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Ming Liao 《Probability Theory and Related Fields》1993,96(2):261-281
Summary We study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in SL(n, R) or GL(n, R). These compact spaces are called boundaries of SL(n, R), which include SO(n), the flag manifold, the sphereS
n–1 and the Grassmannians. The one point motions of these flows are Brownian motions. For almost every, , we determine the set of stable points. This is a random open set whose complement has zero Lebesgue measure. The distance between any two points in the same component of this set tends to zero exponentially fast under the flow. The Lyapunov exponents at stable points are computed explicitly. We apply our results to a stochastic flow onS
n–2 generated by a stochastic differential equation which exhibits some nice symmetry.Research supported in part by Hou Yin Dong Education Foundation of China On leave from Nankai University, Tianjin, China 相似文献
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《Journal of Algebra》2002,247(2):577-615
For coherent families of crystals of affine Lie algebras of type B(1)n, D(1)n, A(2)2n, and D(2)n + 1 we describe the combinatorial R matrix using column insertion algorithms for B, C, D Young tableaux. This is a continuation of previous work by the authors (2000, in “Physical Combinatorics” (M. Kashiwara and T. Miwa, Eds.), Birkhäuser, Boston). 相似文献
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We characterize Lp norms of functions onR
n for 1<p<∞ in terms of their Gabor coefficients. Moreover, we use the Carleson-Hunt theorem to show that the Gabor expansions
of Lp functions converge to the functions almost everywhere and in Lp for 1<p<∞. In L1 we prove an analogous result: the Gabor expansions converge to the functions almost everywhere and in L1 in a certain Cesàro sense. Consequently, we are able to establish that a large class of Gabor families generate Banach frames
for Lp (R
n) when 1≤p<∞. 相似文献
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光滑映射芽的有限决定性是奇点理论中一个重要专题.对函数芽的有限决定性问题,主要是在右等价群及其一些子群作用下来讨论的.本文在[1]和[4]的基础上讨论函数芽在右等价群的正规子群Rr^*(S;n)作用下的有限决定性,并组出函数芽有限Rr^*(S;n)-决定的一个充分必要条件. 相似文献
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E. I. Gordon 《Siberian Mathematical Journal》1988,29(2):198-210
Gorkii. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 2, pp. 45–59, March–April, 1988. 相似文献
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It is known that a ring R is left Noetherian if and only if every left R-module has an injective (pre)cover. We show that (1) if R is a right n-coherent ring, then every right R-module has an (n, d)-injective (pre)cover; (2) if R is a ring such that every (n, 0)-injective right R-module is n-pure extending, and if every right R-module has an (n, 0)-injective cover, then R is right n-coherent. As applications of these results, we give some characterizations of (n, d)-rings, von Neumann regular rings and semisimple rings. 相似文献
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For given graphs , , the -color Ramsey number, denoted by , is the smallest integer such that if we arbitrarily color the edges of a complete graph of order with colors, then it always contains a monochromatic copy of colored with , for some . Let be a cycle of length and a star of order . In this paper, firstly we give a general upper bound of . In particular, for the 3-color case, we have and this bound is tight in some sense. Furthermore, we prove that for all and , and if is a prime power, then the equality holds. 相似文献
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D. Suryanarayana 《Aequationes Mathematicae》1978,18(1-2):322-329
In this paper, we discuss the pairs (f, h) of arithmetical functions satisfying the functional equation in the title, whereF is the product off andh under the Dirichlet convolution; that is,F(n) = Σ d|n ?(d)h(n/d) andS(m n) = Σd|(m, n) ?(d)h(n/d). The well-known Hölder's identity is a special case of this functional equation (?(n) =n, h(n) = μ(n)). We also generalize the functional equation in the title to any arbitrary regular arithmetical convolution and discuss the pairs of solutions (f, h) of the generalized functional equation and pose some problems relating to the characterization of all pairs of solutions. 相似文献
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Liang-yun Zhang 《Siberian Mathematical Journal》2006,47(4):767-778
Given an (H,R)-Lie coalgebra Γ, we construct (H,R T )-Lie coalgebra ΓT through a right cocycle T, where (H,R) is a triangular Hopf algebra, and prove that there exists a bijection between the set of (H,R)-Lie coalgebras and the set of ordinary Lie coalgebras. We also show that if (L, [, ], Δ, R) is an (H,R)-Lie bialgebra of an ordinary Lie algebra then (L T , [, ], ΔT, R T ) is an (H,R T )-Lie bialgebra of an ordinary Lie algebra. 相似文献
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Dragomir Ž. Djoković 《Israel Journal of Mathematics》1977,28(1-2):175-176
IfG is a connected real Lie group and π:G→Aut (V) a continuous irreducible finite-dimensional real representation then we show that π(G) is closed in Aut(V). A similar result is valid in the complex case. 相似文献
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