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    • Handbook of Mathematics

      • 1st Edition
      • July 10, 2014
      • L. Kuipers + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 1 6 8 2 2
      • eBook
        9 7 8 1 4 8 3 1 4 9 2 4 0
      International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examples), Rolle's theorem, and the logarithmic function. The book also discusses extensively the functions of two variables in partial differentiation and multiple integrals. The book then describes the theory of functions, ordinary differential functions, special functions and the topic of sequences and series. The book explains vector analysis (which includes dyads and tensors), the use of numerical analysis, probability statistics, and the Laplace transform theory. Physicists, engineers, chemists, biologists, and statisticians will find this book useful.

    • Lectures in General Algebra

      • 1st Edition
      • July 10, 2014
      • A. G. Kurosh
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 1 7 1 5 7
      • eBook
        9 7 8 1 4 8 3 1 4 9 5 7 8
      Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.

    • Theory of Automata

      • 1st Edition
      • July 10, 2014
      • Arto Salomaa
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 2 1 9 7 0
      • eBook
        9 7 8 1 4 8 3 1 5 4 3 9 8
      Theory of Automata deals with mathematical aspects of the theory of automata theory, with emphasis on the finite deterministic automaton as the basic model. All other models, such as finite non-deterministic and probabilistic automata as well as pushdown and linear bounded automata, are treated as generalizations of this basic model. The formalism chosen to describe finite deterministic automata is that of regular expressions. A detailed exposition regarding this formalism is presented by considering the algebra of regular expressions. This volume is comprised of four chapters and begins with a discussion on finite deterministic automata, paying particular attention to regular and finite languages; analysis and synthesis theorems; equivalence relations induced by languages; sequential machines; sequential functions and relations; definite languages and non-initial automata; and two-way automata. The next chapter describes finite non-deterministic and probabilistic automata and covers theorems concerning stochastic languages; non-regular stochastic languages; and probabilistic sequential machines. The book then introduces the reader to the algebra of regular expressions before concluding with a chapter on formal languages and generalized automata. Theoretical exercises are included, along with ""problems"" at the end of some sections. This monograph will be a useful resource for beginning graduate or advanced undergraduates of mathematics.

    • The Theory of Finitely Generated Commutative Semigroups

      • 1st Edition
      • July 10, 2014
      • L. Rédei
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 2 3 5 2 3
      • Hardback
        9 7 8 0 0 8 0 1 0 5 2 0 8
      • eBook
        9 7 8 1 4 8 3 1 5 5 9 4 4
      The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single "fundamental theorem" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before turning to a discussion of the problem of determining all the F-congruences as the fundamental problem of the proposed theory. The next chapter lays down the foundations of the theory by defining the kernel functions and the fundamental theorem. The elementary properties of the kernel functions are then considered, along with the ideal theory of free semimodules of finite rank. The final chapter deals with the isomorphism problem of the theory, which is solved by reducing it to the determination of the equivalent kernel functions. This book should be of interest to mathematicians as well as students of pure and applied mathematics.

    • The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics

      • 1st Edition
      • Volume 79
      • July 10, 2014
      • G. N. Polozhii
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 6 9 6 5 1
      • eBook
        9 7 8 1 4 8 3 1 8 5 4 6 0
      Pure and Applied Mathematics, Volume 79: The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics presents the numerical solution of two-dimensional and three-dimensional boundary-value problems of mathematical physics. This book focuses on the second-order and fourth-order linear differential equations. Organized into two chapters, this volume begins with an overview of ordinary finite-difference equations and the general solutions of certain specific finite-difference equations. This text then examines the various methods of successive approximation that are used exclusively for solving finite-difference equations. This book discusses as well the established formula of summary representation for certain finite-difference operators that are associated with partial differential equations of mathematical physics. The final chapter deals with the formula of summary representation to enable the researcher to write the solution of the corresponding systems of linear algebraic equations in a simple form. This book is a valuable resource for mathematicians and physicists.

    • A Many-Sorted Calculus Based on Resolution and Paramodulation

      • 1st Edition
      • July 10, 2014
      • Christoph Walther
      • English
      • Paperback
        9 7 8 0 2 7 3 0 8 7 1 8 2
      • eBook
        9 7 8 1 4 8 3 2 5 8 9 3 5
      A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving. This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewriting and unification. The completeness and soundness of the ?RP-calculus, sort theorem, and automated theorem prover for the ?RP-calculus are also elaborated. This publication is a good source for students and researchers interested in many-sorted calculus.

    • Elements of Analytical Dynamics

      • 1st Edition
      • July 10, 2014
      • Rudolph Kurth
      • I. N. Sneddon + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 1 9 3 0 4
      • eBook
        9 7 8 1 4 8 3 1 5 1 7 2 4
      Elements of Analytical Dynamics deals with dynamics, which studies the relationship between motion of material bodies and the forces acting on them. This book is a compilation of lectures given by the author at the Georgia and Institute of Technology and formed a part of a course in Topological Dynamics. The book begins by discussing the notions of space and time and their basic properties. It then discusses the Hamilton-Jacobi theory and Hamilton's principle and first integrals. The text concludes with a discussion on Jacobi's geometric interpretation of conservative systems. This book will be of direct use to graduate students of Mathematics with minimal background in Theoretical Mechanics.

    • An Introduction to Mathematical Analysis

      • 1st Edition
      • July 10, 2014
      • Robert A. Rankin
      • English
      • Paperback
        9 7 8 1 4 8 3 1 6 9 2 2 4
      • eBook
        9 7 8 1 4 8 3 1 8 5 0 3 3
      International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of functions of a single real variable. The title first covers the fundamental idea and assumptions in analysis, and then proceeds to tackling the various areas in analysis, such as limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. The book will be most useful to undergraduate students of mathematical analysis.

    • Regular Figures

      • 1st Edition
      • July 10, 2014
      • L. Fejes Tóth
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 1 9 0 1 4
      • eBook
        9 7 8 1 4 8 3 1 5 1 4 3 4
      Regular Figures concerns the systematology and genetics of regular figures. The first part of the book deals with the classical theory of the regular figures. This topic includes description of plane ornaments, spherical arrangements, hyperbolic tessellations, polyhedral, and regular polytopes. The problem of geometry of the sphere and the two-dimensional hyperbolic space are considered. Classical theory is explained as describing all possible symmetrical groupings in different spaces of constant curvature. The second part deals with the genetics of the regular figures and the inequalities found in polygons; also presented as examples are the packing and covering problems of a given circle using the most or least number of discs. The problem of distributing n points on the sphere for these points to be placed as far as possible from each other is also discussed. The theories and problems discussed are then applied to pollen-grains, which are transported by animals or the wind. A closer look into the exterior composition of the grain shows many characteristics of uniform distribution of orifices, as well as irregular distribution. A formula that calculates such packing density is then explained. More advanced problems such as the genetics of the protean regular figures of higher spaces are also discussed. The book is ideal for physicists, mathematicians, architects, and students and professors in geometry.

    • Lambda-Matrices and Vibrating Systems

      • 1st Edition
      • July 10, 2014
      • Peter Lancaster
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 1 8 5 4 3
      • eBook
        9 7 8 1 4 8 3 1 5 0 9 6 3
      Lambda-Matrices and Vibrating Systems presents aspects and solutions to problems concerned with linear vibrating systems with a finite degrees of freedom and the theory of matrices. The book discusses some parts of the theory of matrices that will account for the solutions of the problems. The text starts with an outline of matrix theory, and some theorems are proved. The Jordan canonical form is also applied to understand the structure of square matrices. Classical theorems are discussed further by applying the Jordan canonical form, the Rayleigh quotient, and simple matrix pencils with latent vectors in common. The book then expounds on Lambda matrices and on some numerical methods for Lambda matrices. These methods explain developments of known approximations and rates of convergence. The text then addresses general solutions for simultaneous ordinary differential equations with constant coefficients. The results of some of the studies are then applied to the theory of vibration by applying the Lagrange method for formulating equations of motion, after the formula establishing the energies and dissipation functions are completed. The book describes the theory of resonance testing using the stationary phase method, where the test is carried out by applying certain forces to the structure being studied, and the amplitude of response in the structure is measured. The book also discusses other difficult problems. The text can be used by physicists, engineers, mathematicians, and designers of industrial equipment that incorporates motion in the design.

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