59 research outputs found
Smarandache Semigroups
The main motivation and desire for writing this book, is the direct appreciation and attraction towards the Smarandache notions in general and Smarandache algebraic structures in particular. The Smarandache semigroups exhibit properties of both a group and a semigroup simultaneously. This book is a piece of work on Smarandache semigroups and assumes the reader to have a good background on group theory
Aspects of fuzzy spaces with special reference to cardinality, dimension, and order-homomorphisms
Aspects of fuzzy vector spaces and fuzzy groups are investigated, including linear independence, basis, dimension, group order, finitely generated groups and cyclic groups. It was necessary to consider cardinality of fuzzy sets and related issues, which included a question of ways in which to define functions between fuzzy sets. Among the results proved, are the additivity property of dimension for fuzzy vector spaces, Lagrange's Theorem for fuzzy groups ( the existing version of this theorem does not take fuzziness into account at all), a compactness property of finitely generated fuzzy groups and an extension of an earlier result on the order-homomorphisms. An open question is posed with regard to the existence of a basis for an arbitrary fuzzy vector space
SMARANDACHE LOOPS
The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absent. This is in marked contrast with group theory where books are abundantly available for all levels: as graduate texts and as advanced research books
Neutrosophic Rings
This book has four chapters. Chapter one is introductory in nature, for it
recalls some basic definitions essential to make the book a self-contained one.
Chapter two, introduces for the first time the new notion of neutrosophic rings
and some special neutrosophic rings like neutrosophic ring of matrix and
neutrosophic polynomial rings. Chapter three gives some new classes of
neutrosophic rings like group neutrosophic rings,neutrosophic group
neutrosophic rings, semigroup neutrosophic rings, S-semigroup neutrosophic
rings which can be realized as a type of extension of group rings or
generalization of group rings. Study of these structures will throw light on
the research on the algebraic structure of group rings. Chapter four is
entirely devoted to the problems on this new topic, which is an added
attraction to researchers. A salient feature of this book is that it gives 246
problems in Chapter four. Some of the problems are direct and simple, some
little difficult and some can be taken up as a research problem.Comment: 154 page
Smarandache Neutrosophic Algebraic Structures
This book has seven chapters. In Chapter one, an elaborate recollection of
Smarandache structures like S-semigroups, S-loops, and S-groupoids is given. It
also gives notions about N-ary algebraic stuctures and their Smarandache
analogue, Neutrosophic structures viz. groups, semigroups, groupoids and loops
are given in Chapter one to make the book a self-contained one. For the first
time, S-neutrosophic groups and S-neutrosophic N-groups are introduced in
Chapter two and their properties are given. S-neutrosophic semigroups and
S-neutrosophic N-semigroups are defined and discussed in Chapter three. Chapter
four defines S-neutrosophic S-loops and S-N-neutrosophic groupoids and their
generalizations are given in Chapter five. Chapter six gives S-neutrosophic
mixed N-structures and their duals. Chapter seven gives 68 problems for any
interested reader.Comment: 202 page
Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures
In this book, for the first time we introduce the notion of neutrosophic
algebraic structures for groups, loops, semigroups and groupoids; and also
their neutrosophic N-algebraic structures.
One is fully aware of the fact that many classical theorems like Lagrange,
Sylow and Cauchy have been studied only in the context of finite groups. Here
we try to shift the paradigm by studying and introducing these theorems to
neutrosophic semigroups, neutrosophic groupoids, and neutrosophic loops.
This book has seven chapters. Chapter one provides several basic notions to
make this book self-contained. Chapter two introduces neutrosophic groups and
neutrosophic N-groups and gives several examples. The third chapter deals with
neutrosophic semigroups and neutrosophic N-semigroups, giving several
interesting results. Chapter four introduces neutrosophic loops and
neutrosophic N-loops. We introduce several new, related definitions. In fact we
construct a new class of neutrosophic loops using modulo integer Z_n, n > 3,
where n is odd. Several properties of these structures are proved using number
theoretic techniques. Chapter five just introduces the concept of neutrosophic
groupoids and neutrosophic N-groupoids. Sixth chapter innovatively gives mixed
neutrosophic structures and their duals. The final chapter gives problems for
the interested reader to solve.Comment: 219 page
Fast iterative methods for variational models in image segmentation
Image segmentation is an important branch of computer vision. It aims at extracting meaningM objects lying in images either by dividing images 5 into contiguous semantic regions, or by extracting one or more specific objects in images such as left kidney in CT image. The image segmentation task is, in general, very difficult to achieve since natural images are diverse and complex, and the way we perceive them varies according to individuals
- …