矩阵方程A^TXB=C的正定和半正定解

给出了矩阵方程Ａ＾ＴＸＢ＝Ｃ在正定和半正定矩阵类中有解的充要条件及解的一般表达式。     

Studies on basicity of alkali metal catron exchanged β and X zeolites by pyrrole-IR spectroscopy

The strength of basic sites has been measured by pyrrole-IR on alkali metal cation exchanged β and X zeolites, as well as NaOH loaded Naβ. The influence of cation type and the structure of zeolites on their basicity has been studied. The acidic and basic properties of the samples were investigated by NH3-TPD and isopropanol reaction. It was shown that the strength of basic sites on samples could be characterized by the shift of vNH band in the pyrrole-IR spectra. The framework oxygen charges were calculated from the Sanderson electronegativity. The changes in basic properties with various alkali metal cation are consistent with the changes of local oxygen charges of the zeolite framework.     

Pseudo-epitaxial C60 films prepared by a hot-wall method

We have used both reflection-geometry and grazing-incidence-geometry X-ray scattering to study thin films of C₆₀ evaporated onto mica substrates via a hot-wall technique. The growth mode yields close-packed C₆₀ planes, which are parallel to the substrate surface and which exhibit out-of-plane correlation lengths of 850 Å. In the film plane the C₆₀ is at best pseudo-epitaxial, with a 0.9° distribution of crystallite orientations, a 450 Å in-plane correlation length, and a 3.7% lattice mismatch, better than obtained by other thin film techniques but far from the accepted definition of single crystal thin film epitaxy.     

随机发展方程适度解的存在唯一性(Ⅱ)

讨论如下Hilbert空间中的半线性随机发展方程的Cauchy问题 dy(t)=[Ay(t) f(t,y(t))]dt G(t,y(t))dw(t) y(O)=V_u的适度解的存在唯一性,在更一般的条件下,得到了该问题的适度解的存在唯一性。     

关于混合型多项式Hammerstein积分方程正解迭代求法

本文给出了混合型多项式Ｈａｍｍｅｒｓｔｅｉｎ积分方程正解的迭代求法，并将所得结果应用到二阶非线性常微分方程的边值问题     

线性双向联想存储器

提出了一个线性双向联想存储器的模型，一组有限个向量对由一线性算子建立起双向联想关系，此线性算于是一个网络的联结权重矩阵。该权矩阵由最小二乘法决定。由权矩阵的解导出一特殊类型的Ｌｙａｐｕｎｏｖ矩阵方程．本文提供了这种Ｌｙａｐｕｎｏｖ矩阵方程的解。     

双层桥梁耦合系统的强迫振动

本文研究作为双层桥模型的梁方程耦合系统，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了一个关于这种系统的解的存在性定理，它类似于ＭｃＫｅｎｎａ和Ｗａｌｔｅｒ文２中关于吊桥方程的一个定理。     

压力淬火过程中锗的相结构研究

 应用高压原位差热方法，直接测量了压力下锗的固化参数─—固化温度与过冷度。高压差热信号表明，当压力大于3 GPa时，锗在凝固过程中可能发生结构相变。X射线结构分析表明，在最终的样品中除GeⅠ相外，还形成GeⅢ相和GeⅣ相。     

Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.