Download or read book Higher Spinor Classes written by J. F. Jardine and published by American Mathematical Soc.. This book was released on 1994 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work defines the higher spinor classes of an orthogonal representation of a Galois group. These classes are higher-degree analogues of the Fröhlich spinor class, which quantify the difference between the Stiefel-Whitney classes of an orthogonal representation and the Hasse-Witt classes of the associated form. Jardine establishes various basic properties, including vanishing in odd degrees and an induction formula for quadratic field extensions. The methods used include the homotopy theory of simplicial presheaves and the action of the Steenrod algebra on mod 2 étale cohomology.
Download or read book Theory of Spinors and Its Application in Physics and Mechanics written by Vladimir A. Zhelnorovich and published by Springer Nature. This book was released on 2019-10-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a systematic exposition of the theory of spinors in finite-dimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in four-dimensional and three-dimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein–Dirac equations, nonlinear Heisenberg’s spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and post-graduate students of physical and mathematical specialties.
Download or read book Clifford Algebras and Spinors written by Pertti Lounesto and published by Cambridge University Press. This book was released on 2001-05-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.
Download or read book Christoffel Functions and Orthogonal Polynomials for Exponential Weights on 1 1 written by A. L. Levin and published by American Mathematical Soc.. This book was released on 1994 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bounds for orthogonal polynomials which hold on the 'whole' interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on [-1,1]. Also presented are uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.
Download or read book Inverse Nodal Problems Finding the Potential from Nodal Lines written by Ole H. Hald and published by American Mathematical Soc.. This book was released on 1996 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.
Download or read book Intersection Pairings on Conley Indices written by Henry L. Kurland and published by American Mathematical Soc.. This book was released on 1996 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is a careful and detailed study of the intersection pairing in the Conley index. The Conley index associates to an isolated invariant set of a semiflow (with some mild compactness conditions) a homotopy type of a space, constructed to be invariant under perturbations of the flow. The homology of this space is the homology Conley index. For a (two-sided) flow, each isolated invariant set has two indices defined: one for the forward flow, and one for the reverse. In general, there is no relationship between these two indices, but when the flow is on an orientable manifold, the two indices can be related by an intersection pairing. It is this pairing that receives a careful and detailed study in this memoir. Results are then applied to the motivating example of the work: the existence of transition layer behavior for two-point boundary value problems of singularly perturbed systems.
Download or read book Anticipative Girsanov Transformations and Skorohod Stochastic Differential Equations written by Rainer Buckdahn and published by American Mathematical Soc.. This book was released on 1994 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a concise exposition of recent developments in anticipative stochastic calculus. The anticipative calculus uses tools from differential calculus and distribution theory on Wiener space to analyze stochastic integrals with integrands which can anticipate the future of the Brownian integrator. In particular, the Skorohod integral, defined as a dual operator to the Wiener space derivative, and the anticipating Stratonovich integrals are fundamental.
Download or read book Shortest Paths for Sub Riemannian Metrics on Rank Two Distributions written by Wensheng Liu and published by American Mathematical Soc.. This book was released on 1995 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sub-Riemannian manifold ([italic capitals]M, E, G) consists of a finite-dimensional manifold [italic capital]M, a rank-two bracket generating distribution [italic capital]E on [italic capital]M, and a Riemannian metric [italic capital]G on [italic capital]E. All length-minimizing arcs on ([italic capitals]M, E, G) are either normal extremals or abnormal extremals. Normal extremals are locally optimal, i.e., every sufficiently short piece of such an extremal is a minimizer. The question whether every length-minimizer is a normal extremal was recently settled by R. G. Montgomery, who exhibited a counterexample. The present work proves that regular abnormal extremals are locally optimal, and, in the case that [italic capital]E satisfies a mild additional restriction, the abnormal minimizers are ubiquitous rather than exceptional. All the topics of this research report (historical notes, examples, abnormal extremals, Hamiltonians, nonholonomic distributions, sub-Riemannian distance, the relations between minimality and extremality, regular abnormal extremals, local optimality of regular abnormal extremals, etc.) are presented in a very clear and effective way.
Download or read book On the Correlation of Multiplicative and the Sum of Additive Arithmetic Functions written by Peter D. T. A. Elliott and published by American Mathematical Soc.. This book was released on 1994 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The correlation of multiplicative arithmetic functions on distinct arithmetic progressions and with values in the complex unit disc, cannot be continually near to its possible maximum unless each function is either very close to or very far from a generalized character. Moreover, under accessible condition the second possibility can be ruled out. As a consequence analogs of the standard limit theorems in probabilistic number theory are obtained with the classical single additive function on the integers replaced by a sum of two additive functions on distinct arithmetic progressions.
Download or read book Subgroup Lattices and Symmetric Functions written by Lynne M. Butler and published by American Mathematical Soc.. This book was released on 1994 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents foundational research on two approaches to studying subgroup lattices of finite abelian p-groups. The first approach is linear algebraic in nature and generalizes Knuth's study of subspace lattices. This approach yields a combinatorial interpretation of the Betti polynomials of these Cohen-Macaulay posets. The second approach, which employs Hall-Littlewood symmetric functions, exploits properties of Kostka polynomials to obtain enumerative results such as rank-unimodality. Butler completes Lascoux and Schützenberger's proof that Kostka polynomials are nonnegative, then discusses their monotonicity result and a conjecture on Macdonald's two-variable Kostka functions.
Download or read book Classification of Direct Limits of Even Cuntz Circle Algebras written by Huaxin Lin and published by American Mathematical Soc.. This book was released on 1995 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove a classification theorem for purely infinite C∗-algebras that is strong enough to show that the tensor products of two different irrational rotation algebras with the same even Cuntz algebra are isomorphic.
Download or read book Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics written by Svante Janson and published by American Mathematical Soc.. This book was released on 1994 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic]G[subscript italic]n, [subscript italic]p and [italic]G[subscript italic]n, [subscript italic]m as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Both normal and non-normal limits are obtained. As examples, applications are given to subgraph counts and to vertex degrees.
Download or read book Solution of the Truncated Complex Moment Problem for Flat Data written by Raúl E. Curto and published by American Mathematical Soc.. This book was released on 1996 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a matricial approach to the truncated complex moment problem, and apply it to the case of moment matrices of flat data type, for which the columns corresponding to the homogeneous monomials in [italic]z and [italic]z̄ of highest degree can be written in terms of monomials of lower degree. We discuss the connection between complex moment problems and the subnormal completion problem for 2-variable weighted shifts, and present in detail the construction of solutions for truncated complex moment problems associated with monomials of degrees one and two.
Download or read book Discretization of Homoclinic Orbits Rapid Forcing and Invisible Chaos written by Bernold Fiedler and published by American Mathematical Soc.. This book was released on 1996 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerically speaking, continuous time dynamical systems do not exist. Rather, a discretized version is studied and interpreted in analogy to the continuous time dynamical system. Over fixed finite time intervals, this analogy is quite close and well understood in terms of discretization errors and sophisticated discretization schemes. Over large or infinite time intervals, this analogy is not so clear, because discretization errors tend to accumulate exponentially with time. In this paper, we specifically investigate the correspondence between continuous and discrete time dynamical systems for homoclinic orbits. By definition, these are orbits which tend to the same stationary point for both large positive and large negative times.
Download or read book m KdV Solitons on the Background of Quasi Periodic Finite Gap Solutions written by Fritz Gesztesy and published by American Mathematical Soc.. This book was released on 1995 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the introductory section, we review the formulation of the Korteweg-de Vries (KdV) equation and of the modified KdV (mKdV) equation as a compatibility condition for a Lax pair of linear operators. We then illustrate Miura's transformation, which maps solutions of the mKdV into solutions of the KdV. We then give a general overview of the concept of soliton solutions relative to general backgrounds, and of the single and double commutation methods. Finally, we present the main results of the article. To avoid the clutter of too many technical details, the paper is organized in four sections and five appendices.
Download or read book Molecular Propagation through Electron Energy Level Crossings written by George Allan Hagedorn and published by American Mathematical Soc.. This book was released on 1994 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal results of this paper involve the extension of the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through generic, minimal multiplicity electron energy level crossings. The Born-Oppenheimer approximation breaks down at electron energy level crossings, which are prevalent in molecular systems. We classify generic, minimal multiplicity level crossings and derives a normal form for the electron Hamiltonian near each type of crossing. We then extend the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through each type of electron energy level crossing.
Download or read book Markov Fields over Countable Partially Ordered Sets Extrema and Splitting written by I. V. Evstigneev and published by American Mathematical Soc.. This book was released on 1994 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various notions of the Markov property relative to a partial ordering have been proposed by both physicists and mathematicians. This work develops techniques for stying Markov fields on partially ordered sets. We introduce random transformations of the index set which preserves the Markov property of the field. These transformations yield new classes of Markov fields starting from relatively simple ones. Examples include a model for crack formation and a model for the distribution of fibres in a composite material.
