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Author : C. T. Dodson
Publisher : Unknown
Page : 264 pages
File Size : 45,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401577773
Author : C. T. J. Dodson
Publisher : Unknown
Page : 244 pages
File Size : 54,7 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39076006533298
Author : C.T. Dodson
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 54,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401577762
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown'The point of a Pin'. van Gulik's TheChinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author : Dovermann Karl Heinz
Publisher : #N/A
Page : 232 pages
File Size : 54,8 Mb
Release : 1992-04-30
Category : Electronic
ISBN : 9789814556132
The articles in the proceedings are closely related to the lectures presented at the topology conference held at the University of Hawaii, August 12-18, 1990. These cover recent results in algebraic topology, algebraic transformation groups, real algebraic geometry, low-dimensional topology, and Nielsen Fixed Point Theory.
Author : Krishan L. Duggal,Ramesh Sharma
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 42,6 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9781461553151
This book provides an upto date information on metric, connection and curva ture symmetries used in geometry and physics. More specifically, we present the characterizations and classifications of Riemannian and Lorentzian manifolds (in particular, the spacetimes of general relativity) admitting metric (i.e., Killing, ho mothetic and conformal), connection (i.e., affine conformal and projective) and curvature symmetries. Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of a comprehensive collection of the works of a very large number of researchers on all the above mentioned symmetries. (b) We have aimed at bringing together the researchers interested in differential geometry and the mathematical physics of general relativity by giving an invariant as well as the index form of the main formulas and results. (c) Attempt has been made to support several main mathematical results by citing physical example(s) as applied to general relativity. (d) Overall the presentation is self contained, fairly accessible and in some special cases supported by an extensive list of cited references. (e) The material covered should stimulate future research on symmetries. Chapters 1 and 2 contain most of the prerequisites for reading the rest of the book. We present the language of semi-Euclidean spaces, manifolds, their tensor calculus; geometry of null curves, non-degenerate and degenerate (light like) hypersurfaces. All this is described in invariant as well as the index form.
Author : C. T. J. Dodson,C.T. Dodson,P.E. Parker,Phillip E. Parker
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 42,5 Mb
Release : 1997-01-31
Category : Mathematics
ISBN : 0792342933
This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. We show how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that we can compute from these. Our approach is to mix illustrative examples with those proofs that actually develop transferable calculational aids. We give extensive appendices with notes on background material, extensive tables of data, and a thorough index. Audience: Graduate students and professionals in mathematics and physics.
Author : L.A. Cordero,C.T. Dodson,Manuel de León
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400912656
It isn't that they can't see the solution. It is Approach your problems from the right end and begin with the answers. Then one day, that they can't see the problem perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chillese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author : Michael Heller
Publisher : World Scientific
Page : 160 pages
File Size : 42,5 Mb
Release : 1992-04-15
Category : Science
ISBN : 9789814506038
The book's principal aim is to clarify fundamental concepts, decipher mathematical structures used to model space-time and relativistic worlds, and to disclose their physical meaning. After each chapter, philosophical implications of the presented material are commented upon. Both special and general theories of relativity are presented in the book with the stress on their global aspects. Although global mathematical methods are extensively used throughout the book, the definitions of new concepts, short comments and examples make reading smooth without the need to consult other textbooks or review papers. Contents:Manifold Model of Space-TimeRelativistic Model of Space-TimeMethod of Fibre BundlesThe Frame Bundle and General RelativityThe Cosmological ProblemGeometry of the Standard Cosmological ModelBibliographical EssayAppendix. Evolution of Dynamical Space-Time TheoriesReferencesSymbol IndexAuthor and Subject Index Readership: Cosmologists, astronomers and theoretical physicists. keywords:Cosmology;Universe;Standard Cosmological Model;Space-Time;General Relativity;Special Relativity;Geometry of Space-Time;Differential Geometry;Fibre Bundles;Methodological Questions of Cosmology;Philosophy of Cosmology
Author : Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 40,5 Mb
Release : 1999
Category : Mathematics
ISBN : 079236001X
This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework.
Author : Jozef Kelemen
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 46,9 Mb
Release : 1991-08-28
Category : Computers
ISBN : 3540545077
This volume contains 6 invited lectures and 13 submitted contributions to the scientific programme of the international workshop Fundamentals of Artificial Intelligence Research, FAIR '91, held at Smolenice Castle, Czechoslovakia, September 8-12, 1991, under the sponsorship of the European Coordinating Committee for Artificial Intelligence, ECCAI. FAIR'91, the first of an intended series of international workshops, addresses issues which belong to the theoretical foundations of artificial intelligence considered as a discipline focused on concise theoretical description of some aspects of intelligence by toolsand methods adopted from mathematics, logic, and theoretical computer science. The intended goal of the FAIR workshops is to provide a forum for the exchange of ideas and results in a domain where theoretical models play an essential role. It is felt that such theoretical studies, their development and their relations to AI experiments and applications have to be promoted in the AI research community.
Author : C. T. J. Dodson,Timothy Poston
Publisher : Springer Science & Business Media
Page : 449 pages
File Size : 41,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783642105142
This treatment of differential geometry and the mathematics required for general relativity makes the subject accessible, for the first time, to anyone familiar with elementary calculus in one variable and with some knowledge of vector algebra. The emphasis throughout is on the geometry of the mathematics, which is greatly enhanced by the many illustrations presenting figures of three and more dimensions as closely as the book form will allow.
Author : M. Crampin,F. A. E. Pirani
Publisher : Cambridge University Press
Page : 408 pages
File Size : 46,9 Mb
Release : 1986
Category : Mathematics
ISBN : 0521231906
An introduction to geometrical topics used in applied mathematics and theoretical physics.
Author : R. Miron
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 54,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9789401733380
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.
Author : Pei-Chu Hu,Chung-Chun Yang
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 46,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401592994
The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.
Author : L. Sabinin
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401144919
During the last twenty-five years quite remarkable relations between nonas sociative algebra and differential geometry have been discovered in our work. Such exotic structures of algebra as quasigroups and loops were obtained from purely geometric structures such as affinely connected spaces. The notion ofodule was introduced as a fundamental algebraic invariant of differential geometry. For any space with an affine connection loopuscular, odular and geoodular structures (partial smooth algebras of a special kind) were introduced and studied. As it happened, the natural geoodular structure of an affinely connected space al lows us to reconstruct this space in a unique way. Moreover, any smooth ab stractly given geoodular structure generates in a unique manner an affinely con nected space with the natural geoodular structure isomorphic to the initial one. The above said means that any affinely connected (in particular, Riemannian) space can be treated as a purely algebraic structure equipped with smoothness. Numerous habitual geometric properties may be expressed in the language of geoodular structures by means of algebraic identities, etc.. Our treatment has led us to the purely algebraic concept of affinely connected (in particular, Riemannian) spaces; for example, one can consider a discrete, or, even, finite space with affine connection (in the form ofgeoodular structure) which can be used in the old problem of discrete space-time in relativity, essential for the quantum space-time theory.