Lucian Drăgoi

Download or read book The "Vertical" Generalization of Goldbach’s Conjecture – An Infinite Class of Conjectures Stronger than Goldbach’s written by Andrei-Lucian Drăgoi and published by Dr. Andrei-Lucian Drăgoi. This book was released on 2021-07-30 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work proposes the generalization of the binary (strong) Goldbach’s Conjecture, briefly called “the Vertical Binary Goldbach’s Conjecture”, which is essentially a meta-conjecture because it states an infinite number of conjectures stronger than Goldbach’s, which all apply on “iterative” primes with recursive prime indexes, with many potential theoretical and practical applications in mathematics and physics) and a very special self-similar property of the primes subset of positive integers.

The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths)

Download The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths) PDF Online Free

Author : Andrei-Lucian Drăgoi
Publisher : Infinite Study
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4./5 ( download)

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Book Synopsis The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths) by : Andrei-Lucian Drăgoi

Download or read book The “Vertical” Generalization of the Binary Goldbach’s Conjecture as Applied on “Iterative” Primes with (Recursive) Prime Indexes (i-primeths) written by Andrei-Lucian Drăgoi and published by Infinite Study. This book was released on with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article proposes a synthesized classification of some Goldbach-like conjectures, including those which are “stronger” than the Binary Goldbach’s Conjecture (BGC) and launches a new generalization of BGC briefly called “the Vertical Binary Goldbach’s Conjecture” (VBGC), which is essentially a metaconjecture, as VBGC states an infinite number of conjectures stronger than BGC, which all apply on “iterative” primes with recursive prime indexes (i-primeths).

Scientia Magna, Vol. 3, No. 1, 2007.

Author : Zhang Wenpeng
Publisher : Infinite Study
ISBN 13 : 1599730251
Total Pages : 123 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Scientia Magna, Vol. 3, No. 1, 2007. by : Zhang Wenpeng

Download or read book Scientia Magna, Vol. 3, No. 1, 2007. written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Third International Conference on Number Theory and Smarandache Problems, 23-25 March 2007, Weinan Teacher's University, China. Papers on Smarandache multi-spaces and mathematical combinatorics, Smarandache stepped functions, cube-free integers as sums of two squares, recurrences for generalized Euler numbers, the generalization of the primitive number function, the Smarandache LCM function and its mean value, a conjecture involving the F. Smarandache LCM function, a new arithmetical function and its asymptotic formula, and other similar topics. Contributors: J. Wang, A. Muktibodh, M. Selariu, X. Zhang, Y. Zhang, M. Liu, R. Zhang, S. Ma, L. Mao, and many others.

Scientia Magna, Vol. 2, No. 2, 2006

Author : Zhang Wenpeng
Publisher : Infinite Study
ISBN 13 : 1599730154
Total Pages : 118 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Scientia Magna, Vol. 2, No. 2, 2006 by : Zhang Wenpeng

Download or read book Scientia Magna, Vol. 2, No. 2, 2006 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of The Second Northwest Conference on Number Theory and Smarandache Problems in China.

Smarandache Notions

Author :
Publisher :
ISBN 13 :
Total Pages : 714 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Smarandache Notions by :

Download or read book Smarandache Notions written by and published by . This book was released on 2001 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 860 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Indian Science Abstracts

Author :
Publisher :
ISBN 13 :
Total Pages : 816 pages
Book Rating : 4.5/5 (721 download)

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Book Synopsis Indian Science Abstracts by :

Download or read book Indian Science Abstracts written by and published by . This book was released on 2000-05 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Unsolved Problems in Number Theory

Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 1475717385
Total Pages : 176 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Unsolved Problems in Number Theory by : Richard Guy

Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second edition sold 2241 copies in N.A. and 1600 ROW. New edition contains 50 percent new material.

Geometric Theorems, Diophantine Equations, and Arithmetic Functions

Author : J. Sándor
Publisher : Infinite Study
ISBN 13 : 1931233519
Total Pages : 302 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Geometric Theorems, Diophantine Equations, and Arithmetic Functions by : J. Sándor

Download or read book Geometric Theorems, Diophantine Equations, and Arithmetic Functions written by J. Sándor and published by Infinite Study. This book was released on 2002 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Prime Numbers

Author : Richard Crandall
Publisher : Springer Science & Business Media
ISBN 13 : 0387289798
Total Pages : 597 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Prime Numbers by : Richard Crandall

Download or read book Prime Numbers written by Richard Crandall and published by Springer Science & Business Media. This book was released on 2006-04-07 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field

Smarandache Rings

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233640
Total Pages : 222 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Rings by : W. B. Vasantha Kandasamy

Download or read book Smarandache Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S.By proper subset one understands a set included in A, different from the empty set, from the unit element if any, and from A.These types of structures occur in our every day?s life, that?s why we study them in this book.Thus, as two particular cases:A Smarandache ring of level I (S-ring I) is a ring R that contains a proper subset that is a field with respect to the operations induced. A Smarandache ring of level II (S-ring II) is a ring R that contains a proper subset A that verifies: ?A is an additive abelian group; ?A is a semigroup under multiplication;?For a, b I A, a?b = 0 if and only if a = 0 or b = 0.

A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (fourth edition)

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599730804
Total Pages : 157 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (fourth edition) by : Florentin Smarandache

Download or read book A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (fourth edition) written by Florentin Smarandache and published by Infinite Study. This book was released on 2005 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: N-Norm and N-conorm are extended in Neutrosophic Logic/Set.

Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233764
Total Pages : 213 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps by : W. B. Vasantha Kandasamy

Download or read book Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003-01-01 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy (the philosophy of neutralities, introduced by FLORENTIN SMARANDACHE), and its connected logic Neutrosophic Logic, which is a further generalization of the theory of Fuzzy Logic. In this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and their Neutrosophic analogue, the Neutrosophic Cognitive Maps (NCMs). Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Neutrosophic Cognitive Maps are generalizations of FCMs, and their unique feature is the ability to handle indeterminacy in relations between two concepts thereby bringing greater sensitivity into the results. Some of the varied applications of FCMs and NCMs which has been explained by us, in this book, include: modeling of supervisory systems; design of hybrid models for complex systems; mobile robots and in intimate technology such as office plants; analysis of business performance assessment; formalism debate and legal rules; creating metabolic and regulatory network models; traffic and transportation problems; medical diagnostics; simulation of strategic planning process in intelligent systems; specific language impairment; web-mining inference application; child labor problem; industrial relations: between employer and employee, maximizing production and profit; decision support in intelligent intrusion detection system; hyper-knowledge representation in strategy formation; female infanticide; depression in terminally ill patients and finally, in the theory of community mobilization and women empowerment relative to the AIDS epidemic.