高维线性插值方法及其在3维温度场计算中的应用

通过分析1维和2维线性插值可以推导出任意斜角直线坐标系下n维线性插值的一般计算公式以及有唯一解的条件,这一结论能够应用于三维温度场计算。可以将n维插值问题归结如下:已知n 1维空间中的n 1个点的坐标以及第n 2个点的n个坐标分量xn 2,1,x n 2,2,,xn 2,n,求解该点的第n 1个坐标分量xn 2,n 1。根据线性插值定义,第n 2个点位于前n 1个点所确定的n维超平面上。根据这一条件列写方程、求解方程可得到插值xn 2,n 1。n维插值问题有唯一解的条件是已知的n 1个点在n维空间中构成的多面体的体积不为0。推导过程在斜角直线坐标系中完成,因而结论具有较大普适性。     

等达因图象的自动采集与识别

文中提出了一种机机械扫描系统．小功率激光器、图象板、相移元件、微机和程序软件组成的等达因图象自动采集与处理系统，用灰度值比较的思想实现了等达因图象的跟踪采集。提出了四幅图象相移法实现等达因图象的自动识别。系统能快速、实时、精确和全自动地实现等达因图象的记录和分析。给出与物体内各点应力状态一一对应的位相图。并用来研究了其他实验方法困难的局部三维效应问题。     

Pure liquids described as concentrated cluster dispersions

The Fulcher-Tammann-Hesse-Vogel equation, ln = A + B/(T – T ₀ ), is shown to be equivalent to the general viscosity-composition relationship, ln _r =k f /(1 – f ), for binary mixtures. The Cailletet-Mathias law of the Rectilinear Diameter is rearranged to represent a density mixture formula for two components. Temperature-independent viscosities and densities can then be calculated for dense, solid cluster fractions, dispersed in a low-density, low-viscosity non-clustered continuous phase. The cluster fraction decreases with temperature. The value ofT ₀ is shown to be related to the liquid- or solid-like behavior of the clusters. For liquids with a vapor pressure < 1 mm Hg at the melting point, the calculated cluster volume fraction suggests close packing of clusters, ranging in shape from monodisperse spheres to polydisperse non-spherical particles. Examples are given for molecular liquids, molten metals, and molten salts. The size of the clusters is estimated from the heat of evaporation.     

On Determining the Percolation Reynolds Number and the Characteristic Linear Dimension for Ideal and Fictitious Porous Media

Various versions of representations of the percolation Reynolds number for porous media with isotropic and anisotropic flow properties are considered. The formulas are derived and the variants are analyzed with reference to model porous media with a periodic microstructure formed by systems of capillaries and packings consisting of spheres of constant diameter (ideal and fictitious porous media, respectively). A generalization of the Kozeny formula is given for determining the capillary diameter in an ideal porous medium equivalent to a fictitious medium with respect to permeability and porosity and it is shown that the capillary diameter is nonuniquely determined. Relations for recalculating values of the Reynolds number determined by means of formulas proposed earlier are given and it is shown that taking the microstructure of porous media into account, as proposed in [1, 2], makes it possible to explain the large scatter of the numerical values of the Reynolds number in processing the experimental data.     

Two lower bounds for the Stanley depth of monomial ideals

Let be two monomial ideals of the polynomial ring . In this paper, we provide two lower bounds for the Stanley depth of . On the one hand, we introduce the notion of lcm number of , denoted by , and prove that the inequality holds. On the other hand, we show that , where denotes the order dimension of the lcm lattice of . We show that I and satisfy Stanley's conjecture, if either the lcm number of I or the order dimension of the lcm lattice of I is small enough. Among other results, we also prove that the Stanley–Reisner ideal of a vertex decomposable simplicial complex satisfies Stanley's conjecture.     

初始状态对自组织演化过程的影响

从实验上系统研究了在强电场下处于介质中的大量金属小球从不同初始状态通过自组织演化为分形的过程;用Sandbox方法定量分析了最终形成的稳定树枝状分形的维数。结果表明:不同初始状态形成分形的过程完全不同,但最终的树枝状分形的维数基本相同。分析认为,小球之间的相互作用存在临界作用距离,不同初始状态相邻小球之间的平均间距不同,因而演化过程不同;而维数相同正是系统耗散相同的体现。     

The minimal dimensions of faithful representations for Heisenberg Lie superalgebras

This paper aims to determine the minimal dimensions and super-dimensions of faithful representations for Heisenberg Lie superalgebras over an algebraically closed field of characteristic zero.     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

Analysis on Fractal Objects

Irregular objects are often modeled by fractals sets. In order to formulate partial differential equations on these nowhere differentiable sets the development of a “new analysis” is necessary. With the help of the model case of the Sierpinski gasket the definition of energy forms and Laplacians on self-similar finitely ramified fractals is explained. Moreover, some results for certain classes of non-self-similar fractals are presented. 2000 Math. Subj. Class.: Primary 28A80, 35J15; Secondary 31C25, 35P05