Mathematical Study for Approximation Models in Radiation Hydrodynamics
Computational Structural Bioinformatics
This book constitutes the proceedings of the Computational Structural Bioinformatics Workshop, CMSB 2024, which took place in Boston, MA, USA, on November 16, 2024. The 7 papers presented in this book were carefully reviewed and selected for inclusion in the proceedings. They deal with relevant problems in classification, modeling and analyzing protein structures and complexes.
Special Integrals
Targeted to upper-undergraduate and graduate students of mathematics, this book discusses special integrals and their applications in finding certain series sums. It starts with the differentiation and the integration methods for summing a series that is applied to find the sum of various binomial and trigonometrical series. It also discusses methods to find the sum of series involving the variables having exponents in integral or fractional powers of 2. Complex variables are freely used to derive several theorems, which result in several special integrals and series sums. Bessel coefficients, Bessel functions, and their various generalizations are also discussed in the book. As a particular case of generalized Bessel functions, pseudo-exponential functions are defined, and their properties are studied in the book. Broadly divided into two parts--Part 1 and Part 2--the book has six chapters in Part 1, whereas Part 2 has six chapters on solutions to the problems in Part 1. To understand the topics in the book, the minimum prerequisites are the knowledge of calculus, complex analysis, and Fourier series.
The Krasnoselskii-Mann Method for Common Fixed Point Problems
This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors. Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a detailed analysis of iterative methods, highlighting their effectiveness in solving complex fixed-point problems. Readers will encounter critical discussions on the behavior of exact and inexact iterates, the role of computational errors, and innovative approaches like remotest set control. This book invites readers to engage with challenging questions about convergence and solution accuracy in mathematical spaces. Ideal for researchers and scholars in mathematics and related fields, this book provides valuable insights into advanced iterative methods for solving fixed-point problems. Whether you are a mathematician specializing in nonlinear analysis or an academic exploring optimization theory, this volume is an essential resource for understanding the latest developments in fixed point theory.
Logic for Dummies
An accessible resource to help you puzzle out logic concepts Logic For Dummies, 2nd Edition explains all the varied ways we use logic in philosophy, science, and everyday life. College students taking a logic course and lifelong learners alike can benefit from this accessible guide to logic concepts--such as syllogisms, constructing proofs and refutations, propositional and predicate logic, symbolic logic, modal and fuzzy logic, deductive and inductive reasoning, and beyond. With real-world examples, fun logic problems, and fully worked out proofs, you have plenty of opportunities to follow along and apply what you've learned. Logic For Dummies, 2nd Edition helps you connect the logical dots! Inside: Grasp formal and informal logic with clear explanations and practice problems See how logic shows up in everyday life and discover how to spot logical fallacies Work through logical proofs and refutations, with answer explanations to strengthen your understanding Sharpen your ability to reason through complex issues with truth tables Logic For Dummies, 2nd Edition is the logical choice for anyone who wants or needs to learn the concepts, theories, and formulas of logical reasoning.
Lectures on Mathematics for Economic and Financial Analysis
The Secret World of Flexagons
The hexaflexagon is a folded paper strip of colored triangles that has long delighted people with how it "magically" changes its appearance when "flexed". This hands-on, comprehensive book goes beyond the hexaflexagon, the standard version of this folded puzzle, exponentially expanding the barely explored field of flexagons as it brings new options and fresh insights to light.● Learn over a dozen different flexes, and make dozens of different flexagons with the aid of step-by-step illustrated directions and templates to copy and print.● Delve into the internal structure of flexagons and discover a universal way to describe and predict their behavior.● Learn how to create your own custom flexagons with a special computer program.● Understand how flexagons are connected to group theory, computer science, and topology.● Have fun decorating flexagons and make flexagon books, puzzles, pop-ups, mazes, and more.Written in a clear, easy-to-understand, and conversational style and enhanced with challenges and tips to broaden your flexagon skills and spark creativity, The Secret World of Flexagons: Fascinating Folded Paper Puzzles is a must for flexagon enthusiasts, teachers, students, libraries, mathematicians, and everyone who loves to solve a good puzzle.
Mathematics For The Curious Mind
Math is more than just numbers-it's the silent force behind everyday decisions and ground breaking innovations. In this engaging and relatable guide, discover how math plays a vital role in careers, from technology and finance to personal life hacks like calculating discounts or budgeting for your next adventure. Packed with humour, real-world examples, and insights from the author's own journey, this book will change the way you view math. It's not a monster to be feared, but a tool that can unlock endless possibilities-whether you're solving equations or navigating life's biggest challenges.About the Author: Aalok Guptaa is an engineer, educator, and passionate math enthusiast, driven by the belief that mathematics is more than just a subject-it's a key to unlocking one's potential. With years of experience in teaching, his mission is to simplify math, making it accessible and relevant for everyday life and career growth. Founder of Kkhyatis Edtech, Aalok's unique approach blends his love for numbers with practical applications, helping students achieve academic success while preparing them for future innovations in fields like AI, robotics, and data science.
The Doctrine of Triangles
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry's rich historical past full circle into the modern era.
Biofuel Production, Performance, and Emission Optimization
Comp Formal Euclidean Geom (V1)
This book explores three computational formalisms for solving geometric problems. Part I introduces a trigonometric-based formalism, enabling calculations of distances, angles, and areas using basic trigonometry. Part II focuses on complex numbers, representing points in the plane to manipulate geometric properties like collinearity and concurrency, making it particularly useful for planar problems and rotations. Part III covers vector formalism, applying linear algebra to both plane and solid geometry. Vectors are effective for solving problems related to perpendicularity, collinearity, and the calculation of distances, areas, and volumes.Each formalism has its strengths and limitations, with complex numbers excelling in the plane and vectors being more versatile in three-dimensional space. This book equips readers to choose the best approach for various geometric challenges. This book, designed for math majors, especially future educators, is also valuable for gifted high school students and educators seeking diverse proofs and teaching inspiration.
Non-K瓣hler Complex Surfaces and Strongly Pseudoconcave Surfaces
Convex Functions and Their Applications
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.
Dependence Models Via Hierarchical Structures
Bringing together years of research into one useful resource, this text empowers the reader to creatively construct their own dependence models. Intended for senior undergraduate and postgraduate students, it takes a step-by-step look at the construction of specific dependence models, including exchangeable, Markov, moving average and, in general, spatio-temporal models. All constructions maintain a desired property of pre-specifying the marginal distribution and keeping it invariant. They do not separate the dependence from the marginals and the mechanisms followed to induce dependence are so general that they can be applied to a very large class of parametric distributions. All the constructions are based on appropriate definitions of three building blocks: prior distribution, likelihood function and posterior distribution, in a Bayesian analysis context. All results are illustrated with examples and graphical representations. Applications with data and code are interspersed throughout the book, covering fields including insurance and epidemiology.
Approximation Theory and Applications
Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics. The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure. However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice. This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields. Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics. Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access.
Minimum Gamma-Divergence for Regression and Classification Problems
This book introduces the gamma-divergence, a measure of distance between probability distributions that was proposed by Fujisawa and Eguchi in 2008. The gamma-divergence has been extensively explored to provide robust estimation when the power index γ is positive. The gamma-divergence can be defined even when the power index γ is negative, as long as the condition of integrability is satisfied. Thus, the authors consider the gamma-divergence defined on a set of discrete distributions. The arithmetic, geometric, and harmonic means for the distribution ratios are closely connected with the gamma-divergence with a negative γ. In particular, the authors call the geometric-mean (GM) divergence the gamma-divergence when γ is equal to -1. The book begins by providing an overview of the gamma-divergence and its properties. It then goes on to discuss the applications of the gamma-divergence in various areas, including machine learning, statistics, and ecology. Bernoulli, categorical, Poisson, negative binomial, and Boltzmann distributions are discussed as typical examples. Furthermore, regression analysis models that explicitly or implicitly assume these distributions as the dependent variable in generalized linear models are discussed to apply the minimum gamma-divergence method. In ensemble learning, AdaBoost is derived by the exponential loss function in the weighted majority vote manner. It is pointed out that the exponential loss function is deeply connected to the GM divergence. In the Boltzmann machine, the maximum likelihood has to use approximation methods such as mean field approximation because of the intractable computation of the partition function. However, by considering the GM divergence and the exponential loss, it is shown that the calculation of the partition function is not necessary, and it can be executed without variational inference.
Mathematics in Architecture, Art, Nature, and Beyond
There is little opportunity in classrooms today for teachers to explore the amazing applications of mathematics outside the curriculum. This book is intended to show how mathematics manifests itself in areas that most people are unaware of. One can even revel in the history of how our number system evolved and how that has enabled us to define the beauty in mathematics as well as in art, architecture, nature, and beyond.The first two chapters of this book introduce the Fibonacci numbers and investigate their amazing relationships and applications in our general environment. The following four chapters focus on the Golden Ratio and the Golden Rectangle, exploring how they manifest all around us, often hiding in plain sight: in everything from architectural wonders such as the Taj Mahal to coin design, and from Greek vases to petal formation. We conclude our enjoyable journey through these mathematical wonders by considering conic sections and how they explain many aspects of everyday life, such as radar dishes, headlight reflectors, and whispering halls. This exposure to aspects of mathematics that are usually bypassed in the school curriculum will provide high school students, teachers, and general readers with an opportunity to truly appreciate the power and beauty of mathematics.
Four-Dimensional Paper Constructions Mobius, Klein & Boy
Explore four-dimensional paper constructions inspired by the work of great mathematicians like M繹bius, Klein, Boy, Hopf, and others. These creations will help you visualize four-dimensional space and beyond, transporting you to higher-dimensional spaces. This book is designed to solidify your foundations in various areas of mathematics and physics, with a particular focus on topology.If you are familiar with higher-dimensional spaces from loving sci-fi stories, you may find the four-dimensional illustrations in this book especially intuitive. Imagine starting on Earth and traveling straight up into the universe -- where would you end up? Perhaps you would travel in one direction only to eventually return to your starting point. Can you imagine what happens during the course of this trip? By engaging with these four-dimensional paper constructions, you will gain a deeper understanding of this fascinating journey.
Measure Theory for Analysis and Probability
This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, Radon-Nikodym and Jordan-Hahn theorems, providing a detailed account of ���� spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions. The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulcea's theorem and Kolmogorov's consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts.
Engaging Young Student Math (V3)
Engaging Young Students in Mathematics through Competitions presents a wide range of topics relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Following the earlier two volumes, contributors explore a wide variety of fascinating problems of the type often presented at mathematics competitions. In this new third volume, many chapters are directly related to the challenges involved in organizing competitions under Covid-19, including many positive aspects resulting from the transition to online formats. There are also sections devoted to background information on connections between the mathematics of competitions and their organization, as well as the competitions' interplay with research, teaching and more.The various chapters are written by an international group of authors involved in problem development, many of whom were participants of the 9th Congress of the World Federation of National Mathematics Competitions in Bulgaria in 2022. Together, they provide a deep sense of the issues involved in creating such problems for competition mathematics and recreational mathematics.
Amusements in Mathematics
Unlock the Enigma of Numbers with a Timeless Classic! Dive into the captivating world of ""Amusements in Mathematics"" by the legendary Henry Ernest Dudeney, a masterpiece that has enchanted puzzle enthusiasts for generations. This extraordinary collection of mathematical puzzles and brainteasers, once out of print for decades, is now beautifully republished by Alpha Editions, making it a must-have collector's edition for both the curious minds of today and the inquisitive thinkers of tomorrow. From mind-bending riddles to ingenious conundrums, Dudeney's brilliance shines through every page, offering a delightful challenge to both novice and seasoned puzzle solvers. Whether you're looking to sharpen your problem-solving skills or simply seeking an entertaining escape into the world of numbers, this book promises hours of intellectual amusement. Don't miss your chance to own a piece of mathematical history that has stood the test of time. Rediscover the joy of puzzles with ""Amusements in Mathematics"" and let your imagination soar!
Approximation & Regular Methods Operator-Function Equations
This book presents an overview of the most recent research and results in the field of approximation and regularisation methods for operator-functional equations, and explores their applications in electrical and power engineering. It presents the state of the art in building operator theory, regularised numerical methods, and in the verification of mathematical models for dynamical models based on integral and differential equations. Special attention is paid to Volterra models, a powerful tool for modelling hereditary dynamics.This book begins by exploring the solvability of singular integral equations, and moves on to study approximation methods for linear operator equations and nonlinear integral equations. Following this, it examines loaded equations and bifurcation analysis, before concluding with an investigation of the applications of the contents of the book in electrical engineering and automation. Each chapter provides an overview and analysis of the relevant problem statements, outlines current methods within the field, and identifies future directions for research.With an interdisciplinary approach, this book is essential reading for anyone interested in operator-functional equations. Graduate students and professors in the fields of applied mathematics, physics, material science, and numerical analysis will find this work insightful and valuable, as will industry professionals in related fields.
Math Mammoth Grade 3 Answer Keys, International Version
