Square-Free Factorizations. Some Cryptological and Other Mathematical Aspects
Set Dynamic Equations on Time Scales
The process of authoring this book is inspired by the recent increased activity of research on dynamic equations on time scales and other closely related areas. This monograph is the first published book that attempts to provide a comprehensive view of the theory and applications of set dynamic equations on time scales. The main focus of the book is the qualitative theory of set dynamic equations and their applications to fuzzy dynamic equations. The key topics include the solvability of set dynamic equations, stability of set dynamic equations, and applications to certain types of fuzzy dynamic equations.There are five chapters in the book, through which the authors examine a wide scope of the concept of set dynamic equations and their applications. Each chapter focuses on theory and proofs to enrich the reader's understanding of the topic.This book will be particularly useful to those experts who work in applied analysis, in general. It will also be a good reference for computer scientists since it covers fuzzy dynamic equations. Researchers and graduate students at various levels interested in learning about set dynamic equations and related fields will find this text a valuable resource of both introductory and advanced material.
Graph-Theoretic Concepts in Computer Science
This book constitutes the refereed proceedings of the 50th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2024, held in Gozd Martuljek, Slovenia in June 2024, The 31 papers presented in this volume were carefully reviewed and selected from 89 submissions. Additionally, this volume also contains a survey on approximation algorithms for tree-width, path-width, and tree-depth prepared by Hans Bodlander, who delivered the Test of Time Award talk at WG 2024. The WG 2024 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science or by extracting new graph-theoretic problems from applications.
Geometry by Its Transformations
This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years. The book starts with the background needed from Euclid's Elements, followed by chapters on transformations, including dilation (similitude), homology, homogeneous coordinates, projective geometry, inversion, the M繹bius transformation, and transformation geometry as in French schoolbooks of 1910. Projective geometry is presented by tracing its path through the work of J. V. Poncelet, J. Steiner, and K. G. C. von Staudt. Extensive exercises are included, many from the period studied. The prerequisites for approaching this course are knowledge of high school geometry and enthusiasm for mathematical demonstration. This textbook is ideal for a college geometry course, for self-study, or as preparation for the study of modern geometry.
Beyond Simplicity
Go Beyond Simplicity And Embrace Complexity! In this compelling book, discover why engaging with complex issues beyond your work is crucial and gain practical guidance on how to do so effectively. Prepare to unlock a world of opportunity as you learn how to maintain unwavering motivation on this transformative journey. The once daunting complexity will unravel before your eyes, revealing new horizons you never thought possible. You will witness a remarkable transformation, as the previously intricate becomes clear, and even the most formidable challenges become within reach. Sharpen your understanding of the world and effortlessly grasp interconnections. Equipped with this newfound ability, you will confidently tackle novel problems, drawing insightful analogies from a range of subjects. As you delve into this enlightening read, you may find yourself wondering why you hadn't embarked on this journey sooner. You will learn: - The contemporary importance of mastering complex concepts- Strategies for studying and comprehending complex subjects- Techniques for conceptual and systems thinking- Streamlined methods for organizing information- Practical applications for making sense of the universe- Key areas of focus for future growth- And much more...! With technological advancements reshaping our world, staying ahead of the curve requires honing critical thinking, analytical skills, and abstract reasoning capabilities. The purpose of this book is to illuminate the significance of embracing complex and abstract concepts.
Almost Periodicity and Almost Automorphy
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an "ordinary differential equation" with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.
Cie IGCSE and O Level Complete Maths Core 6e Teacher Handbook
Cie IGCSE and O Level Complete Maths Extended 6e Teacher Handbook
Introduction to Enumerative and Analytic Combinatorics
These award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author's goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field.
Discrete Mathematics
This book aims to provide an introduction to select topics in discrete mathematics at a level appropriate for first or second year undergraduate math and computer science majors. This course serves both as a survey of the topics in discrete math and as the "bridge" course for math majors.
Advances in Fuzzy Logic and Artificial Neural Networks
In a world where uncertainty and complexity dominate decision-making processes, Advances in Neural Networks and Fuzzy Logic presents groundbreaking studies exploring the potential of these Artificial Intelligence approaches to solve real-world problems. The chapters cover applications across various fields, such as robust galaxy classification, simulations in weighted finite automata, stock price prediction, large-scale water purification selection, speech deficiency detection in children, and supply chain management. Advanced techniques such as deep neural networks, fuzzy clustering, SHAP, LIME, and Hesitant Fuzzy Linguistic Term Sets are explored. This reprint is helpful for researchers, engineers, and students who wish to understand the latest advancements in and practical applications of neural networks and fuzzy logic. Within these pages, you will discover how these technologies solve complex problems and foster more transparent and reliable decision-support systems, as well as the state of the art in Artificial Intelligence, where neural networks and fuzzy logic converge to tackle modern challenges with innovation and precision.
Analytical and Numerical Solution Methods Heat Transfer Problems
The calculating engine
The calculating engine" is a classic book, that has held significant value throughout history, and to ensure its timeless wisdom is never lost, Alpha Editions has carefully preserved it by republishing it in a modern, accessible format for both present and future generations. Thoughtfully reformatted, retyped, and newly designed, this edition offers a clear and readable text-free from scanned copies of the original work. Alpha Editions is dedicated to breathing new life into antique and classic books, making these literary treasures available once again for readers who cherish history, culture, and timeless knowledge.
Journal of Applied Logics. IfCoLog Journal of Logics and their Applications. Volume 12, number 1, January 2025. Special Issue
A Beginner's Guide to Mathematical Proof
A Beginner's Guide to Mathematical Proof prepares mathematics majors for the transition to abstract mathematics, and introduces a wider readership of quantitative science students to the mathematical structures underlying more applied topics with an accessible, step-by-step approach requiring minimal mathematical prerequisites.
The Math Book
Math's infinite mysteries unfold in this updated edition of the award-winning The Math Book. Beginning millions of years ago with ancient "ant odometers," and moving through time to our modern-day quest for higher dimensions, prolific polymath Clifford Pickover covers major milestones in mathematical history. Among the numerous concepts readers will encounter as they dip into this inviting anthology: cicada-generated prime numbers, magic squares, and the butterfly effect. Each topic is presented in a lavishly illustrated spread, including formulas and real-world applications of the theorems. This reissue includes four new entries: 2013 (Bounded Gaps Between Primes), 2015 (Erdős Discrepancy Problem Solved), 2016 (Sphere Packing in Dimension 8), and 2023 (Einstein Tiles and Beyond). Each topic is presented in a lavishly illustrated spread, including formulas and real-world applications of the theorems.
Analysis and Probability on Graphs
Analysis and Probability on graphs is an introduction to random graphs, Markov chains on digraphs, entropy of Markov Chains, and discrete Lyapunov exponents and Hausdorff dimension, requiring only minimal background in probability, mathematical analysis, and graphs. This textbook includes constructive discussions about the motivation of basic concepts, and many worked-out problems in each chapter, making it ideal for classroom use or self-study.
General Topology
This book is dedicated to metric spaces and their topology. The book starts with ZFC axioms. The real number system is constructed by both the Dedekind cut and the Cauchy sequence approach. The various examples and properties of metric spaces and normed linear spaces are discussed. The different distances between the sets are highlighted. The research work on metric-preserving maps and isometries on different p-norms has been discussed. Homeomorphism and different equivalent metrics have also been discussed. A detailed description of a metric on the product and the quotient set is also provided. The completion of a metric space as a universal property and applications of the Baire Category Theorem are covered. A special focus is on compactness and the relation between a compact metric space, the Hilbert Cube, and the Cantor set. The properties of connected and path-connected metric spaces are provided.
Best IDEAS
This Special Issue presents selected papers by leading international experts on various database engineered applications. The leading experts include Schahram Dustdar, who served as an invited speaker at several International Database Engineered Applications Symposia, and the authors of the two highest-ranked papers from the 27th International Database Engineered Applications Symposium from Heraklion, Crete, Greece. The authors of this Special Issue present their ideas in twelve full journal articles that were reviewed for both the quality and readability of their contents. Hence, this Special Issue is a valuable resource on topics ranging from federated databases, data analytics and data mining, and data prediction and imputation to various aspects of temporal databases and genome databases.
Finite Element Analysis of Structures Using MATLAB
"Finite Element Analysis of Structures using MATLAB" is an essential guide for students delving into the world of finite element analysis. This comprehensive resource offers clear explanations, relevant examples, and practical MATLAB code to enhance understanding and application. From the historical foundation of Finite Element Analysis to the exploration of thin and thick plates and structural dynamics. This comprehensive resource spans twelve chapters and two appendices. Appendix A provides MATLAB code for problem-solving, while Appendix B guides you through using ABAQUS. Begin with a historical introduction and explore the essentials of finite element analysis. Dive into nodes, elements, interpolation functions, and FEA formalization. Focus on one-dimensional and two-dimensional elements and learn numerical integration with Gaussian quadrature. Discover axisymmetric and three-dimensional elements, and apply FEA to analyze thin and thick plates. Explore structural dynamics and vibrations in the final chapter. Appendix A contains MATLAB code for seventeen numerical examples, and Appendix B offers a step-by-step ABAQUS procedure. 'Finite Element Analysis of Structures using MATLAB' is your ultimate resource for practical understanding. Whether it's coursework or deeper exploration, this book with clear explanations and relevant examples is your invaluable companion."
Graceful Labeling of Few Types of Graphs and Their Applications
Curves and Surfaces with Applications in Cagd
Carefully refereed and edited papers on the most current developments in the theory and applications of curves and surfaces. This volume, with its companion volume, contains a selection of papers presented at the Third International Conference on Curves and Surfaces which was held in June 1996 at Chamonix, France. Each book contains several invited survey lectures prepared by leading experts in the fields of approximation theory, computer- aided geometric design, numerical analysis, and wavelets. In addition, each book includes a number of closely related full-length research papers which have been refereed and meticulously edited. These books should be of great interest to mathematicians, engineers, and computer scientists working in the field of Approximation Theory, Computer-Aided Geometric Design (CAGD), Computer Graphics, Numerical Analysis, CAD/CAM, and application areas.
Augmented and Virtual Reality in Mathematics Education
Augmented and virtual reality (AR/VR) are technologies of increasing importance in our society. In the field of mathematics education, these innovative technologies may offer a wide range of opportunities to support immersive, individual, and active learning processes. At the same time, many new challenges arise that need to be mastered by teachers and students in the classroom. With this book we want to contribute to the discourse by presenting innovative insights by bringing parties from research and practice together. The papers cover a wide range of relevant topics including cooperation and communication, STEM and modelling, development and application of design criteria, spatial geometry and imagination or teacher-trainings. The contributions include in-depth theoretical considerations, concrete developed applications and learning environments, and findings from empirical studies.
Mathematical Modeling of the Human Respiratory Control System
