Distributed Generation and Reliability of Local Distribution System
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.
Modelling returns in South Africa using Jump Diffusion Processes
Applied Statistics with Python
Applied Statistics with Python concentrates on applied and computational aspects of statistics, focussing on conceptual understanding and Python-based calculations. It compiles multiple aspects of applied statistics, teaching useful skills in statistics and computational science.
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."
Set Theo & Found Math (V1-2nd Ed)
This book presents both axiomatic and descriptive set theory, targeting upper-level undergraduate and beginning graduate students. It aims to equip them for advanced studies in set theory, mathematical logic, and other mathematical fields, including analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered through the text.This new edition includes additional topics on trees, ordinal functions, and sets, along with numerous new exercises. The presentation has been improved, and several typographical errors have been corrected.
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.
Graceful Labeling of Few Types of Graphs and Their Applications
Mathematical Methods for Curves and Surfaces II
Contains more than fifty carefully refereed and edited full-length papers on the theory and applications of mathematical methods arising out of the Fourth International Conference on Mathematical Methods in Computer Aided Geometric Design, held in Lillehammer, Norway, in July 1997.
Mathematical Models in Medical and Health Science
A unique assemblage of cutting-edge research on mathematical models in biology and medicine. This book is composed of refereed and carefully edited research articles derived from the Conference on Mathematical Models in Medical and Health Sciences, held at Vanderbilt University in conjunction with the thirteenth annual Shanks Lectures Series (May 1997).
Real Analysis
Can the limitations of the Riemann integral be overcome? What is its relationship with modern analysis?The theory of Lebesgue integration is a crucial component in the development of modern analysis. This book is an in-depth real analysis textbook, which introduces the basic theory of modern analysis and the basic skills of analysis. Based on the knowledge of real analysis, the theory of interpolation of operators and the Fourier transform theory are further introduced systematically. The main contents include: abstract measures and integrals, measure and topology, Lebesgue integration on Rn, the interpolation of operators on Lp(Rn), Hardy-Littlewood maximal function, convolution and the Fourier transform. They play an important role in harmonic analysis, partial differential equations, probability and numerical analysis. This book is moderately difficult and detailed, focusing on the combination of abstract and concrete, and training readers to skillfully use modern analysis.This textbook is an excellent reference book for readers studying the fields of Harmonic analysis and partial differential equations. It is intended for advanced undergraduate and graduate students in university mathematics, as well as mathematicians and physicists in general.
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.
Advanced Topics on Semilinear Evolution Equations
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fr矇chet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.
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.
Quantum Machine Learning and Optimisation in Finance - Second Edition
The proof by contradiction of the negation of Riemann Hypothesis
Data Structures and Algorithms In Graphics and Geometry
Data Structures and Algorithms in Graphics and Geometry provides a comprehensive exploration of the intersection between computer graphics, computational geometry, and algorithm design. This book delves into the fundamental data structures and algorithms essential for solving complex problems in graphics and geometry-related applications. From representing geometric objects and spatial data to performing geometric computations and rendering techniques, readers are equipped with the knowledge and tools needed to tackle challenges in areas such as computer-aided design, computer graphics, robotics, and geographic information systems (GIS). Through theoretical foundations, practical implementations, and algorithmic analysis, the book offers insights into optimizing performance and efficiency in graphics and geometry algorithms. Whether you're a computer scientist, software engineer, or researcher in the field of computer graphics and computational geometry, this book serves as an invaluable resource for understanding and applying data structures and algorithms in diverse graphical and geometric contexts.
?tale Cohomology
An authoritative introduction to the essential features of 矇tale cohomology A. Grothendieck's work on algebraic geometry is one of the most important mathematical achievements of the twentieth century. In the early 1960s, he and M. Artin introduced 矇tale cohomology to extend the methods of sheaf-theoretic cohomology from complex varieties to more general schemes. This work found many applications, not only in algebraic geometry but also in several different branches of number theory and in the representation theory of finite and p-adic groups. In this classic book, James Milne provides an invaluable introduction to 矇tale cohomology, covering the essential features of the theory. Milne begins with a review of the basic properties of flat and 矇tale morphisms and the algebraic fundamental group. He then turns to the basic theory of 矇tale sheaves and elementary 矇tale cohomology, followed by an application of the cohomology to the study of the Brauer group. After a detailed analysis of the cohomology of curves and surfaces, Milne proves the fundamental theorems in 矇tale cohomology--those of base change, purity, Poincar矇 duality, and the Lefschetz trace formula--and applies these theorems to show the rationality of some very general L-series.
Convergence Structures and Applications to Analysis
No detailed description available for "Convergence Structures and Applications to Analysis".
Convergence Structures 1984
No detailed description available for "Convergence Structures 1984".
Theory of Nonlinear Operators
No detailed description available for "Theory of Nonlinear Operators".
Parcella'84
No detailed description available for "Parcella'84".
Category and Measure
Topological spaces in general, and the real numbers in particular, have the characteristic of exhibiting a 'continuity structure', one that can be examined from the vantage point of Baire category or of Lebesgue measure. Though they are in some sense dual, work over the last half-century has shown that it is the former, topological view, that has pride of place since it reveals a much richer structure that draws from, and gives back to, areas such as analytic sets, infinite games, probability, infinite combinatorics, descriptive set theory and topology. Keeping prerequisites to a minimum, the authors provide a new exposition and synthesis of the extensive mathematical theory needed to understand the subject's current state of knowledge, and they complement their presentation with a thorough bibliography of source material and pointers to further work. The result is a book that will be the standard reference for all researchers in the area.
Lotka-Volterra-Approach to Cooperation and Competition in Dynamic Systems
No detailed description available for "Lotka-Volterra-Approach to Cooperation and Competition in Dynamic Systems".
Singular Ordinary Differential Operators and Pseudodifferential Equations
No detailed description available for "Singular Ordinary Differential Operators and Pseudodifferential Equations".
Mathematics for Engineers
This book offers a comprehensive treatment of the core mathematical topics required for a modern engineering degree. The book begins with an introduction to the basics of mathematical reasoning and builds up the level of complexity as it progresses.
Linear Algebra with its Applications
This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a subject that has found the broadest range of applications in all branches of mathematics, physical and social sciences, and engineering.
Depth-bounded Reasoning. Classical Propositional Logic
The "cost of reasoning", i.e., the cognitive or computational effort required by non-ideal, resource-bounded (human or artificial) agents in order to perform non-trivial inferences, is a crucial issue in philosophy, AI, economics and cognitive (neuro)science. Accounting for this fundamental variable in modelling real-world reasoning and decision-making is one of the most important and difficult challenges in the theory of rationality. With this volume, we are launching a series that, under the general title of "Logic and Bounded Rationality", aims to create a community of researchers from several areas that wish to cooperate towards a systematic logical view of bounded rationality.However, a key stumbling block for any effort in this direction, is that a basic component of many reasoning and decision making tasks, namely deductive reasoning in propositional logic, is computationally hard. Hence, in this first volume of the series we offer a novel view of classical propositional logic. We present an "informational semantics" for the classical operators whose proof-theoretical presentation is a system of classical natural deduction that, unlike Gentzen's and Prawitz's systems, yields a simple way of measuring the "depth" of an inference. This approach leads to defining, in a natural way, a sequence of tractable depth-bounded deduction systems. As recent applications in formal argumentation and non-monotonic reasoning suggest, our approach provides a plausible model for representing rational agents with increasing, albeit limited, computational resources.
Computational Global Macro
Computational Global Macro offers investors a new paradigm for the analysis of geopolitical risk. By drawing on game theory, machine learning, and causal inference, the book provides investors with a novel framework for analyzing the political and economic interactions between global actors. In doing so, it presents a counterpoint to the often informal and speculative approach to geopolitical analysis that is prevalent in the research produced by investment firms. The book will thus serve as a valuable reference for investment professionals, students, and academics seeking to apply sophisticated quantitative tools to the development of their macro views.
An Introduction to Applied Numerical Analysis
The book has two overarching goals. The first goal is to introduce different available numerical procedures for finding solutions to linear equations, roots of polynomial equations, interpolation and approximation, numerical differentiation and integration, differential equations, and error analysis. The second goal is to translate theory into practice through applying commonly used numerical methods in mathematics, physical sciences, biomedical sciences, and engineering.This book was crafted in an informal and user-friendly manner to motivate the study of the material being covered. Ample figures and numerical tables are presented to enhance the reader's ease of understanding of the material under consideration.
Catalan Numbers
Catalan numbers, named after the French-Belgian mathematician Eug癡ne Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical, and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be of interest to professionals, students, and a general audience.The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.
