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Academic Press

  • Numerical Methods of Mathematical Optimization

    With ALGOL and FORTRAN Programs
    • 1st Edition
    • Hans P. Künzi + 2 more
    • Werner Rheinboldt
    • English
    Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods. Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition to the theoretical considerations, several algorithms of importance to the numerical application of optimization theory are described. The next chapter explains the computer programs used in actual optimization, which have the form of procedures or subroutines. The book concludes with an analysis of ALGOL and FORTRAN, paying particular attention to their use in global optimization procedures as well as for the simplex and duoplex methods and the decomposition, Gomory, Beale, and Wolfe algorithms. This monograph will be helpful to students and practitioners of computer science and applied mathematics.

  • Integral Geometry and Representation Theory

    • 1st Edition
    • I. M. Gel'fand + 2 more
    • English
    Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.

  • Elementary Calculus

    • 1st Edition
    • P.R. Masani + 2 more
    • Ralph P. Boas
    • English
    Elementary Calculus presents a three semester introductory course on calculus. This book reveals the conceptual development of the calculus, taking into cognizance the technical and applied sides and standards of clarity and rigor that prevail in mathematics. The topics discussed include the basic laws of numbers, classification of real functions, and concept of instantaneous velocity. The limits of functions defined on intervals, derivatives of the trigonometric functions, and standard logarithmic function are also reviewed. This text likewise considers integration by substitution, lengths of plane curves, and simple harmonic motion. This publication is designed for students who have a knowledge of elementary trigonometry, and either have had a one semester course on analytic or coordinate geometry or might take such a course with calculus.

  • Topology

    Volume I
    • 1st Edition
    • K. Kuratowski
    • English
    Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations such as the exponential topology and quotient topology. The next chapter is devoted to the study of metric spaces, starting with more general spaces, having the limit as its primitive notion. The space is assumed to be metric separable, and this includes problems of cardinality and dimension. Dimension theory and the theory of Borei sets, Baire functions, and related topics are also discussed. The final chapter is about complete spaces and includes problems of general function theory which can be expressed in topological terms. The book includes two appendices, one on applications of topology to mathematical logics and another to functional analysis. This monograph will be helpful to students and practitioners of algebra and mathematics.

  • Robustness in Statistics

    • 1st Edition
    • Robert L. Launer + 1 more
    • English
    Robustness in Statistics contains the proceedings of a Workshop on Robustness in Statistics held on April 11-12, 1978, at the Army Research Office in Research Triangle Park, North Carolina. The papers review the state of the art in statistical robustness and cover topics ranging from robust estimation to the robustness of residual displays and robust smoothing. The application of robust regression to trajectory data reduction is also discussed. Comprised of 14 chapters, this book begins with an introduction to robust estimation, paying particular attention to iteration schemes and error structure of estimators. Sensitivity and influence curves as well as their connection with jackknife estimates are described. The reader is then introduced to a simple analog of trimmed means that can be used for studying residuals from a robust point-of-view; a class of robust estimators (called P-estimators) based on the location and scale-invariant Pitman estimators of location; and robust estimation in the presence of outliers. Subsequent chapters deal with robust regression and its use to reduce trajectory data; tests for censoring of extreme values, especially when population distributions are incompletely defined; and robust estimation for time series autoregressions. This monograph should be of interest to mathematicians and statisticians.

  • Chemistry and Methods of Enzymes

    • 3rd Edition
    • James B. Sumner + 1 more
    • English
    Chemistry and Methods of Enzymes, Third Edition focuses on the processes, methodologies, and reactions in enzyme chemistry, as well as kinetics, nucleases, esterases, and carbohydrates. The publication first underscores the general properties of enzymes, including chemical nature, occurrence, numerical characterization of enzyme concentration, kinetics of enzyme reactions, preparation of commercial enzymes, purification and preservation of enzymes, relations of vitamins to enzymes, and zymogens and kinases. The text then takes a look at esterases and carbohydrates. Topics include pectin depolymerase, heparinase, xylanase, chitinase, dextranase, trehalase, nucleotide phosphatases, glucosulfatase, and gastric lipase. The manuscript examines nucleases, nuclein deaminases, amidases, proteolytic enzymes, and hydrases. Discussions focus on enolase, aconitase, peptidases as metalloproteins, glutaminases, aspartase, urease, adenosine deaminase, and nucleoside phosphorylase. The book also elaborates on iron and copper enzymes, dehydrogenases containing coenzymes I and II, and yellow enzymes. The text is a dependable source of data for chemists and researchers wanting to dig deeper into the chemistry and methods of enzymes.

  • Nonlinear Phenomena in Mathematical Sciences

    Proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, Held at the University of Texas at Arlington, Arlington, Texas, June 16–20, 1980
    • 1st Edition
    • V. Lakshmikantham
    • English
    Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.

  • Protein and Amino Acid Requirements of Mammals

    • 1st Edition
    • Anthony A. Albanese
    • English
    Protein and Amino Acid Requirements of Mammals focuses on the determination of the protein and amino acid requirements of various mammals, including man in particular. The selection first offers information on some species and age differences in amino acid requirements and the methods of measuring the nutritive value of protein hydrolysates and amino acid mixtures. Discussions focus on assay methods based on protein regeneration; specificity of amino acid requirements; amino acid requirements for nitrogen equilibrium in the adult; and composition of tissue proteins and amino acid requirements for growth. The text then examines the laboratory evaluation of amino acid mixtures and protein hydrolysates and dietary proteins and synthesis of tissue proteins. Topics include role of dietary proteins in the hypertrophy of gonads, effect of dietary proteins on repletion of liver proteins, and effect of dietary proteins on the synthesis of plasma proteins. The publication examines the protein and amino acid requirements of man, including qualitative amino acid requirements of various species, growth and protein and amino acid needs, and metabolic interactions of essential and nonessential amino acids. The selection is a dependable reference for researchers interested in the determination of the protein and amino acid requirements of mammals, including man.

  • Discrete Computational Structures

    • 1st Edition
    • Robert R. Korfhage
    • Werner Rheinboldt
    • English
    Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasizes combinatorics and probability. Examples show different techniques of the general process of enumerating objects. Combinatorics cover permutations, enumerators for combinations, Stirling numbers, cycle classes of permutations, partitions, and compositions. The book cites as example the interplay between discrete mathematics and computing using a system of distinct representatives (SDR) problem. The problem, originating from group theory, graph theory, and set theory can be worked out by the student with a network model involving computers to generate and analyze different scenarios. The book is intended for sophomore or junior level, corresponding to the course B3, "Introduction to Discrete Structures," in the ACM Curriculum 68, as well as for mathematicians or professors of computer engineering and advanced mathematics.

  • Group Theory and Its Applications

    • 1st Edition
    • Ernest M. Loebl
    • English
    Group Theory and Its Applications focuses on the applications of group theory in physics and chemistry. The selection first offers information on the algebras of lie groups and their representations and induced and subduced representations. Discussions focus on the functions of positive type and compact groups; orthogonality relations for square-integrable representations; group, topological, Borel, and quotient structures; and classification of semisimple lie algebras in terms of their root systems. The text then takes a look at the generalization of Euler's angles and projective representation of the Poincare group in a quaternionic Hilbert space. The manuscript ponders on group theory in atomic spectroscopy, group lattices and homomorphism, and group theory in solid state physics. Topics include band theory of solids, lattice vibrations in solids, stationary states in the quantum theory of matter, coupled tensors, and shell structure. The text then examines the group theory of harmonic oscillators and nuclear structure and de Sitter space and positive energy. The selection is a dependable reference for physicists and chemists interested in group theory and its applications.

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