Author: A.H. Zemanian
Publisher: Courier Corporation
ISBN: 0486151948
Category : Mathematics
Languages : en
Pages : 404
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Book Description
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Author: J. Durbin
Publisher: SIAM
ISBN: 0898710073
Category : Mathematics
Languages : en
Pages : 73
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Book Description
Presents a coherent body of theory for the derivation of the sampling distributions of a wide range of test statistics. Emphasis is on the development of practical techniques. A unified treatment of the theory was attempted, e.g., the author sought to relate the derivations for tests on the circle and the two-sample problem to the basic theory for the one-sample problem on the line. The Markovian nature of the sample distribution function is stressed, as it accounts for the elegance of many of the results achieved, as well as the close relation with parts of the theory of stochastic processes.
Author: J. Durbin
Publisher: SIAM
ISBN: 9781611970586
Category : Mathematics
Languages : en
Pages : 70
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Book Description
Presents a coherent body of theory for the derivation of the sampling distributions of a wide range of test statistics. Emphasis is on the development of practical techniques. A unified treatment of the theory was attempted, e.g., the author sought to relate the derivations for tests on the circle and the two-sample problem to the basic theory for the one-sample problem on the line. The Markovian nature of the sample distribution function is stressed, as it accounts for the elegance of many of the results achieved, as well as the close relation with parts of the theory of stochastic processes.
Author: Lawrence J. Gitman
Publisher:
ISBN:
Category : Business & Economics
Languages : en
Pages : 1455
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Book Description
Introduction to Business covers the scope and sequence of most introductory business courses. The book provides detailed explanations in the context of core themes such as customer satisfaction, ethics, entrepreneurship, global business, and managing change. Introduction to Business includes hundreds of current business examples from a range of industries and geographic locations, which feature a variety of individuals. The outcome is a balanced approach to the theory and application of business concepts, with attention to the knowledge and skills necessary for student success in this course and beyond. This is an adaptation of Introduction to Business by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.
Author: Abraham de Moivre
Publisher:
ISBN:
Category : Annuities
Languages : en
Pages : 374
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Book Description
Author: Qi-Ming He
Publisher: Springer Science & Business Media
ISBN: 1461473306
Category : Computers
Languages : en
Pages : 363
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Book Description
Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions. New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.
Author: Guy Latouche
Publisher: Springer Science & Business Media
ISBN: 146144909X
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Matrix-analytic and related methods have become recognized as an important and fundamental approach for the mathematical analysis of general classes of complex stochastic models. Research in the area of matrix-analytic and related methods seeks to discover underlying probabilistic structures intrinsic in such stochastic models, develop numerical algorithms for computing functionals (e.g., performance measures) of the underlying stochastic processes, and apply these probabilistic structures and/or computational algorithms within a wide variety of fields. This volume presents recent research results on: the theory, algorithms and methodologies concerning matrix-analytic and related methods in stochastic models; and the application of matrix-analytic and related methods in various fields, which includes but is not limited to computer science and engineering, communication networks and telephony, electrical and industrial engineering, operations research, management science, financial and risk analysis, and bio-statistics. These research studies provide deep insights and understanding of the stochastic models of interest from a mathematics and/or applications perspective, as well as identify directions for future research.
Author: Antonio Puliafito
Publisher: Springer
ISBN: 3319923781
Category : Technology & Engineering
Languages : en
Pages : 315
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Book Description
This book covers ideas, methods, algorithms, and tools for the in-depth study of the performance and reliability of dependable fault-tolerant systems. The chapters identify the current challenges that designers and practitioners must confront to ensure the reliability, availability, and performance of systems, with special focus on their dynamic behaviors and dependencies. Topics include network calculus, workload and scheduling; simulation, sensitivity analysis and applications; queuing networks analysis; clouds, federations and big data; and tools. This collection of recent research exposes system researchers, performance analysts, and practitioners to a spectrum of issues so that they can address these challenges in their work.
Author: Dick Russell
Publisher:
ISBN: 9780199148387
Category : Mathematics
Languages : en
Pages : 206
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Book Description
Split into sections on Pure Mathematics, Statistics, Mechanics, and Discrete Mathematics this one book is the essential study companion for all your AS Mathematics students. Ideal either as a class text or as a useful revision guide* Mathematical concepts and principles presented in a clear, straightforward style* Each section includes a wealth of examination style questions and answers* Suitable for any specification - the book features an AS specification mapping grid so you can feel confident that your specification is covered
Author: András Horváth
Publisher: John Wiley & Sons
ISBN: 1848219458
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Phase type distributions are widely applicable modeling and statistical tools for non-negative random quantities. They are built on Markov chains, which provide a simple, intuitive stochastic interpretation for their use. Phase Type Distribution starts from the Markov chain-based definition of phase type distributions and presents many interesting properties, which follow from the basic definition. As a general family of non-negative distributions with nice analytical properties, phase type distributions can be used for approximating experimental distributions by fitting or by moments matching; and, for discrete event simulation of real word systems with stochastic timing, such as production systems, service operations, communication networks, etc. This book summarizes the up-to-date fitting, matching and simulation methods, and presents the limits of flexibility of phase type distributions of a given order. Additionally, this book lists numerical examples that support the intuitive understanding of the analytical descriptions and software tools that handle phase type distributions.
