岩石类材料裂纹分叉非规则性几何的分形效应

本文考察了岩石裂纹(从晶粒尺寸的微裂纹到几千米的断层构造)的分叉在几何上存在的非规则性,在文献[10,11]的基础上,应用分形(fractal)几何建立了裂纹分叉的分形模型,分析了裂纹分叉的分形效应,从几何的角度研究了裂纹分叉使断裂韧性提高的物理力学现象,导出了一个比smith公式更合理的断裂韧性计算式。     

Determination of Spherical Area Measures by Means of Dilation Volumes

For a large class of compact sets X in ℝ^d which can be represented as finite unions of sets of positive reach, the spherical area measure of order d — 1 is determined by the volumes of dilations of X with infinitesimal multiples of all rotations of a suitable convex test set. For spherical area measures of lower orders, a similar result is obtained by approximating the set X by the closures of the complements of close parallel bodies.     

黄河小浪底坝区泥化夹层分布及其抗剪试验方法的分析

在大量地质勘探试验研究资料的基础上 ,分析研究了形成泥化夹层的母岩和地质构造力 ,泥化夹层的类型及其粒度成分以及泥化夹层的分布规律。还分析研究了不同试验方法对泥化夹层抗剪强度的影响 ,并着重分析研究了我院研制的控制膨胀饱和固结慢剪的试验成果。     

MgO缺陷和不规则表面吸附CO的能带和电子结构研究

采用从头算程序优化MgO表面三种不同配位位置吸附CO构型,并用扩展休克尔紧束缚(EHT)晶体轨道方法对MgO的缺陷和不规则表面吸附CO的可能构型进行能带计算,讨论了能带结构及组成,不同构型吸附前后能带和成键性质的变化,以及吸附前后的电荷转移和吸附键的变化规律。研究结果发现,CO的C端更有利于在MgO固体表面的吸附,具有氧缺陷结构的MgO更有利于吸附分解CO。     

A NOTE ON FINITE ELEMENT WAVELETS

1. IotroductionThe study of mu1ti-wavelets was initiated by Goodman, Lee and Tang[2]. Later, acharacterization of sca1ing functions and wavelets was established by Goodman and Lee[3].In [4] GoodInan constructed multi-wavelets that satisfy certain interpolating conditions.Geronimo, Hardin and Massopust[5] used fractal interpolation to construct orthogonal scal-ing functions gh1 and gh2 (with multiplicity r = 2) that are both symmetric and colltinuousbut nondifferentiable. Strang and Strela…     

On a Problem of Daubechies

   Abstract. We solve a problem posed by Daubechies [12] by showing the nonexistence of orthonormal wavelet bases with good time-frequency localization associated with irrational dilation factors.     

On certain modified boundary value problems for ordinary differential equations with irregular singularity

We consider a linear second-order differential equation with irregularly singular point at the beginning of the interval. For the corresponding homogeneous differential equation, we obtain the asymptotics of the solutions and their derivatives near the singular point. Using some modified Green functions and taking into account the asymptotics, we consider three boundary value problems with various boundary conditions (including a weighted one) at the singular point, proving theorems on the existence and uniqueness of the solutions and giving their structure. Lithuanian Mathematical Journal, Vol. 49, No. 1, 2009, pp. 109–121     

矩阵酉扩张的刻划

本文用奇异值刻划了具有指定阶酉扩张的矩阵类，同时讨论了矩阵的正规扩张问题