CMS/CAIMS Books in Mathematics – serie

This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models.

This monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models.

This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field.

This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field.

This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator.

This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator.

This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice.

This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice.

This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.The material provided should aid practitioners significantly to solve their problems.

This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.The material provided should aid practitioners significantly to solve their problems.

The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes.

The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes.

The main difference between a bank balance sheet management problem and a typical portfolio optimization problem is that the former involves multiple risks.

The main difference between a bank balance sheet management problem and a typical portfolio optimization problem is that the former involves multiple risks.

In mathematical modeling of processes occurring in logistics, management science, operations research, networks, mathematical finance, medicine, and control theory, one often encounters optimization problems involving more than one objective function so that Multiobjective Optimization (or Vector Optimization, initiated by W.

In mathematical modeling of processes occurring in logistics, management science, operations research, networks, mathematical finance, medicine, and control theory, one often encounters optimization problems involving more than one objective function so that Multiobjective Optimization (or Vector Optimization, initiated by W.

Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Édouard Lucas between 1876 and 1880, that they are now named after him.

Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Édouard Lucas between 1876 and 1880, that they are now named after him.

The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions. In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces.

The first approach consists of the method of analytical and classical solutions, and the second approach consists of the method of weak (variational) solutions. In connection with the approach of weak solutions, the book also provides an introduction to distributions, Fourier transform and Sobolev spaces.

This book is about semisimple Banach algebras with a focus on those that are commutative. Some of the questions dealt with in the book are: Whether the introduced Banach algebras are BSE-algebras, whether they have BSE norms, whether they have the separating ball property or some variant of it, and whether they are Arens regular.

This book is about semisimple Banach algebras with a focus on those that are commutative. Some of the questions dealt with in the book are: Whether the introduced Banach algebras are BSE-algebras, whether they have BSE norms, whether they have the separating ball property or some variant of it, and whether they are Arens regular.

Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.

Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs.

This book offers a comprehensive introduction to various aspects of functional analysis and operator algebras. In Part I, readers will find the foundational material suitable for a one-semester course on functional analysis and linear operators.

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years.

This third edition presents an expanded and updated treatment of convex analysis methods, incorporating many new results that have emerged in recent years. These additions are essential for grasping the practical applications of convex function theory in solving contemporary real-world problems.To reflect these advancements, the material has been meticulously reorganized, with a greater emphasis on topics relevant to current research. Additionally, great care has been taken to ensure that the text remains accessible to a broad audience, including both students and researchers focused on the application of mathematics.Ideal for undergraduate courses, graduate seminars, or as a comprehensive reference, this book is an indispensable resource for those seeking to understand the extensive potential of convex function theory.

Here, we re-examine most of the key topics Beiler covered, while introducing fresh updates and insights rooted in computational number theory.The authors aim to present efficient computer algorithms to tackle various problems that arise in the theory of numbers, providing a deeper and more modern perspective on these timeless puzzles.

Scientific computing is essential for tackling complex problems across many domains—but how can scientists develop high-performance and high-quality software that scales efficiently? This book serves as an accessible introduction to extreme-scale computing, specifically designed for domain scientists who may not have formal computer science training but need to harness the power of C++ and parallel computing for large-scale applications.The book begins by covering the fundamentals of scientific computing software management, including essential tools like Linux, Git, and CMake, before diving into a detailed exploration of C++ for extreme-scale computing. Readers familiar with languages like Python will gain the necessary skills to transition to C++ and build scalable, efficient software.  Beyond basic programming, this book delves into hardware-aware computing, teaching readers how to optimize software performance by understanding the underlying architecture of modern computational systems. It then introduces parallel computing techniques, covering MPI for distributed memory parallelism, shared memory parallelism, CUDA for GPU programming, and Kokkos for performance portability.Further chapters focus on efficient I/O, debugging, and profiling, which all address aspects of the critical challenge of performance optimization in extreme-scale computing. The book concludes with an overview of popular libraries for extreme-scale computing, equipping readers with the tools they need to solve real-world computational problems.  With a balance of theory, practical applications, and illustrative case studies, this book provides domain scientists with a comprehensive roadmap to mastering extreme-scale computing and developing highly parallel and performant software.