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Mathematics (179 Books)


The category of mathematics are works on the abstract study of subjects encompassing quantity, structure, space, change, and more; it has no generally accepted definition.

 
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International Journal of Mathematical Combinatorics : Volume 2, Ju...

By: Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

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International Journal of Mathematical Combinatorics : Volume 2, Ap...

By: Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

The Characterization of Symmetric Primitive Matrices with Exponent n − 2 Junliang Cai Abstract: In this paper the symmetric primitive matrices of order n with exponent n − 2 are completely characterized by applying a combinatorial approach, i.e., mathematical combinatorics ([7]). Key words: primitive matrix, primitive exponent, graph.

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International Journal of Mathematical Combinatorics : Volume 1, Ma...

By: Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

Sequences on Graphs with Symmetries Linfan Mao Chinese Academy of Mathematics and System Science, Beijing, 10080, P.R.China Beijing Institute of Civil Engineering and Architecture, Beijing, 100044, P.R.China E-mail: maolinfan@163.com Abstract: An interesting symmetry on multiplication of numbers found by Prof.Smarandache recently. By considering integers or elements in groups on graphs, we extend this symmetry on graphs and find geometrical symmetries. For extending...

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International Journal of Mathematical Combinatorics : Volume 1, Ap...

By: Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

x4: Radio labeling of P3n for n is less than or equal to 5 or n = 7 In this section we determine radio numbers of cube path of small order as a special case.

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International Journal of Mathematical Combinatorics : Volume 1, Ap...

By: Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

Abstract: In this paper we find the interrelations and the hidden pattern of the problems faced by the PWDs and their caretakers using Fuzzy Relational Maps (FRMs). Here we have taken the problems faced by the rural persons with disabilities in Melmalayanur and Kurinjipadi Blocks, Tamil Nadu, India. This paper is organized with the following four sections. Section one is introductory in nature giving the overall contents from the survey made about PWDs in the above said ...

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International Journal of Mathematical Combinatorics : Volume 1, Ja...

By: Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandachemulti-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topic...

Abstract: Let G be a group having a partially closed subset S such that S contains the identity element of G and each element in S has an inverse in S. Such subsets of G are called halfsubgroups of G. If a halfsubgroup S generates the group G, then S is called a halfsubgroup generating the group or hsgg in short. In this paper we prove some results on hsggs of a group. Order class of a group are special halfsubgroupoids. Elementary abelian groups are characterized as gro...

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International Journal of Mathematical Combinatorics : Volume 1, Oc...

By: Linfan Mao

Generally, combinatorics deals with twofold: Question 1.1. to determine or find structures or properties of configurations, such as those structure results appeared in graph theory, combinatorial maps and design theory,..., etc.. Question 1.2. to enumerate configurations, such as those appeared in the enumeration of graphs, labeled graphs, rooted maps, unrooted maps and combinatorial designs,...,etc..

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Groups as Graphs

By: Florentin Smarandache; W. B. Vasantha Kandasamy

This book has four chapters. Chapter one is introductory in nature. The reader is expected to have a good background of algebra and graph theory in order to derive maximum understanding of this research. The second chapter represents groups as graphs. The main feature of this chapter is that it contains 93 examples with diagrams and 18 theorems. In chapter three we describe commutative semigroups, loops, commutative groupoids and commutative rings as special graphs. The ...

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Fuzzy Linguistic Topological Spaces

By: Florentin Smarandache; W. B. Vasantha Kandasamy

This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The final chapter suggests over 100 problems and some of them are at research level.

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Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their ...

By: Florentin Smarandache; W. B. Vasantha Kandasamy

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem.

1.2 Definition of Fuzzy Cognitive Maps In this section we recall the notion of Fuzzy Cognitive Maps (FCMs), which was introduced by Bart Kosko in the year 1986. We also give several of its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices. DEFINITION 1.2.1: An FCM is a directed graph ...

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Fuzzy Analysis of School Dropouts and Their Life After

By: Florentin Smarandache; W. B. Vasantha Kandasamy

In this book authors study and analyze the problem of school dropouts and their life after. The problems can by no means be analyzed by collecting the numerical data. For such data can only serve as information beyond that the data can be of no use, for the school dropouts suffer an environment change after becoming a school dropout. Thus the emotions of the school dropout; is technically involved.

The basic tools used in the analysis of the problem of school dropout and their life after are described briefly in this chapter. We provide also the references for these concepts. Bart Kosko introduced the Fuzzy Cognitive Maps (FCMs) in the year 1986. 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. FCM was a fuzzy extension of the c...

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Frate Cu Meridianele Si Paralelele : Volume 6

By: Florentin Smarandache

În perioada 24-25 aprilie 2010 s-a desfăşurat A Şasea Conferinţă Internaţională în Teoria Numerelor şi Noţiuni Smarandache la Universitatea Normală din Tianshui, China. Organizatorii conferinţei au fost prof. univ. dr. Zhang Wenpeng de la Universitatea Nordvest din Xi’an şi prof. univ. dr. Wangsheng He de la Universitatea Normală din Tianshui. Lucrările conferinţei au fost publicate într-un volum special în care se găsesc şi articole matematice despre noţiuni legate de c...

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Finite Neutrosophic Complex Numbers

By: Florentin Smarandache; W. B. Vasantha Kandasamy

This book is organized into 5 chapters. The first chapter introduces real neutrosophic complex numbers. Chapter two introduces the notion of finite complex numbers; algebraic structures like groups, rings etc are defined using them. Matrices and polynomials are constructed using these finite complex numbers. Chapter three introduces the notion of neutrosophic complex modulo integers. Algebraic structures using neutrosophic complex modulo integers are built and around 90 ...

In this chapter we for the first time we define the notion of integer neutrosophic complex numbers, rational neutrosophic complex numbers and real neutrosophic complex numbers and derive interesting properties related with them.

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Extensica : Fotojurnal Instantaneu Din Canton

By: Florentin Smarandache

Professor Florentin Smrandache is invited to spend a period of three months time at the Research Institute of Extension Engineering at Guangdong University of Technology in China in order to conduct research on extenics.

Cu moralul extrem de ridicat, alerg pe autostrada I-40 din Gallup spre aeroportul din Albuquerque. Urlă muzica. Ferestrele deschise. Muzică populară românească, din Banat şi Oltenia, la casetă. Am înregistraţi şi pe cântăreţii mei din Bălceşti: Vasile Oprea (Vasilică a lu’ Tirina, vecinul meu), Mărin Covrig (coleg de şcoală primară şi generală), Gheorghe Lupu (mai mare cu doi ani ca mine, stătea peste drum de casa mea).

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Extenics in Higher Dimensions

By: Florentin Smarandache

During my research period in the Summer of 2012 at the Research Institute of Extenics and Innovation Methods, from Guangdong University of Technology, in Guangzhou, China, I have introduced the Linear and Non-Linear Attraction Point Principle and the Network of Attraction Curves, have generalized the 1D Extension Distance and the 1D Dependent Function to 2D, 3D, and in general to n-D Spaces, and have generalized Qiao-Xing Li’s and Xing-Sen Li’s definitions of the Locatio...

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Exploring the Extension of Natural Operations on Intervals, Matric...

By: Florentin Smarandache; W. B. Vasantha Kandasamy

This book extends the natural operations defined on intervals, finite complex numbers and matrices. Secondly the authors introduce the new notion of finite complex modulo numbers just defined as for usual reals. Finally we introduced the notion of natural product Xn on matrices. This enables one to define product of two column matrices of same order. We can find also product of m*n matrices even if m not does equal n. This natural product Xn is nothing but the usual prod...

In this chapter we just give a analysis of why we need the natural operations on intervals and if we have to define natural operations existing on reals to the intervals what changes should be made in the definition of intervals. Here we redefine the structure of intervals to adopt or extend to the operations on reals to these new class of intervals.

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Erasure Techniques in MRD Codes

By: Florentin Smarandache; W. B. Vasantha Kandasamy

In this book the authors study the erasure techniques in concatenated Maximum Rank Distance (MRD) codes. The authors for the first time in this book introduce the new notion of concatenation of MRD codes with binary codes, where we take the outer code as the RD code and the binary code as the inner code.

We want to find efficient algebraic methods to improve the realiability of the transmission of messages. In this chapter we give only simple coding and decoding algorithms which can be easily understood by a beginner. Binary symmetric channel is an illustration of a model for a transmission channel. Now we will proceed onto define a linear code algebraically.

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Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists

By: Florentin Smarandache

This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the ...

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Dual Numbers

By: Florentin Smarandache; W. B. Vasantha Kandasamy

In this book the authors study dual numbers in a special way. The main aim of this book is to find rich sources of new elements g such that g2 = 0. The main sources of such new elements are from Zn, n a composite number. We give algebraic structures on them. This book is organized into six chapters. The final chapter suggests several research level problems. Fifth chapter indicates the applications of dual numbers. The forth chapter introduces the concept of interval dua...

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DSm Vector Spaces of Refined Labels

By: W. B. Vasantha Kandasamy; Florentin Smarandache

This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly any n-dimensional space of refined labels can be easily studied as a matter of routine.

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