Bücher der Reihe Forum for Interdisciplinary Mathematics

This book collects chapters on contemporary topics on metric fixed point theory and its applications in science, engineering, fractals, and behavioral sciences. The book presents the study of common fixed points in a generalized metric space and fixed point results with applications in various modular metric spaces.

The book focuses on how to implement discrete wavelet transform methods in order to solve problems of reaction-diffusion equations and fractional-order differential equations that arise when modelling real physical phenomena.

It provides a comprehensive overview of channel coding, covering modern techniques such as turbo codes, low-density parity-check (LDPC) codes, space-time coding, polar codes, LT codes, and Raptor codes as well as the traditional codes such as cyclic codes, BCH, RS codes, and convolutional codes.

This book contains select papers on mathematical analysis and modeling, discrete mathematics, fuzzy sets, and soft computing. All the papers were presented at the international conference on FIM28-SCMSPS20 virtually held at Sri Sivasubramaniya Nadar (SSN) College of Engineering, Chennai, India, and Stella Maris College (Autonomous), Chennai, from November 23-27, 2020. The conference was jointly held with the support of the Forum for Interdisciplinary Mathematics. Both the invited articles and submitted papers were broadly grouped under three heads: Part 1 on analysis and modeling (six chapters), Part 2 on discrete mathematics and applications (six chapters), and Part 3 on fuzzy sets and soft computing (three chapters).

This edited book provides invited and reviewed contributions in mathematical, physical and experimental modelling and simulations in all fluid mechanics branches. Contributions explore the emerging and state-of-the-art tools in the field authored by well-established researchers to derive improved performance of modelling and simulations. Serving the multidisciplinary fluid mechanics community, this book aims to publish new research work that enhances the prediction and understanding of fluid mechanics and balances from academic theory to practical applications through modelling, numerical studies, algorithms and simulation. The book offers researchers, students and practitioners significant insights on modelling and simulations in fluid mechanics. It offers readers a range of academic contributions on fluid mechanics by researchers that have become leaders in their field. The research work presented in this book will add values to the existing literature in terms of what needs to be done better to direct modelling and simulations towards a growing and rapidly developing field.

This monograph discusses the theoretical and practical development of multicriteria decision making (MCDM). The main purpose of MCDM is the construction of systematized strategies for the "optimisation" of feasible options, as well as the justification of why some alternatives can be declared "optimal". However, at time, we must make decisions in an uncertain environment and such inconvenience gives rise to a much more elaborate scenario. This book highlights models where this lack of certainty can be flexibly fitted in and goes on to explore valuable strategies for making decisions under a multiplicity of criteria. Methods discussed include bipolar fuzzy TOPSIS method, bipolar fuzzy ELECTRE-I method, bipolar fuzzy ELECTRE-II method, bipolar fuzzy VIKOR method, bipolar fuzzy PROMETHEE method, and two-tuple linguistic bipolar fuzzy Heronian mean operators. This book is a valuable resource for researchers, computer scientists, and social scientists alike.

This book's aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie-Simpson numerical algorithm, models represented by nonlinear reaction-diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.

This book facilitates both the theoretical background and applications of fuzzy, intuitionistic fuzzy and rough, fuzzy rough sets in the area of data science. This book provides various individual, soft computing, optimization and hybridization techniques of fuzzy and intuitionistic fuzzy sets with rough sets and their applications including data handling and that of type-2 fuzzy systems. Machine learning techniques are effectively implemented to solve a diversity of problems in pattern recognition, data mining and bioinformatics. To handle different nature of problems, including uncertainty, the book highlights the theory and recent developments on uncertainty, fuzzy systems, feature extraction, text categorization, multiscale modeling, soft computing, machine learning, deep learning, SMOTE, data handling, decision making, Diophantine fuzzy soft set, data envelopment analysis, centrally measures, social networks, VolterräFredholm integro-differential equation, Caputo fractional derivative, interval optimization, decision making, classification problems. This book is predominantly envisioned for researchers and students of data science, medical scientists and professional engineers.

In commemoration of the bicentennial of the birth of the "e;lady who gave the rose diagram to us"e;, this special contributed book pays a statistical tribute to Florence Nightingale. This book presents recent phenomenal developments, both in rigorous theory as well as in emerging methods, for applications in directional statistics, in 25 chapters with contributions from 65 renowned researchers from 25 countries. With the advent of modern techniques in statistical paradigms and statistical machine learning, directional statistics has become an indispensable tool. Ranging from data on circles to that on the spheres, tori and cylinders, this book includes solutions to problems on exploratory data analysis, probability distributions on manifolds, maximum entropy, directional regression analysis, spatio-directional time series, optimal inference, simulation, statistical machine learning with big data, and more, with their innovative applications to emerging real-life problems in astro-statistics, bioinformatics, crystallography, optimal transport, statistical process control, and so on.

This book contains select invited chapters on the latest research in numerical fluid dynamics and applications. The book aims at discussing the state-of-the-art developments and improvements in numerical fluid dynamics. All the chapters are presented for approximating and simulating how these methods and computations interact with different topics such as shock waves, non-equilibrium single and two-phase flows, elastic human-airway, and global climate. In addition to the fundamental research involving novel types of mathematical sciences, the book presents theoretical and numerical developments in fluid dynamics. The contributions by well-established global experts in fluid dynamics have brought different features of numerical fluid dynamics in a single book. The book serves as a useful resource for high-impact advances involving computational fluid dynamics, including recent developments in mathematical modelling, numerical methods such as finite volume, finite difference and finite element, symbolic computations, and open numerical programs such as OpenFOAM software. The book addresses interdisciplinary topics in industrial mathematics that lie at the forefront of research into new types of mathematical sciences, including theory and applications. This book will be beneficial to industrial and academic researchers, as well as graduate students, working in the fields of natural and engineering sciences. The book will provide the reader highly successful materials and necessary research in the field of fluid dynamics.

This book's aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments.

This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.

In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds.

This book presents the understanding of how the different forms of regulatory mechanisms, like birth and death, competition, consumption and the like, result in changes in the stability and dynamics of ecological systems. It deals with a profound and unique insight into the mathematical richness of basic ecological models. Organised into eight chapters, the book discusses the models of mathematical ecology, the dynamical models of single-species system in a polluted environment, the dynamical behaviour of different nonautonomous two species systems in a polluted environment, the influence of environmental noise in Gompertzian and logistic growth models, stability behaviour in randomly fluctuating versus deterministic environments of two interacting species, stochastic analysis of a demographic model of urbanization and stability behaviour of a social group by means of loop analysis, thermodynamic criteria of stability and stochastic criteria of stability. The book will be useful tothe researchers and graduate students who wish to pursue research in mathematical ecology.

A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems.

This book is a collection of invited and reviewed chapters on state-of-the-art developments in interdisciplinary mathematics.

This book systematically classifies the mathematical formalisms of computational models that are required for solving problems in mathematics, engineering and various other disciplines.

This book presents recent developments in statistical methodologies with particular relevance to applications in forestry and environmental sciences.

In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds.

This book provides comprehensive information on the conceptual basis of wavelet theory and it applications.

This book provides an introduction to the mathematical aspects of Euler's elastic theory and its application. The remaining chapters discuss the modeling of membranes, mylar balloons, rotating liquid drops, Hele-Shaw cells, nerve fibers, Cole's experiments, and membrane fusion.

The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained.

This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications. Key topics covered include Sharkovsky¿s theorem on periodic points, Thron¿s results on the convergence of certain real iterates, Shield¿s common fixed theorem for a commuting family of analytic functions and Bergweiler¿s existence theorem on fixed points of the composition of certain meromorphic functions with transcendental entire functions. Generalizations of Tarski¿s theorem by Merrifield and Stein and Abian¿s proof of the equivalence of Bourbaki¿Zermelo fixed-point theorem and the Axiom of Choice are described in the setting of posets. A detailed treatment of Ward¿s theory of partially ordered topological spaces culminates in Sherrer fixed-point theorem. It elaborates Mankäs proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy¿Kowalevsky theorem for partial differential equations and the central limit theorem. It also provides a proof of the converse of the contraction principle due to Jachymski, a proof of fixed point theorem for continuous generalized contractions, a proof of Browder¿Gohde¿Kirk fixed point theorem, a proof of Stalling's generalization of Brouwer's theorem, examine Caristi's fixed point theorem, and highlights Kakutani's theorems on common fixed points and their applications.

It provides an extensive overview of geometric programming methods within a unifying framework, and presents an in-depth discussion of the modified geometric programming problem, fuzzy geometric programming, as well as new insights into goal geometric programming.

The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC).