有关对偶方程的充要条件

本文给出了多维马氏过程的对偶过程存在的充分必要条件,在多维跳过程的情形下,本文给出了用Q-对来验证对偶过程是否存在的条件。     

非线性规划的Ω共轭对偶理论

本文通过推广凸共轭函数和次梯度的概念,建立了非线性规划问题的一类对偶理论——Ω共轭对偶理论.研究结果表明,许多关于非线性最优化对偶性方面的结论都是本文的特殊情况.     

群体多目标最优化的Lagrange对偶性

本文建立了目标和约束为不对称的群体多目标最优化问题的Lagrange对偶规划，在问题的联合弱有效解意义下，得到群体多目标最优化Lagrange型的弱对偶定理、基本对偶定理、直接对偶定理和逆对偶定理。     

求解线性规划的对偶算法

单纯形法一般采用行变换进行计算.本文给出了两种列变换的计算方法,一种与原始单纯形法等价,一种与对偶单纯形法等价,本文称之为对偶方法.这两种方法不引入松弛变量或剩余变量,计算规模小,有明显竞争优势.     

对偶平行体与对偶Steiner点

结合平行体及径向加的定义,给出了星体的对偶平行体.研究了对偶平行体与平均弦长之间的关系,并得出了对偶平行类在某度量下的性质,此外,还证明了对偶Steiner点在对偶平行类上的连续性及赋值性质.     

变量有广义界线性规划的直接对偶单纯形法

本文讨论变量有广义界线性规划问题借助标准形线性规划同单纯形法技术，建立问题的一个直接对偶单纯形法。分析了方法的性质，给出了初始对偶可行基的计算方法，并用实例说明方法的具体操作。     

关于对偶Steiner多项式的根的注记

受凸体的Steiner多项式的启发,定义了星体的对偶Steiner多项式,并利用对偶Aleksandrov-Fenchel不等式讨论了对偶Steiner多项式的根.进而,得到了关于对偶Steiner多项式的根的一些不等式,这些不等式恰好是关于Steiner多项式的根的不等式的对偶形式.     

关于有界BCK—代数的主对偶理想的一个定理

本文给出了ＢＣＫ－代数主对偶理想的一个定理，使得［３］中定理２作为本定理的一个特例。     

对偶Brunn-Minkowski型不等式

本文研究了对偶Brunn-Minkowski不等式问题.利用对偶混合体和Blaschke径向和的性质,建立了对偶混合体均质积分的Brunn-Minkowski不等式的隔离形式,推广了对偶Brunn-Minkowski理论的几个不等式.     

Billingsley's packing dimension

For a stochastic process on a finite state space, we define the notion of a packing measure based on the naturally defined cylinder sets. For any two measures , , corresponding to the same stochastic process, if

then we prove that

     

概率空间上有限测度的维数及其分布

设（Ω，Ｆ，μ）为概率空间，ｖ为（Ω，Ｆ）上的有限测度的密度定理，并研究了ｖ的维数及维数分布的若干性质。     

Dimension scales of bicompacta

We introduce the notion of a (stable) dimension scale d-sc(X) of a space X, where d is a dimension invariant. A bicompactum X is called dimensionally unified if dim F = dim_G F for every closed F ? X and for an arbitrary abelian group G. We prove that there exist dimensionally unified bicompacta with every given stable scale dim-sc.     

A Note on Projective and Flat Dimensions and the Bieri-Neumann-Strebel-Renz Σ-Invariants

Let G be a finitely generated group, and A a ?[G]-module of flat dimension n such that the homological invariant Σ ⁿ (G, A) is not empty. We show that A has projective dimension n as a ?[G]-module. In particular, if G is a group of homological dimension hd(G) = n such that the homological invariant Σ ⁿ (G, ?) is not empty, then G has cohomological dimension cd(G) = n. We show that if G is a finitely generated soluble group, the converse is true subject to taking a subgroup of finite index, i.e., the equality cd (G) = hd(G) implies that there is a subgroup H of finite index in G such that Σ^∞(H, ?) ≠ ?.     

Multifractal analysis of the occupation measures of a kind of stochastic processes

Let {X(t), 0t1} be a stochastic process whose range is a random Cantor-like set depending on an -sequence (0<<1) and μ is the occupation measure of X(t). In this paper we examine the multifractal structure of μ and obtain the fractal dimensions of the sets of points of where the local dimension of μ is different from . It is interesting to notice that the final results of this paper are identical to those for the occupation measure of a stable subordinator with index , yet the stochastic process under consideration in this work is not even a Markov process.     

Asymptotic cones and Assouad-Nagata dimension

We prove that the dimension of any asymptotic cone over a metric space does not exceed the asymptotic Assouad-Nagata dimension of . This improves a result of Dranishnikov and Smith (2007), who showed for all separable subsets of special asymptotic cones , where is an exponential ultrafilter on natural numbers.

We also show that the Assouad-Nagata dimension of the discrete Heisenberg group equals its asymptotic dimension.

     

关于FP-内射维数的一个注记

Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.     

Gorenstein Flat and Cotorsion Dimensions of Unbounded Complexes

In this article, we define and study the Gorenstein flat dimension and Gorenstein cotorsion dimension for unbounded complexes over GF-closed rings by constructions of resolutions of unbounded complexes. The behavior of the dimensions under change of rings is investigated.     

Dimension Results for Space-anisotropic Gaussian Random Fields

Let X = {X(t) ∈ R~d, t ∈ R~N} be a centered space-anisotropic Gaussian random field whose components satisfy some mild conditions. By introducing a new anisotropic metric in R~d, we obtain the Hausdorff and packing dimension in the new metric for the image of X. Moreover, the Hausdorff dimension in the new metric for the image of X has a uniform version.     

螺线的Steinhaus维数

Ｄｕｐａｉｎ Ｙ,Ｆｒａｎｃｅ Ｍ．Ｍ．和 Ｔｒｉｃｏｔ Ｃ．［１］利用积分几何中的经典的Ｓｔｅｉｎｈａｕｓ定理,引入 Ｓｔｅｉｎｈａｕｓ维数,并研究了螺线的 Ｓｔｅｉｎｈａｕｓ维数与盒维数的关系．本文深入这一研究,对Ｓｔｅｉｎｈａｕｓ维数的值域,单调性等基本性质作了进一步的考察．