Download or read book Explicit Formulas written by Jay Jorgenson and published by Springer. This book was released on 2006-11-14 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.
Download or read book Fractal Geometry and Number Theory written by Michel L. Lapidus and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B.) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.
Download or read book Broadband Matching Theory And Implementations 3rd Edition written by Wai-kai Chen and published by World Scientific. This book was released on 2015-10-13 with total page 879 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition presents a unified, up-to-date and detailed account of broadband matching theory and its applications to the design of broadband matching networks and amplifiers. A special feature is the addition of results that are of direct practical value. They are design curves, tables and explicit formulas for designing networks having Butterworth, Chebyshev or elliptic, Bessel or maximally flat group-delay response. These results are extremely useful as the design procedures can be reduced to simple arithmetic. Two case studies towards the end of the book are intended to demonstrate the applications to the practical design of modern filter circuits.
Download or read book A Course in Analytic Number Theory written by Marius Overholt and published by American Mathematical Soc.. This book was released on 2014-12-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Download or read book Algebraic Number Theory written by Serge Lang and published by Springer Science & Business Media. This book was released on 1994-06-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—-MATHEMATICAL REVIEWS
Download or read book Logic and Its Applications written by Mohua Banerjee and published by Springer Science & Business Media. This book was released on 2010-12-14 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 4th Indian Conference on Logic and Its Applications, ICLA 2011, held in Delhi, India, in January 2011. The 14 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 34 submissions. The papers present current research in all aspects of formal logic ranging from pure and applied logic to history of logic.
Download or read book The Adventure of Reason written by Paolo Mancosu and published by OUP Oxford. This book was released on 2014-01-09 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.
Download or read book Mathematical Modelling Applied Analysis and Computation written by Jagdev Singh and published by Springer Nature. This book was released on 2019-08-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.
Download or read book The Development of Modern Logic written by Leila Haaparanta and published by OUP USA. This book was released on 2009-06-18 with total page 1005 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains newly-commissioned articles covering the development of modern logic from the late medieval period (fourteenth century) through the end of the twentieth-century. It is the first volume to discuss the field with this breadth of coverage and depth. It will appeal to scholars and students of philosophical logic and the philosophy of logic.
Download or read book Transmutations Singular and Fractional Differential Equations with Applications to Mathematical Physics written by Elina Shishkina and published by Academic Press. This book was released on 2020-07-24 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. - Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods - Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details - Enables researchers, lecturers and students to find material under the single "roof"
Download or read book Zeta Functions of Graphs written by Audrey Terras and published by Cambridge University Press. This book was released on 2010-11-18 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory meets number theory in this stimulating book. Ihara zeta functions of finite graphs are reciprocals of polynomials, sometimes in several variables. Analogies abound with number-theoretic functions such as Riemann/Dedekind zeta functions. For example, there is a Riemann hypothesis (which may be false) and prime number theorem for graphs. Explicit constructions of graph coverings use Galois theory to generalize Cayley and Schreier graphs. Then non-isomorphic simple graphs with the same zeta are produced, showing you cannot hear the shape of a graph. The spectra of matrices such as the adjacency and edge adjacency matrices of a graph are essential to the plot of this book, which makes connections with quantum chaos and random matrix theory, plus expander/Ramanujan graphs of interest in computer science. Created for beginning graduate students, the book will also appeal to researchers. Many well-chosen illustrations and exercises, both theoretical and computer-based, are included throughout.
Download or read book Pipe Flow written by Donald C. Rennels and published by John Wiley & Sons. This book was released on 2022-05-10 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pipe Flow Provides detailed coverage of hydraulic analysis of piping systems, revised and updated throughout Pipe Flow: A Practical and Comprehensive Guide provides the information required to design and analyze piping systems for distribution systems, power plants, and other industrial operations. Divided into three parts, this authoritative resource describes the methodology for solving pipe flow problems, presents loss coefficient data for a wide range of piping components, and examines pressure drop, cavitation, flow-induced vibration, and other flow phenomena that affect the performance of piping systems. Throughout the book, sample problems and worked solutions illustrate the application of core concepts and techniques. The second edition features revised and expanded information throughout, including an entirely new chapter that presents a mixing section flow model for accurately predicting jet pump performance. This edition includes additional examples, supplemental problems, and a new appendix of the speed of sound in water. With clear explanations, expert guidance, and precise hydraulic computations, this classic reference text remains required reading for anyone working to increase the quality and efficiency of modern piping systems. Discusses the fundamental physical properties of fluids and the nature of fluid flow Demonstrates the accurate prediction and management of pressure loss for a variety of piping components and piping systems Reviews theoretical research on fluid flow in piping and its components Presents important loss coefficient data with straightforward tables, diagrams, and equations Includes full references, further reading sections, and numerous example problems with solution Pipe Flow: A Practical and Comprehensive Guide, Second Edition is an excellent textbook for engineering students, and an invaluable reference for professional engineers engaged in the design, operation, and troubleshooting of piping systems.
Download or read book Handbook of Finite Fields written by Gary L. Mullen and published by CRC Press. This book was released on 2013-06-17 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and
Download or read book Information Security Practice and Experience written by Robert Deng and published by Springer Nature. This book was released on 2021-12-16 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 16th International Conference on Information Security Practice and Experience, ISPEC 2021, held in Nanjing, China, in December 2021. The 23 full papers presented in this volume were carefully reviewed and selected from 94 submissions. The conference focus on new information security technologies, including their applications and their integration with IT systems in various vertical sectors.
Download or read book Higher Ramanujan Equations and Periods of Abelian Varieties written by Tiago J. Fonseca and published by American Mathematical Society. This book was released on 2023-01-18 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Simulation of Communication Systems written by Philip Balaban and published by Springer. This book was released on 2012-12-06 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation may be defined as the discipline whose objective is to imitate one or more aspects of reality in a way that is as close to that reality as possible; indeed, an apt synonym that is gaining some currency is artificial reality. Under this definition, simulation is a very old discipline. Probably the first applications of simulation were to scale models of various types of dynamical structures or mechanical devices. Man has always looked for ways to "try things out" before building the real thing; this is the motivation behind any form of simulation. Thus, simulation of communication systems is concerned with imitating some aspects of the behavior of communication systems. It is implicit in our use of simulation that the medium (so to speak) for carrying it out is the digital computer. Computer-based modeling and simulation of communication systems has only developed in the last 20 years or so, since the advent of modern digital computers. A variety of modeling and simulation techniques have been developed and described in widely scattered journals, but until now there has not been a single volume devoted to the subject. We have tried to provide a unified framework that describes both the disciplines involved and the methods of modeling and simulating communication systems and subsystems. In the electronic era, the first type of computer simulation, in today's use of the term, took shape in the form of analog computers.
