The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations

We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. We prove the convergence and stability of the scheme in L ₂ and C norms. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005.     

求解一类变形变分不等式的投影收缩算法及其性质

对一类变形的变分不等式：求，使得提出了一类投影收缩算法，并得到了该算法的收敛性及相关性质．     

Ba（n，x）~（134）Cs，~（134）Ba（n，2n）~（133）Ba，

用中子活化法相对于５４Ｆｅ（ｎ，Ｐ）５４Ｍｎ反应，在１３．５０—１４．８０ＭｅＶ中子能区测量了Ｂａ（ｎ，ｘ）１３４Ｃｓ，１３４Ｂａ（ｎ，２ｎ）１３３Ｂａ，１４０Ｃｅ（ｎ，２ｎ）１３９Ｃｅ，１４２Ｃｅ（ｎ，２ｎ）１４１Ｃｅ和２３Ｎａ（ｎ，２ｎ）２２Ｎａ的反应截面．并将所测的结果和其他作者的结果进行了比较，中子能量是用９０Ｚｒ（ｎ，２ｎ）８９ｍ＋ｇＺｒ反应和９３Ｎｂ（ｎ，２ｎ）９２ｍＮｂ反应截面比法测定的。     

Vibrational control of crystal growth from liquid phase

Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase.     

A globally convergent Newton method for solving strongly monotone variational inequalities

Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.     

关于多正解问题的某些研究

本文以ｆｐ 同伦方法为工具，借助于一些适当的变换，研究有序的（Ｂ）空间中的集值映象方程的多正解问题；在文中的有关工作中，还使用了集值映象的拟导数的某些性质．     

Research on sound radiation from body in free field

I.IntroductionWhenastructurcvibratcs,itsvibratingsurfacewillmakesurroundingmediummovetogethcrwithit.Ifthernotionissofastthatthcmediumroundthestructureproduccaloca1contractionandcxpansionandthcypropagatefaraway,thesoundradiationisformed.Itispossiblctodcscribeanalytica11ytheradiationfic1dofsimplyandregularlyshapcdsourcessuchaspointsoundsourccs,spherica1soundsourccsandinflnite1engthllnearsoundsourccs,butitisa1mostimpossib1ctosolvetheradiationfiledbyanyanalyt-ica1methodforsourcesofvcrycomplicateds…     

Extended convergence results for the method of multipliers for nonstrictly binding inequality constraints

In this paper, we extend the classical convergence and rate of convergence results for the method of multipliers for equality constrained problems to general inequality constrained problems, without assuming the strict complementarity hypothesis at the local optimal solution. Instead, we consider an alternative second-order sufficient condition for a strict local minimum, which coincides with the standard one in the case of strict complementary slackness. As a consequence, new stopping rules are derived in order to guarantee a local linear rate of convergence for the method, even if the current Lagrangian is only asymptotically minimized in this more general setting. These extended results allow us to broaden the scope of applicability of the method of multipliers, in order to cover all those problems admitting loosely binding constraints at some optimal solution. This fact is not meaningless, since in practice this kind of problem seems to be more the rule rather than the exception.In proving the different results, we follow the classical primaldual approach to the method of multipliers, considering the approximate minimizers for the original augmented Lagrangian as the exact solutions for some adequate approximate augmented Lagrangian. In particular, we prove a general uniform continuity property concerning both their primal and their dual optimal solution set maps, a property that could be useful beyond the scope of this paper. This approach leads to very simple proofs of the preliminary results and to a straight-forward proof of the main results.The author gratefully acknowledges the referees for their helpful comments and remarks. This research was supported by FONDECYT (Fondo Nacional de Desarrollo Científico y Technológico de Chile).     

高阶半线性抛物型方程组的生命跨度

其中m,P,q>1．利用试验函数方法,首先推导一些积分不等式,然后对方程组爆破解的生命跨度 [0,T)给出估计．