基于聚类分析和鉴别信息的教学效果评价模型分析

应用聚类分析算法和鉴别信息方法构建一个评价大学生学业水平与学生管理措施之间的相关性模型,基于平均数、中位数、及格率、优秀率和区分度等指标提出一个评价教学改革措施有效性的指标,并分析指标的有效性。将这一方法应用于包含多个课程的9年累计成绩数据,分析成绩变化与相关管理措施的相关性,验证模型的有效性。     

Hopf Bifurcation for Non—smooth Planar Dynamical Systems

The purpose of this paper is to study the Hopf bifurcation property of the non-smooth planar dynamical systemwhere the individual functions K± R2 x I R2 at the right-hand side for some interval I containing 0 are smooth enough and given byThe parameter dependent matrices Aa(A) are assumed to be of the formwhere a 0 and w±() > 0. And the nonlinear terms in equation (??) are assumed to be smooth enough and have the formIn a standard way we extend the system (??) to a differential inclusion …     

近似求解Cahn-Hilliard方程的拟谱方法

利用拟谱方法研究了非线性Cahn-Hilliard方程解的近似, 分析了半离散与全离散近似解的收敛性和稳定性, 并给出收敛速度的估计. 同时还讨论了半离散问题解的爆破现象.     

Generalized Hopf Bifurcation for Non-smooth Planar Dynamical Systems： the Corner Case

Piece-wise smooth systems are an important class of ordinary differential equations whosedynamics are known to exhibit complex bifurcation scenarios and chaos. Broadly speaking,piece-wise smooth systems can undergo all the bifurcation that smooth ones can. Moreinterestingly, there is a whole class of bifurcation that are unique to piece-wise smoothsystems, such as the bifurcation caused by the geometric shape of the region in which thevector field is analyzed. For example (see Figure 1), the region is divided into two partsI and Ⅱ by a discontinuity boundary which contains a corner at O. When an orbit crossthe corner, border-collision bifurcation may occur (cf. [1]). The present paper deals withthe mechanics of the generalized Hopf bifurcation when the stationary point locates at thecorner.     

8-形同宿轨道附近的同宿轨分支性质

In this paper we investigate the homoclinic bifurcation properties near an eight-figure homoclinic orbit of co-dimension two of a planar dynamical system. The corresponding local bifurcation diagram is also illustrated by numerical computation.     

A Petrov－Galerkin Method with Linear Trial and Quadratic Test Spaces for Parabolic Convection－Diffusion Problems

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鞍结同宿轨道附近分支现象的数值分析

主要采用数值分析的方法研究一个化学反应方程中鞍结 同宿轨道附近的分支性质, 包括平衡点、 周期解和双曲同宿轨道等分支现象及其稳定性.     

高维离散动力系统中Hopf不变流形的存在性

研究高维离散动力系统中 Hopf不变流形 (周期不变流形 )的存在性 .利用不动点处的特征值结构 ,应用 Fredholm算子理论 ,直接证明高维映射的 Hopf不变流形的存在性 ,同时给出相应不变流形的渐近表达式     

偏微分方程数值解课程的思索

探讨《偏微分方程数值解》课程教学改革的思考与体会,主要包括教学方法和教学模式的改革,加强背景知识的介绍,将科研前沿带入课堂,将MATLAB融入教学以及考核方式的改革等。