Estimation over Curves of the Functions Given by Dirichlet Series on a Half-Plane

We study the maximal term of the Hadamard composition of Dirichlet series with real exponents. We obtain a lower estimate for the sum of a Dirichlet series over a curve arbitrarily approaching the convergence line.     

无简并微扰论公式的研究

本文介绍了Ｗｉｇｎｅｒ公式，Ｇｏｌｄｓｔｏｎｅ公式与Ｓｃｈｒｏｄｉｎｇｅｒ公式及其递推形式，比较表明，Ｓｃｈｒｏｄｉｎｇｅｒ公式的递推形式更容易利用计算机程序实现。文中还给出了逐级计算非连通项到任意级的方法。     

A numerical study of flow over a confined backward-facing step

Numerical solutions using the SIMPLE algorithms for laminar flow over a backward-facing step are presented. Five differencing schemes were used: hybrid; quadratic upwind (QUICK); second-order upwind (SOUD); central-differencing and a novel scheme named second-order upwind biased (SOUBD). The SOUBD scheme is shown to be part of a family of schemes which include the central-differencing, SOUD and QUICK schemes for uniform grids. The results of the backward-facing step problem are presented and are compared with other numerical solutions and experimental data to evaluate the accuracy of the differencing schemes. The accuracy of the differencing schemes was ascertained by using uniform grids of various grid densities. The QUICK, SOUBD and SOUD schemes gave very similar accurate results. The hybrid scheme suffered from excessive diffusion except for the finest grids and the central-differencing scheme only converged for the finest grids.     

妊娠晚期羊水中微量元素测定及其与胎儿生长发育关系的研究

对１０２名足月正常妊娠第一胎的产妇妊娠晚期羊水中６种微量元素（锌、铜、锰、铁、钙、镁）首次进行了测定，并通过对出生新生儿生长发育的监测探讨其与胎儿生长发育的关系。妊娠晚期羊水中６种微量元素含量（±Ｓ／×１０－５）分别为：Ｚｎ２．２９±１．７７，Ｃｕ０．１４±０．１４，Ｍｎ０．１３±０．２３，Ｆｅ３．６９±２．７０，Ｃａ８２．５４±７４．１８，Ｍｇ１８．７１±１１．０９．男女新生儿其母羊水中微量元素含量比较无显著差异，Ｐ≥０．０５．与文献报道中期妊娠羊水中所含微量元素比较有增加趋势．６种微量元素相互关系中．与锌、钙呈正相关外，锌与铜、锰、铁、镁呈负相关．低体重组与低身长组新生儿孕母羊水中锌含量明显低于高体重组和高身长组，有显著差异，Ｐ≤０．０１．铁在高身长组含量增高，与低身长组比较有显著差异，Ｐ≤０．０５．锰于低体重组含量升高，与高体重组比较有显著差异，Ｐ≤０．０１．镁与铜于低身长组含量升高，与高身长组比较有显著差异，Ｐ分别≤０．０５与０．０１．可见高铜、高锰、高镁可致胎儿生长发育迟缓．     

Parabolic Equations with Measurable Coefficients

We investigate the unique solvability of second order parabolic equations in non-divergence form in , p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables. The second author was partially supported by NSF Grant DMS-0140405.     

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

留数定理在拓扑相变中的应用

留数定理是高校物理专业必修课程数学物理方法中的一个重要定理.传统教学中关于该定理的讲授着重于数学公式的推导和数学思想的传达,而对于其在具体物理问题上的应用鲜有涉及.本文以一维Su-Schrieffer-Heeger模型的拓扑相变问题为例,阐明了如何利用留数定理解析得到二阶位移量的表达式并用该物理量表征拓扑相变.在讲授留数定理的教学过程中引入具体物理问题的分析实例,可以使学生更深刻地理解数学定理中的物理内涵.     

T-STRESS IN PIEZOELECTRIC SOLID

The non-singular and bounded terms for stresses near the crack tip were investigated. The crack problem in a transversely isotropic piezoelectric solid for the plane problem was dealt with. The principle of superposition and the Plemelj formulation were introduced. The non-singular terms are given by solving Rieman-Hilbert problem. It is shown that the non-singular terms are influenced by the elastic and electric constants.