A Guide to Mathematical Tables


Book Description

A Guide to Mathematical Tables is a supplement to the Guide to Mathematical Tables published by the U.S.S.R. Academy of Sciences in 1956. The tables contain information on subjects such as powers, rational and algebraic functions, and trigonometric functions, as well as logarithms and polynomials and Legendre functions. An index listing all functions included in both the Guide and the Supplement is included. Comprised of 15 chapters, this supplement first describes mathematical tables in the following order: the accuracy of the table (that is, the number of decimal places or significant figures); the limits of variation of the argument and the interval of the table; and the serial number of the book or journal in the reference material. The second part gives the author, title, publishing house, and date and place of publication for books, and the name of the journal, year of publication, series, volume and number, page and author and title of the article cited for journals. Topics range from exponential and hyperbolic functions to factorials, Euler integrals, and related functions. Sums and quantities related to finite differences are also tabulated. This book will be of interest to mathematicians and mathematics students.







The Mathematical Theory of Information


Book Description

The general concept of information is here, for the first time, defined mathematically by adding one single axiom to the probability theory. This Mathematical Theory of Information is explored in fourteen chapters: 1. Information can be measured in different units, in anything from bits to dollars. We will here argue that any measure is acceptable if it does not violate the Law of Diminishing Information. This law is supported by two independent arguments: one derived from the Bar-Hillel ideal receiver, the other is based on Shannon's noisy channel. The entropy in the 'classical information theory' is one of the measures conforming to the Law of Diminishing Information, but it has, however, properties such as being symmetric, which makes it unsuitable for some applications. The measure reliability is found to be a universal information measure. 2. For discrete and finite signals, the Law of Diminishing Information is defined mathematically, using probability theory and matrix algebra. 3. The Law of Diminishing Information is used as an axiom to derive essential properties of information. Byron's law: there is more information in a lie than in gibberish. Preservation: no information is lost in a reversible channel. Etc. The Mathematical Theory of Information supports colligation, i. e. the property to bind facts together making 'two plus two greater than four'. Colligation is a must when the information carries knowledge, or is a base for decisions. In such cases, reliability is always a useful information measure. Entropy does not allow colligation.




Simulation of Local Area Networks


Book Description

A fast-growing area in the communications industry is the internetworking of an ever-increasing proliferation of computers, particularly via local area networks (LANs). The LAN is a resource-sharing data communications network being used by many offices to interchange information such as electronic mail, word processing, and files among computers and other devices. This unique book shows the user how to establish the performance characteristics of a LAN before putting it to use in a particular type of situation. Simulation of Local Area Networks consists of eight chapters, each with its own extensive list of references. The first chapter provides a brief review of local area networks, and the second chapter gives the analytical models of popular LANs-token-passing bus and ring networks, CSMA/CD LANs, and star networks. Chapter 3 covers general principles of simulation, and Chapter 4 discusses fundamental concepts in probability and statistics relating to simulation modeling. Materials in Chapters 3 and 4 are specifically applied in developing simulation models on token-passing LANs, CSMA/CD LANs, and star LANs in Chapters 5 through 7. The computer code in Chapters 5, 6, and 7 is divided into segments, and a detailed explanation of each segment is provided. The last chapter reviews special-purpose languages such as GPSS, SIMSCRIPT, GASP, SIMULA, SLAM, and RESQ. Helpful criteria for language selection are included. The entire code is put together in the appendixes. This book has two major advantages over existing texts. First, it uses C, a well-developed general-purpose language that is familiar to most analysts. Second, the text specifically applies the simulation principles to local area networks. No other book available shows the systems analyst how to evaluate the performance of existing or proposed systems under different kinds of conditions.







Monte Carlo Methods for Electromagnetics


Book Description

Until now, novices had to painstakingly dig through the literature to discover how to use Monte Carlo techniques for solving electromagnetic problems. Written by one of the foremost researchers in the field, Monte Carlo Methods for Electromagnetics provides a solid understanding of these methods and their applications in electromagnetic computation. Including much of his own work, the author brings together essential information from several different publications. Using a simple, clear writing style, the author begins with a historical background and review of electromagnetic theory. After addressing probability and statistics, he introduces the finite difference method as well as the fixed and floating random walk Monte Carlo methods. The text then applies the Exodus method to Laplace’s and Poisson’s equations and presents Monte Carlo techniques for handing Neumann problems. It also deals with whole field computation using the Markov chain, applies Monte Carlo methods to time-varying diffusion problems, and explores wave scattering due to random rough surfaces. The final chapter covers multidimensional integration. Although numerical techniques have become the standard tools for solving practical, complex electromagnetic problems, there is no book currently available that focuses exclusively on Monte Carlo techniques for electromagnetics. Alleviating this problem, this book describes Monte Carlo methods as they are used in the field of electromagnetics.




The Central


Book Description