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Dimension Theory: A Selection of Theorems and Counterexamples (Atlantis Studies in Mathematics #7)
by Michael G. CharalambousThis book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Dimensional Analysis
by J. C. GibbingsFor experiments, dimensional analysis enables the design, checks the validity, orders the procedure and synthesises the data. Additionally it can provide relationships between variables where standard analysis is not available. This widely valuable analysis for engineers and scientists is here presented to the student, the teacher and the researcher. It is the first complete modern text that covers developments over the last three decades while closing all outstanding logical gaps. Dimensional Analysis also lists the logical stages of the analysis, so showing clearly the care to be taken in its use while revealing the very few limitations of application. As the conclusion of that logic, it gives the author's original proof of the fundamental and only theorem. Unlike past texts, Dimensional Analysis includes examples for which the answer does not already exist from standard analysis. It also corrects the many errors present in the existing literature by including accurate solutions. Dimensional Analysis is written for all branches of engineering and science as a teaching book covering both undergraduate and postgraduate courses, as a guide for the lecturer and as a reference volume for the researcher.
Dimensional Analysis
by Qing-Ming TanDimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author's research group over the past forty years at the Chinese Academy of Sciences. The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields. Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.
Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists
by Bahman ZohuriThis ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book's coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book's theoretical explanations and step-by-step mathematical solutions to practical implementations.
Dimensions Math 6B
by Bill Jackson Kow Cheong YanDimensions Math is a series designed to teach middle school students foundational skills in mathematics. It follows the Singapore Mathematics Framework and covers the content standards in the United States Common Core State Standards for mathematics. This series empowers students to solve problems and master concepts through the thoughtful use of different approaches. It facilitates students’ understanding and internalization of concepts and encourages deep exploration of topics. Students will enjoy learning math through this comprehensive system and be motivated to study, discover, and apply knowledge in real-life situations.
Dimensions Math Textbook 5B
by Singapore Math Inc Various RolesThe Dimensions Math® Pre-Kindergarten to Grade 5 series is based on the pedagogy and methodology of math education in Singapore. The curriculum develops concepts in increasing levels of abstraction, emphasizing the three pedagogical stages: Concrete, Pictorial, and Abstract. Each topic is introduced, then thoughtfully developed through the use of problem solving, student discourse, and opportunities for mastery of skills.
Dimensionstheorie (essentials)
by Jörg NeunhäusererDieses Essential gibt eine kompakte Einführung in die Dimensionstheorie. Die topologische Dimension und mehrere fraktale Dimensionen werden definiert und anhand von Beispielen erläutert. Lesende lernen grundlegende Sätze über die Dimension von kartesischen Produkten, Projektionen, Schnitten und arithmetischen Summen kennen. Weiterhin wird eine Vielfalt von Anwendungen der Dimensionstheorie in der Zahlentheorie, der Geometrie, der Analysis, den dynamischen Systemen und der Stochastik vorgestellt.
Dinaric Perspectives on TIMSS 2019: Teaching and Learning Mathematics and Science in South-Eastern Europe (IEA Research for Education #13)
by Barbara Japelj Pavešić Paulína Koršňáková Sabine MeinckThis open access book brings together national experts from across the Dinaric region to rigorously review IEA’s Trends in International Mathematics and Science Study (TIMSS) 2019 grade four data to develop a multidimensional and culturally sensitive perspective on their TIMSS 2019 primary-level results. The Dinaric region, named after the Dinaric Alps, is located in South-eastern Europe, and stretches through Croatia, Bosnia and Herzegovina, Serbia, Montenegro, Kosovo[1], Albania, and North Macedonia. IEA’s TIMSS has been an invaluable resource for monitoring international trends in mathematics and science achievement at grades four and eight since 1995. The TIMSS 2019 administration of the test to grade four students, provided a unique opportunity for analysis within shared regional settings and enabled the construction of this first report based on international study results from the region, prepared by the National Research Coordinators in collaboration with IEA. [1] This designation is without prejudice to positions on status and is in line with UNSCR 1244/1999 and the ICJ Opinion on the Kosovo declaration of independence.
Dingers: The 101 Most Memorable Home Runs in Baseball History
by Joshua Shifrin Tommy SheaFrom splitters to spitters; from a frozen rope to the suicide squeeze; from extra innings to no hitters, baseball is truly a great game. But nothing hypes up a crowd like a home run, a round tripper, a big bomb . . . the long ball! Hitting the ball out of the park is one of the greatest feats in baseball, and doing so in the clutch can make an average player a hero overnight.In Dingers, authors Joshua Shifrin and Tom Shea break down the 101 most memorable home runs in baseball history, telling their stories and how they affected the game of baseball. Whether it’s "The Shot Heard ’Round the World” or Hank Aaron’s 715th blast, readers will get an inside scoop on some of the most famous moments that now live in baseball lore.Whether you were there when Reggie Jackson hit three-straight home runs in Game 6 of the 1977 World Series, watched Joe Carter’s 1993 World Series-winning home run live, or have seen highlights from Bill Mazeroski’s memorable shot in Game 7 of the 1960 World Series, Dingers is for baseball fans young and old. Relive the moments you cherish to the ones you’ve only heard tales about.Skyhorse Publishing, as well as our Sports Publishing imprint, are proud to publish a broad range of books for readers interested in sports-books about baseball, pro football, college football, pro and college basketball, hockey, or soccer, we have a book about your sport or your team.Whether you are a New York Yankees fan or hail from Red Sox nation; whether you are a die-hard Green Bay Packers or Dallas Cowboys fan; whether you root for the Kentucky Wildcats, Louisville Cardinals, UCLA Bruins, or Kansas Jayhawks; whether you route for the Boston Bruins, Toronto Maple Leafs, Montreal Canadiens, or Los Angeles Kings; we have a book for you. While not every title we publish becomes a New York Times bestseller or a national bestseller, we are committed to publishing books on subjects that are sometimes overlooked by other publishers and to authors whose work might not otherwise find a home.
Dinos Love Numbers: Maths is easy with dinosaurs!
by Adam FrostIntroduce young readers to the magical world of numbers with this fun, dinosaur-themed picture book!Packed with amazing dinosaur facts and awe-inspiring numbers, Dinos Love Numbers looks at shapes, fractions, addition, subtraction, measurements and so much more. Wherever you go you will bump noses with numbers, rub shoulders with shapes or have a chance meeting with multiplication, and guess what: numbers are SUPER fun. Don't believe me? Try this for dinosaur-loving-size...Which dino was as heavy as 10 elephants? (It's the Alamosaurus, of course!)Who would win in a dino race? (A Velociraptor. Speedy!)Which dinosaur is THREE TIMES the length of a great white shark? (A Megalodon. It was ENORMOUS!)The perfect picture book for all maths-loving kids, dinosaur-loving kids and those kids who are not sure about numbers, Dinos Love Numbers has fun illustrations and is packed with super-cool prehistoric creatures to make maths fun for children aged 5+.
Diophantine Analysis
by Jorn SteudingWhile its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine ap
Diophantine Analysis
by Jörn SteudingThis collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject. The topics range from Baker's method of bounding linear forms in logarithms (authored by Sanda Bujačić and Alan Filipin), metric diophantine approximation discussing in particular the yet unsolved Littlewood conjecture (by Simon Kristensen), Minkowski's geometry of numbers and modern variations by Bombieri and Schmidt (Tapani Matala-aho), and a historical account of related number theory(ists) at the turn of the 19th Century (Nicola M. R. Oswald). Each of these notes serves as an essentially self-contained introduction to the topic. The reader gets a thorough impression of Diophantine Analysis by its central results, relevant applications and open problems. The notes are complemented with many references and an extensive register which makes it easy to navigate through the book.
Diophantine Approximation and Dirichlet Series (Texts and Readings in Mathematics #80)
by Hervé Queffelec Martine QueffelecThe second edition of the book includes a new chapter on the study of composition operators on the Hardy space and their complete characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet series and their composition operators, and connections between these two domains which often occur through the Kronecker approximation theorem and the Bohr lift. The book initially discusses Harmonic analysis, including a sharp form of the uncertainty principle, Ergodic theory and Diophantine approximation, basics on continued fractions expansions, and the mixing property of the Gauss map and goes on to present the general theory of Dirichlet series with classes of examples connected to continued fractions, Bohr lift, sharp forms of the Bohnenblust–Hille theorem, Hardy–Dirichlet spaces, composition operators of the Hardy–Dirichlet space, and much more. Proofs throughout the book mix Hilbertian geometry, complex and harmonic analysis, number theory, and ergodic theory, featuring the richness of analytic theory of Dirichlet series. This self-contained book benefits beginners as well as researchers.
Diophantine Approximations (Dover Books on Mathematics)
by Ivan NivenThis self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discussion. Each chapter concludes with a bibliographic account of closely related work; these sections also contain the sources from which the proofs are drawn.
Diophantine Equations and Power Integral Bases: Theory and Algorithms
by István GaálWork examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.
Diophantine m-tuples and Elliptic Curves (Developments in Mathematics #79)
by Andrej DujellaThis book provides an overview of the main results and problems concerning Diophantine m-tuples, i.e., sets of integers or rationals with the property that the product of any two of them is one less than a square, and their connections with elliptic curves. It presents the contributions of famous mathematicians of the past, like Diophantus, Fermat and Euler, as well as some recent results of the author and his collaborators.The book presents fragments of the history of Diophantine m-tuples, emphasising the connections between Diophantine m-tuples and elliptic curves. It is shown how elliptic curves are used in solving some longstanding problems on Diophantine m-tuples, such as the existence of infinite families of rational Diophantine sextuples. On the other hand, rational Diophantine m-tuples are used to construct elliptic curves with interesting Mordell–Weil groups, including curves of record rank with agiven torsion group. The book contains concrete algorithms and advice on how to use the software package PARI/GP for solving computational problems.This book is primarily intended for researchers and graduate students in Diophantine equations and elliptic curves. However, it can be of interest to other mathematicians interested in number theory and arithmetic geometry. The prerequisites are on the level of a standard first course in elementary number theory. Background in elliptic curves, Diophantine equations and Diophantine approximations is provided.
Direct Integral Theory
by O. A. NielsenThis book covers various topics related to direct integral theory, including Borel spaces, direct integral of Hilbert spaces and operators, direct integrals of representations, direct integrals and types of von Neumann algebras, and measures on the quasi-dual representations.
Direct Sum Decompositions of Torsion-Free Finite Rank Groups
by Theodore G. FaticoniWith plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups
Direct and Indirect Boundary Integral Equation Methods (Monographs And Surveys In Pure And Applied Mathematics Ser. #107)
by Christian ConstandaThe computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering. Boundary integral equation methods (BIEM's) have certain advantages over other procedures for solving such problems: BIEM's are powerful, applicable to a wide variety of situations, elegant, and ideal for numerical treatment. Certain fundamental constructs in BIEM's are also essential ingredients in boundary element methods, often used by scientists and engineers.However, BIEM's are also sometimes more difficult to use in plane cases than in their three-dimensional counterparts. Consequently, the full, detailed BIEM treatment of two-dimensional problems has been largely neglected in the literature-even when it is more than marginally different from that applied to the corresponding three-dimensional versions.This volume discusses three typical cases where such differences are clear: the Laplace equation (one unknown function), plane strain (two unknown functions), and the bending of plates with transverse shear deformation (three unknown functions). The author considers each of these with Dirichlet, Neumann, and Robin boundary conditions. He subjects each to a thorough investigation-with respect to the existence and uniqueness of regular solutions-through several BIEM's. He proposes suitable generalizations of the concept of logarithmic capacity for plane strain and bending of plates, then uses these to identify contours where non-uniqueness may occur. In the final section, the author compares and contrasts the various solution representations, links them by means of boundary operators, and evaluates them for their suitability for
Direct and Inverse Scattering for the Matrix Schrödinger Equation (Applied Mathematical Sciences #203)
by Tuncay Aktosun Ricardo WederAuthored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrödinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
Direct and Inverse Sturm-Liouville Problems: A Method of Solution (Frontiers in Mathematics)
by Vladislav V. KravchenkoThis book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems.The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.
Direct and Projective Limits of Geometric Banach Structures. (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Patrick Cabau Fernand PelletierThis book describes in detail the basic context of the Banach setting and the most important Lie structures found in finite dimension. The authors expose these concepts in the convenient framework which is a common context for projective and direct limits of Banach structures. The book presents sufficient conditions under which these structures exist by passing to such limits. In fact, such limits appear naturally in many mathematical and physical domains. Many examples in various fields illustrate the different concepts introduced. Many geometric structures, existing in the Banach setting, are "stable" by passing to projective and direct limits with adequate conditions. The convenient framework is used as a common context for such types of limits. The contents of this book can be considered as an introduction to differential geometry in infinite dimension but also a way for new research topics. This book allows the intended audience to understand the extension to the Banach framework of various topics in finite dimensional differential geometry and, moreover, the properties preserved by passing to projective and direct limits of such structures as a tool in different fields of research.
Directed Algebraic Topology and Concurrency
by Lisbeth Fajstrup Eric Goubault Emmanuel Haucourt Samuel Mimram Martin RaussenThis monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis. Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs. The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than "just" the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account. The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.
Direction Dependence in Statistical Modeling: Methods of Analysis
by Alexander Von Eye Wolfgang Wiedermann Engin A. Sungur Daeyoung KimCovers the latest developments in direction dependence research Direction Dependence in Statistical Modeling: Methods of Analysis incorporates the latest research for the statistical analysis of hypotheses that are compatible with the causal direction of dependence of variable relations. Having particular application in the fields of neuroscience, clinical psychology, developmental psychology, educational psychology, and epidemiology, direction dependence methods have attracted growing attention due to their potential to help decide which of two competing statistical models is more likely to reflect the correct causal flow. The book covers several topics in-depth, including: A demonstration of the importance of methods for the analysis of direction dependence hypotheses A presentation of the development of methods for direction dependence analysis together with recent novel, unpublished software implementations A review of methods of direction dependence following the copula-based tradition of Sungur and Kim A presentation of extensions of direction dependence methods to the domain of categorical data An overview of algorithms for causal structure learning The book's fourteen chapters include a discussion of the use of custom dialogs and macros in SPSS to make direction dependence analysis accessible to empirical researchers.
Directional and Multivariate Statistics: A Volume in Honour of Ashis SenGupta
by Barry C. Arnold Arnab Kumar Laha Somesh Kumar Kunio ShimizuThis book contains select chapters on a range of topics in directional statistics, multivariate statistical inference, financial statistics, statistical machine learning and reliability inference. At the 43rd Annual Convention of the Indian Society for Probability and Statistics (ISPS) held in Prayagraj (formerly Allahabad), Uttar Pradesh, India, from 6–8 February 2024, attribute was paid to Prof. Ashis SenGupta on the occasion of his 70th birthday. He has pioneered research on directional statistics in the modern era in India and enhanced it worldwide and contributed significantly to the advancement of the following topics: Highly flexible distributions on manifolds Statistical machine learning in data science Big data on manifolds Optimal multiparameter, multivariate statistical inference Reliability inference and stress-dependent-strength models Directional statistics for highly volatile financial models Cylindrical, spherical and toroidal regression analysis Innovative applications of emerging real-life directional data