A Study Of Matrices, Elementary Divisors, And The Classification Of Collineations
Recent Developments in Spectral and Approximation Theory
New Perspectives on Optimization Algorithms Research
Optimization processes are present in nearly all human activities, aiming to reduce time and expenses, conserve resources, and maximize efficiency. Classical numerical optimization methods were initially employed in more complex or elaborate problems. This class of methods was convenient to use when equations could correctly and completely formulate all the attributes of the problem to be optimized and whose search space for the solution had convexity characteristics and was not multimodal. Expressing a problem completely through equations is often a difficult (if not impossible) task because linguistic values or employing quantities that are not easily dealt with by classical optimization methods can only describe certain limitations and barriers. Irregular and non-convex search spaces also present problems for classical methods, especially those with multiple local minima and maxima, as they can lead to suboptimal solutions. In this context, researchers in optimization have presented new techniques to overcome these barriers, introducing new concepts and methods that enable working with problems that are not well-defined and in multimodal search spaces. Many of these techniques utilize artificial intelligence methods, and it is possible to optimize problems where their limitations are not clearly defined or where their search spaces contain different local maxima and minima. This book is a contribution in this sense. In it, the reader will find two sections. The first, titled "Methodologies", presents the frontier of state-of-the-art optimization techniques and their applications to various problems. The second section, titled "Applications," presents examples of practical applications of modern techniques in optimizing issues, which can be easily adapted to others with similar characteristics. Thus, the reader can use this book to optimize their problems by applying the solutions presented in the chapters and adapting them to their specific issues.
The System of Calculating Diameter, Circumference, Area, and Squaring the Circle
Computational Methods for Inverse Problems and Applications
Advances in Poisson Geometry
This book presents recent advances in topics related to Poisson geometry originating from lectures given at the "Poisson School" held in 2022 at the CRM in Barcelona. The purpose is to give both an introduction to this active field of research as well as highlight new trends in related topics. The texts cover both classical results, known to experts in the field, as well as recent and previously unpublished mathematical results. Graduate students and early-stage researchers with basic knowledge in differential and symplectic geometry, together with established researchers that are keen to dive into this rapidly growing field of research, will find this book a useful resource.
Some Integral Equations Related to Abel's Equation and the Hilbert Transform
On Condition Numbers and the Distance to the Nearest Ill-posed Problem
Using the Kth Nearest Neighbor Clustering Procedure to Determine the Number of Subpopulations
On the Formulation and Analysis of Numerical Methods for Time Dependent Transport Equations
A Note on the Integral Equation of the First Kind With a Cauchy Kernel
On Invariant Surfaces and Bifurcation of Periodic Solutions of Ordinary Differential Equations
Some Integral Equations Related to Abel's Equation and the Hilbert Transform
Applied Engineering Mathematics
The publication of this book is motivated by the need to present the latest research & advancements in the fields of Fluid/Solid Mechanics, Nonlinear Dynamics, and Differential Equations in Applied Mathematics. This book gathers the work of leading experts, offering cutting-edge findings addressing existing challenges in the field. It covers a broad spectrum of topics, including advanced computational methods/mathematical modeling/different Mathematical methods & their applications in many scientific disciplines like predicting the nature and behavior of physical systems in engineering. These problems often require solving differential equations governing fluid flow, heat transfer, and structural deformation, often simultaneously, among other topics. Each chapter delves into specific problems, showcasing interdisciplinary approaches & demonstrating the practical impact of mathematical research on real-world issues. This book is a great resource for scholars, professionals, and researchers as it offers a comprehensive overview of cutting-edge methodologies & innovative solutions. It aims to stimulate additional investigation, promote interdisciplinary collaboration & make substantial contributions to advancing knowledge.
Information-Oriented Logic
The book introduces a new form of mathematical logic called "Information Oriented Logic" (IOL). It demonstrates that IOL is capable of solving various classical and non-classical logic problems that cannot be solved by traditional methods of logic. In this book, it is argued that two meaningful declarative sentences or symbols can make the same statement if they express the same thing or referent in different ways. The book treats a piece of information as the referent for a meaningful declarative sentence, thus inventing information-oriented logic. As a result, this book provides a comprehensive guide to this logic. Unlike traditional logic, which uses declarative sentences as the result of logical expressions, this new logic uses pieces of information. The book is intended for undergraduate and graduate students, as well as scholars applying mathematical logic to various fields such as philosophy, linguistics, ontology, information theory, computer science, etc. Additionally, it provides a new mereology in which all implications of a piece of information are its parts.
