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71.
We characterize the best model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct best model geometries in an appropriate sense – these are the maximally symmetric trees. The first theorem gives several equivalent conditions on a bounded valence, cocompact tree T without valence 1 vertices saying that T is maximally symmetric. The second theorem gives general constructions for maximally symmetric trees, showing for instance that every virtually free group has a maximally symmetric tree for a model geometry. 相似文献
72.
Zofia Stepien/snm> 《Geometriae Dedicata》2002,93(1):37-45
We prove the formality property of any homogeneous space G/G
generated by an automorphism of finite order of a compact simple Lie group G. 相似文献
73.
Matthias Birkner José Alfredo Ló pez-Mimbela Anton Wakolbinger 《Proceedings of the American Mathematical Society》2002,130(8):2431-2442
We present a probabilistic approach which proves blow-up of solutions of the Fujita equation in the critical dimension . By using the Feynman-Kac representation twice, we construct a subsolution which locally grows to infinity as . In this way, we cover results proved earlier by analytic methods. Our method also applies to extend a blow-up result for systems proved for the Laplacian case by Escobedo and Levine (1995) to the case of -Laplacians with possibly different parameters .
74.
Simon Gindikin Bernhard Krö tz 《Transactions of the American Mathematical Society》2002,354(8):3299-3327
In this paper we define a distinguished boundary for the complex crowns of non-compact Riemannian symmetric spaces . The basic result is that affine symmetric spaces of can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.
75.
In the last decades it was observed that Clifford algebras and geometric product provide a model for different physical phenomena. We propose an explanation of this observation based on the theory of bounded symmetric domains and the algebraic structure associated with them. The invariance of physical laws is a result of symmetry of the physical world that is often expressed by the symmetry of the state space for the system implying that this state space is a symmetric domain. For example, the ball of all possible velocities is a bounded symmetric domain. The symmetry on this ball follow from the symmetry of the space-time transformations between two inertial systems, which fixes the so-called symmetric velocity between them. The Lorenz transformations acts on the ball Sof symmetric velocities by conformal transformations. The ball Sis a spin ball (type IV in Cartan's classification). The Lie algebra of this ball is defined a triple product that is closely related to geometric product. The relativistic dynamic equations in mechanics and for the Lorenz force is described by this Lie algebra and the triple product. 相似文献
76.
Ngaiming Mok 《Compositio Mathematica》2002,132(3):289-309
Let be an irreducible bounded symmetric domain and Aut() be a torsion-free discrete group of automorphisms, X /. We study the problem of algebro-geometric and differential-geometric characterizations of certain compact holomorphic geodesic cycles S X. We treat special cases of the problem, pertaining to a situation in which S is a compact holomorphic curve, and to the case where is a classical domain dual to the hyperquadric. In both cases we consider algebro-geometric characterizations in terms of tangent subspaces. As a consequence we derive effective pinching theorems where certain complex submanifolds S X are proven to be totally geodesic whenever their scalar curvatures are pinched between certain computed universal constants, independent of the volume of the submanifold S, giving new examples of the gap phenomenon for the characterization of compact holomorphic geodesic cycles.Research funded by a CERG grant from Research Grants Council of Hong Kong. 相似文献
77.
1.引言19世纪Hamilton提出经典力学的一种基本的方程形式.记P=Mq表示动量,q表示位移,于是动能T=1/2(p,M-1 p),并将总能量H=T+V位能)表示为p,q的函数:于是经典力学的标准形式-Newton形式称为Hamilton正则方程.(1.1)是ZI维相空间或称辛空间中的相变量(PI,...,P。,ql;...,qn)'的一阶微分方程组.其中q-(ql,...;qrt)'是位置向量,dq,、I。。。。。q=i=(ql,...,qh)'是速度向量,dt'"""。'。'。。。l、。。d"q,....、,-,-… 相似文献
78.
Consider a closed Jackson type network in which each queue has a single exponential server. Assume that N customers are moving among k queues. We establish simple closed form bounds on the network throughput (both lower and upper), which are sharper than those that are currently available. Numerical evaluation indicates that the improvements are significant. 相似文献
79.
Miroslav Englis 《Proceedings of the American Mathematical Society》1999,127(11):3259-3268
Let be a Cartan domain of rank and genus and , , the Berezin transform on ; the number can be interpreted as a certain invariant-mean-value of a function around . We show that a Lebesgue integrable function satisfying , , must be -harmonic. In a sense, this result is reminiscent of Delsarte's two-radius mean-value theorem for ordinary harmonic functions on the complex -space , but with the role of radius played by the quantity .
80.
Genkai Zhang 《Acta Appl Math》2002,73(1-2):79-94
We give a brief survey on the study of constructions of invariant differential operators on Riemannian symmetric spaces and of combinatorial and analytical properties of their eigenvalues, and pose some open questions. 相似文献