The Semiclassical Limit in the Quantum Drift-Diffusion Equations with Isentropic Pressure

The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.     

半线性双调和方程解的存在性

考虑了有界光滑区域ΩR~d,d=2,3上的一类半线性双调和方程.非线性项φ（｜▽u｜）是由｜▽u｜~p产生的.应用Schaefer不动点定理证明了当d=2（或d=3）,p满足2≤p〈∞（或2≤p≤6）时,该问题的解是存在的,并且解是局部唯一的.     

由一道模拟考题引发的再思考

本刊2013年11、12期(上半月)刊载了侯典峰、董雁飞两位老师的文章《一道模拟考题的求解思维层次》,文中从四个不同的角度对一道模拟考题进行了解法剖析,让人深受启发,然而四种解法计算量都较大,且未能完全揭示问题的背景,略有遗憾.数学知识有机联系,纵横交错,求解问题即使解答正确合理,未必是最佳思路,有时需要迎难而上,冲破桎梏,拨开迷雾.题目三个顶点均在椭圆上的三角形称为椭圆的内接三角形,已知点A是椭圆的一个短轴的     

A TRIANGULAR FINITE VOLUME ELEMENT METHOD FOR A SEMILINEAR ELLIPTIC EQUATION

In this paper we extend the idea of interpolated coefficients for a semilinear problem to the triangular finite volume element method. We first introduce triangular finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. We then derive convergence estimate in Hi-norm, L2-norm and L∞-norm, respectively. Finally an example is given to illustrate the effectiveness of the proposed method.     

严格循环的算子代数

设X是半自共轭的Banach空间,而A是B(X)的严格循环的交换子代数,考虑算子代数A的一些性质,这些性质与算子代数的自反性有关,而且这些性质为讨论A的自反性提供了理论基础.     

梯度磁电弹材料界面的Stoneley波波速研究

研究均匀弹性半空间(y ≤ 0)和功能梯度磁电弹半空间(y≥0)界面的Stoneley波的波速.基于弹性介质和磁电弹介质的本构方程、运动方程和界面连续条件,得到了弹性半空间(y≤0)和磁电弹半空间(y≥0)界面处的Stoneley界面波波速方程,并讨论了梯度系数对波速的影响.研究结果对于界面波器件的研制提供理论依据.     

基于半参数回归模型的最小一乘局部线性算法

根据最小一乘准则,推导出最小一乘局部线性估计的计算方法,并通过对模拟数据的计算和分析,对比最小一乘核算法和最小二乘局部线性算法,验证了最小一乘局部线性算法是一种有效的,稳健的估计方法,并且有降低边界效应的作用．     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

CYCLIC AND NEGACYCLIC CODES OF LENGTH 2p^s OVER Fp^m ＋ uFp^m

In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m ＋ uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.     

CONSTRUCTING POINTED WEAK HOPF ALGEBRAS BY ORE-EXTENSION

The main work of this article is to give a nontrivial method to construct pointed semilattice graded weak Hopf algebra At =n i =0Aαi tfrom a Clifford monoid S = [Y; Gα, φα,β ]by Ore-extensions, and to obtain a co-Frobenius semilattice graded weak Hopf algebra H(S, n, c, χ, a, b) through factoring At by a semilattice graded weak Hopf ideal.