https://doi.org/10.1142/12645 | January 2022
Pages: 300
ISBN: 978-981-124-938-9 (hardcover)
The book presents an updated study of hypergroups, being structured on 12 chapters in starting with the presentation of the basic notions in the domain: semihypergroups, hypergroups, classes of subhypergroups, types of homomorphisms, but also key notions: canonical hypergroups, join spaces and complete hypergroups. A detailed study is dedicated to the connections between hypergroups and binary relations, starting from connections established by Rosenberg and Corsini. Various types of binary relations are highlighted, in particular equivalence relations and the corresponding quotient structures, which enjoy certain properties: commutativity, cyclicity, solvability.
A special attention is paid to the fundamental beta relationship, which leads to a group quotient structure. In the finite case, the number of non-isomorphic Rosenberg hypergroups of small orders is mentioned. Also, the study of hypergroups associated with relations is extended to the case of hypergroups associated to n-ary relations. Then follows an applied excursion of hypergroups in important chapters in mathematics: lattices, Pawlak approximation, hypergraphs, topology, with various properties, characterizations, varied and interesting examples. The bibliography presented is an updated one in the field, followed by an index of the notions presented in the book, useful in its study.
Preface
Semihypergroups
Hypergroups
Subhypergroups
Homomorphisms and Isomorphisms
Fundamental Relations
More about the Corresponding Quotient Structures
Join Spaces, Canonical Hypergroups and Lattices
Rosenberg Hypergroups
Hypergroups and n-ary Relations
Approximations in Hypergroups
Links between Hypergraphs and Hypergroups
Topological Hypergroups
Bibliography
Index
Advanced undergraduate and graduate students, researchers and practitioners in the fields of algebra, group theory and algebraic hyperstructures.
https://doi.org/10.1142/12719 | March 2022
Pages: 200
ISBN: 978-981-125-210-5 (hardcover)
ISBN: 978-981-125-249-5 (softcover)
This book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors.
It contains the basic notions of abstract algebra through solved exercises as well as a "True or False" section in each chapter.
Each chapter also contains an essential background section, which makes the book easier to use.
Logic, sets et al.
Mappings
Binary Relations
Groups
Rings and Fields
Polynomials and Rational Fractions
First and second year mathematics and computer science students interested in abstract algebra. Also good for instructors.
https://doi.org/10.1142/q0345 | April 2022
Pages: 560
ISBN: 978-1-80061-171-9 (hardcover)
Based on notes written during the teacher's many years of teaching, Analysis in Euclidean Space mainly covers Differentiation and Integration theory in several real variables, but also an array of closely related areas including measure theory, differential geometry, classical theory of curves geometric measure theory, integral geometry, and others.
With several original results, new approaches and an emphasis on concepts and rigorous proofs, the book is suitable for undergraduate students, particularly in mathematics and physics, who are interested in acquiring a solid grounding in analysis and expanding their background. There are many examples and exercises inserted in the text for the student to work independently.
Analysis in Euclidian Space comprises twenty chapters, each with an introduction summarizing its contents, and an additional chapter containing miscellaneous exercises. Teachers may use the varied chapters of this book for different undergraduate courses in analysis. The only prerequisites are a basic course in linear algebra and a standard first-year calculus course in differentiation and integration. As the book progresses, the difficulty increases such that some of the later sections may be appropriate for graduate study.
Introduction
Euclidean Space
Continuous Functions
Coordinate Systems, Curves and Surfaces
Differentiation
Higher Order Derivatives
The Inverse and Implicit Function Theorems
Regular Sub-Manifolds
Ordinary Differential Equations
Linear Partial Differential Equations
Orthogonal Families of Curves and Surfaces
Measuring Sets: The Riemann Integral
The Lebesgue Integral
Fubini's Theorem and Change of Variables
Integration on Sub-Manifolds
Line Integrals and Flux
The Basic Theorems of Vector Analysis
Conservative and Solenoidal Fields
Harmonic Functions
The Divergence and Rotational Equations: Poisson's Equation
The Dirichlet and Neumann Problems
Additional Exercises
Can be used as a textbook for undergraduate students studying differentiation theory in several real variables, measure and integration in several real variables, ordinary differential equations, linear partial differential equations, vector analysis, and curves and surfaces. Graduate students may use this book for an introduction to geometric measure theory and integral geometry, as well as advanced topics in vector analysis.
https://doi.org/10.1142/12594 | April 2022
Pages: 450
ISBN: 978-981-124-857-3 (hardcover)
ISBN: 978-981-124-933-4 (softcover)
Whenever the topic of mathematics is mentioned, people tend to indicate their weakness in the subject as a result of not having enjoyed its instruction during their school experience. Many students unfortunately do not have very positive experiences when learning mathematics, which can result from teachers who have a tendency "to teach to the test". This is truly unfortunate for several reasons. First, basic algebra and geometry, which are taken by almost all students, are not difficult subjects, and all students should be able to master them with the proper motivational instruction. Second, we live in a technical age, and being comfortable with basic mathematics can certainly help you deal with life's daily challenges. Other, less tangible reasons, are the pleasure one can experience from understanding the many intricacies of mathematics and its relation to the real world, experiencing the satisfaction of solving a mathematical problem, and discovering the intrinsic beauty and historical development of many mathematical expressions and relationships. These are some of the experiences that this book is designed to deliver to the reader.
The book offers 101 mathematical gems, some of which may require a modicum
of high school mathematics and others, just a desire to carefully apply
oneself to the ideas. Many folks have spent years encountering mathematical
terms, symbols, relationships and other esoteric expressions. Their origins
and their meanings may never have been revealed, such as the symbols +,
-, =, ・ and many others. This book provides a delightful insight into
the origin of mathematical symbols and popular theorems such as the Pythagorean
Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities,
intriguing number relationships, and some of the different mathematical
procedures in various countries. The book uses a historical and cultural
approach to the topics, which enhances the subject matter and greatly adds
to its appeal. The mathematical material can, therefore, be more fully
appreciated and understood by anyone who has a curiosity and interest in
mathematics, especially if in their past experience they were expected
to simply accept ideas and concepts without a clear understanding of their
origins and meaning. It is hoped that this will cast a new and positive
picture of mathematics and provide a more favorable impression of this
most important subject and be a different experience than what many may
have previously encountered. It is also our wish that some of the fascination
and beauty of mathematics shines through in these presentations.
Introduction
Numbers and Symbols
Arithmetic Curiosities
Aspects of Measurement
Geometric Novelties
Probability
A Potpourri of Mathematical Topics
General readership as well as to teachers and students of mathematics at the secondary level.
https://doi.org/10.1142/12580 | June 2022
Pages: 260
ISBN: 978-981-124-809-2 (hardcover)
This volume presents recent developments in geometric structures on Riemannian manifolds and their discretization. With chapters written by recognized experts, these discussions focus on contact structures, Kﾃ､hler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.
For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.
Magnetic Curves in Quasi-Sasakian Manifolds of Product Type (Marian Ioan MUNTEANU and Ana Irina NISTOR)
Motion of Charged Particles in a Compact Homogeneous Sasakian Manifold (Osamu IKAWA)
A Note on Legendre Trajectories on Sasakian Space Forms (Qingsong SHI and Toshiaki ADACHI)
Non Naturally Reductive Einstein Metrics on the Symplectic Group via Quaternionic Flag Manifolds (Andreas ARVANITOYEORGOS and Yusuke SAKANE)
A Lie Theoretic Interpretation of Realizations of Some Contact Metric Manifolds (Takahiro HASHINAGA, Akira KUBO, Yuichiro TAKETOMI and Hiroshi TAMARU)
About Code Equivalence ・A Geometric Approach (Iliya BOUYUKLIEV and Stefka
BOUYUKLIEVA)
An Algorithm for Computing the Covering Radius of a Linear Code Based on
Vilenkin hrestenson Transform (Paskal PIPERKOV, Iliya BOUYUKLIEV and Stefka
BOUYUKLIEVA)
Geometric Properties of Non-Flat Totally Geodesic Surfaces in Symmetric Spaces of Type A (Misa OHASHI and Kazuhiro SUZUKI)
On the Relationships Between Hopf Fibrations and Cartan Hypersurfaces in Spheres (Hideya HASHIMOTO)
Bochner Curvature of Cotangent Bundles with Natural Diagonal Kaehler Structures (Simona-Luiza DRUTA-ROMANIUC)
Isotropicity of Surfaces with Zero Mean Curvature Vector in 4-dimensional Spaces (Naoya ANDO)
Geometry of Lie Hypersurfaces in a Complex Hyperbolic Space (Sadahiro MAEDA and Hiromasa TANABE)
Kaehler Graphs Whose Principal Graphs are of Cartesian Product Type (Toshiaki ADACHI)
In Memory of Professor Akihiko Morimoto (Naoko MORIMOTO and Toshiaki ADACHI)
In Memory of Professor Georgi Ganchev (Velichka MILOUSHEVA)
Graduate students and researchers in the fields of differential geometry and discrete mathematics.