Riemann面上带cusp奇点的共形度量

Riemann面上带有奇点的度量是复几何中重要的研究对象.对Riemann面上带有cusp奇点且满足面积和Calabi能量有限的共形度量进行研究，得到HCMU度量在cusp奇点附近精确的表达式.     

重心坐标系下三次C样条奇拐点分析

介绍三次C样条和重心坐标,同时给出重心坐标系下三次C样条的参数表示形式,利用仿射不变量来研究三次C样条奇拐点存在判别条件,并且对仿射不变量p的各种情况进行讨论,同时简化奇拐点判别条件。     

Uncertainty analysis for peer assessment: oral presentation skills for final year project

Peer assessment plays an important role in engineering education for an active involvement in the assessment process, developing autonomy, enhancing reflection, and understanding of how to achieve the learning outcomes. Peer assessment uncertainty for oral presentation skills as part of the FYP assessment is studied. Validity and reliability for complex assessments were conceptualised in the context of quantification, hierarchical system of uncertainties, aleatory uncertainty, and epistemic uncertainty. Systems as assessment methods were also conceptualised to define elements (i.e. examiner, examinee, and difficulty) as variables or/and constants, and to study the uncertainty behaviour of the peer assessment within the framework of the parametric uncertainty model. As a result, a singularity, at which the hierarchical structure of uncertainties breaks down, and its related behaviour were theoretically predicted and experimentally verified. Also, a validity paradox, when the ‘difficulty’ level is sufficiently lowered, was found to be possible and verified for oral presentation skills. It may be useful for understanding fundamental characteristics of the peer assessment in which epistemic uncertainties are dependent on how the assessment is close to the singularity point.     

一类带有奇异位势的强奇性偏微分方程的正解的性质

主要讨论矩阵型强奇异偏微分方程      

Beyond Rational Autonomy: Levinas and the Incomparable Worth of the Student as Singular Other

This article explores the question: Why are students of worth? Educationally, an answer often involves a Kantian response: They are of worth because they are always ends and never means. This response is usually connected to a notion of autonomy interpreted as individual, rational self-determination. The article argues for a different answer. The essay begins with a recent educational example of construing worth as rational autonomy. Meira Levinson, in her book The Demands of Liberal Education (1999), argues for a version of rational autonomy which is taken in the essay as a Kantian response to the question. The essay then turns to Kant’s own understanding of intrinsic human worth as ends. Although the essay agrees in general with the notion of end, it criticizes Kant’s version of rational autonomy. Instead, it argues for a notion of worth as irreplaceable singularity. Both the critique of the Kantian answer and theessay’salternative are shaped by the philosophy of Emmanuel Levinas. Here technical notions of “the other,” proximity and singularity are brought to bear on the question of human worth. The Levinasian alternative, so the essay argues, better answers the question of student worth by highlighting the incomparability of the student as a singular other.     

具有奇点和时滞的p-Laplacian方程的正周期解

利用重合度理论,研究一类具有奇点和时滞的 p-Laplacian方程,获得其正周期解存在性新的充分条件,推广和改进了已有文献中的相关结论。     

解决高校课堂教学模式单一化问题的策略研究

随着生产力的提高,科学技术的快速发展,知识经济突飞猛进,社会对高等教育提出了更高的要求,特别是建立全新的人才培养模式。然而高校教学模式单一化问题制约着高校教学模式的改革与发展,因此,高校要积极探索、实践多样化、综合性的教学模式,从而提高课堂的教学质量,构建新型的教学与人才培养模式。     

关于场论中旋度的两个重要问题

本文指出了场论中旋度这一名称由来的缺陷,并作了改进,同时提出了研究奇点旋度的重要性及奇点旋度的算法。通过对几个典型物理场旋度的计算和分析,给出了利用场论理论研究一般物理场有关性质的方法。     

具有摩擦支承边界矩形薄板的局部分岔

建立了具有摩擦支承边界的矩形薄板在面内载荷作用下的动力学方程 ,利用L S方法和奇异性理论对系统进行了局部分叉研究 ,讨论了非退化情况下Z2 分叉问题 .利用数值模拟给出了开折参数局部分叉集图和分叉响应曲线及物理参数平面上的分叉响应规律 ,其结果与解析和实验研究有很好的一致性 .     

球对称均匀星的引力坍缩

本文首先从一般的角度讨论了球对称均匀星的引力坍缩问题,并且将该问题总结为求解两个一阶非线性的微分方程组;然后具体计算了当星体的状态方程为p=βζ(此处β是一个常数)时的坍缩解;最后我们对该问题作了进一步的讨论并指出外部观察者是无法观察星体坍缩到Schwarzschild半径之后的情况。