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。     

The G-biliaison class of symmetric determinantal schemes

We consider a family of schemes, that are defined by minors of a homogeneous symmetric matrix with polynomial entries. We assume that they have maximal possible codimension, given the size of the matrix and of the minors that define them. We show that these schemes are G-bilinked to a linear variety of the same dimension. In particular, they can be obtained from a linear variety by a finite sequence of ascending G-biliaisons on some determinantal schemes. We describe the biliaisons explicitly in the proof of Theorem 2.3. In particular, it follows that these schemes are glicci.     

Free Entropy Dimensions of Some von Neumann Algebras

In this paper, we estimate the free entropy dimension of the group yon Neumann algebra L（Zt）, which is less than 1/t,2 ≤t ≤ ＋∞. This data is identical with the free dimension defined by Dykema.     

裁元齐次Moran集的Hausdorff维数

将齐次Moran集迭代过程中的k项序列集Dk={(i1,...,ik):1≤ij≤nj,1≤j≤k}裁减为Dk={(i1,...,ik):1≤ij≤nj, ij≠2 unless ij-1=1, 2≤j≤k},相应的集合称为裁元齐次Moran集．本文确定了一类裁元齐次Moran集的Hausdorff维数．     

STATISTICALLY FRACTAL STRENGTH THEORY FOR BRITTLE MATERIALS

Based on the hypothesis of the fractal distribution of crack sizes in brittle materials andthe weakest link principle,the relationship between the fractal dimension of the size-frequency distri-bution of cracks and the Weibull Modulus is derived,which reveals the geometrical nature of theWeibull Modulus.The influences of the size distribution and the orientation distribution of cracks aswell as the irregularity of the crack propagation on the strength are all taken into account.Finally,ageneral expression for the statistical strength of brittle materials in complex tensile stress state is ob-tained.     

The HAUSDORFF DIMENSION AND MEASURE OF THE GENERALIZED MORAN FRACTALS AND FOURIER SERIES

ＴｈｅＨＡＵＳＤＯＲＦＦＤＩＭＥＮＳＩＯＮＡＮＤＭＥＡＳＵＲＥＯＦＴＨＥＧＥＮＥＲＡＬＩＺＥＤＭＯＲＡＮＦＲＡＣＴＡＬＳＡＮＤＦＯＵＲＩＥＲＳＥＲＩＥＳ￥ＲＥＮＦＵＴｈＯ；ＬＩＡＮＧＪＩＮＲＯＮＧＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈ...     

2+1维SU(2)规范场真空波函数的红外形式

本文提出一种确定规范场真空波函数的尝试方法．所得之波函数能有效地描述缓变组态．     

Topological classification of linear hyperbolic cocycles

In this paper linear hyperbolic cocycles are classified by the relation of topological conjugacy. Roughly speaking, two linear cocycles are conjugate if there exists a homeomorphism which maps their trajectories into each other. The problem of classification of discrete-time deterministic hyperbolic dynamical systems was investigated by Robbin (1972). He proved that there exist 4d classes ofd-dimensional deterministic discrete hyperbolic dynamical systems. We obtain a criterion for topological conjugacy of two linear hyperbolic cocycles and show that the number of classes depends crucially on the ergodic properties of the metric dynamical system over which they are defined. Our result is a generalization of the deterministic theorem of Robbin.     

Investigation of use of reach-back characteristics method for 2D dispersion equation

The use of the Holly-Preissmann two-point scheme has been very popular for the calculation of the dispersion equation. The key to this scheme is to use the characteristics method incorporating the Hermite cubic interpolation technique to approximate the trajectory foot of the characteristics. This method can avoid the excessive numerical damping and oscillation associated with most finite difference schemes for advection computation. On the basis of the fundamental idea of the Holly-Preissmann two-point scheme, a new technique is introduced herein for the computation of the two-dimensional dispersion equation. This new scheme allows the characteristics projecting back several time steps to fall on the spatial or temporal axis, while the characteristics foot is still solved by the Holly-Preissmann two-point method. The diffusion portion of the dispersion equation is solved by the commonly used Crank-Nicholson method. The calculation for these two processes consisting of advection and diffusion is carried out separately but consecutively in one time step, a method known as the split operator algorithm. A hypothetical model was constructed to demonstrate the applicability of this new technique for the calculation of the pure advection and dispersion equation in two dimensions.