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2631-2640 of 2668 results in All results

Applications of Finite Groups

  • 1st Edition
  • January 1, 1959
  • J. S. Lomont
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 6 8 9 6 - 5
Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

Matrix Calculus

  • 3rd Edition
  • January 1, 1959
  • E. Bodewig
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 7 4 9 8 - 0
Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well as the decomposition of the matrix into two triangular matrices, choice of another pivotal element, Gauss-Doolittle process, Aitken's triple product, neighbor systems, errors and exactness of the solution, and complex systems. The publication also elaborates on the characteristic equation of the iteration processes, type of convergence of the iteration methods, speeding-up convergence by changing matrix, and methods for electronic computers. The determination of eigenvectors, pure methods, progressive algorithms, and deflation are also discussed. The manuscript is a helpful reference for researchers interested in matrix calculus.

Homology Theory on Algebraic Varieties

  • 1st Edition
  • January 1, 1958
  • Andrew H. Wallace
  • I. N. Sneddon
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 5 2 6 0 - 8
Homology Theory on Algebraic Varieties, Volume 6 deals with the principles of homology theory in algebraic geometry and includes the main theorems first formulated by Lefschetz, one of which is interpreted in terms of relative homology and another concerns the Poincaré formula. The actual details of the proofs of these theorems are introduced by geometrical descriptions, sometimes aided with diagrams. This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The next two chapters focus on singular sections and hyperplane sections, focusing on the choice of a pencil in the latter case. The reader is then introduced to Lefschetz's first and second theorems, together with their corresponding proofs. The Poincaré formula and its proof are also presented, with particular reference to clockwise and anti-clockwise isomorphisms. The final chapter is devoted to invariant cycles and relative cycles. This volume will be of interest to students, teachers, and practitioners of pure and applied mathematics.

Selected Constants Oxydo-Reduction Potentials

  • 1st Edition
  • January 1, 1958
  • G. Charlot
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 2 3 7 9 - 7
Selected Constants: Oxydo-Reduction Potentials contains Tables of the most probable value of the normal oxidation-reduction potential, or of the formal or apparent potential, of a given oxidation-reduction system. This book is prepared under the sponsorship of the Commission on Electrochemical Data of the Section of Analytical Chemistry of the International Union of Pure and Applied Chemistry. It is included in a general program of the Section of Analytical Chemistry. Entry items are classified in alphabetical order. This book will be of value to specialized and non-specialized chemists, teachers, and students.

Jets, Wakes, and Cavities

  • 1st Edition
  • January 1, 1957
  • Zarantonello Eduardo H. + 1 more
  • English
  • eBook
    9 7 8 - 0 - 3 2 3 - 1 6 2 7 1 - 5
Applied Mathematics and Mechanics, Volume 2: Jets, Wakes, and Cavities provides a systematic discussion of jets, wakes, and cavities. This book focuses on the general aspects of ideal fluid theory and examines the engineering applications of fluid dynamics. Organized into 15 chapters, this volume starts with an overview of the different types of jets and explores the atomization of jets in carburetors in connection with gasoline engine design. This text then emphasizes the formal treatment of special flows and examines the flows that are bounded by flat plates and free streamlines. Other chapters consider the flows that are bounded by the cavity behind a symmetric wedge. This book discusses as well the intuitive momentum and similarity considerations. The final chapter deals with several surprising physical complications. Mathematician, physicists, engineers, and readers interested in the fields of applied mathematics, experimental physics, hydraulics, and aeronautics will find this book extremely useful.

Integral Equations

  • 1st Edition
  • Volume 4
  • January 1, 1957
  • S. G. Mikhlin
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 2 6 2 7 - 9
Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.

Elementary Analysis

  • 1st Edition
  • January 1, 1956
  • K. S. Snell + 1 more
  • W. J. Langford + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 3 7 0 8 - 7
Elementary Analysis, Volume 1 introduces the reader to elementary analysis in an informal manner and provides the practical experience in algebraic and analytic operations to lay a sound foundation of basic skills. The preliminary ideas are illustrated by applications to the simpler algebraic functions. Emphasis is on fundamental principles, rather than manipulative techniques. This volume is comprised of 14 chapters and begins with a discussion on number systems, covering concepts ranging from number scales to rational and real numbers, binary operations, and deductive methods. The following chapters deal with sets, vectors and congruences, and functions. Exponential and logarithmic functions, the straight line, and linear function are also considered. The remaining chapters focus on the quadratic function; the principle of mathematical induction and its applications; differentiation and the inverse process; and integration and its applications. Differential equations are presented, along with the definite integral. This book will be of particular value to teachers and students in training colleges.