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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Arches

    Tables for Statistical Analyses
    • 1st Edition
    • Jan Szymczyk
    • Jerzy Mutermilch
    • English
    Arches: Tables for Statistical Analyses presents a table used for simplifying the calculations of numerical determination of the magnitude of the internal forces in various cross-sections. After the evaluation of the redundancies, one of the stages in the analysis of statistically indeterminate arches is for the investigator to determine the magnitudes of the normal forces and bending moments at various cross-sections. A large number of sections should be considered in order for the investigator to get an accurate picture of the distribution of the generalized internal forces. Such number of sections varies between 10 and 20. To simplify the calculations, the book supplements the main tables for the vertical and horizontal components of reactions by auxiliary tables. These auxiliary tables give the magnitudes of normal forces and bending moments for cases usually encountered in actual practice. The book also explains the use of coefficients in the analysis of two-pinned arches with unyielding supports. The text can be useful for mathematicians, statisticians, and scientific investigators who have to deal with the analysis of numerical data.

  • Conceptual Information Processing

    • 1st Edition
    • Roger C. Schank
    • English
    Fundamental Studies in Computer Science, 3: Conceptual Information Processing discusses a theory of natural language and implementation of that theory on a computer, focusing basically on an Artificial Intelligence approach to linguistics. This book aims to write computer programs that could understand and generate sentences, which is intended as a first step towards the long range goal of a computer that can communicate with people in natural language. The topics covered include computational linguistics, conceptual dependency theory, history of the analyzer, representation in memory, and structure of BABEL. This publication is a good reference for researchers and specialists working in the field of computer science.

  • Non-Linear Transformations of Stochastic Processes

    • 1st Edition
    • P. I. Kuznetsov + 2 more
    • English
    Non-Linear Transformations of Stochastic Processes focuses on the approaches, methodologies, transformations, and computations involved in the non-linear transformations of stochastic processes. The selection first underscores some problems of the theory of stochastic processes and the transmission of random functions through non-linear systems. Discussions focus on the transformation of moment functions for the general non-linear transformation; conversion formulas for correlation functions; transformation of moment functions for the simplest type of non-linear transformation; and normalization of the linear system of probability distribution laws. The text then ponders on quasi-moment functions in the theory of random processes and correlation functions in the theory of the Brownian motion generalization of the Fokker-Planck equation. The manuscript elaborates on the correlation functions of random sequences of rectangular pulses; method of determining the envelope of quasi-harmonic fluctuations; and the problem of measuring electrical fluctuations with the aid of thermoelectric devices. The book then examines the effect of signal and noise on non-linear elements and the approximate method of calculating the correlation function of stochastic signals. The selection is a dependable source of information for researchers interested in the non-linear transformations of stochastic processes.

  • Digital Computer Design

    Logic, Circuitry, and Synthesis
    • 1st Edition
    • Edward L. Braun
    • English
    Digital Computer Design: Logic, Circuitry, and Synthesis focuses on the logical structure, electronic realization, and application of digital information processors. The manuscript first offers information on numerical symbols, fundamentals of computing aids, quantization, representation of numbers in an electronic digital computer, and computer applications. The text then ponders on the nature of automatic computation and Boolean algebra. Discussions focus on the advantages of a Boolean algebraic description of a digital computer; clock pulse generators and timing circuits; sequential switching networks; elements of information processing systems and types of digital computers; and automatic sequencing methods. The book elaborates on circuit descriptions of switching and storage elements and large capacity storage systems. Topics include static magnetic storage, dynamic delay line storage, cathode-ray storage, vacuum tube systems of circuit logic, and magnetic core systems of circuit logic. The publication also examines the system design of GP computers, digital differential analyzer, and the detection and correction of errors. The text is a valuable source of data for mathematicians and engineers interested in digital computer design.

  • Symplectic Geometry

    • 1st Edition
    • Carl Ludwig Siegel
    • English
    Symplectic Geometry focuses on the processes, methodologies, and numerical approaches involved in symplectic geometry. The book first offers information on the symplectic and discontinuous groups, symplectic metric, and hermitian forms. Numerical calculations are presented to show the values and transformations of these groups. The text then examines the fundamental domain of the modular group and the volume of the fundamental domain of the modular group. Equations and matrices are provided to show the fundamental domain and volume of the fundamental domain of the modular group. The publication ponders on commensurable groups and unit groups of quinary quadratic forms. Numerical analyses are also offered to show the values and characteristics of commensurable and unit groups. The text is a helpful reference for researchers interested in symplectic geometry.

  • Additive and Polynomial Representations

    • 1st Edition
    • David H. Krantz + 2 more
    • English
    Additive and Polynomial Representations deals with major representation theorems in which the qualitative structure is reflected as some polynomial function of one or more numerical functions defined on the basic entities. Examples are additive expressions of a single measure (such as the probability of disjoint events being the sum of their probabilities), and additive expressions of two measures (such as the logarithm of momentum being the sum of log mass and log velocity terms). The book describes the three basic procedures of fundamental measurement as the mathematical pivot, as the utilization of constructive methods, and as a series of isomorphism theorems leading to consistent numerical solutions. The text also explains the counting of units in relation to an empirical relational structure which contains a concatenation operation. The book notes some special variants which arise in connection with relativity and thermodynamics. The text cites examples from physics and psychology for which additive conjoint measurement provides a possible method of fundamental measurement. The book will greatly benefit mathematicians, econometricians, and academicians in advanced mathematics or physics.

  • Readings in Fuzzy Sets for Intelligent Systems

    • 1st Edition
    • Didier J. Dubois + 2 more
    • English
    Readings in Fuzzy Sets for Intelligent Systems is a collection of readings that explore the main facets of fuzzy sets and possibility theory and their use in intelligent systems. Basic notions in fuzzy set theory are discussed, along with fuzzy control and approximate reasoning. Uncertainty and informativeness, information processing, and membership, cognition, neural networks, and learning are also considered. Comprised of eight chapters, this book begins with a historical background on fuzzy sets and possibility theory, citing some forerunners who discussed ideas or formal definitions very close to the basic notions introduced by Lotfi Zadeh (1978). The reader is then introduced to fundamental concepts in fuzzy set theory, including symmetric summation and the setting of fuzzy logic; uncertainty and informativeness; and fuzzy control. Subsequent chapters deal with approximate reasoning; information processing; decision and management sciences; and membership, cognition, neural networks, and learning. Numerical methods for fuzzy clustering are described, and adaptive inference in fuzzy knowledge networks is analyzed. This monograph will be of interest to both students and practitioners in the fields of computer science, information science, applied mathematics, and artificial intelligence.

  • A Guidebook to Fortran on Supercomputers

    • 1st Edition
    • John M. Levesque + 1 more
    • English
    A Guidebook to Fortran on Supercomputers presents in detail both the underlying architecture of supercomputers and the manner by which a compiler maps Fortran code onto that architecture. This book outlines the constructs preventing full optimization and provides specific strategies for restructuring a program. Organized into four chapters, this book begins with an overview of the basic concepts of vector, scalar, and parallel processing. This text then provides an in-depth look at the architectural features of a variety of existing machines, with emphasis to the features common to many of them. Other chapters consider the optimization techniques used by compilers and how a programmer can take advantage of this knowledge in restructuring existing programs and in the development of new applications. The final chapter presents examples of loops from real-world programs, with a discussion of the inherent problems. This book is a valuable resource for scientists, engineers, students, and research workers.

  • Uncertainty in Artificial Intelligence

    Proceedings of the Eighth Conference (1992), July 17–19, 1992, Eighth Conference on Uncertainty in Artificial Intelligence, Stanford University
    • 1st Edition
    • Didier J. Dubois + 2 more
    • English
    Uncertainty in Artificial Intelligence: Proceedings of the Eighth Conference (1992) covers the papers presented at the Eighth Conference on Uncertainty in Artificial Intelligence, held at Stanford University on July 17-19, 1992. The book focuses on the processes, methodologies, technologies, and approaches involved in artificial intelligence. The selection first offers information on Relative Evidential Support (RES), modal logics for qualitative possibility and beliefs, and optimizing causal orderings for generating DAGs from data. Discussions focus on reversal, swap, and unclique operators, modal representation of possibility, and beliefs and conditionals. The text then examines structural controllability and observability in influence diagrams, lattice-based graded logic, and dynamic network models for forecasting. The manuscript takes a look at reformulating inference problems through selective conditioning, entropy and belief networks, parallelizing probabilistic inference, and a symbolic approach to reasoning with linguistic quantifiers. The text also ponders on sidestepping the triangulation problem in Bayesian net computations; exploring localization in Bayesian networks for large expert systems; and expressing relational and temporal knowledge in visual probabilistic networks. The selection is a valuable reference for researchers interested in artificial intelligence.

  • Entire Functions

    • 1st Edition
    • A. I. Markushevich
    • English
    Entire Functions focuses on complex numbers and the algebraic operations on them and the basic principles of mathematical analysis. The book first elaborates on the concept of an entire function, including the natural generalization of the concept of a polynomial and power series. The text then takes a look at the maximum absolute value and the order of an entire function, as well as calculations for the coefficients of power series representing a given function, use of integrals, and complex numbers. The publication elaborates on the zeros of an entire function and the fundamental theorem of algebra and Picard’s little theorem. Calculations for the zeros of an entire function and numerical representations of Liouville's theorem and Picard’s little theorem are presented. The book also examines algebraic relationships and addition theorems, including an explanation of Weierstrass' theorem and Picard’s little theorem. The manuscript is a vital reference for students interested in the numerical approaches involved in entire functions.

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