Download or read book On the Pseudo Smarandache Squarefree function and Smarandache function written by Xuhui Fan and published by Infinite Study. This book was released on with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this paper is using the elementary methods to study the mean value properties of the Pseudo-Smarandache-Squarefree function and Smarandache function, and give two sharper asymptotic formulas for it.
Download or read book A Set of New Smarandache Functions Sequences and Conjectures written by Felice Russo and published by Infinite Study. This book was released on 2000 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the mean value of the Pseudo Smarandache function written by Lin Cheng and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer k.
Download or read book Research on Smarandache Problems in Number Theory collected papers Vol I written by Wenpeng Zhang and published by Infinite Study. This book was released on 2005-01-01 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory is an ancient subject, but we still cannot answer many simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new problems implicated and are still promoting the development of number theory and mathematics.American-Romanian number theorist Florentin Smarandache introduced hundreds of interest sequences and arithmetical functions, and presented many problems and conjectures in his life. In 1991, he published a book named Only problems, Not solutions!. He presented 105 unsolved arithmetical problems and conjectures about these functions and sequences in it. Already many researchers studied these sequences and functions from his book, and obtained important results.This book, Research on Smarandache Problems in Number Theory (Collected papers), contains 41 research papers involving the Smarandache sequences, functions, or problems and conjectures on them.All these papers are original. Some of them treat the mean value or hybrid mean value of Smarandache type functions, like the famous Smarandache function, Smarandache ceil function, or Smarandache primitive function. Others treat the mean value of some famous number theoretic functions acting on the Smarandache sequences, like k-th root sequence, k-th complement sequence, or factorial part sequence, etc. There are papers that study the convergent property of some infinite series involving the Smarandache type sequences. Some of these sequences have been first investigated too. In addition, new sequences as additive complement sequences are first studied in several papers of this book.Most authors of these papers are my students. After this chance, I hope they will be more interested in the mysterious integer and number theory!More future papers by my students will focus on the Smarandache notions, such as sequences, functions, constants, numbers, continued fractions, infinite products, series, etc. in number theory!List of the Contributors:Zhang Wenpeng, Xu Zhefeng, Zhang Xiaobeng, Zhu Minhui, Gao Nan, Guo Jinbao, He Yanfeng, Yang Mingshun, Li Chao, Gao Jing, Yi Yuan, Wang Xiaoying, Lv Chuan, Yao Weili, Gou Su, He Xiaolin, Li Hailong, Liu Duansen, Li Junzhuang, Liu Huaning, Zhang Tianping, Ding Liping, Li Jie, Lou Yuanbing, Zhao Xiqing, Zhao Xiaopeng, Yang Cundian, Liang Fangchi
Download or read book Smarandache Notions Journal Vol 13 written by Jack Allen and published by Infinite Study. This book was released on 2002-12-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The books are published by Smarandache Notions Journal. It is an electronic and hard-copy journal of research in mathematics. Besides this, occasionally It publishes papers of research in physics, philosophy, literary essays and creation, linguistics, and art work. Initially the journal was called "Smarandache Function Journal". Since 1996 to present the original journal was extended to the "Smarandache Notions Journal". It is annually published in the United States by the American Research Press in 1000 copies and on the internet.
Download or read book On the pseudo Smarandache function written by Henry Ibstedt and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study originates from questions posed on alternating iterations involving the pseudo-Smarandache function Z(n) and the Euler function. Interesting questions have been resolved through the surprising involvement of Fermat numbers
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.
Download or read book Smarandache Chinese written by Yuan Yi and published by Infinite Study. This book was released on 2006-01-01 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers and definitions in Chinese language related to Smarandache n-structures, generalized palindromes, functions, sequences, numbers, neutrosophic logic/set/probability/statistics, Smarandache geometries, etc.
Download or read book Scientia Magna Vol 4 No 4 2008 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on an equation involving the Smarandache function and its positive integer solutions, the Smarandache kn-digital subsequence, the Smarandache 3n-digital sequence and the Zhang Wenpeng's conjecture, the quintic supported spline wavelets with numerical integration and similar topics. Contributors: A. A. Majumdar, B. Chen, C. Shi, S. Wang, L. Zhang, A. Saeid, M. Haveshki, T. Veluchamy, P.S.Sivakkumar, and others.
Download or read book NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS VOLUME 9 NUMBER 2 2003 written by Aldo Peretti and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles, notes and problems on Smarandache Function, Pseudo-Smarandache function, Smarandache-simple functions, Inferior Smarandache Prime Part, Smarandache double factorial function, Generalized Smarandache Palindrome, Smarandache problems, Smarandache circular sequence etc.
Download or read book Sequences of Numbers Involved in Unsolved Problems written by Florentin Smarandache and published by Infinite Study. This book was released on 2006-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. The book contains definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. ( on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes/squares/cubes/factorials, almost primes, mobile periodicals, functions, tables, prime/square/factorial bases, generalized factorials, generalized palindromes, etc. ).
Download or read book Smarandache Notions written by and published by . This book was released on 2002 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientia Magna Vol 3 No 3 2007 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: Papers on some faces of Smarandache semigroups' concept in transformation semigroups' approach, the hybrid power mean of the character sums and the general Kloosterman sums, an equation involving the square sum of natural numbers and Smarandache primitive function, Some Dirichlet series involving special sequences, and other similar topics. Contributors: F. Ayatollah, G. Feng, N. Quang, P. Tuan, A.A.K. Majumdar, Y. Wang, B.E. Carvajal-Gamez, C. Aguilar-Chavez, L. Cheng, and many others.
Download or read book Scientia Magna Vol 3 No 4 2007 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on the mean value of the Smarandache LCM function, Pseudo-Smarandache-Squarefree function, the irrational root sieve sequence, assessment method for weight of experts at interval judgment, miscellaneous remark on problems involving Mersenne primes, a successive linear programming algorithm for SDP relaxation of binary quadratic programming, and other similar topics. Contributors: X. Pan, B. Liu, H. Liu, A. R. Gilani, B. N. Waphare, N. T. Quang, P. D. Tuan, S. Hussain, B. Ahmad, A. Jing , F. Liang, J. Wang, and many others.
Download or read book Smarandache Function Journal vol 14 2004 written by Sabin Tabirca and published by Infinite Study. This book was released on with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Download or read book Comments and Topics on Smarandache Notions and Problems written by Kenichiro Kashihara and published by Infinite Study. This book was released on 1996 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smarandache Function Journal vol 9 1998 written by V. Seleacu and published by Infinite Study. This book was released on with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
