关于一类电-力振动模型的建模与分析

从电学、力学的基本原理出发,通过数学方法建立和分析了一种电-力振动模型。这是一种较复杂的电力混合作用的线性振动系统,由模型的特殊结构(类扬声器结构)作者确立了两种磁场,即感生磁场和外磁场两者正交独立,并规定了电学、力学两种不同物理量的坐标取向关系。该模型需要求得三阶正系数常微分方程的收敛解,再求得包含暂态、稳态项的完整解。另外,文章从能量和做功的角度,通过对电压电流间的相位差分析,对所建模型的正确性作了论证,同时也为这类建模引荐了一种论证手段。     

A finite element analysis of the flange earrings of strong anisotropic sheet metals in deep-drawing processes

Flange earrings of strong anisotropic sheet metals in deep-drawing process are numerically analyzed by the elastic-plastic large deformation finite element formulation based on a discrete Kirchhoff triangle plate shell element model. A Barlat-Lian anisotropic yield function and a quasi-flow corner theory are used in the present formulation. The numerical results are compared with the experimental ones of cylindrical cup drawing process. The focus of the present researches is on the numerical analysis and the constraining scheme of the flange earring of circular sheets with strong anisotropy in square cup drawing process. The project supported by the National Natural Science Foundation of China (19832020) and Provincial Natural Science Foundation of Jilin, China (200000519)     

Maximum Order of Triangle‐Free Graphs with a Given Rank

The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle‐free graphs with a given rank and characterize all such graphs achieving the maximum order.     

量子计算正三角形腔内的氢负离子光剥离截面

用传统量子力学方法研究了横截面为正三角形的腔内氢负离子光剥离, 得到了光剥离截面随能量变化的解析表达公式. 该公式还给出了剥离截面的阈值行为. 进一步研究发现, 当氢负离子处于正三角形一角附近时, 用量子力学方法得到的结果与氢负离子处于60°角域内时使用闭合轨道理论得到的结果一致.     

A version of Orlicz-Pettis Theorem for quasi-homogeneous operator space

A version of Orlicz-Pettis Theorem is established for multiplier convergent series and quasi-homogeneous operator. Applications to spaces of quasi-homogeneous operators are given.     

A characterization of Möbius transformations by use of hyperbolic regular polygons

In this paper we present a new characterization of Möbius transformations by use of hyperbolic regular polygons.     

非线性不等式组的光滑近似方法及其收敛性

将非线性不等式组的求解转化成非线性最小二乘问题,利用引入的光滑辅助函数,构造新的极小化问题来逐次逼近最小二乘问题.在一定的条件下,文中所提出的光滑高斯-牛顿算法的全局收敛性得到保证.适当条件下,算法的局部二阶收敛性得到了证明.文后的数值试验表明本文算法有效.     

On an empty triangle with the maximum area in planar point sets

Let P be a finite set of points in general position in the plane. We evaluate the ratio between the maximum area of an empty triangle of P and the area of the convex hull of P.     

广义的约当-冯诺依曼型常数和正规结构

本文引入了一个广义的约当-冯诺依曼型常数,并研究了它的相关性质,同时还利用广义的约当-冯诺依曼型常数,弱正交系数μ(X)和Domínguez-Benavides系数R(1,X),对Banach空间中的弱收敛序列系数WCS(X)进行了估计,从而得到了空间具有正规结构的一些充分条件.这些结论严格推广了最近一些文献中的结果.     

Construction and studies of a new class of reciprocal trees: interknitting of the Pascal's triangle

A method of construction of a new class of trees with reciprocal pairs of eigenvalues (λ, 1/λ) has been developed. They are derived from star graphs and can be symbolized as K _{1, n ?1} + n(p) + mK ₂ (1 ≤ m ≤ n ? 1 except for n = 1). The trees are minimally Kekulenoid and hence contain reciprocal pairs of eigenvalues in their eigenspectra. The characteristic polynomial coefficients of these trees with given values of n and m are shown to be obtainable by appropriate use of the Pascal's triangle. A general formula for this purpose has been developed. An analytical formula for the Wiener indices of such trees in terms of m and n has been derived and some consequences of this formula are presented. The relevance of these trees to real molecular structures is discussed. The trees have been shown to be useful in observing the subspectrallity of two series of IPR fullerenes of formulae C_{50+10 n} and C_{60+12 n} (n is a positive integer).