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Bent Functions: Fundamentals and Results
by Sihem MesnagerThis book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results. This book uniquely provides a necessary comprehensive coverage of bent functions. It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.
Berechenbarkeit: Berechnungsmodelle und Unentscheidbarkeit (essentials)
by Karl-Heinz ZimmermannIn diesem essential werden wesentliche Konzepte der Berechenbarkeitstheorie erörtert. Zunächst werden unterschiedliche Modelle der Berechenbarkeit eingeführt und ihre semantische Gleichwertigkeit gezeigt. Dieses Resultat steht in Einklang mit der Church-Turing-These, nach der jede intuitiv berechenbare Funktion partiell-rekursiv ist. Neben zentralen Instrumenten der Berechenbarkeit, wie etwa der Gödelisierung von berechenbaren Funktionen und der Existenz universeller berechenbarer Funktionen, stehen unentscheidbare Probleme im Fokus, wie etwa das Halteproblem sowie das Wortproblem für die Term-Ersetzung. Semi-entscheidbare Mengen werden beleuchtet und die zentralen Sätze von Rice und Rice-Shapiro werden skizziert.
Berechnungen in der Chemie und Verfahrenstechnik mit Excel und VBA
by Wolfgang Schmidt Shichang WangMit diesem Arbeitsbuch lernt der Anwender numerische Methoden in Excel-VBA kennen und zur Lösung von Problemen und Aufgabenstellungen aus Chemie und Verfahrenstechnik einzusetzen. Dabei steht die Anwendung auf einfache, grundlegende verfahrenstechnische Berechnungsmethoden im Vordergrund. Nach einer kurzen Einführung in Excel, Makros und die VBA-Programmierung, werden mathematische Methoden behandelt, die zur Berechnung verfahrenstechnischer und chemischer Problemstellungen erforderlich sind. Das Kernstück dieses Bandes ist die Anwendung des Gelernten auf reale Probleme aus dem Laboralltag, z.B. Gasgleichungen, Verbrennungs- und Polymerisationsrechnung.
The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics (Static & Dynamic Game Theory: Foundations & Applications)
by Mindia E. Salukvadze Vladislav I. ZhukovskiyThe goal of this book is to elaborate on the main principles of the theory of the Berge equilibrium by answering the following two questions: What are the basic properties of the Berge equilibrium? Does the Berge equilibrium exist, and how can it be calculated? The Golden Rule of ethics, which appears in Christianity, Judaism, Islam, Buddhism, Confucianism and other world religions, states the following: “Behave towards others as you would like them to behave towards you." In any game, each party of conflict seeks to maximize some payoff. Therefore, for each player, the Golden Rule is implemented through the maximization of his/her payoff by all other players, which matches well with the concept of the Berge equilibrium. The approach presented here will be of particular interest to researchers (including undergraduates and graduates) and economists focused on decision-making under complex conflict conditions. The peaceful resolution of conflicts is the cornerstone of the approach: as a matter of fact, the Golden Rule precludes military clashes and violence. In turn, the new approach requires new methods; in particular, the existence problems are reduced to saddle point design for the Germeier convolution of payoff functions, with further transition to mixed strategies in accordance with the standard procedure employed by E. Borel, J. von Neumann, J. Nash, and their followers. Moreover, this new approach has proven to be efficient and fruitful with regard to a range of other important problems in mathematical game theory, which are considered in the Appendix.
The Bergman Kernel and Related Topics: Hayama Symposium on SCV XXIII, Kanagawa, Japan, July 2022 (Springer Proceedings in Mathematics & Statistics #447)
by Kengo Hirachi Takeo Ohsawa Shigeharu Takayama Joe KamimotoThis volume consists of 15 papers contributing to the Hayama Symposium on Complex Analysis in Several Variables XXIII, which was dedicated to the 100th anniversary of the creation of the Bergman kernel. The symposium took place in Hayama and Tokyo in July 2022. Each article is closely related to the Bergman kernel, covering topics in complex analysis, differential geometry, representation theory, PDE, operator theory, and complex algebraic geometry. Specifically, some papers address the L2 extension operators from a newly opened viewpoint after solving Suita's conjecture for the logarithmic capacity. They are also continuations of quantitative solutions to the openness conjecture for the multiplier ideal sheaves. The study involves estimates for the solutions of the d-bar equations, focusing on the existence of compact Levi-flat hypersurfaces in complex manifolds. The collection also reports progress on various topics, including the existence of extremal Kähler metrics on compact manifolds, Lp variants of the Bergman kernel, Wehrl-type inequalities, homogeneous Kähler metrics on bounded homogeneous domains, asymptotics of the Bergman kernels, and harmonic Szegő kernels and operators on the Bergman spaces and Segal-Bargmann spaces. Some of the papers are written in an easily accessible way for beginners. Overall, this collection updates how a basic notion provides strong insights into the internal relationships between independently found phenomena.
Berkovich Spaces and Applications (Lecture Notes in Mathematics #2119)
by Johannes Nicaise Antoine Ducros Charles FavreWe present an introduction to Berkovich's theory of non-archimedean analytic spaces that emphasizes its applications in various fields. The first part contains surveys of a foundational nature, including an introduction to Berkovich analytic spaces by M. Temkin, and to étale cohomology by A. Ducros, as well as a short note by C. Favre on the topology of some Berkovich spaces. The second part focuses on applications to geometry. A second text by A. Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under a proper map are coherent, and B. Rémy, A. Thuillier and A. Werner provide an overview of their work on the compactification of Bruhat-Tits buildings using Berkovich analytic geometry. The third and final part explores the relationship between non-archimedean geometry and dynamics. A contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems in dimension 1 and 2. Finally a survey by J. -P. Otal gives an account of Morgan-Shalen's theory of compactification of character varieties. This book will provide the reader with enough material on the basic concepts and constructions related to Berkovich spaces to move on to more advanced research articles on the subject. We also hope that the applications presented here will inspire the reader to discover new settings where these beautiful and intricate objects might arise.
Bernoulli Numbers and Zeta Functions (Springer Monographs in Mathematics)
by Tsuneo Arakawa Tomoyoshi Ibukiyama Masanobu KanekoTwo major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen-von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler-Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the doub le zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.
Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science
by Aubrey ClaytonThere is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach—that is, to incorporate prior knowledge when reasoning with incomplete information—in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.
Bernstein Operators and Their Properties
by Jorge BustamanteThis book provides comprehensive information on the main aspects of Bernstein operators, based on the literature to date. Bernstein operators have a long-standing history and many papers have been written on them. Among all types of positive linear operators, they occupy a unique position because of their elegance and notable approximation properties. This book presents carefully selected material from the vast body of literature on this topic. In addition, it highlights new material, including several results (with proofs) appearing in a book for the first time. To facilitate comprehension, exercises are included at the end of each chapter. The book is largely self-contained and the methods in the proofs are kept as straightforward as possible. Further, it requires only a basic grasp of analysis, making it a valuable and appealing resource for advanced graduate students and researchers alike.
Bertrand Russell, Feminism, and Women Philosophers in his Circle (History of Analytic Philosophy)
by Landon D. C. Elkind Alexander Mugar KleinThis book examines Bertrand Russell’s complicated relationships to the women around him, and to feminism more generally. The essays in this volume offer scholarly reassessments of these relationships and their import for the history of feminism and of analytic philosophy.Russell is a founder of analytic philosophy. He has also been called a feminist due to his public, decades-long advocacy for women’s rights and equality of the sexes. But his private behavior towards wives and sexual partners, and his apparently dismissive (occasionally public) responses to some women philosophers, raises the question of what sort of feminist (or chauvinist) Russell actually was.Focusing on women in Russell’s circle of acquaintance, including feminist activists and his philosophical interlocutors, this book casts new light on a timeless thinker’s feminism and the women who played critical roles in the making of analytic philosophy.
Bertrand’s Paradox and the Principle of Indifference (Routledge Studies in the Philosophy of Mathematics and Physics)
by Nicholas ShackelEvents between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference.Bertrand's Paradox and the Principle of Indifference will appeal to scholars and advanced students working in the philosophy of mathematics, epistemology, philosophy of science, probability theory and mathematical physics.
Bessel Functions and Their Applications
by B G KorenevBessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro
Bessel Processes, Schramm-Loewner Evolution, and the Dyson Model (SpringerBriefs in Mathematical Physics #11)
by Makoto KatoriThe purpose of this book is to introduce two recent topics in mathematical physics and probability theory: the Schramm-Loewner evolution (SLE) and interacting particle systems related to random matrix theory. A typical example of the latter systems is Dyson's Brownian motion (BM) model. The SLE and Dyson's BM model may be considered as "children" of the Bessel process with parameter D, BES(D), and the SLE and Dyson's BM model as "grandchildren" of BM. In Chap. 1 the parenthood of BM in diffusion processes is clarified and BES(D) is defined for any D ≥ 1. Dependence of the BES(D) path on its initial value is represented by the Bessel flow. In Chap. 2 SLE is introduced as a complexification of BES(D). Rich mathematics and physics involved in SLE are due to the nontrivial dependence of the Bessel flow on D. From a result for the Bessel flow, Cardy's formula in Carleson's form is derived for SLE. In Chap. 3 Dyson's BM model with parameter β is introduced as a multivariate extension of BES(D) with the relation D = β + 1. The book concentrates on the case where β = 2 and calls this case simply the Dyson model. The Dyson model inherits the two aspects of BES(3); hence it has very strong solvability. That is, the process is proved to be determinantal in the sense that all spatio-temporal correlation functions are given by determinants, and all of them are controlled by a single function called the correlation kernel. From the determinantal structure of the Dyson model, the Tracy-Widom distribution is derived.
The Best American Infographics 2016
by Gareth Cook Robert Krulwich“When it comes to infographics…the best work in this field grabs those eyes, keeps them glued, and the grip is sensual—and often immediate. A good graphic says ‘See what I see!’ and either you do or you don’t. The best ones…pull you right in, and won’t let you go.” —From the introduction by Robert Krulwich The year’s most “awesome” (RedOrbit) infographics reveal aspects of our world in often startling ways—from a haunting graphic mapping the journey of 15,790 slave ships over 315 years, to a yearlong data drawing project on postcards that records and cements a trans-Atlantic friendship. The Best American Infographics 2016 covers the realms of social issues, health, sports, arts and culture, and politics—including crisp visual data on the likely Democratic/Republican leanings of an array of professions (proving that your urologist is far more likely to be a Republican than your pediatrician). Here once again are the most innovative print and electronic infographics—“the full spectrum of the genre—from authoritative to playful” (Scientific American). ROBERT KRULWICH is the cohost of Radiolab and a science correspondent for NPR. He writes, draws, and cartoons at Curiously Krulwich, where he synthesizes scientific concepts into colorful, one-of-a-kind blog posts. He has won several Emmy awards for his work on television, and has been called “the most inventive network reporter in television” by TV Guide.
The Best Apple Crisp in the World
by Charnan SimonJake wants to learn how to make his grandmother’s apple crisp! The only problem is she doesn’t use a recipe. With his uncle’s help, he must figure out the ingredients and measurements.
The Best Bug Parade (MathStart #Level 1)
by Stuart J. MurphyA variety of different bugs compare their relative sizes while going on parade
Best Evidence Structural Interventions for HIV Prevention
by Josefina J. Card Charles B. Collins Rachel E Golden Emily N Newman Shayna D CunninghamProviding detailed information on structural HIV prevention interventions, this book is intended for health care practitioners and researchers to plan, implement, and evaluate such interventions in their own communities. As defined by the CDC, structural interventions focus on the physical, social, cultural, political, economic, legal, and/or policy aspects of the environment. Designed to reach a large number of individuals, structural interventions usually occur across entire communities, cities, or countries. As a result, the resources required to initiate structural interventions can far exceed those required for smaller-scale behavioral programs. However, changes from structural interventions have the potential to last over time, even after the programs have ended, resulting in effective use of public and private prevention resources. Because the reach of structural interventions is typically larger than that of individual- or group-focused interventions (for example, the 100% Condom Use Program, which was implemented countrywide in Thailand), their influence may be equally--if not more--significant.This book is a resource for health practitioners, educators, and researchers who seek HIV/AIDS structural prevention programs that have been shown to be effective in their regions or for their target populations (e.g. injection drug users, commercial sex workers, or the general public). With extensive case studies, the book classifies interventions according to the desired outcomes (specific behavior or policy changes) so that the reader may focus on examples of programs with similar goals and target populations to their own. Addresses the quintessential public health ethical dilemma regarding which types of environmental changes should be mandatory via legislation and which should be voluntary, promoted via programmatic, practice, and policy change.
Best Matching Theory & Applications (Automation, Collaboration, & E-Services #3)
by Shimon Y. Nof Mohsen MoghaddamMismatch or best match? This book demonstrates that best matching of individual entities to each other is essential to ensure smooth conduct and successful competitiveness in any distributed system, natural and artificial. Interactions must be optimized through best matching in planning and scheduling, enterprise network design, transportation and construction planning, recruitment, problem solving, selective assembly, team formation, sensor network design, and more. Fundamentals of best matching in distributed and collaborative systems are explained by providing: #65533; Methodical analysis of various multidimensional best matching processes #65533; Comprehensive taxonomy, comparing different best matching problems and processes #65533; Systematic identification of systems' hierarchy, nature of interactions, and distribution of decision-making and control functions #65533; Practical formulation of solutions based on a library of best matching algorithms and protocols, ready for direct applications and apps development. Designed for both academics and practitioners, oriented to systems engineers and applied operations researchers, diverse types of best matching processes are explained in production, manufacturing, business and service, based on a new reference model developed at Purdue University PRISM Center: "The PRISM Taxonomy of Best Matching". The book concludes with major challenges and guidelines for future basic and applied research in the area of best matching.
The Best of All Possible Worlds: A Life of Leibniz in Seven Pivotal Days
by Michael KempeA biography of the polymath Gottfried Wilhelm Leibniz told through seven critical days spanning his life and revealing his contributions to our modern world. Gottfried Wilhelm Leibniz (1646–1716) was the Benjamin Franklin of Europe, a “universal genius” who ranged across many fields and made breakthroughs in most of them. Leibniz invented calculus (independently from Isaac Newton), conceptualized the modern computer, and developed the famous thesis that the existing world is the best that God could have created. In The Best of All Possible Worlds, historian and Leibniz expert Michael Kempe takes us on a journey into the mind and inventions of a man whose contributions are perhaps without parallel in human history. Structured around seven crucial days in Leibniz’s life, Kempe’s account allows us to observe him in the act of thinking and creating, and gives us a deeper understanding of his broad-reaching intellectual endeavors. On October 29, 1675, we find him in Paris, diligently working from his bed amid a sea of notes, and committing the integral symbol—the basis of his calculus—to paper. On April 17, 1703, Leibniz is in Berlin, writing a letter reporting that a Jesuit priest living in China has discovered how to use Leibniz’s binary number system to decipher an ancient Chinese system of writing. One day in August 1714, Leibniz enjoys a Viennese coffee while drawing new connections among ontology and biology and mathematics. The Best of All Possible Worlds transports us to an age defined by rational optimism and a belief in progress, and will endure as one of the few authoritative accounts of Leibniz’s life available in English.
The Best of Corwin: Differentiated Instruction in Literacy, Math, and Science
by Leslie E. LaudContent-specific DI guidance from the best minds in education In this collection, current research on the most effective differentiation practices for differentiating instruction in literacy, mathematics, and scienceis brought alive through the many strategies and examples. Topics covered include: Reading and writing: A comprehensive array of models for differentiating reading instruction; gradual release of responsibility to accelerate progress; and multi-tiered writing instruction Mathematics: Support for both low- and high-achieving students, including interventions and challenges, and the implementation of RTI in math instruction Science: Models and methods for increasing student achievement through differentiated science inquiry
The Best of Times: Math Strategies that Multiply
by Greg TangNEW YORK TIMES bestselling author Greg Tang takes on the times tables, teaching kids innovative ways to multiply numbers and derive answers WITHOUT memorization.Four is very fast to do when you multiply by 2.Here's a little good advice --please just always double twice!BEST OF TIMES gives kids an intuitive understanding of multiplication, encouraging them to arrive at answers on their own rather than memorizing the times tables. A child who can multiply by two, for instance, can multiply by four and even eight! Likewise, times six builds on times two and times three.With his common-sense approach, Greg Tang encourages kids to solve problems creatively, building both their skills and their confidence.
The Best of Times: Math Strategies That Multiply
by Greg Tang Harry BriggsNEW YORK TIMES bestselling author Greg Tang takes on the times tables, teaching kids innovative ways to multiply numbers and derive answers WITHOUT memorization. Four is very fast to do when you multiply by 2. Here's a little good advice -- please just always double twice! BEST OF TIMES gives kids an intuitive understanding of multiplication, encouraging them to arrive at answers on their own rather than memorizing the times tables. A child who can multiply by two, for instance, can multiply by four and even eight! Likewise, times six builds on times two and times three. With his common-sense approach, Greg Tang encourages kids to solve problems creatively, building both their skills and their confidence.
Best Practice Guideline for Statistical Analyses of Fatigue Results (IIW Collection)
by Guy Parmentier Michel Huther Isabel Huther Fabien LefebvreThis book provides a comprehensive guidance for the use of sound statistical methods and for the evaluation of fatigue data of welded components and structures obtained under constant amplitude loading and used to produce S-N curves. Recommendations for analyzing fatigue data are available, although they do not deal with all the statistical treatments that may be required to utilize fatigue test results, and none of them offers specific guidelines for analyzing fatigue data obtained from tests on welded specimens. For an easy use, working sheets are provided to assist in the proper statistical assessment of experimental fatigue data concerning practical problems giving the procedure and a numerical application as illustration.
Best Practices for Teaching Mathematics: What Award-Winning Classroom Teachers Do
by Randi B. StoneSpark students' interest in math with intriguing and winning strategies that include animated learning icons, money-based systems, human number lines, "sweet" solutions, and much more.
Best Practices in Logistic Regression
by Jason W. OsborneJason W. Osborne’s Best Practices in Logistic Regression provides students with an accessible, applied approach that communicates logistic regression in clear and concise terms. The book effectively leverages readers’ basic intuitive understanding of simple and multiple regression to guide them into a sophisticated mastery of logistic regression. Osborne’s applied approach offers students and instructors a clear perspective, elucidated through practical and engaging tools that encourage student comprehension.