广义Sierpinski集

本文考察了包括平面上的各种广义 Cantor集 ,Sierpinski集和包括某些连续不可微曲线在内的广义 Sierpinski集 .由相似变换 ,导出了它们的级数表达式 ,并利用它和字符串空间的对应关系 ,计算出它们的Hausdorff维数     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

运动水平平板上混合对流的群论分析

本文用变换群理论对运动水平平板混合对流边界层流动的动量、能量和浓度扩散方程进行了分析，得到了与X4/(7-5n)成正比的壁面温度分布和浓度分布，同时壁面运动速度正比于X(3-n)／(7-5n)时存在相似性解．导出了相似性解方程，用四阶Runge－Kutta方法进行了计算，给出了Pr＝0．72　和Sc，K1，K2，K3参数下的速度、温度和浓度分布，得出了各参数对流场、温度场的影响。     

On the Second Law of Thermodynamics and the Piston Problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio m/M is a very small parameter, where m is the mass of one particle of the gaz and M is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation in a previous work, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.     

Differential density matrix overlap: an index for assessment of electron correlation in atoms and molecules

Summary A new index, called the differential density matrix overlap (DDMO), is proposed for assessment of the electron correlation effects in atoms and molecules. DDMO can be easily calculated as the negative value of the correlation energy derivative with respect to the relative position of the occupied and virtual orbitals. DDMO is transparent to physical interpretation. It can serve as a tool for analyzing the accuracy of approximate electron correlation methods and the validity of the Hartree-Fock wavefunction as the zeroth-order approximation. The properties of DDMO are discussed using test calculations on 11 atoms and molecules as an example.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

用解析方法建立两个三角形的亲似对应(Ⅰ)

本文解决的是射影几何中建立两个三角形亲似对应的问题.本文对亲似对应问题进行了分析,根据亲似对应的特点,将问题简化,并在此基础上推导出建立两个三角形亲似对应的数学公式及计算方法.     

数字图书馆FAQ服务的探讨

探讨了在数字图书馆中逐渐普及FAQ服务的意义 .通过对国内部分图书馆主页的访问调查 ,剖析了目前国内的数字图书馆FAQ服务存在的问题 ,如缺乏对用户的深入研究 ,缺乏对问题的分析选择 ,还有设计上存在的问题等 .主张要在充分研究用户的心理和行为的基础上开发和开展FAQ服务 ,并对FAQ的开发步骤做了简要的介绍     

矩阵的合同、相似与二次型

矩阵的合同关系、相似关系都是等价关系，它们虽然不同。但又有联系．对称矩阵是这两个知识点的交汇点。即两个实对称矩阵合同当且仅当它们相似．进一步得到二次型可以通过一个正交变换化为标准型。这一理论是高等代数教科书的重要内容。然而．现行的教科书对该理论的证明至少涉及到二次型、线性空间、线性变换和欧氏空间的内容．本文利用欧氏空间的正交性质给出这一理论新的简洁证明。以供教学参考之用。     

城市规划辅助审批系统中的相似度研究

城市规划的审批是一件难于量化的工作，它受政治经济等多方面因素影响，是城市规划领域关注的一大焦点．本文尝试将CBR技术用于城市规划辅助审批，让政府的审批依据达到历史与现实的统一．实现CBR的一个关键是相似度的设计，本文结合城市规划辅助审批领域的特点，设计了可行的方案，并应用于实际的办公系统中．