A NOTE ON REARRANGEMENTS OF SERIES IN BANACH SPACES

We generalize Kadec‘s and Yan Zikun‘s resuhs in [1],[2] to prove; in every infinite dimensional real Banach space Y there exist an infinite dimensional subspace X and a series ∑xn such that ∑xn has property(N) in X. but(the domain of sums of this series) S(∑xn) is not a convex set.     

Frame multiresolution analysis and infinite trees in Banach spaces on locally compact abelian groups

We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaceson locally compact abelian groups including modulation spaces.     

紧—凸性与紧—光滑性

本文首先通过暴露集和暴露泛函的概念引入卫闭凸集的紧－严格凸、紧－强凸、紧－一致凸及紧－非常凸等概念。用对偶映射给出了Ｂａｎａｃｈ空间的两种新光滑性－紧－一致光滑与紧－非常光滑。然后特别研究了Ｂａｎａｃｈ空间的紧－非常凸与紧－非常光滑。此外还得到关于对偶映射的两个新结果。     

集值测度的延拓定理

讨论了集值测度的若干基本性质，在此基础上，研究了集值测度凸性，紧性及其靠拢定理，特别是到紧凸值集值测度的延拓定理。     

THE ABSTRACT CAUCHY PROBLEM AND A GENERALIZATION OF THE LUMER-PHILLIPS THEOREM

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙｔｈｅｔｈｅｏｒｙｏｆＣｓｅｍｉｇｒｏｕｐｓｈａｓｅｘｔｅｎｓｉｖｅｌｙｄｅｖｏｌｏｐｏｅｄｂｙｍａｎｙａｕｔｈｏｒｓ（ｓｅｅ［２－８,１４］）,ｂｕｔａｎａｔｕｒａｌａｎｄｉｍｐｏｒｔａｎｔｑｕｅｓｔ...     

MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES

This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

本文对Ｊ．－Ｐ．Ａｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓｋａ最近关于自反严格凸Ｂａｎａｃｈ空间中闭凸集值映射最小选择连续的于个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱ｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓｋａ的条件下闭凸集值映射最小选择的连续性,其次对Ｊ．Ｐ．Ａｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓｋａ的结果给出了一个新的简单证明,最后用反例说明本文给出的条件Ｊ．Ｐ．Ａｕｂｉｎ与Ｈ．Ｆｒａｎｋｏｗｓａｋａ条     

关于多目标分式规划

Abstract. In this paper some optimality criteria are proved and some Mond-Weir type duality theorem for multiobjective fractional programming problems defined in a Banach space is obtained.     

无限维离散时间代数Riccati方程的非负解

本文研究了无限维离散时间代数Ｒｉｃｃａｔｉ方程（ＤＡＲＥ）的非负自伴解，给出了（ＤＡＲＥ）有非负 自伴解的充要条件．对幂可稳定化的离散时间系统∑ｄ（Ａ，Ｂ，－），若Ａ是可逆的，Ｂ是紧的，给出 了（ＤＡＲＥ）的非负解集的参数化刻画，并以Ａ的有限维的含于反稳定的不可观察子空间中的不变子 空间为参数．该结果把［５］中关于有限维系统∑ｄ（Ａ，Ｂ，－）的结果推广到了一般的系统∑ｄ（Ａ，Ｂ，－） 中．最后，还给出了∑ｄ（Ａ，Ｂ，－）具有非负稳定化解的充要条件．     

TWO DIMENSIONAL RIEMANN PROBLEM FOR GAS DYNAMICS SYSTEM IN THREE PIECES

1.IntroductionItiswellknownthattheRiemannproblemplaysanessentialroleindevelopingone-dimensionaltheoryofhyperbolicconservationlaws[3]anditisthesimplestoneofgeneralCauchyproblemandmucheasiertoclarifytheexplicitstructureofitssolutions.Ontheotherhand,the...     

时变种群扩散系统最优生育率控制的非线性问题

本文讨论了一类时变种群扩散系统最优生育率控制的非线性问题，证明了最优生育率控制的存在性，给出了控制为最优的必要条件及其最优性组，本结果可为种群扩散系统最优控制问题的实际研究提供物理理论基础。     

证券价格长期波动控制系统的最优控制策略

探讨证券价格长期波动控制系统的最优控制问题.建立了在有效市场条件下证券价格长期波动的控制系统模型.为了使证券价格和内在价值按照人们预期的目标变化,探讨了对它们服从的系统采用经典信息结构下的随机最优控制策略问题.设计了使系统的输出跟踪证券内在价值的估计值,同时使调节控制的幅度尽可能小的性能指标,给出了最优控制策略的求解公式和计算过程,并给出了考虑系统性能的计算过程,对相应结果进行了分析.主要结论是:当价值对价格的均衡回归调整不足,或投资者对前期价值的增值预期乐观时,最优控制策略所起的作用在加强;而当价值对价格的均衡回归调整过度,或投资者对前期价值的增值预期悲观时,最优控制策略所起的作用在减弱.这些结果可以为完善证券市场和上市公司的监管提供理论依据     

A POSTERIORI ERROR ESTIMATE OF OPTIMAL CONTROL PROBLEM OF PDE WITH INTEGRAL CONSTRAINT FOR STATE

In this paper, we study adaptive finite element discretization schemes for an optimal control problem governed by elliptic PDE with an integral constraint for the state. We derive the equivalent a posteriori error estimator for the finite element approximation, which particularly suits adaptive multi-meshes to capture different singularities of the control and the state. Numerical examples are presented to demonstrate the efficiency of a posteriori error estimator and to confirm the theoretical results.     

一类中立型时变非线性控制系统的镇定与控制

本文利用专著（１）￣（３）中的有关方法,讨论了一类具有滞后的中立型时变非线性控制系统的镇定与次优控制问题,得出了滞后量与非线性项的估计公式,并推广了文（４）,（５）的结果。     

OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE

In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur's theorem and optimality condition is derived by means of normal cone.     

PERIODIC SOLUTION FOR A CLASS OF NEUTRAL HIGHER DIMENSIONAL DIFFERENTIAL SYSTEM WITH DELAY

This paper,using the theory of exponential dichotomy and fixed point theo- rem,discusses the existence of periodic solution for a class of neutral higher dimensional differential system with delay,the result extends and improves the result of paper[6].     

一类随机时延网络控制系统的神经网络自适应容错控制

针对一类随机时延网络控制系统,提出一种基于RBF神经网络自适应动态补偿的容错控制策略.该方法通过在线估计时延将系统建模为随机切换系统,并在模型参考自适应方法的基础上设计RBF神经网络动态补偿容错控制器,利用Lyapunov稳定性理论给出神经网络补偿器的在线权值学习算法,以保证网络控制系统在故障情况下的跟踪性能和状态一致最终有界稳定.最后通过仿真验证了该方法的有效性.     

分数阶抛物方程控制系统最优控制的稳定性

本文研究了一类分数阶抛物方程的最优控制问题,主要讨论了其最优控制与最优值的稳定性.利用了凸方法获得了获得了这类问题最优控制的稳定性结果,并且推广了在参考文献[3]中的最优控制稳定性结论.