Number Theory Commons^™

G-Neutrosophic Space, Mumtaz Ali, Florentin Smarandache, Munazza Naz, Muhammad Shabir

Branch Mathematics and Statistics Faculty and Staff Publications

The Concept of a G-space came into being as a consequence of Group action on an ordinary set. Over the history of Mathematics and Algebra, theory of group action has emerged and proven to be an applicable and effective framework for the study of different kinds of structures to make connection among them.

Generalized Interval Neutrosophic Soft Set And Its Decision Making Problem, Said Broumi

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, we introduce the concept of generalized interval neutrosophic soft set and study their operations. Finally, we present an application of generalized interval neutrosophic soft set in decision making problem.

Super Special Codes Using Super Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes. This book has four chapters. In chapter one basic properties of codes and super matrices are given. A new type of super special vector space is constructed in chapter two of this book. Three new classes of super special codes namely, super special row code, super special column code and super special codes are introduced in chapter three. Applications of these …

Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers. In this book the authors introduce the new notion of superbimatrices and generalize it to super trimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerized world. The main difference between simple bimatrices and super bimatrices is that in case of simple bimatrices we have only one type of product defined on them, whereas in case …

Reservation For Other Backward Classes In Indian Central Government Institutions Like Iits, Iims And Aiims – A Study Of The Role Of Media Using Fuzzy Super Frm Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government. This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central …

N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …

Special Classes Of Set Codes And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book the authors introduce the notion of set codes, set bicodes and set n-codes. These are the most generalized notions of semigroup n-codes and group n-codes. Several types of set ncodes are defined. Several examples are given to enable the reader to understand the concept. These new classes of codes will find applications in cryptography, computer networking (where fragmenting of codes is to be carried out) and data storage (where confidentiality is to be maintained). We also describe the error detection and error correction of these codes. The authors feel that these codes would be appropriate to the …

Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Neutrality And Many-Valued Logics, Florentin Smarandache, Andrew Schumann

Branch Mathematics and Statistics Faculty and Staff Publications

ThisbookwrittenbyA. Schumann &F. Smarandache isdevotedtoadvances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes’ axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0,1] which are larger than zero, but smaller than each positive real number. Robinson applied this idea into modern mathematics in [117] and developed so-called non-standard analysis. In the framework of non-standard analysis there were obtained many interesting results examined in [37], [38], [74], [117].

There exists also a different version of mathematical analysis in that Archimedes’ axiom is rejected, namely, p-adic analysis (e.g., …

Auxiliary Information And A Priori Values In Construction Of Improved Estimators, Florentin Smarandache, Rajesh Singh, Pankaj Chauhan, Nirmala Sawan

Branch Mathematics and Statistics Faculty and Staff Publications

This volume is a collection of six papers on the use of auxiliary information and a priori values in construction of improved estimators. The work included here will be of immense application for researchers and students who employ auxiliary information in any form. Below we discuss each paper: 1. Ratio estimators in simple random sampling using information on auxiliary attribute. Prior knowledge about population mean along with coefficient of variation of the population of an auxiliary variable is known to be very useful particularly when the ratio, product and regression estimators are used for estimation of population mean of a …

Neutrosophic Rings, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we define the new notion of neutrosophic rings. The motivation for this study is two-fold. Firstly, the classes of neutrosophic rings defined in this book are generalization of the two well-known classes of rings: group rings and semigroup rings. The study of these generalized neutrosophic rings will give more results for researchers interested in group rings and semigroup rings. Secondly, the notion of neutrosophic polynomial rings will cause a paradigm shift in the general polynomial rings. This study has to make several changes in case of neutrosophic polynomial rings. This would give solutions to polynomial equations for …

Sequences Of Numbers Involved In Unsolved Problems, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Here it is a long list of sequences, functions, unsolved problems, conjectures, theorems, relationships, operations, etc. Some of them are inter-connected. 1) Consecutive Sequence: 1,12,123,1234,12345,123456,1234567,12345678,123456789,12345678910, 1234567891011,123456789101112,12345678910111213,... How many primes are there among these numbers? In a general form, the Consecutive Sequence is considered in an arbitrary numeration base B.

References:

Student Conference, University of Craiova, Department of Mathematics, April 1979, "Some problems in number theory" by Florentin Smarandache.

Arizona State University, Hayden Library, "The Florentin Smarandache papers" special collection, Tempe, AZ 85287-1006, USA.

The Encyclopedia of Integer Sequences", by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, …

Fuzzy And Neutrosophic Analysis Of Women With Hiv/Aids, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Fuzzy theory is one of the best tools to analyze data, when the data under study is an unsupervised one, involving uncertainty coupled with imprecision. However, fuzzy theory cannot cater to analyzing the data involved with indeterminacy. The only tool that can involve itself with indeterminacy is the neutrosophic model. Neutrosophic models are used in the analysis of the socio-economic problems of HIV/AIDS infected women patients living in rural Tamil Nadu. Most of these women are uneducated and live in utter poverty. Till they became seriously ill they worked as daily wagers. When these women got admitted in the hospital …

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (In Traditional Chinese), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

A Unifying Field In Logics: Neutrosophic Logic Neutrosophy, Neutrosophic Set, Neutrosophic Probability (Chinese Translation), Florentin Smarandache, Feng Liu

Branch Mathematics and Statistics Faculty and Staff Publications

中智学为何诞生? 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借此对学科正式 命名并引入中国。 科学是真理吗? 比如, 当今信息科学的突出问题之一就是知识表达、知识处理及知识交流中的逻辑单一性: 不是真就是假, 从而不 能面对任何矛盾和冲突。由此, 人工智能、计算机网络、数据库、信息工程, 乃至电子商务、电子政务多多少少在走死 胡同。从表面上看, 它是模糊数学或协调逻辑的问题, 而从本质上看, 它属于结构性问题, 涉及到对哲学、逻辑学、集 合论、概率论、认知科学、信息科学基本概念以及众多相关领域的重新认识、重新塑造问题。 众所周知, 我国学习西方, 只图表面, 而不注重科学的内在结构, 不懂科学的概念和原理中也有基础设施 (换句话 说, 就是基础设施的基础设施), 从而建不起高楼大厦, 更谈不上科学上的自主, 从而形成盲目跟从西方的弊病。 科学, 这个被认为是永恒的真理, 其本质上没有半点永恒, 相反, 它时刻处于新老交替、新陈代谢、自我否定、自 我淘汰的动态之中——即使存在什么永恒的真理, 也终究会被后人推翻。科学实际上是一种战争, 而中智学正是关于它 的战略战术的科学。 当今世界上高深的科学莫过于爱因斯坦的相对论, 然而一切的一切, 都是建立在恒定光速的基础上——它正 在被现代的人们推翻!

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …

Algebra În Exercijii Şi Probleme Pentru Liceu, Florentin Smarandache, Ion Goian, Raisa Grigor, Vasila Marin

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Definitions, Solved And Unsolved Problems, Conjectures, And Theorems In Number Theory And Geometry, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

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 problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again.

Asupra Unor Noi Functii În Teoria Numerelor, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritmetica, la etapa aritmeticii superioare din perioada Renasterii, cand teoria …

Smarandache Type Functions Obtained By Duality, Florentin Smarandache, C Dumitrescu, N Varlan, St Zamfir, E Radescu, N Radescu

Branch Mathematics and Statistics Faculty and Staff Publications

we extend the Smarandache function from the set N* of positive integers to the set Q of rationals

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …

Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Problemes Avec Et, Sans Problemes!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.