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131.
132.
Robert Piziak 《Foundations of Physics》1990,20(6):651-665
A quadratic space is a generalization of a Hilbert space. The geometry of certain kinds of subspaces (closed, splitting, etc.) is approached from the purely lattice theoretic point of view. In particular, theorems of Mackey and Kaplansky are given purely lattice theoretic proofs. Under certain conditions, the lattice of closed elements is a quantum proposition system (i.e., a complete orthomodular atomistic lattice with the covering property). 相似文献
133.
134.
We study the limiting behavior of the solution of with a Neumann boundary condition or an appropriate Dirichlet condition. The analysis is based on “energy methods”. We assume that the initial data has a “transition layer structure”, i.e., u? ≈ ±+M 1 except near finitely many transition points. We show that, in the limit as ? → 0, the solution maintains its transition layer structure, and the transition points move slower than any power of ?. 相似文献
135.
We prove that a branched immersion of a surface with boundary into a differentiable manifold has no false branch points (in fact, no ramified points) if the immersion induces an isomorphism of fundamental groups and some other natural hypotheses are satisfied. This result has immediate applications to Plateau's problem.Work done while the first author was a visiting member of the Max-Planck-Institut für Mathematik at Bonn. Both authors acknowledge the support of Max-Planck-Institut für Mathematik, Bonn and Schwerpunkt Geometrie at Mathematisches Institut, University of Heidelberg 相似文献
136.
We study the linear system =Ax+Bu from a differential geometric point of view. It is well-known that controllability of the system is related to the one-parameter family of operators et
B. We use this to give a proof of the classical controllability conditions in terms of the differential geometry of certain curves in n. We then view (t)=Im(et
B) as a curve in appropriate Grassmannian and see that, in local coordinates, is an integral curve of the flow induced by a matrix Riccati equation. We obtain qualitative geometric conditions on that are equivalent to the controllability of the system. To get quantitiative results, we lift to a curve l' in a splitting space, a generalized Grassmannian, which has the advantage of being a reductive homogeneous space of the general linear group, GL(n). Explicit and simple expressions concerning the geometry of are computed in terms of the Lie algebra of GL(n), and these are related to the controllability of the system.James Wolper was a visiting professor in the Department of Mathematics at Texas Tech University while much of this research was conducted. He would like to express appreciation for the hospitality he received during his visit. 相似文献
137.
Robert Hermann 《Acta Appl Math》1988,12(1):35-78
This paper will attempt to unify diverse material from physics and engineering in terms of differential forms on manifolds. A variational system will be defined by means of a scalar-valued differential form on a manifold and an ideal in the Grassmann algebra of differential forms on that manifold to serve as constraints. Two types of extremal submanifolds will be defined. The first-called the Euler-Lagrange extremals-will be defined by a method that is the generalization of the classical methods in the calculus of variations. The second—a generalization of a method used by Cartan in his treatise Leçons sur les invariants intégraux-will define extremals as integral submanifolds of an exterior differential system invariently attached to the variational system. As examples, the variational systems attached to string theories in Riemannian manifolds and Yang-Mills fields will be discussed from this differential form point of view. Finally, as application, the differential geometric properties and definition of energy will be presented from the differential form point of view.This work was supported by a grant from the Applied Mathematics program of the National Science Foundation. 相似文献
138.
Robert Keener 《Probability Theory and Related Fields》1988,80(1):1-20
Summary Let P be a distribution in the plane and define the renewal measure R=P
*nwhere * denotes convolution. The main results of this paper are three term asymptotic expansions for R far from the origin. As an application, expansions are obtained for distributions in linear boundary crossing problems.Research supported by NSF grants MCS-8102080 and DMS-8504708 相似文献
139.
Robert J. Budzyński Sławomir Klimek Paweł Sadowski 《Communications in Mathematical Physics》1989,120(3):481-499
Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of 1 and develop elements of its representation theory. 相似文献
140.
In this paper we prove results in resonance scattering for the Schrödinger operatorP
v=–h
2+V, V being a smooth, short range potential onR
n
. More precisely, for energy near a trapping energy level 0 for the classical system defined by the Hamiltonianp(x,)=
2+V(x), we prove that the scattering phase and the scattering cross sections associated to (P
v, P0) have the Breit-Wigner form (Lorentzian line shape) in the limith0. 相似文献