关于复合函数极限几个定理的探讨

本文对复合函数的极限做了细致的讨论，给出了6个定理。     

微分中值定理的一种统一证明方法

利用闭区间上连续函数的介值定理、单调有界定理及极限的性质,统一地证明了广义微分中值定理,其余的微分中值定理可以作为广义微分中值定理的特例给出。     

Wilkinson定理扰动界的改进估计

Wilkinson定理是代数特征值问题中的一个经典定理,文章给出了Wilkinson定理的结果中关于扰动矩阵上界的另一种估计形式,并指出该形式对Wilkinson定理具有一定的改进。     

非线性边界条件的Burgers－KdV方程的静态解

对几类非线性边值条件，讨论了Ｂｕｒｇｅｒｓ－ＫｄＶ方程的边值问题的静态解的存在性和解的个数．借助不动点定理，证明了该边值问题至少有一个，至多有有限个静态解．     

Z-空间上的有界线性泛函的性质

文章在次范整线性空间中利用Hahn-Banach扩张定理给出泛函存在定理,分隔性定理,这些定理推广赋范线性空间的泛函存在定理、分隔性定理.     

无穷多项和求极限问题的探讨

针对求极限过程中的一个难点———无穷多项和求极限 ,可通过先求和、夹逼定理、无穷小分析法、定积分等四种方法加以解决。     

Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow(a lumped vortex model)

For purpose of easy identification of the role of free vortices on the lift and drag and for purpose of fast or engineering evaluation of forces for each individual body,we will extend in this paper the Kutta–Joukowski(KJ) theorem to the case of inviscid flow with multiple free vortices and multiple airfoils. The major simplification used in this paper is that each airfoil is represented by a lumped vortex,which may hold true when the distances between vortices and bodies are large enough. It is found that the Kutta–Joukowski theorem still holds provided that the local freestream velocity and the circulation of the bound vortex are modified by the induced velocity due to the outside vortices and airfoils. We will demonstrate how to use the present result to identify the role of vortices on the forces according to their position,strength and rotation direction. Moreover,we will apply the present results to a two-cylinder example of Crowdy and the Wagner example to demonstrate how to perform fast force approximation for multi-body and multi-vortex problems. The lumped vortex assumption has the advantage of giving such kinds of approximate results which are very easy to use. The lack of accuracy for such a fast evaluation will be compensated by a rigorous extension,with the lumped vortex assumption removed and with vortex production included,in a forthcoming paper.     

相似定理在复合材料结构件上的应用

为尽量减少复合材料结构件的试验研究成本,除非必须使用原尺寸的结构试验件之外,通常情况下都采用结构件的缩比件进行所需要的结构强度试验。通过试验和计算的对比分析,阐明了相似定理在正交各向异性的复合材料结构上应用的合理性。     

顺序加载下的积累疲劳强度最优可靠度设计

介绍了零件在受到顺序加载下的几组载荷作用的积累，疲劳强度最优可靠度的设计计算方法，并地迈因纳定理（Miner‘s rule)应用范围做了一定补充。     

Lagrange中值定理的证明

通过从Lagrange中值定理的结论、条件、几何意义三个方面的分析，提出了构造辅助函数的思路和方法，并利用辅助函数证明了Lagrange中值定理。