Download or read book Behavior of Distant Maximal Geodesics in Finitely Connected Complete 2 dimensional Riemannian Manifolds written by Takashi Shioya 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: This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas.
Download or read book The Geometry of Total Curvature on Complete Open Surfaces written by Katsuhiro Shiohama and published by Cambridge University Press. This book was released on 2003-11-13 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.
Download or read book Finite Rational Matrix Groups written by Gabriele Nebe and published by American Mathematical Soc.. This book was released on 1995 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of finite rational matrix groups reduces to the investigation of the maximal finite irreducible matrix groups and their natural lattices, which often turn out to have rather beautiful geometric and arithmetic properties. This book presents a full classification in dimensions up to 23 and with restrictions in dimensions and p +1 and p-1 for all prime numbers p. Nonmaximal finite groups might act on several types of lattices and therefore embed into more than one maximal finite group. This gives rise to a simplicial complex interrelating the maximal finite groups and measuring the complexity of the dimension. Group theory, integral representation theory, arithmetic theory of quadratic forms and algorithmic methods are used.
Download or read book Completely Prime Maximal Ideals and Quantization written by William M. McGovern and published by American Mathematical Soc.. This book was released on 1994 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let [Fraktur lowercase]g be a complex simple Lie algebra of classical type, [italic capital]U([Fraktur lowercase]g) its enveloping algebra. We classify the completely prime maximal spectrum of [italic capital]U([Fraktur lowercase]g). We also construct some interesting algebra extensions of primitive quotients of [italic capital]U([Fraktur lowercase]g), and compute their Goldie ranks, lengths as bimodules, and characteristic cycles. Finally, we study the relevance of these algebras to D. Vogan's program of "quantizing" covers of nilpotent orbits [script]O in [Fraktur lowercase]g[superscript]*.
Download or read book Pseudofunctors on Modules with Zero Dimensional Support written by I-Chiau Huang and published by American Mathematical Soc.. This book was released on 1995 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudofunctors with values on modules with zero dimensional support are constructed over the formally smooth category and residually finite category. Combining those pseudofunctors, a pseudofunctor over the category whose objects are Noetherian local rings and whose morphisms are local with finitely generated residue field extensions is constructed.
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 On Finite Groups and Homotopy Theory written by Ran Levi 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: In part 1 we study the homology, homotopy, and stable homotopy of [capital Greek]Omega[italic capital]B[lowercase Greek]Pi[up arrowhead][over][subscript italic]p, where [italic capital]G is a finite [italic]p-perfect group. In part 2 we define the concept of resolutions by fibrations over an arbitrary family of spaces.
Download or read book The Cohen Macaulay and Gorenstein Rees Algebras Associated to Filtrations written by Shirō Gotō and published by American Mathematical Soc.. This book was released on 1994 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first, this volume was intended to be an investigation of symbolic blow-up rings for prime ideals defining curve singularities. The motivation for that has come from the recent 3-dimensional counterexamples to Cowsik's question, given by the authors and Watanabe: it has to be helpful, for further researches on Cowsik's question and a related problem of Kronecker, to generalize their methods to those of a higher dimension. However, while the study was progressing, it proved apparent that the framework of Part I still works, not only for the rather special symbolic blow-up rings but also in the study of Rees algebras R(F) associated to general filtrations F = {F[subscript]n} [subscript]n [subscript][set membership symbol][subscript bold]Z of ideals. This observation is closely explained in Part II of this volume, as a general ring-theory of Rees algebras R(F). We are glad if this volume will be a new starting point for the further researchers on Rees algebras R(F) and their associated graded rings G(F).
Download or read book The Full Set of Unitarizable Highest Weight Modules of Basic Classical Lie Superalgebras written by Hans Plesner Jakobsen and published by American Mathematical Soc.. This book was released on 1994 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work contains a complete description of the set of all unitarizable highest weight modules of classical Lie superalgebras. Unitarity is defined in the superalgebraic sense, and all the algebras are over the complex numbers. Part of the classification determines which real forms, defined by anti-linear anti-involutions, may occur. Although there have been many investigations for some special superalgebras, this appears to be the first systematic study of the problem.
Download or read book Random Perturbations of Hamiltonian Systems written by Mark Iosifovich Freĭdlin and published by American Mathematical Soc.. This book was released on 1994 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random perturbations of Hamiltonian systems in Euclidean spaces lead to stochastic processes on graphs, and these graphs are defined by the Hamiltonian. In the case of white-noise type perturbations, the limiting process will be a diffusion process on the graph. Its characteristics are expressed through the Hamiltonian and the characteristics of the noise. Freidlin and Wentzell calculate the process on the graph under certain conditions and develop a technique which allows consideration of a number of asymptotic problems. The Dirichlet problem for corresponding elliptic equations with a small parameter are connected with boundary problems on the graph.
Download or read book Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity I written by Eldar Straume and published by American Mathematical Soc.. This book was released on 1996 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. By enlarging this simple numerical invariant, but suitably restricted, one gradually increases the complexity of orbit structures of transformation groups. This is a natural program for classical space forms, which traditionally constitute the first canonical family of testing spaces, due to their unique combination of topological simplicity and abundance in varieties of compact differentiable transformation groups.
Download or read book Some Special Properties of the Adjunction Theory for 3 Folds in mathbb P 5 written by Mauro Beltrametti and published by American Mathematical Soc.. This book was released on 1995 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work studies the adjunction theory of smooth 3-folds in P]5. Because of the many special restrictions on such 3-folds, the structure of the adjunction theoretic reductions are especially simple, e.g. the 3-fold equals its first reduction, the second reduction is smooth except possibly for a few explicit low degrees, and the formulae relating the projective invariants of the given 3-fold with the invariants of its second reduction are very explicit. Tables summarizing the classification of such 3-folds up to degree 12 are included. Many of the general results are shown to hold for smooth projective n-folds embedded in P]N with N 2n -1.
Download or read book The Major Counting of Nonintersecting Lattice Paths and Generating Functions for Tableaux written by Christian Krattenthaler and published by American Mathematical Soc.. This book was released on 1995 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of counting nonintersecting lattice paths by the major index and its generalizations is developed. We obtain determinantal expressions for the corresponding generating functions for families of nonintersecting lattice paths with given starting points and given final points, where the starting points lie on a line parallel to [italic]x + [italic]y = 0. In some cases these determinants can be evaluated to result in simple products. As applications we compute the generating function for tableaux with [italic]p odd rows, with at most [italic]c columns, and with parts between 1 and [italic]n. Moreover, we compute the generating function for the same kind of tableaux which in addition have only odd parts. We thus also obtain a closed form for the generating function for symmetric plane partitions with at most [italic]n rows, with parts between 1 and [italic]c, and with [italic]p odd entries on the main diagonal. In each case the result is a simple product. By summing with respect to [italic]p we provide new proofs of the Bender-Knuth and MacMahon (ex-)conjectures, which were first proved by Andrews, Gordon, and Macdonald. The link between nonintersecting lattice paths and tableaux is given by variations of the Knuth correspondence.
Download or read book Deformation Theory of Pseudogroup Structures written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 1966 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Iterating the Cobar Construction written by Justin R. Smith and published by American Mathematical Soc.. This book was released on 1994 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a new invariant of a CW-complex called the m-structure and uses it to perform homotopy-theoretic computations. The m-structure of a space encapsulates the coproduct structure, as well as higher-coproduct structures that determine Steenrod-operations. Given an m-structure on the chain complex of a reduced simplicial complex of a pointed simply-connected space, one can equip the cobar construction of this chain-complex with a natural m-structure. This result allows one to form iterated cobar constructions that are shown to be homotopy equivalent to iterated loop-spaces.
Download or read book An Extension of the Galois Theory of Grothendieck written by André Joyal and published by American Mathematical Soc.. This book was released on 1984 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we compare, in a precise way, the concept of Grothendieck topos to the classical notion of topological space. The comparison takes the form of a two-fold extension of the idea of space.
Download or read book Principal Currents for a Pair of Unitary Operators written by Joel D. Pincus and published by American Mathematical Soc.. This book was released on 1994 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of interrelationships between rectifiable currents associated to n-tuples of operators with commutators or multicommutators satisfying trace class conditions is the exploration of a non commutative spectral theory in which there is still a significant degree of localization at points in the current support - viewed as a non commutative spectrum. This memoir is a systematic development of the theory of principal functions in this the noncommutative case, and it generalizes extensive previous work of R. Carey and Pincus.
