完备非紧流形上的射线与Busemann函数

讨论了完备非紧正则黎曼流形上的Busemann函数间的关系，并用于讨论流形的几何拓扑性质．     

LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits \mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.     

FOURIER-TRANSFORM RAMAN AND INFRARED SPECTRA AND VIBRATIONAL ASSIGNMENT FOR SOLID GLUTARIMIDE

Abstract

The FT-Raman and FT-IR spectra of crystalline glutarimide and its N-deuterated derivative have been recorded in the range 4000-100 cm^?1. A complete vibrational assignment is given for all internal modes and is supported by normal coordinate analysis based on a general valence force field. The calculated frequencies are in very good agreement with experiment. A close similarity is found for frequencies of the corresponding vibrations of glutarimide and uracils in the solid state. It is concluded that the strength of hydrogen bonding in glutarimide is very similar to that in crystalline pyrimidine nucleic bases.     

数学师范生教育科研能力培养的思考

在分析国内数学师范生教育科研现状的基础上,提出培养数学师范生教育科研能力的几点意见,主要有：转变观念,重视师范生教育科研能力的培养;完善培养目标,规范论文与研究报告的写作;通过指导阅读书籍、报刊、学位论文等,培养学生对教育问题的敏感性；以专业课程为依托,实现教育科研与专业学习的有机结合；充分利用教育实习,实现教育科研与教学活动的紧密结合;让师范生参与教学法老师的教育科研项目,加深其时科研的体会和感受.     

移动交界面流固耦合传热的数值稳定性分析

研究了交界面移动情况下流固耦合稳态传热的数值稳定性问题.考虑Dirichlet-Robin组合边界条件,用速度表征交界面的移动情况,流体域和固体域分别采用有限体积法和有限单元法进行离散及数值求解,利用Goudonov-Ryabenkii理论正则模态分析方法重点研究了交界面移动时数值方法的稳定性,最终获得了一条由耦合系数和移动速度组成的最优曲线,并且证明了当耦合系数和移动速度在这条曲线上取值时,离散的求解域能够达到最快的收敛速度及绝对的稳定性特征.为设计人员进行数值仿真时选取合理的参数提供了参考.     

(λ,μ)-模糊粗糙子群

本文根据(λ,μ)-模糊正规子群定义了新的同余关系,由此提出了(λ,μ)-模糊粗糙子群和(λ,μ)-模糊粗糙正规子群的概念,并研究了它们的性质.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

方差可能无穷的“中度偏离”单位根过程的复合分位数估计

考虑一类"中度偏离"单位根过程,y_t=q_ny_t-1+u_t,其中qn=1+c/(k_n),k_n=o(n),c为一非零常数,{u_t}为随机扰动项序列.在允许扰动项方差无穷的条件下,构造q_n的复合分位数估计,并得到了该估计的渐近分布.最后通过数值模拟,在扰动项服从t(2)分布下,说明了该估计的稳健和有效性.