共查询到20条相似文献,搜索用时 546 毫秒
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Ⅰ.組合数級数与它的和由组合公式: C_x~r=x(x-1)(x-2)…(x-r+1)/r!, C_(ax+b)~r=(ax+b)(ax+b-1)(ax+b-2)…(ax+b-r+1)/r!, C_(a_0x~s+a_1x~(s-1)+…+a_s)~r=(a_0x~s+a_1x~(s-1)+…+a_s)..(a_0x~s+a_1x~(s-1)+…+ a_s-1)(a_0x~s++a_1x~(s-1)+…+a_s-2)… ..(a_0x~s+a_1x~(s-1)+…+a_s-r+1)/r!, 可知C_x~r,C_(ax+b)~r为x的r次函数,C_(a_0x~s+a_1x~(s-1)+…+a_s)~r为x的rs次函数。因此当x取連續整数时,C_x~r,c_(ax+b)~r的数列是r阶等差級数;C_(a_0x~s+a_1x~(s-1)+…+as)~r的数列是rs阶等差級数。或者說:从連續整数或等差級数(x取連續整数时ax+b的数列是等差級数)中取r的組合数的数列是r阶等差級数;从s阶等差級数(x取連續整数时a_0x~s+a_1x~(s-1)+…+a_s的数列是s阶等差級数)中取r的組合数的数列是rs阶等差級数。 相似文献
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Don Hadwin 《Journal of Functional Analysis》2009,256(7):2027-2068
The notion of topological free entropy dimension of n-tuple of elements in a unital C∗ algebra was introduced by Voiculescu. In the paper, we compute topological free entropy dimension of one self-adjoint element and topological free orbit dimension of one self-adjoint element in a unital C∗ algebra. We also calculate the values of topological free entropy dimensions of any families of self-adjoint generators of some unital C∗ algebras, including irrational rotation C∗ algebra, UHF algebra, and minimal tensor product of two reduced C∗ algebras of free groups. 相似文献
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We show that a monomial ideal I in a polynomial ring S has projective dimension ≤ 1 if and only if the minimal free resolution of S∕I is supported on a graph that is a tree. This is done by constructing specific graphs which support the resolution of the S∕I. We also provide a new characterization of quasi-trees, which we use to give a new proof to a result by Herzog, Hibi, and Zheng which characterizes monomial ideals of projective dimension 1 in terms of quasi-trees. 相似文献
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We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on Rn. We show that the classical probability entropy dimension of a measure is related with diverse other notions of dimension. First, it can be viewed as a kind of fractal dimension. Second, if one extends Bochner's inequalities to a measure by requiring that microstates around this measure asymptotically satisfy the classical Bochner's inequalities, then we show that the classical probability entropy dimension controls the rate of increase of optimal constants in Bochner's inequality for a measure regularized by convolution with the Gaussian law as the regularization is removed. We introduce a free analogue of the Bochner inequality and study the related free entropy dimension quantity. We show that it is greater or equal to the non-microstates free entropy dimension. 相似文献
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MichalDOST/~L DonHADWIN 《数学学报(英文版)》2003,19(3):419-472
In this paper we define a very simple invariant η(V^-) for a k-tuple V^-of unitaries in a finite factor von Neumann algebra, and we show how this invariant can replace free entropy in many of the important applications. We also introduce a notion of metric free entropy and some related concepts.We include proofs, using η, of the theorems of Liming Ge and of D. Voiculescu, respectively, on the primeness of and on the absence of Cartan snbalgebras in the noncommutative free group factors. 相似文献
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L. Yu. Polyakova 《Siberian Mathematical Journal》2007,48(6):1038-1045
We construct a free resolution for a free partially commutative monoid and, using this resolution, estimate the homological dimension of the monoid. 相似文献
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随机微分方程dX_t=(δf~2(t)-h(t)X_t)dt+2f(t) │X_t│~(1/2)dBt,(X_0=x,δ>0)的解X_t是一种推广的δ(δ>0)维Bessel过程.文章对于任意停时τ给出了‖sup0≤t≤τη(t)X_t‖p的L~p估计,其中η:R_+→R_+是一个R+上的可微函数,而且满足微分方程dη/dt-h(t)η=-η~2f~2(t),η(0)=1. 相似文献
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In the current article, we prove the crossed product C*-algebra by a Rokhlin action of finite group on a strongly quasidiagonal C*-algebra is strongly quasidiagonal again. We also show that a just-infinite C*-algebra is quasidiagonal if and only if it is inner quasidiagonal. Finally, we compute the topological free entropy dimension in just-infinite C*-algebras. 相似文献
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G. C. Bell A. N. Dranishnikov 《Transactions of the American Mathematical Society》2006,358(11):4749-4764
We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite-dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpotent and polycyclic groups in terms of their Hirsch length. We are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups, amalgamated free products and the hyperbolization of metric spaces possessing the Higson property.
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Kenley Jung 《Geometric And Functional Analysis》2007,17(4):1180-1200
Suppose F is a finite tuple of selfadjoint elements in a tracial von Neumann algebra M. For α > 0, F is α-bounded if where is the free packing α-entropy of F introduced in [J3]. M is said to be strongly 1-bounded if M has a 1-bounded finite tuple of selfadjoint generators F such that there exists an with . It is shown that if M is strongly 1-bounded, then any finite tuple of selfadjoint generators G for M is 1-bounded and δ0(G) ≤ 1; consequently, a strongly 1-bounded von Neumann algebra is not isomorphic to an interpolated free group factor and δ0 is an invariant for these algebras. Examples of strongly 1-bounded von Neumann algebras include (separable) II
1-factors which have property Γ, have Cartan subalgebras, are non-prime, or the group von Neumann algebras of . If M and N are strongly 1-bounded and M ∩ N is diffuse, then the von Neumann algebra generated by M and N is strongly 1-bounded. In particular, a free product of two strongly 1-bounded von Neumann algebras with amalgamation over
a common, diffuse von Neumann subalgebra is strongly 1-bounded. It is also shown that a II
1-factor generated by the normalizer of a strongly 1-bounded von Neumann subalgebra is strongly 1-bounded.
Received: November 2005, Revision: March 2006, Accepted: March 2006 相似文献
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本文研究了分支特征为ψ(x,z)=γz1+β(0<β≤1)形式的超一致椭圆扩散过程,当初始值X0(dx)为底过程的某类不变测度时,给出了当空间维数d满足βd≤2时,超过程Xt依分布收敛于0测度,当βd>2时,Xt则依分布收敛于一个非退化的随机测度. 相似文献