New Version of the Newton Method for Nonsmooth Equations

In this paper, an inexact Newton scheme is presented which produces a sequence of iterates in which the problem functions are differentiable. It is shown that the use of the inexact Newton scheme does not reduce the convergence rate significantly. To improve the algorithm further, we use a classical finite-difference approximation technique in this context. Locally superlinear convergence results are obtained under reasonable assumptions. To globalize the algorithm, we incorporate features designed to improve convergence from an arbitrary starting point. Convergence results are presented under the condition that the generalized Jacobian of the problem function is nonsingular. Finally, implementations are discussed and numerical results are presented.     

An Experimental Study of Liquid Jets Interacting with Cross Airflows

The primary break‐up of liquid jets in cross flows has been studied experimentally. An open‐circuit wind tunnel was employed in which the airflow was generated by a centrifugal fan. The test section, positioned 3 m downstream of the fan, was made of clear acrylic resin to allow optical access and visualization. The working liquid used in the present experiment was an aero‐engine lubrication oil, which was injected perpendicularly into the air flow, via a nozzle placed in the top wall of the test‐section. The study of the primary break‐up mechanisms of the jet involved three parameters, the oil viscosity, and the jet and air cross flow velocities, which were varied independently. Two different break‐up regimes were observed and identified; arcade break‐up and bag break‐up. These were separated by a transition zone. Transverse and longitudinal (or streamwise) penetrations of the jet before the liquid breakup were also measured. The correlation proposed by Wu et al. to predict the jet transverse penetration before the break‐up of the liquid, as a function of the liquid/airflow momentum‐flux ratio, was found to be applicable only to liquids with low viscosity. An empirical extension to this equation has been produced.     

Banach空间上的不连续映射的不动点定理

本文把著名的Ｓｃｈａｕｄｅｒ定理推广到不连续映射的情形，主要的结果表明对任一Ｂａｎａｃｈ空间中的任一给定的紧凸子集上的任一自映射，可以在紧凸集上找一点ｘ，使‖ｘ－ｆ（ｘ）‖不超过函数的固定的不连续测量，这一结果推广了Ｓｃｈａｕｄｅｒ定理和文［１］的结果     

Gwinner变分不等式和隐变分不等式

本文在研究Gwinner变分不等式的基础上，利用新的集值映象不动点定理，探讨一类具广泛意义的隐变分不等式问题，改进了迄今相关结果中对紧性条件的要求，在非紧设置下获得了解的存在性定理．     

射线引起DNA双链断裂的统计分布

辐射过程引起的生物细胞的DNA双链断裂是一种很重要的细胞损伤过程.射线在细胞中能量沉积比较大时,DNA双链断裂的碎片分布会偏离随机断裂模型给出的结果,为此发展了新的模型分析方法-统计碎裂模型.根据统计物理学的原理和方法，放射性射线照射细胞后，将射线的能量传递给细胞中的DNA分子，当沉积的能量比较大时，体系会经过一个弛豫过程，DNA碎片大小l按照统计规律分布.体系熵值取极大的分布是最可几的分布，从而得到了辐射导致DNA双链断裂后碎裂片段随其大小l的分布函数exp(αl+βl²)，它对应于 两种成分，一种成分随碎裂片段的大小l的增大而迅速减小，这对应于分布函数中的exp(βl ²)项，对于质量比较小的碎裂片段，这种成分是主要贡献；另外一种成分随碎 裂片段的大小l的增大而缓慢减小，这对应于分布函数中的exp(αl)项，对于质量比较大的 碎裂片段，这种成分是主要贡献.根据实验所测的碎裂片段分布，通过数值解法解积分方程 ，将热力学参数α，β解出，与实验结果进行比较，实验的结果支持了DNA双链断裂后碎裂 片段分布的统计碎裂模型. 关键词： 熵 统计碎裂模型 DNA双链断裂     

On Quasimonotone Variational Inequalities

In this paper, we study variational inequalities with multivalued mappings. By employing Fan's lemma, we establish the existence result for the dual formulation of variational inequalities with semistrictly quasimonotone mappings. We also show that similar results for quasimonotone variational inequalities do not hold.     

Singular values, quasiconformal maps and the Schottky upper bound

Some properties and asymptotically sharp bounds are obtained for singdar values of Ramanujan’s generalized modular equation. from which infinite-product representations of the Hersch-Pfluger ϕdimtortion function ϕ _K (r) and the Agard η-distortion function η _K (t) follow. By these results, the explicit quasiconformal Schwan lemma is improved, several properties are obtained for the Schottky upper bound, and a conjecture on the linear distortion function λ (K) is proved to be true.     

拟共形映照和线性局部连通集

本文证明了Ｒｎ中线性局部连通集定义中的两个性质分别在保持无穷远点不变的拟共形映照下是不变的，并且指出保持无穷远点不变的条件是必不可少的．反过来，设ｆ是Ｒｎ上的同胚，ｆ（　）＝　，若线性局部连通集定义中的任意一条性质在ｆ下不变，则ｆ必是拟共形映照．     

Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping.     

关于满足强分离开集条件的自相似集的Hausdorff测度

设E是Rn中由相似压缩S1,S2,…,Sm所确定的满足开集条件的自相似集,其Hausdorff维数为s,其s-维Hausdorff测度记为Hs(E).利用部分估计原理得到了本文的主要结果:若E满足强分离开集条件,则在E中存在一个压缩拷贝串序列{Ui}和紧集U(|U|>0),使得Hs(U)等于|U|s,并且{Ui}按Hausdorff度量收敛到U,进而证明了由U可以构造一个数列,使得该数列正好收敛到Hs(E);另外,引入了自相似集的相似压缩不动点,得到了等式Hs(E∩U)=|U|s 成立的一个必要条件.