Hemen Dutta – författare

Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strategies to control the occurrence and reoccurrence of viruses. The models included in this book can be used to study the dynamics of different viruses, searching for control measures, and epidemic models under various effects and environments. This book covers different models and methods of modeling, including data-driven approaches. The authors and editors are experienced researchers, and each chapter has been designed to provide readers with leading-edge information on topics discussed. Includes models to describe global and local dynamics of various viruses Provides readers with control strategies for occurrence and reoccurrence of viruses Includes epidemic models under various effects and environments Provides readers with a robust set of mathematical tools and techniques for epidemiological modeling

This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.

This book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension.Features Offers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean AlgebraProvides end of chapter solved examples and practice problemsDelivers materials on valid arguments and rules of inference with illustrationsFocuses on algebraic structures to enable the reader to work with discrete structures

Recognized as a "Recommended" title by Choice for their October 2020 issue.Choice is a publishing unit at the Association of College & Research Libraries (ACR&L), a division of the American Library Association. Choice has been the acknowledged leader in the provision of objective, high-quality evaluations of nonfiction academic writing. This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences.Presents theory, methods, and applications in a balanced mannerIncludes the basic developments with full detailsContains the most recent advances and offers enough references for further studyWritten in a self-contained style and provides proof of necessary resultsOffers research problems to help early career researchers prepare research proposalsMathematical Methods in Engineering and Applied Sciences makes available for the audience, several relevant topics in one place necessary for crucial understanding of research problems of an applied nature. This should attract the attention of general readers, mathematicians, and engineers interested in new tools and techniques required for developing more accurate mathematical methods and modelling corresponding to real-life situations.

Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problemsThis book is written for individual researchers, educators, students, and department libraries.

Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problemsThis book is written for individual researchers, educators, students, and department libraries.

Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.

This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic. Features Includes basic and essential topics of real analysisAdopts a reasonable approach to make the subject easier to learnContains many solved examples and exercise at the end of each chapterPresents a quick review of the fundamentals of set theoryCovers the real number systemDiscusses the basic concepts of metric spaces and complete metric spaces

This book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension.Features Offers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean AlgebraProvides end of chapter solved examples and practice problemsDelivers materials on valid arguments and rules of inference with illustrationsFocuses on algebraic structures to enable the reader to work with discrete structures

Methods of Mathematical Modeling: Advances and Applications delves into recent progress in this field, highlighting innovative methods and their uses in different domains. This book covers convergence analysis involving nonlinear integral equations and boundary value problems, Navier-Stokes equations in Sobolev-Gevrey spaces, magneto-hydrodynamics of ternary nanofluids with heat transfer effects, vortex nerve complexes in video frame shape approximation, hybrid schemes for computing hyperbolic conservation laws, and solutions to new fractional differential equations. Additionally, the book examines dynamics of Leslie-Gower type predator-prey models and models for the dynamics of generic crop and water availability.Readers will find diverse approaches, techniques, and applications needed for modeling various physical and natural systems. Each chapter is self-contained, encouraging independent study and application of the modeling examples to individual research projects. This book serves as a valuable resource for researchers, students, educators, scientists, and practitioners involved in different aspects of modeling.Provides new mathematical methods and techniques for modeling various physical and natural systemsIncludes new hybrid computational schemes and procedures for handling wave interactionsIncludes advanced-level convergence analysis and generalized Navier-Stokes equationsProvides readers with the dynamics of predator-prey, generic crop, and water availability models

In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and operators acting on them. The construction of these operators itself is interesting and provides new types of Hilbert-space operators. Also, by considering spectral-theoretic properties of these operators, the authors illustrate how "free-Hilbert-space� Operator Theory is different from the classical Operator Theory. More interestingly, the authors demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how "inside� actions of operator algebra deform the free-probabilistic information-in particular, the semicircular law. Presents the spectral properties of three types of operators on a Hilbert space, in particular how these operators affect the semicircular law Demonstrates how the semicircular law is deformed by actions "from inside", as opposed to actions "from outside" considered by previous theory Explores free Hilbert spaces and their modeling applications Authored by two leading researchers in Operator Theory and Operator Algebra

Mathematical Modeling in Bioscience: Theory and Applications provides readers with tools and techniques for mathematical modeling in bioscience through a wide range of novel and intriguing topics. The book concentrates on larger elements of mathematical modeling in bioscience, including topics such as modeling of the Topp--Leone new power generalized Weibull-G distribution family, vector-borne disease modeling, transmission modeling of SARS-COV-2 among other infectious diseases, pattern formulation models, compartmental models for HIV/AIDS transmission, population models, irrigation scheduling models, and predator--prey models. The readers will discover a variety of new methods, approaches, and techniques, as well as a wide range of applications demonstrating key concepts in bioscience modeling. This book provides a leading-edge resource for researchers in a variety of scientific fields who are interested in mathematical modeling, including mathematics, statistics, biology, biomedical engineering, computer science, and applied sciences.Provides key concepts for advanced mathematical methods for modeling in bioscienceIncludes statistical, delay, random, and stochastic mathematical modelsFocuses on broader aspects of mathematical models in bioscienceProvides the readers with several types of dynamic representative applications

Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.

The aim of Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties is to discuss primarily about different kinds of summable spaces, compute their duals and then characterize several matrix classes transforming one summable space into other. The book also discusses several geometric properties of summable spaces, as well as dealing with the construction of summable spaces using Orlicz functions, and explores several structural properties of such spaces. Each chapter contains a conclusion section highlighting the importance of results, and points the reader in the direction of possible new ideas for further study.Features Suitable for graduate schools, graduate students, researchers and faculty, and could be used as a key text for special Analysis seminars Investigates different types of summable spaces and computes their duals Characterizes several matrix classes transforming one summable space into other Discusses several geometric properties of summable spaces Examines several possible generalizations of Orlicz sequence spaces

This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.

Recognized as a "Recommended" title by Choice for their October 2020 issue.Choice is a publishing unit at the Association of College & Research Libraries (ACR&L), a division of the American Library Association. Choice has been the acknowledged leader in the provision of objective, high-quality evaluations of nonfiction academic writing. This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences. Presents theory, methods, and applications in a balanced manner Includes the basic developments with full details Contains the most recent advances and offers enough references for further study Written in a self-contained style and provides proof of necessary results Offers research problems to help early career researchers prepare research proposals Mathematical Methods in Engineering and Applied Sciences makes available for the audience, several relevant topics in one place necessary for crucial understanding of research problems of an applied nature. This should attract the attention of general readers, mathematicians, and engineers interested in new tools and techniques required for developing more accurate mathematical methods and modelling corresponding to real-life situations.

The book explores a range of mathematical topics essential for application in engineering and applied sciences. It explores both the theoretical and practical aspects, providing a comprehensive foundation for the development of robust theories applicable to engineering and applied sciences.Mathematical Analysis for Engineering and Applied Sciences: Foundational and Fundamental Aspects discusses the essential mathematical principles that underpin the fields of applied science and engineering. This comprehensive book explores a blend of pure and applied mathematics, demonstrating how mathematical tools and techniques can be utilized to create a wide range of models for practical applications in these disciplines. It addresses the challenges of handling complex phenomena and provides algorithms, methods, and logical concepts that are invaluable for bioengineering, cryptosystems, surface modeling, and various other engineering applications.Individual researchers, educators, students, and department libraries will find this book of interest.

An introductory course in summability theory for students, researchers, physicists, and engineersIn creating this book, the authors’ intent was to provide graduate students, researchers, physicists, and engineers with a reasonable introduction to summability theory. Over the course of nine chapters, the authors cover all of the fundamental concepts and equations informing summability theory and its applications, as well as some of its lesser known aspects. Following a brief introduction to the history of summability theory, general matrix methods are introduced, and the Silverman-Toeplitz theorem on regular matrices is discussed. A variety of special summability methods, including the Nörlund method, the Weighted Mean method, the Abel method, and the (C, 1) - method are next examined. An entire chapter is devoted to a discussion of some elementary Tauberian theorems involving certain summability methods. Following this are chapters devoted to matrix transforms of summability and absolute summability domains of reversible and normal methods; the notion of a perfect matrix method; matrix transforms of summability and absolute summability domains of the Cesàro and Riesz methods; convergence and the boundedness of sequences with speed; and convergence, boundedness, and summability with speed.• Discusses results on matrix transforms of several matrix methods• The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory• Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods• Matrix transforms of summability domains of regular perfect matrix methods are examined• Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutionsAn Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation.ANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia.HEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India.P.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.

An authoritative text that presents the current problems, theories, and applications of mathematical analysis researchMathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research.This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc.Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information providedOffers references that help readers advance to further studyWritten for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

A guide to the new research in the field of fractional order analysisFractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy.Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculusOffers a balance of theory, methods, and applicationsPuts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological modelsHelps make research more relevant to real-life applicationsWritten for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.

This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. The book is useful for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. It provides a good balance while dealing with the basic and essential topics that enable the reader to learn the more advanced topics easily. It includes many examples and end of chapter exercises including hints for solutions in several critical cases. The book is ideal for students, instructors, as well as those doing research in areas requiring a basic knowledge of Real Analysis. Those more advanced in the field will also find the book useful to refresh their knowledge of the topic. Features Includes basic and essential topics of real analysisAdopts a reasonable approach to make the subject easier to learnContains many solved examples and exercise at the end of each chapterPresents a quick review of the fundamentals of set theoryCovers the real number systemDiscusses the basic concepts of metric spaces and complete metric spaces

This volume is a collection of chapters that present several key principles and theories, as well as their potential uses in the development of mathematical models in areas like waves, thermodynamic, electromagnetics, fluid dynamics, and catastrophes. The techniques and methodologies used in this book, on the other hand, should have a long-term impact and be applicable to a wide range of different topics of study and research. Each chapter should also help readers in gaining a better knowledge of the underlying and connected concepts. The companion volume (Contemporary Mathematics, Volume 787) is devoted to theory and application.

This volume is a collection of chapters that present key ideas and theories, as well as their rigorous applications, required for the development of mathematical models in areas such as travelling waves, epidemiology, the chemotaxis system, atrial fibrillation, and vortex nerve complexes. The techniques, methodologies and approaches adopted in this book have relevance in several other fields including physics, biology, and sociology. Each chapter should also assist readers in comfortably comprehending the related and underlying ideas. The companion volume (Contemporary Mathematics, Volume 786) is devoted to principle and theory.

Mathematical Modelling: Principle and Theory (Volume 786) is a collection of chapters that present several key principles and theories, as well as their potential uses in the development of mathematical models in areas like waves, thermodynamic, electromagnetics, fluid dynamics, and catastrophes. The techniques and methodologies used in this book, on the other hand, should have a long-term impact and be applicable to a wide range of different topics of study and research. Each chapter should also help readers in gaining a better knowledge of the underlying and connected concepts.Mathematical Modelling: Theory and Application (Volume 787) is a collection of chapters that present key ideas and theories, as well as their rigorous applications, required for the development of mathematical models in areas such as travelling waves, epidemiology, the chemotaxis system, atrial fibrillation, and vortex nerve complexes. The techniques, methodologies and approaches adopted in this book have relevance in several other fields including physics, biology, and sociology. Each chapter should also assist readers in comfortably comprehending the related and underlying ideas.

This book presents several aspects of research on mathematics that have significant applications in engineering, modelling and social matters, discussing a number of current and future social issues and problems in which mathematical tools can be beneficial.

This book presents several aspects of research on mathematics that have significant applications in engineering, modelling and social matters, discussing a number of current and future social issues and problems in which mathematical tools can be beneficial.

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research.

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research.

Focusing on computational methods in science, mathematical tools applied to engineering, mathematical modeling and new aspects of analysis, the book discusses the applications of mathematical modelling in areas such as health science, engineering, computer science, social science, and economics.