Preparation of Papers

In this paper, we study the local uniqueness of the solutions to the extended linear complementarity problem (XLCP, Ref. 1) by means of a concept which is an extension of the nondegenerate matrix in the standard LCP. Then, we give some special characterizations for the local uniqueness of the solutions to the horizontal linear complementarity problem (HLCP).     

剪力墙的面外刚度对建筑结构计算结果的影响

剪力在钢筋混凝土建筑结构中有着广泛的应用,在计算时一般都忽略剪力面外刚度的贡献。本文利用一种同时具有面内刚度和面外刚度的剪力墙模型,研究了剪力墙的面外刚度对整体结构的控制位移和固有频率的影响。结果表明,剪力面外刚度的贡献与剪力墙之间的耦合程度以及是要用刚性楼板假定有关,在大型复杂的纵横剪力墙结构中,剪力墙面外刚度的贡献不可忽略。     

微裂纹屏蔽机理的力学理论

简述了微裂纹屏蔽的力学理论和主要结论．分析了与这些理论有关的两种研究途径中的四种假设的正当性和适用范围．对相互矛盾的结论做了讨论．介绍了作者在这一领域的研究成果,并尝试将这方面的研究推广到复合材料和界面裂纹问题中．      

Existence and uniqueness of global strong solutions of two models in atmospheric dynamics

In this paper, the author proves by the methods of energy estimates the existence and uniqueness of global strong solutions of barotropic nondivergent model and baroclinic quasi-geostrophic quasi-nondivergent model. The two models are fundamental ones in atmospheric dynamics. The results here generalize the outcome given by the author in [3]–[5] and verify a conjecture posed by Zeng Qing-cun in [1].     

用产品工艺假定推算两大部类构成的充要条件

依据投入产出表使用产品工艺假定推算社会再生产的两大部类构成,比使用产业部门工艺假定推算更符合马克思政治经济学原理.使用产品工艺假定推算在数学上可以归结为一个带非负约束的二次规划问题.运用参数线性规划方法能够证明这样的推算存在一个充分必要条件.这一充分必要条件对于通常使用产品工艺假定与产业部门工艺假定的组合进行推算,也有作用.     

Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions

We consider a class of analytic area-preserving mappings C^m-smoothly depending on a parameter. Without imposing on any non-degeneracy assumption, we prove a formal KAM theorem for the mappings, which implies many previous KAM-type results under some non-degeneracy conditions. Moreover, by this formal KAM theorem, we can also obtain some new interesting results under some weaker non-degeneracy conditions. Thus, the formal KAM theorem can be regarded as a general KAM theorem for areapreserving mappings.     

Reduction of round-off errors in chemical kinetics

In this paper, a modification of chemical kinetics is introduced in order to reduce round-off errors in stiff source terms. Fast chemical processes close to partial equilibrium are often composed of different contributions that cancel each other out (for example forward and backward reactions). These contributions tend to be very large compared to their sum. Thus, computer evaluation of the chemical source term can lead to serious round-off errors due to cancellation. This can cause severe convergence problems within Newton's method when simulating the process with implicit integration methods and thus lead to additional step size reduction. Here, a method is presented that reduces the round-off error by making a slight change to the model. Furthermore, this change is smooth and does not change the dimension, so that it is also possible to apply the method locally when solving partial differential equations. Numerical examples presented in this paper verify the approach.     

Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs

An example of an SDP (semidefinite program) exhibits a substantial difficulty in proving the superlinear convergence of a direct extension of the Mizuno—Todd—Ye type predictor—corrector primal-dual interior-point method for LPs (linear programs) to SDPs, and suggests that we need to force the generated sequence to converge to a solution tangentially to the central path (or trajectory). A Mizuno—Todd—Ye type predictor—corrector infeasible-interior-point algorithm incorporating this additional restriction for monotone SDLCPs (semidefinite linear complementarity problems) enjoys superlinear convergence under strict complementarity and nondegeneracy conditions. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

Weakness and improvement on Wang–Li–Tie’s user-friendly remote authentication scheme

In an open network environment, the remote authentication scheme using smart cards is a very practical solution to validate the legitimacy of a remote user. In 2003, Wu and Chieu presented a user-friendly remote authentication scheme using smart cards. Recently, Wang, Li, and Tie found that Wu–Chieu’s scheme is vulnerable to the forged login attack, and then presented an improvement to eliminate this vulnerability. In our opinion, the smart card plays an important role in those schemes. Therefore, we demonstrate that Wang–Li–Tie’s scheme is not secure under the smart card loss assumption. If an adversary obtains a legal user’s smart card even without the user’s corresponding password, he can easily use it to impersonate the user to pass the server’s authentication. We further propose an improved scheme to overcome this abuse of the smart card.     

Projected Gradient Type Method of Centers for Constrained Optimization

本文提出了一种求解约束优化问题的新算法—投影梯度型中心方法．在连续可微和非退化的假设条件下，证明了其全局收敛性．本文算法计算简单且形式灵活．