Physical Sciences and Mathematics Commons^™

Finite Neutrosophic Complex Numbers, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book for the first time the authors introduce the notion of real neutrosophic complex numbers. Further the new notion of finite complex modulo integers is defined. For every C(Zn) the complex modulo integer iF is such that 2 Fi = n – 1. Several algebraic structures on C(Zn) are introduced and studied. Further the notion of complex neutrosophic modulo integers is introduced. Vector spaces and linear algebras are constructed using these neutrosophic complex modulo integers. This book is organized into 5 chapters. The first chapter introduces real neutrosophic complex numbers. Chapter two introduces the notion of finite complex …

Dsm Vector Spaces Of Refined Labels, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The study of DSm linear algebra of refined labels have been done by Florentin Smarandache, Jean Dezert, and Xinde Li.

In this book the authors introduce the notion of DSm vector spaces of refined labels. The reader is requested to refer the paper as the basic concepts are taken from that paper [35]. 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 …

Algebraic Structures Using Super Interval Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.

This book has seven chapters. Chapter one is introductory in nature, just introducing the super interval matrices or interval super matrices. In chapter two essential operations on super interval matrices are defined. Further in this chapter algebraic structures are defined on these super interval matrices using these operation. Using these super interval matrices semirings and semivector spaces …

Algebraic Structures Using Natural Class Of Intervals, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Authors in this book introduce a new class of intervals called the natural class of intervals, also known as the special class of intervals or as natural intervals. These intervals are built using increasing intervals, decreasing intervals and degenerate intervals. We say an interval [a, b] is an increasing interval if a < b for any a, b in the field of reals R. An interval [a, b] is a decreasing interval if a > b and the interval [a, b] is a degenerate interval if a = b for a, b in the field of reals R. The natural class of intervals consists of the collection of increasing intervals, decreasing intervals and the degenerate intervals. Clearly R is contained in the natural …

Interval Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval semigroups, interval matrix semigroups and interval polynomial semigroups are defined and discussed. This book has eight chapters. The main feature of this book is that we suggest 241 problems in the eighth chapter. In this book the authors have defined 29 new concepts and illustrates them with 231 examples. Certainly this will find several applications. The authors deeply acknowledge Dr. Kandasamy for the proof reading …

Neutrosophic Interpretation Of The Analects Of Confucius, Florentin Smarandache, Fu Yuhua

Branch Mathematics and Statistics Faculty and Staff Publications

This book is the companion volume of "Neutrosophic Interpretation of Tao Te Ching,” its purpose is to extend the foundation and application range of “The Analects of Confucius.” The reasons for this are as follows. Firstly, we are willing to point out that The Analects of Confucius already has some limitations, because many questions we are interested in cannot be answered within “The Analects of Confucius.” For example, The Analects of Confucius basically discussed the matters in China, however considering all possible situations it should matter in foreign countries as well, i.e. the “global village.” This was impossible in Confucian …

Neutrosophic Interpretation Of Tao Te Ching, Florentin Smarandache, Fu Yuhua

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of this book is to extend the foundation and application range of 'Tao Te Ching'. The reasons for this are as follows. Firstly, we are willing to point out that 'Tao Te Ching' already has some limitation, because many questions we are interested in cannot be answered within 'Tao Te Ching'. For example, 'Tao Te Ching' basically discussed the matters in China, however considering all possible situations it should matter in foreign countries as well, i.e. the “global village”. This was impossible in Lao Tzu’s time. Secondly, if the original “Tao Te Ching” is regarded as “Positive Tao …