Finite difference method and its convergent error analyses for thermistor problem

The thermistor problem is an initial-boundary value problem of coupled nonlinear differential equations. The nonlinear PDEs consist of a heat equation with the Joule heating as asource and a current conservation equation with temperature-dopendent electrical conductivity.This problem has important opplicatioJls in industry. In this paper, A new finite differencescheme is proposed on nonuniform rectangular partition for the thermistor problem. In the theo-retical analyses,the second-order error estimates are obtained for electrical potential in discrete L^2 and H^1 norms,and for the temperature in L^2 norm. In order to get these second-order errorestimates,the Joule heating source is used in a changed equivalent form.     

混合序列的强大数律

讨论了混合序列部分和的强收敛性,所得结果推广和改进了文献[1]、[2],并推广了Marcinkiewicz强大数律．     

弹性力学的平衡差分解法

本文从基本的平衡方程出发,导出了含边界条件的弹性力学差分方程;给出了平面问题,梁弯曲问题,薄板弯曲问题的具体形式和算例。这种方法适用各种边界和荷载情况,而且放松了对位移连续性的要求。     

The Inequality Between Two Distributions: Applications to the Analysis of Diversity Data

A new measure called diversity difference is proposed for the inequality of a pair of distributions. The diversity difference measure satisfies eight properties of a measure of inequality. This measure is simple to calculate and provides easily interpreted results.Existing inequality measures examine the distribution of a single variable whose data are arranged in a monotonic order. The new measure can employ multiple variables and does not require each to be monotonic but can be used if the data happen to be monotonic. The pair of distributions is useful for organizational diversity data because one of the distributions represents the actual proportions of employees in any class or set of classes and the other distribution is the benchmark or anchoring distribution. Data from the measure can be displayed in diversity difference trees for quick interpretation.The diversity difference measure can be arranged to define a Lorenz curve. An example with three classes (gender, race, and age) is employed to provide examples of the measure, the resulting Lorenz curve, and the disparity ratio.     

误差为鞅差序列的半参数回归模型估计的相合性

设半参数回归模型Ｙ（ｎ）ｉ＝β·ｘ（ｎ）ｉ＋ｇ（ｔ（ｎ）ｉ）＋Ｅ（ｎ）ｉ,ｉ＝１,２,…,ｎ,本文由最小二乘法和一般加权方法定义的β、ｇ（ｔ）的估计量βｎ,ｇｎ（ｔ）,在误差为鞅差序列下获得了βｎ,ｇｎ（ｔ）的ｒ（≥２）阶平均相合性．     

一类非线性二阶差分方程解的振动性

本文建立了非线性二阶差分方程的若干振动准则,所得结果改进了文［５］中相应的定理．     

差动型激光自混合干涉式位移测量系统

提出了一种利用激光自混合干涉效应的差动式位移测量系统, 建立了系统的数学模型,经仿真分析及实验验证表明： 和单激光管结构相比, 该系统位移分辨力提高了二倍, 达 １／４ 光波波长, 且能大大减小光反馈强度引起的噪声及温度干扰。     

Quantum Phase and Phase Difference for Fermion

In this paper, from the index theorem, we present the Hermitian phase operator for fermion, give its eigenvalues and orthogonal, normalized and complete eigenstates. Furthermore, we also get the phase difference operator for two fermions and discuss its quantum properties.     

The construction of large element in finite element method

In the usual finite element method, the order of the interpolation in an element is kept unchanged, and the accuracy is raised by subdividing the grid denser and denser. Alternatively, in the large element method, the grid is kept unchanged, and the terms of approximate series in the element are increased to raise the accuracy.In this paper, a method for constructing large elements is presented. When using this method, two sets of variables, one set defined inside the element, and the other defined on the boundary of the element, are adopted. Then, these two sets of variables are combined by the hybrid-penalty function method. This method can be applied to any elliptic equations in a domain with arbitrary shape and arbitrary complex boundary condition. It is proved with strict mathematical method in this paper, that in general cases, the accuracy of this method is much higher than that of the usual element and the large element method presented in [7]. Therefore, the degrees of freedom needed in this method are much fewer than those in the two methods if the same accuracy is preserved.     

Cyclic star products and universalities in symbolic dynamics of trimodal maps

Cyclic star products for the triple superstable kneading (TSSK) sequences are presented for symbolic dynamics of trimodal maps of endomorphisms on the interval. Feigenbaum’s metric universalities in unimodal maps are generalized to trimodal maps. Four equal-value universal convergent rates {δ_a,δ_c,δ_η,δ_a,c,η} and three universal scaling factors {_C,_D,_E} are first obtained.