随机环境中马氏链状态的各种常返性与暂留性

考虑到随机环境中马氏链的状态在受到环境因素各种条件的影响下,引入了随机环境中马氏链状态的各种常返性与暂留性概念,讨论了这些常返性与暂留性的相互关系,从而说明随机环境中马氏链状态的常返性与暂留性和经典马氏链状态的常返性与暂留性有着显著的区别.     

局部凸空间的正规性

本文建立局部凸拓扑向量空间的正规性、完全正规性和单调正规性的等价条件．作为这些结果的应用，研究了函数空间的单调正规性和可度量性．     

经验似然的冗余性

提出经验似然的冗余性和偏冗余性的概念,讨论了相应的冗余性等价条件,将GMM的冗余性结果推广到经验似然估计,同时模拟实验结果也证实了经验似然的冗余性和偏冗余性对估计的影响.     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

次正规子群与有限群的超可解性

通过Sylow子群的极大子群和次正规性,利用极小阶反例的方法,得出群p-幂零性和超可解性的结论.本文的创新改进之处在于结合Sylow子群的极大子群和次正规性,研究p-幂零性和超可解性的相关结论.     

平均跟踪性与双曲线性同胚

本文研究了双曲线性自同胚的平均跟踪性,利用双曲线性映射的性质和压缩映射定理,得到了在有界的Banach空间上的双曲线性自同胚具有平均跟踪性.另外,证明了在一般的度量空间上的压缩映射也具有平均跟踪性.     

Musielak—Orlicz空间L^p（x）（Ω）的若干凸性

本文研究了一类特殊的Musielak-Orlicz空间Lp(x)(Ω)赋予Luxemburg范数时的严格凸性,局部一致凸性,弱局部一致凸性,中点局部一致凸性与一致凸性.利用Banach空间几何学中刻画凸性的一般方法,并结合一般Musielak-Orlicz空间凸性的判别准则,获得了用p(x)刻画空间Lp(x)(Ω)赋予Luxemburg范数时,上述几种凸性的充分必要条件.     

求sum from i=1 to n(f(x_i))的值的方法

有些函数值的求和问题,表面上看,与周期性、等差性、等比性无关,但事实上隐含着周期性、等差性、等比性,一旦将其周期性、等差性、等比性揭示,问题便迎刃而解.笔者就从何处揭示这些隐含的特性,从哪里入手找到撬动这些特性的支点,作一些探析,以飨读者.     

半直线上随机环境中可逗留随机游动的常返性

本文主要讨论了在独立但不同分布环境下，半直线上可逗留随机环境中随机游动的常返性和非常返性，并进一步研究了常返性中的正常返性和零常返性．     

一类二阶非线性差分方程的振动性与渐近性

研究了一类二阶非线性差分方程解的振动性与渐近性,建立了三个新的振动性与渐近性定理,推广和改进了已知的一些结果.     

A modified quasi-boundary value method for ill-posed problems

In this paper, we study a final value problem for first order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.     

平衡问题解的存在性

主要研究平衡问题解的存在性.通过对目标函数和可行集合的渐近分析,给出拟单调平衡问题解集非空的条件.进而用类似的方法研究了向量平衡问题解存在的条件,并将其应用到向量优化问题上.     

强向量均衡问题与不动点问题的粘性逼近算法

讨论了强向量均衡问题与非扩张映射不动点问题的公共解.首先,给出了强向量均衡问题的辅助问题,并在适当的条件下,证明了其解的存在性和唯一性结果.然后,利用这些结果,提出了强向量均衡问题与非扩张映射不动点问题公共解的粘性逼近算法,并进一步证明了,在适当的条件下,由该算法产生的迭代序列强收敛于强向量均衡问题和非扩张映射不动点问题的公共解.     

Analysis of nonlinear BVPs motivated by fluid film flow over a surface

We study a coupled nonlinear boundary value problem which has been shown to have applications to fluid flow and heat transfer in a fluid film over a stretching surface for set values of the model parameters (one of which determines the size of the problem domain). For arbitrary values of these parameters we are able to establish the existence and uniqueness of a class of monotone solutions. Perturbation solutions are then constructed and used to approximate certain invariants for the solutions. We then study a related boundary value problem formed by imposing an additional boundary condition on one of the governing equations (which results in an ill-posed problem), and we arrive at conditions allowing for solutions to this four-parameter problem to agree with the solutions to the three-parameter problem.     

A symmetry problem from probability

We examine solutions of two related boundary value problems for smooth domains in Euclidean space which arise from variational problems in probability. We show that the existence of solutions to each problem implies that the domain is a sphere.

     

Statistical causality,martingale problems and local uniqueness

The paper considers a statistical concept of causality in continuous time in the filtered probability spaces which is based on the Granger’s definition of causality. The given causality concept is then applied to the solution of the martingale problem (associated with the stochastic differential equation driven with semimartingales). More precisely, we show that the given causality concept is closely connected to the concept of extremality of measures for the solutions of the martingale problem, for the stopped martingale problem and for the local martingale problem. We also show the equivalence between some models of causality and local uniqueness (for the solutions of the martingale problem).     

The forward and inverse problems for a fractional boundary value problem

In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered.     

Fractional knapsack problems

The fractional knapsack problem to obtain an integer solution that maximizes a linear fractional objective function under the constraint of one linear inequality is considered. A modification of the Dinkelbach's algorithm [3] is proposed to exploit the fact that good feasible solutions are easily obtained for both the fractional knapsack problem and the ordinary knapsack problem. An upper bound of the number of iterations is derived. In particular it is clarified how optimal solutions depend on the right hand side of the constraint; a fractional knapsack problem reduces to an ordinary knapsack problem if the right hand side exceeds a certain bound.     

On variational perturbations of control problems: Minimum-time problem and minimum-effort problem

In order to obtain numerical solutions for an abstract optimal control problem, one approximates the abstract operations in a computationally feasible manner. After having found an approximate optimal solution, the question is whether a sequence of these approximate optimal solutions converges to an optimal solution of the original problem. In this work, we are concerned with this type of convergence on the time-optimal control problem for a class of linear systems with distributed parameters and on the minimum-effort problem.     

F-互补问题及其与极小元问题的等价性

本文在Ｂａｎａｃｈ空间中引进了 Ｆ－互补问题,讨论了这一问题解的存在性,在向量格中,给出了Ｆ－互补问题的可行集是 ∧ －子格的条件,研究了Ｆ－互补问题与最小元问题的等价性。