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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Mathematical Modeling in Bioscience

    Theory and Applications
    • 1st Edition
    • Hemen Dutta
    • English
    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.

  • Statistical Modeling and Robust Inference for One-shot Devices

    • 1st Edition
    • Narayanaswamy Balakrishnan + 1 more
    • English
    The study of one-shot devices such as automobile airbags, fire extinguishers, or antigen tests, is rapidly becoming an important problem in the area of reliability engineering. These devices, which are destroyed or must be rebuilt after use, are a particular case of extreme censoring, which makes the problem of estimating their reliability and lifetime challenging. However, classical statistical and inferential methods do not consider the issue of robustness.Statistic... Modeling and Robust Interference for One-shot Devices offers a comprehensive investigation of robust techniques of one-shot devices under accelerated-life tests. With numerous examples and case studies in which the proposed methods are applied, this book includes detailed R codes in selected chapters to help readers implement their own codes and use them in the proposed examples and in their own research on one-shot devicetesting data. Researchers, mathematicians, engineers, and students working on acceleratedlife testing data analysis and robust methodologies will find this to be a welcome resource.

  • Generalized Quantum Calculus with Applications

    • 1st Edition
    • Svetlin G. Georgiev + 1 more
    • English
    Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula.Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.

  • Approximation Theory and Applications

    Piecewise Linear and Generalized Functions
    • 1st Edition
    • Sergei Aliukov
    • English
    Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics. The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure. However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice. This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields. Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics. Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access.

  • Irreducible Tensorial Sets

    • 1st Edition
    • U. Fano + 1 more
    • H. S. W. Massey + 1 more
    • English
    Irreducible Tensorial Sets discusses mathematical methods originating from the theory of coupling and recoupling of angular momenta in atomic physics that constitute an extension of vector and tensor algebra. The book presents a unified treatment with a compact system of notations from different approaches, such as group theory, algebra, and quantum mechanical transformation theory. It discusses irreducible tensorial sets that cover different sets of quantities such as tensor components and states of atomic systems. It also explains quantum mechanical applications, coupling and recoupling of atomic and nuclear states, the Wigner-Eckart theorem, and the products of tensorial sets of operators. The text shows how to calculate the interaction energy between atomic systems couple with one another with a constant total angular momentum. The book also explains the correlations which are functions of the Euler angles between the frame of reference in which a radiation is observed and a frame of reference attached to the orienting radiation or field. It then cites sample problems related to the angular distribution of radiations. The book will prove useful for physicists, for mathematicians, or for readers with some knowledge in theoretical physics, particularly on theory of groups and quantum mechanics.

  • Role of Internet of Things and Machine Learning in Smart Healthcare

    • 1st Edition
    • Volume 137
    • English
    Role of Internet of Things and Machine Learning in Smart Healthcare, Volume 137 of the Advances in Computers series, presents detailed coverage of innovations in computer hardware, software, theory, design, and applications. Published since 1960, this series provides contributors with a medium to explore their subjects in greater depth and breadth than typical journal articles. Additionally, the book discusses the basic concepts of the Internet of Things (IoT) and Machine Learning (ML), along with their various applications in smart healthcare. It proposes novel techniques by integrating IoT, cloud computing, and ML algorithms to efficiently manage e-healthcare data and improve security. The volume also addresses research challenges and probable future directions in smart healthcare using IoT and ML, making it a comprehensive resource for researchers, practitioners, and students interested in advancing healthcare technologies.

  • Computer-Aided Diagnosis (CAD) Tools and Applications for 3D Medical Imaging

    • 1st Edition
    • Volume 136
    • English
    Computer-Aided Diagnosis (CAD) Tools and Applications for 3D Medical Imaging, Volume 136 in the Advances in Computers series, presents detailed coverage of innovations in computer hardware, software, theory, design, and applications. Chapters in this updated release include Introduction to Computer-aided diagnosis (CAD) tools and applications, Enhancement of three-dimensional medical images, Machine Learning Based Techniques for Computer Aided Diagnosis, AI-based image processing techniques for the automatic segmentation of human organs, Watermarking over medical images, Compressive Sensing for 3D Medical Image Compression, and more.Additional chapters cover Image encryption of medical images, Image Registration for 3D Medical Images, Texture-based computations for processing volumetric dental image, Language Processing in the Brain :an fMRI Study, Research challenges and emerging futuristic evolution for 3D medical image processing, Software based medical image analysis, and Automated 3D Visualization and Volume Estimation of Hepatic Structures for Treatment Planning of Hepatocellular Carcinoma.

  • Agent-Based Models with MATLAB

    • 1st Edition
    • Erik Cuevas + 3 more
    • English
    Agent-Based Models with MATLAB introduces Agent-Based Modeling (ABM), one of the most important methodologies for complex systems modeling. The book explores computational implementations and accompanying MATLAB software code as a means of inspiring readers to apply agent-based models to solve a diverse range of problems. It comes with a large amount of software code that accompanies the main text, and the modeling systems described in the book are implemented using MATLAB as the programming language. Despite the heavy mathematical components of Agent-Based Models and complex systems, it is possible to utilize these models without in-depth understanding of their mathematical fundamentals.This book enables computer scientists, mathematicians, researchers, and engineers to apply ABM in a wide range of research and engineering applications. It gradually advances from basic to more advanced methods while reinforcing complex systems through practical, hands-on applications of various computational models.

  • Mathematical Methods in Medical and Biological Sciences

    • 1st Edition
    • Harendra Singh + 1 more
    • English
    Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish　profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits.In addition, the book provides leading-edge developments and insights for a range of applications, including epidemiological modeling of pandemic dynamics, viral infection developments, cancer developments, blood oxygen dynamics, HIV infection spread, reaction-diffusion models, polio infection spread, and chaos modeling with fractional order derivatives.

  • Encyclopedia of Mathematical Physics

    • 2nd Edition
    • Richard Szabo + 1 more
    • English
    Encyclopedia of Mathematical Physics, Second Edition provides a complete resource for researchers, students, and lecturers with an interest in mathematical physics. The book enables readers to access basic information on topics peripheral to their own areas by providing a repository of core information that can be used to refresh even the experienced researcher’s memory and aid teachers in directing students to entries relevant to their course-work. The impressive amount of information in this work - approximately 270 chapters - has been distilled, organized into 10 distinct sections and presented as a complete reference tool to the userThe book is a stimulus for new researchers working in mathematical physics—or in areas using the methods originating from work in mathematical physics—providing them with focused, high-quality background information.

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