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??In this paper, we consider the optimal dividend problem in the spectrally positive L\'{e}vy model with regime switching. By an auxiliary optimal problem, the principle of dynamic programming and the fluctuation theory of L\'{e}vy processes, we show that optimal strategy is a modulated barrier strategy. The value function and the optimal dividend barrier are obtained by iteration.     

Model updating for undamped gyroscopic systems with connectivity constraints

ABSTRACT

An important and difficult aspect for the finite element model updating problem is to make the updated model have physical meaning, that is, the connectivity of the original model should be preserved in the updated model. In many practical applications, the system matrices generated by discretization of a distributed parameter system with the finite element techniques are often very large and sparse and are of some special structures, such as symmetric and band structure (diagonal, tridiagonal, pentadiagonal, seven-diagonal, etc.). In this paper, the model updating problem for undamped gyroscopic systems with connectivity constraints is considered. The method proposed not only preserves the connectivity of the original model, but also can update the analytical matrices with different bandwidths, which can meet the needs of different structural dynamic model updating problems. Numerical results illustrate the efficiency of the proposed method.     

Optimal control of a two-dimensional contact problem

We consider a frictionless contact problem with unilateral constraints for a 2D bar. We describe the problem, then we derive its weak formulation, which is in the form of an elliptic variational inequality of the first kind. Next, we establish the existence of a unique weak solution to the problem and prove its continuous dependence with respect to the applied tractions and constraints. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result.     

Conditions for graphs to be path partition optimal

The path partition number of a graph is the minimum number of edges we have to add to turn it into a Hamiltonian graph, and the separable degree is the minimum number of edges we have to add to turn it into a 2-connected graph. A graph is called path partition optimal if its path partition number is equal to its separable degree. We study conditions that guarantee path partition optimality. We extend several known results on Hamiltonicity to path partition optimality, in particular results involving degree conditions and induced subgraph conditions.     

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

In this article,we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients.The authors use a new method introduced by Duzaar and Grotowski,to prove partial regularity for weak solutions,based on a generalization of the technique of harmonic approximation and directly establish the optimal Ho¨lder exponent for the derivative of a weak solution on its regular set.     

Compressible navier-stokes-poisson equations

This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed.     

状态和控制均含时滞的受外界扰动的线性系统的最优控制

主要研究一类受外界持续扰动且状态和控制含不同时滞的线性系统的最优控制,首先通过变量代换,将系统化为控制不含时滞的滞后型微分系统.接着使用最优控制的极大值原理的必要条件,得到含超前和滞后项的两点边值问题.为了得到最优控制律的解析解,引进一个灵敏参数ε,得到两点边值问题序列,通过迭代法,得到最优控制律的解析解.并对外界扰动状态构造降维观测器,来实现最优控制律的物理可实现性.最后实例验证了上述方法的有效性.     

具有热储备的并行可修系统的最优控制

研究了并行可修复系统,在Banach空间中正解的存在唯一性,并以范数指标函数衡量控制标量为标准的最优控制.     

关于高等教育学费的优化模型探讨

给出了高校学费的优化模型,该模型对于高校标准学费的制定有着一定的借鉴意义.对模型的求解,采用了数据拟合和多元线性回归的方法,并通过计算机模拟的方法来对结果加以检验,检验结果表明模型是合理的.整个求解过程借助了MATLAB6.5,求解过程极其便利可行.     

可修复人机储备系统最优控制

讨论了一个运行部件和一个储备部件组成的可修复系统的最优控制问题.