共查询到20条相似文献,搜索用时 390 毫秒
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L Foissy 《Bulletin des Sciences Mathématiques》2003,127(6):505-548
We introduce a functor from the category of braided spaces into the category of braided Hopf algebras which associates to a braided space V a braided Hopf algebra of planar rooted trees . We show that the Nichols algebra of V is a subquotient of . We construct a Hopf pairing between and , generalising one of the results of [Bull. Sci. Math. 126 (2002) 193-239]. When the braiding of c is given by c(vi⊗vj)=qi,jvj⊗vi, we obtain a quantification of the Hopf algebras introduced in [Bull. Sci. Math. 126 (2002) 193-239; 126 (2002) 249-288]. When qi,j=qai,j, with q an indeterminate and (ai,j)i,j the Cartan matrix of a semi-simple Lie algebra , then is a subquotient of . In this case, we construct the crossed product of with a torus and then the Drinfel'd quantum double of this Hopf algebra. We show that is a subquotient of . 相似文献
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R. Nair 《Indagationes Mathematicae》2003,14(2):233-240
Let a = (aii=1∞ be a strictly increasing sequence of natural numbers and let be a space of Lebesgue measurable functions defined on [0,1). Let <y> denote the fractional part of the real number y. We say that a is an ∗ sequence if for each f ?
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《Advances in Mathematics》2003,174(2):227-235
A set of the form , where is convex and denotes the integer lattice, is called a convex lattice set. It is known that the Helly number of d-dimensional convex lattice sets is 2d. We prove that the fractional Helly number is only d+1: For every d and every α∈(0,1] there exists β>0 such that whenever F1,…,Fn are convex lattice sets in such that for at least index sets I⊆{1,2,…,n} of size d+1, then there exists a (lattice) point common to at least βn of the Fi. This implies a (p,d+1)-theorem for every p?d+1; that is, if is a finite family of convex lattice sets in such that among every p sets of , some d+1 intersect, then has a transversal of size bounded by a function of d and p. 相似文献
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Mitsuru Uchiyama 《Journal of Functional Analysis》2006,231(1):221-244
Let P+ be the set of all non-negative operator monotone functions defined on [0,∞), and put . Then and . For a function and a strictly increasing function h we write if is operator monotone. If and and if and , then . We will apply this result to polynomials and operator inequalities. Let and be non-increasing sequences, and put for t≧a1 and for t≧b1. Then v+?u+ if m≦n and : in particular, for a sequence of orthonormal polynomials, (pn-1)+?(pn)+. Suppose 0<r,p and s=0 or 1≦s≦1+p/r. Then 0≦A≦B implies for 0<α≦r/(p+r). 相似文献
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Let be the anticipating smooth semimartingale and be its generalized local time. In this paper, we give some estimates about the quasi sure property of Xt and its quadratic variation process t〈X〉. We also study the fractional smoothness of and prove that the quadratic variation process of can be constructed as the quasi sure limit of the form , where is a sequence of subdivisions of [a,b], , i=0,1,…,n2. 相似文献
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Mirko Lepovi? 《Discrete Mathematics》2007,307(6):730-738
Let G be a simple graph of order n. Let and , where a and b are two nonzero integers and m is a positive integer such that m is not a perfect square. We say that Ac=[cij] is the conjugate adjacency matrix of the graph G if cij=c for any two adjacent vertices i and j, for any two nonadjacent vertices i and j, and cij=0 if i=j. Let PG(λ)=|λI-A| and denote the characteristic polynomial and the conjugate characteristic polynomial of G, respectively. In this work we show that if then , where denotes the complement of G. In particular, we prove that if and only if PG(λ)=PH(λ) and . Further, let Pc(G) be the collection of conjugate characteristic polynomials of vertex-deleted subgraphs Gi=G?i(i=1,2,…,n). If Pc(G)=Pc(H) we prove that , provided that the order of G is greater than 2. 相似文献
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In this paper we study the existence and qualitative property of standing wave solutions for the nonlinear Schrödinger equation with E being a critical frequency in the sense that . We show that if the zero set of W−E has several isolated connected components Zi(i=1,…,m) such that the interior of Zi is not empty and ∂Zi is smooth, then for ?>0 small there exists, for any integer k,1?k?m, a standing wave solution which is trapped in a neighborhood of , where is any given subset of . Moreover the amplitude of the standing wave is of the level . This extends the result of Byeon and Wang (Arch. Rational Mech. Anal. 165 (2002) 295) and is in striking contrast with the non-critical frequency case , which has been studied extensively in the past 20 years. 相似文献
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Reza Sazeedeh 《Journal of Pure and Applied Algebra》2008,212(1):275-280
Let R=?n∈N0Rn be a Noetherian homogeneous ring with local base ring (R0,m0) and irrelevant ideal R+, let M be a finitely generated graded R-module. In this paper we show that is Artinian and is Artinian for each i in the case where R+ is principal. Moreover, for the case where , we prove that, for each i∈N0, is Artinian if and only if is Artinian. We also prove that is Artinian, where and c is the cohomological dimension of M with respect to R+. Finally we present some examples which show that and need not be Artinian. 相似文献
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Estimation of the location parameters of a p×1 random vector with a spherically symmetric distribution is considered under quadratic loss. The conditions of Brandwein and Strawderman [Ann. Statist. 19(1991) 1639-1650] under which estimators of the form dominate are (i) where -h is superharmonic, (ii) is nonincreasing in R, where has a uniform distribution in the sphere centered at with a radius R, and (iii) . In this paper, we not only drop their condition (ii) to show the dominance of over but also obtain a new bound for a which is sometimes better than that obtained by Brandwein and Strawderman. Specifically, the new bound of a is 0<a<[μ1/(p2μ-1)][1-(p-1)μ1/(pμ-1μ2)]-1 with for i=-1,1,2. The generalization to concave loss functions is also considered. Additionally, we investigate estimators of the location parameters when the scale is unknown and the observation contains a residual vector. 相似文献
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In this paper, we develop a stochastic calculus related to a fractional Brownian sheet as in the case of the standard Brownian sheet. Let be a fractional Brownian sheet with Hurst parameters H=(H1,H2), and (2[0,1],B(2[0,1]),μ) a measure space. By using the techniques of stochastic calculus of variations, we introduce stochastic line integrals along all sufficiently smooth curves γ in 2[0,1], and four types of stochastic surface integrals: , i=1,2, , , , . As an application of these stochastic integrals, we prove an Itô formula for fractional Brownian sheet with Hurst parameters H1,H2∈(1/4,1). Our proof is based on the repeated applications of Itô formula for one-parameter Gaussian process. 相似文献
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Joachim Toft 《Bulletin des Sciences Mathématiques》2003,127(2):101-132
We study , of all such that for every ?∈C∞0, where denotes the twisted convolution. We prove that certain boundedness for are completely determined of the behaviour for a at origin, for example that , and that if a(0)<∞, then a∈L2∩L∞. We use the results in order to determine wether positive pseudo-differential operators belong to certain Schatten-casses or not. 相似文献