Sierpinski Gasket上布朗运动的维数性质

本文研究Sierpinski Gasket上的布朗运动X的象集、图集的Hausdorff维数性质,证明了存在零概率集Ⅳ,若ω∈Nc,则对任意紧集F(?)[0,∞),有(i)dimX(F+t)=min(α-1dimF,df),a.e.t>0,(ii)dimGrX|F+t=min(α-1dimF,(1-α)df+dimF),a.e.t>0,其中ds=log3/log2,α=log2/log5.

SG(2,2)上布朗运动的维数性质

本文研究分形集合ＳＧ（２，２）上布朗运动的维数性质，得到了ＳＧ（２，２）上布朗运动的样本图以及象集的Ｈａｕｓｄｏｒｆｆ维数与盒维数．

一种新的Z_p几何指标理论及其应用

给出一种广义Zp几何指标理论,它是刘嘉荃,王志强,徐远通,Michalek R和Tarantello G等学者介绍的Zp指标的推广.对于某些非线性系统,该指标可以用来讨论其多重周期解和次调和解的存在性.利用广义Zp几何指标,结合Kaplan-Yorke的耦合系统方法,文章给出一类微分差分方程多重周期解存在性的一个条件.

The algorithm of 3D multi-scale volumetric curvature and its application

To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. We also propose a fast algorithm for computing 3D volumetric curvature. In comparison to conventional volumetric curvature attributes, its main improvements and key algorithms introduce multi-frequency components expansion in time-frequency domain and the corresponding multi-scale adaptive differential operator in the wavenumber domain, into the volumetric curvature calculation. This methodology can simultaneously depict seismic multi-scale features in both time and space. Additionally, we use data fusion of volumetric curvatures at various scales to take full advantage of the geologic features and anomalies extracted by curvature measurements at different scales. The 3D MSVC can highlight geologic anomalies and reduce noise at the same time. Thus, it improves the interpretation efficiency of curvature attributes analysis. The 3D MSVC is applied to both land and marine 3D seismic data. The results demonstrate that it can indicate the spatial distribution of reservoirs, detect faults and fracture zones, and identify their multi-scale properties.

Some New Properties of Wigner Function Studied in Entangled State Representation

Based on the Wigner operator in the entangled state representation we study some new important propertiesof Wigner function for bipartite entangled systems,such as size of an entangled state,upper bound of Wigner functions,etc.These discussions demonstrate the beauty and elegance of the entangled state representation.

Effects of negative index medium defect layers on the transmission properties of one-dimensional photonic crystal

The photonic band gap structure of 1D photonic crystal with a negative index medium defect layer is studied by using the transfer matrix method. Investigations show that the introdufion of negative index medium defect layer and the increase of the negative index value will result in an extension of the band gap. Moreover, by increasing the negative index, the width of defect layer and the numbers of period photonic crystal, the width of defect modes will be narrowed, which is advantaged to obtain optical filters with narrow band. Finally, the effects of absorption on the properties of band gap and on defect modes have been discussed.

Magnetic and Magneto-Optical Properties in Paramagnetic NdF3 Under High Magnetic Field

In this paper, we first theoretically report the magnetic and magneto-opticalproperties in paramagnetic media under high external magnetic field. Considering the action of theexternal magnetic Geld H_e and indirect exchange interaction H_v, the characteristic of the magneticsaturation and the property of the Faraday rotation to be nonlinear with external magnetic Geld arepresented in paramagnetic NdF_3. In terms of our theory, the indirect exchange interaction plays auimportant role in the magnetization M and the Faraday rotation θ in NdF_3 under high externalmagnetic Geld. The theory is in good agreement with experimental results. On the other hand, areasonable explanation for the temperature dependence of the ratio of the Verdet constant to themagnetic susceptibility V/x is obtained.

Investigation on thermophysical properties of reactive powder concrete

The thermophysical properties,such as thermal conductivity,thermal diffusivity,specific heat capacity and linear thermal expansion of reactive powder concrete(RPC) with different steel fiber volumetric fractions are investigated by means of high temperature tests. The thermophysical characteristics of RPC with different fiber volumes under different temperatures are analyzed and compared with those of the common high-strength concrete and high-performance concrete. The empirical relationships of thermophysical properties with temperature and fiber volume are identified. By the heat transfer and solid physics methods,the microscopic physical mechanism of heat transfer process and heat conduction properties of RPC are investigated,and the theoretical formulas of specific heat capacity and thermal expansion coefficient are derived,respectively. The effects of temperature and steel fibers on the specific heat capacity and the thermal expansion coefficient are quantitatively analyzed and the discriminant conditions are provided. It is shown that the experimental results are consistent with the theoretical prediction.

Asymptotic properties of Lasso in high-dimensional partially linear models

We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.