September 2022
Pages: 692
ISBN: 978-981-126-012-4 (hardcover)
This is the first monograph devoted to clean ring and matrix theory. It aims to study a theory of expressing an element in a ring as the sum of some special ones, such as idempotents, units, nilpotents, tripotents, involutions, etc. A matrix over such rings is thereby expressed as the sum of some special matrices. Also another topics on the behaviors of topological properties and *-properties of such rings are investigated.
The book is based on the results of various published papers, particularly, by the authors'. It is accessible for students familiar with general abstract algebra, while the topics are interesting for researchers in the field of ring, matrix and operator theory.
Strongly Clean Conditions
Matrices over Commutative Rings
Triangular and Generalized Matrix Rings
Strong J-Cleanness
Strong Nil-cleanness
Classes of Strongly Clean Rings
Clean Properties
Rings Generated by Certain Elements
Weakly Clean and Weakly Nil-clean Properties
Periodic and Weakly Periodic Rings
Conditions on Zero-divisors
Topological Structures
Rings of Continuous Functions
Rings with Involutions
The Generalized Drazin Inverse
Graduate students and researchers in algebra and analysis, especially, ring and matrix theory, operator theory. Researchers in applied and computation related to generalized inverse.
September 2022
Pages: 328
ISBN: 978-981-126-110-7 (hardcover)
Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.
This book is the first to introduce fractal calculus and provides a basis for the research and development of this framework. It is suitable for undergraduate and graduate students in mathematics and physics who have mastered general mathematics, quantum physics, and statistical mechanics, as well as researchers dealing with fractal structures in various disciplines.
Introduction to Analysis of Fractals
Basic Tools
Fractal Cantor Like Sets
Fractal Calculus
Local Fractal Differential Equations
Stability of Fractal Differential Equations
Generalization of Fractal Calculus
Application of Fractal Calculus
Appendix
Undergraduate and graduate students in mathematics and physics who has mastered general mathematics, quantum physics, and statistical mechanics; researchers dealing with fractal structures in various disciplines
November 2022
Pages: 350
ISBN: 978-981-125-854-1 (hardcover)
This is a book for a second course in linear algebra whereby students are assumed to be familiar with calculations using real matrices. To facilitate a smooth transition into rigorous proofs, it combines abstract theory with matrix calculations.
This book presents numerous examples and proofs of particular cases of important results before the general versions are formulated and proved. This is highly effective to create the needed depth of understanding a general theory by detailing a proof of a particular case that encapsulates the main idea of a general theorem. Using the knowledge gained from a particular case, it can be easily extended to prove another particular case or a general case. For some theorems, there are two or even three proofs provided. In this way, students stand to gain and study important results from different angles and, at the same time, see connections between different results presented in the book.
Vector Spaces
Linear Transformations
Inner Product Spaces
Reduction of Endomorphisms
Appendices:
Permutations
Complex Numbers
Polynomials
Infinite Dimensional Inner Product Spaces
Undergraduate students taking a second course in linear algebra.
November 2022
Pages: 290
ISBN: 978-981-126-104-6 (hardcover)
ISBN: 978-981-126-210-4 (softcover)
The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.
The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions.
The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.
Introduction to Patterns:
Geometrical Configurations
Piecewise Functions
Analytical Formulations
Recursive Sequences
Piecewise Sequences
Periodic Cycles
Geometrical Configurations:
Patterns at Same Scale
Patterns at Different Scales
Alternating & Piecewise Patterns
Summation of Areas
Sequences, Products & Summations:
Linear Sequences
Quadratic Sequences
Summation?Type Sequences
Geometric Sequences
Product?Type Sequences
Alternating & Piecewise Sequences
Summations & Proof by Induction:
3Linear & Geometric Summations
Proof by Induction
Traits of Pascal's Triangle:
Horizontal Identities
Diagonal Identities
Binomial Expansion
Recursive Relations:
Formulating a Recursive Relation
Obtaining an Explicit Solution
Non-autonomous Recursive Sequences
Periodic Traits:
Autonomous Recursive Sequences
Multiplicative Form
Additive Form
Multiplicative & Additive Forms
High school and undergraduate levels in mathematics for Non-STEM disciplines, Pattern Recognition, Discrete Mathematics, Difference Equations.
November 2022
Pages: 250
ISBN: 978-981-125-294-5 (hardcover)
This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and stochastic resetting processes, which can be easily followed by the reader, who will be able to reproduce the obtained results. The book will be intended for advanced undergraduate and graduate students and researchers in physics, mathematics and other natural sciences due to the various examples which will be provided in the book.
Mathematical background
Fox H-function and Related Functions
Elements of Random Walk Theory
Anomalous Diffusion: Application of Mittag-Leffler and Fox H-functions
Random Search: Application of Mittag-Leffler and Fox H-functions
Various Applications of Mittag-Leffler and Fox H-functions
Appendix A: Functional Calculus
Advanced undergraduate and graduate students, researchers in the fields of stochastic processes, fractional calculus, anomalous diffusion, random search, stochastic resetting, econophysics.
December 2022
Pages: 350
ISBN: 978-981-125-529-8 (hardcover)
This comprehensive compendium discusses the basics of graph theory to its application, focusing on the application of graph theory to mobile communications.
A mobile communication connects a mobile terminal and a base station wirelessly, and the base station enables communications all over the world via a wired and satellite communication system. This means that the mobile communication system includes wire and wireless technologies, and also hardware such as analog electric circuits, digital circuits and a software part such as computer algorithms.
This useful reference text deeply studies how the network structure influences the performance of the corresponding system.
Basic Concept of Graphs
Trees, Cotrees and Hybrid Trees
Matrix and Application of Trees
Graphical Views of Electrical and Electronic Networks
Operators in Signal Flow Graphs
Location Problems on Graphs and Networks
Cellular Systems in Mobile Communication Systems
Channel Assignment Problems
Mobility and Communication Traffic
Multi-Hop Communication
Researchers, professionals, academics, undergraduate and graduate students in circuits & systems, communications and electrical and electronic engineering.