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Full-Text Articles in Number Theory
Nidus Idearum. Scilogs, I: De Neutrosophia, Florentin Smarandache
Nidus Idearum. Scilogs, I: De Neutrosophia, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). In this first books of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others …
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …
Algebraic Structures On Finite Complex Modulo Integer Interval C([0, N)), Florentin Smarandache, W.B. Vasantha Kandasamy
Algebraic Structures On Finite Complex Modulo Integer Interval C([0, N)), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors introduce the notion of finite complex modulo integer intervals. Finite complex modulo integers was introduced by the authors in 2011. Now using this finite complex modulo integer intervals several algebraic structures are built. Further the concept of finite complex modulo integers itself happens to be new and innovative for in case of finite complex modulo integers the square value of the finite complex number varies with varying n of Zn. In case of finite complex modulo integer intervals also we can have only pseudo ring as the distributive law is not true, in general in C([0, …
Special Pseudo Linear Algebras Using [0,N), Florentin Smarandache, W.B. Vasantha Kandasamy
Special Pseudo Linear Algebras Using [0,N), Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book we introduce some special type of linear algebras called pseudo special linear algebras using the interval [0, n). These new types of special pseudo interval linear algebras has several interesting properties. Special pseudo interval linear algebras are built over the subfields in Zn where Zn is a S-ring. We study the substructures of them. The notion of Smarandache special interval pseudo linear algebras and Smarandache strong special pseudo interval linear algebras are introduced. The former Sspecial interval pseudo linear algebras are built over the Sring itself. Study in this direction has yielded several interesting results. S-strong special …
Soft Neutrosophic Algebraic Structures And Their Generalization - Vol. 1, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir
Soft Neutrosophic Algebraic Structures And Their Generalization - Vol. 1, Florentin Smarandache, Mumtaz Ali, Muhammad Shabir
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors introduced the notions of soft neutrosophic algebraic structures. These soft neutrosophic algebraic structures are basically defined over the neutrosophic algebraic structures which means a parameterized collection of subsets of the neutrosophic algebraic structure. For instance, the existence of a soft neutrosophic group over a neutrosophic group or a soft neutrosophic semigroup over a neutrosophic semigroup, or a soft neutrosophic field over a neutrosophic field, or a soft neutrosophic LA-semigroup over a neutrosophic LAsemigroup, or a soft neutosophic loop over a neutrosophic loop. It is interesting to note that these notions are defined over finite and …
Set Theoretic Approach To Algebraic Structures In Mathematics - A Revelation, Florentin Smarandache, W.B. Vasantha Kandasamy
Set Theoretic Approach To Algebraic Structures In Mathematics - A Revelation, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors bring out how sets in algebraic structure can be used to construct most generalized algebraic structures, like set linear algebra/vector space, set ideals in rings and semigroups. This sort of study is not only innovative but infact very helpful in cases instead of working with a large data we can work with a considerably small data. Thus instead of working with a vector space or a linear algebra V over a field F we can work with a subset in V and a needed subset in F, this can save both time and economy. The concept …
Special Dual Like Numbers And Lattices, Florentin Smarandache, W.B. Vasantha Kandasamy
Special Dual Like Numbers And Lattices, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors introduce a new type of dual numbers called special dual like numbers. These numbers are constructed using idempotents in the place of nilpotents of order two as new element. That is x = a + bg is a special dual like number where a and b are reals and g is a new element such that g2 =g. The collection of special dual like numbers forms a ring. Further lattices are the rich structures which contributes to special dual like numbers. These special dual like numbers x = a + bg; when a and b …
Interval Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy
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 …