Mathematical Analysis in Interdisciplinary Research

This contributed volume presents research and expository papers in mathematical analysis and its applications to various fields, covering optimal control problems, communication networks, emergency evacuation, cooperative and noncooperative systems, and more. It is useful for graduate students and researchers in theoretical and interdisciplinary research.

Format: Hardback
Length: 1060 pages
Publication date: 11 March 2022
Publisher: Springer Nature Switzerland AG

This comprehensive volume presents an extensive collection of research and expository papers covering a wide range of topics in mathematical analysis and its diverse applications across various fields. It serves as a state-of-the-art resource, offering cutting-edge knowledge on a diverse array of subjects. The book is particularly valuable for graduate students and researchers engaged in theoretical and interdisciplinary research. The focus of the book is on several key areas, including:

Optimal Control Problems: This section explores the analysis and solution of optimal control problems, where the objective is to find the optimal control policies that maximize a given performance criterion while satisfying certain constraints. The topics covered include dynamic programming, Pontryagin's maximum principle, linear programming, and nonlinear control systems.

Optimal Maintenance of Communication Networks: This area focuses on developing efficient algorithms and models for maintaining communication networks, such as wireless networks, optical networks, and power grids. The topics covered include network optimization, routing, capacity planning, and fault detection and recovery.

Optimal Emergency Evacuation with Uncertainty: This section addresses the challenges of designing optimal evacuation strategies in the presence of uncertainty, such as natural disasters, terrorist attacks, or pandemics. The topics covered include evacuation planning, risk assessment, and decision-making under uncertainty.

Cooperative and Noncooperative Partial Differential Systems: This section explores the analysis and solution of partial differential equations (PDEs) that involve multiple agents or stakeholders. The topics covered include cooperative game theory, Nash equilibrium, and distributed optimization.

Variational Inequalities and General Equilibrium Models: This section examines the study of variational inequalities and their applications in modeling economic systems, social systems, and biological systems. The topics covered include game theory, optimization, and control theory.

Anisotropic Elasticity and Harmonic Functions: This section focuses on the study of anisotropic materials, such as rubber, plastic, and biological tissues, and their response to external forces. The topics covered include elasticity theory, differential equations, and boundary value problems.

Nonlinear Stochastic Differential Equations: This section explores the analysis and solution of nonlinear stochastic differential equations (SDEs) that model complex systems with randomness. The topics covered include stochastic differential equations, Brownian motion, and Markov processes.

Operator Equations: This section examines the study of operator equations, which are a class of PDEs that arise in various applications, including physics, engineering, and mathematics. The topics covered include partial differential equations, operator theory, and applications to physics.

Max-Product Operators of Kantorovich Type: This section explores the theory of max-product operators, which are a class of operators that arise in the study of partial differential equations and have applications in various fields, including physics, economics, and mathematics. The topics covered include partial differential equations, operator theory, and applications to physics.

Perturbations of Operators: This section examines the analysis and solution of perturbations of operators, which are a fundamental concept in the study of partial differential equations. The topics covered include perturbation theory, stability analysis, and applications to physics and engineering.

Integral Operators: This section explores the theory of integral operators, which are a class of operators that arise in the study of partial differential equations and have applications in various fields, including physics, engineering, and mathematics. The topics covered include integral equations, operator theory, and applications to physics.

Dynamical Systems Involving Maximal Monotone Operators: This section examines the analysis and solution of dynamical systems that involve maximal monotone operators, which are a class of operators that play a crucial role in the study of partial differential equations and their applications. The topics covered include dynamical systems, partial differential equations, and applications to physics and engineering.

The Three-Body Problem: This section explores the study of the three-body problem, which is a classical problem in physics that involves the motion of three celestial bodies under the influence of gravitational and electromagnetic forces. The topics covered include celestial mechanics, classical mechanics, and numerical simulations.

Deceptive Systems: This section examines the study of deceptive systems, which are systems that appear to be simple but have complex underlying dynamics. The topics covered include complex systems, chaos theory, and applications to physics and engineering.

Hyperbolic Equations: This section explores the analysis and solution of hyperbolic equations, which are a class of PDEs that arise in various applications, including physics, engineering, and mathematics. The topics covered include hyperbolic equations, differential equations, and applications to physics.

Strongly Generalized Preinvex Functions: This section examines the theory of strongly generalized preinvex functions, which are a class of functions that have important applications in optimization, control theory, and mathematical economics. The topics covered include optimization, partial differential equations, and applications to economics.

Dirichlet Characters: This section explores the theory of Dirichlet characters, which are a fundamental concept in the study of partial differential equations and their applications in various fields, including physics, engineering, and mathematics. The topics covered include partial differential equations, operator theory, and applications to physics.

Probability Distribution Functions: This section examines the theory of probability distribution functions, which are a fundamental concept in statistics and probability theory. The topics covered include probability theory, statistics, and applications to economics and finance.

Applied Statistics: This section explores the application of statistical methods and techniques to various fields, including economics, biology, and social sciences. The topics covered include statistical analysis, data modeling, and applications to real-world problems.

Integral Inequalities: This section examines the theory of integral inequalities, which are a class of mathematical inequalities that arise in various applications, including optimization, control theory, and mathematical economics. The topics covered include optimization, partial differential equations, and applications to economics.

Generalized Convexity: This section explores the theory of generalized convexity, which is a fundamental concept in optimization and control theory. The topics covered include convex analysis, optimization, and applications to economics and finance.

Global Hyperbolicity of Spacetimes: This section examines the theory of global hyperbolicity of spacetimes, which is a fundamental concept in general relativity and cosmology. The topics covered include spacetime geometry, differential equations, and applications to astrophysics.

Douglas-Rachford Methods: This section explores the theory of Douglas-Rachford methods, which are a class of numerical methods for solving differential equations. The topics covered include numerical analysis, differential equations, and applications to physics and engineering.

Fixed Point Problems: This section examines the theory of fixed point problems, which are a fundamental concept in mathematics and have applications in various fields, including optimization, control theory, and mathematical economics. The topics covered include fixed point theory, optimization, and applications to economics and finance.

The General Rodrigues Problem: This section explores the theory of the general Rodrigues problem, which is a fundamental problem in celestial mechanics and has applications in various fields, including astrophysics and space exploration. The topics covered include celestial mechanics, differential equations, and applications to astrophysics.

Banach Algebras: This section explores the theory of Banach algebras, which are a class of algebraic structures that have important applications in mathematics, physics, and engineering. The topics covered include algebraic structures, linear algebra, and applications to physics and engineering.

Affine Group: This section explores the theory of affine group, which is a fundamental concept in geometry and algebra. The topics covered include geometry, algebra, and applications to physics and engineering.

Gibbs Semigroup: This section explores the theory of Gibbs semigroup, which is a class of stochastic processes that have important applications in physics, chemistry, and biology. The topics covered include stochastic processes, probability theory, and applications to physics and biology.

Relator Spaces: This section explores the theory of relator spaces, which are a class of mathematical structures that have important applications in mathematics, physics, and engineering. The topics covered include mathematical structures, linear algebra, and applications to physics and engineering.

Sparse Data Representation: This section explores the theory of sparse data representation, which is a technique for efficiently storing and processing large amounts of data with limited storage capacity. The topics covered include data compression, data storage, and applications to data analysis and machine learning.

Meier-Keeler Sequential Contractions: This section explores the theory of Meier-Keeler sequential contractions, which are a class of operators that have important applications in optimization, control theory, and mathematical economics. The topics covered include optimization, partial differential equations, and applications to economics.

Hybrid Contractions: This section explores the theory of hybrid contractions, which are a class of operators that have important applications in optimization, control theory, and mathematical economics. The topics covered include optimization, partial differential equations, and applications to economics.

Polynomial Equations: This section explores the theory of polynomial equations, which are a fundamental concept in mathematics and have applications in various fields, including physics, engineering, and mathematics. The topics covered include algebraic equations, linear algebra, and applications to physics and engineering.

In addition to presenting the state-of-the-art knowledge, some of the works published within this volume also provide guidelines for further research and propose new directions and open problems in the field. This volume serves as a valuable resource for graduate students, researchers, and practitioners interested in mathematical analysis and its diverse applications.

Weight: 1748g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030847203
Edition number: 1st ed. 2021