一种改进边界元法在弹性扭转问题中的应用

本文用一种改进边界元法分析与计算了椭圆截面等直杆的扭转问题.并与边界元法的解进行比较,其结果极为符合.然而,改进边界元法较边界元法所需要的数据量少得多,计算时间也将大大减少了.因此,本文方法对求解Poisson方程问题是一种经济而行之有效的数值计算方法.     

Operator Matrix Forms of Positive Operators

If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2）of operators on Hibert spaces is given,we proved that the operator ～↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R（A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet.     

Monomial bases for -Schur algebras

Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of and its associated monomial basis, we investigate -Schur algebras as ``little quantum groups". We give a presentation for and obtain a new basis for the integral -Schur algebra , which consists of certain monomials in the original generators. Finally, when , we interpret the Hecke algebra part of the monomial basis for in terms of Kazhdan-Lusztig basis elements.

     

A Decision Criterion for the Optimal Number of Clusters in Hierarchical Clustering

Clustering has been widely used to partition data into groups so that the degree of association is high among members of the same group and low among members of different groups. Though many effective and efficient clustering algorithms have been developed and deployed, most of them still suffer from the lack of automatic or online decision for optimal number of clusters. In this paper, we define clustering gain as a measure for clustering optimality, which is based on the squared error sum as a clustering algorithm proceeds. When the measure is applied to a hierarchical clustering algorithm, an optimal number of clusters can be found. Our clustering measure shows good performance producing intuitively reasonable clustering configurations in Euclidean space according to the evidence from experimental results. Furthermore, the measure can be utilized to estimate the desired number of clusters for partitional clustering methods as well. Therefore, the clustering gain measure provides a promising technique for achieving a higher level of quality for a wide range of clustering methods.     

关于对偶扩张代数有限维数的注记

没A是一个有限维代数，R为A的对偶扩张代数．本我们讨论R的有限维数findim R of R，证明了，在—般情况下findim R≠2findim A，这就回答了惠昌常教授所提的一个问题．     

烃类烟粒红外复折射率的测定与应用

测定了室温下烃类(乙炔、乙烷)烟粒的红外复折射率,并讨论了所获数据在测量烟浓度与烟粒大小分类、计算光谱吸收系数及在特定浓度与温度下评估烟雾辐射率方面的应用。     

The numerical approximation of center manifolds in Hamiltonian systems

In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip.     

THE APPLICATION OF HIGH RESOLUTION SOLID STATE NMR IN ADSORPTION SYSTEMS

High resolution solid state NMR techniques(such as MAS,CP/MAS andCRAMPS)were employed to study the nature of organic molecules adsorbed onporous solids. A magic angle spinning system was achieved for sealed samples with a spinning speed from 2KHz to 4.2KHz.Using this technique,high resolution ~1HMAS spectra of organic molecules and H_2S adsorbed on charcoal were obtained.EXperimental results suggest that for high coverage of adsorbed organic molecules,the spectral lines were resolved very well.But for low coverage,the spectrallines could not be separated completely.As the organic molecules condensed in     

自由电子激光光导的数值模拟与分析

从一维自由电子激光理论出发,唯象地考虑衍射效应,计算和分析了光导效应的特点和规律;针对曙光一号装置的自由电子激光参数,利用二维理论对光场剖面、填充因子、光场半径等进行了数值模拟;根据计算结果分析和讨论了影响光导的因素和实验条件。