修理工单重定期休假可修系统更换模型研究

针对修理工带有单重休假的单部件可修系统,提出了一种新的维修更换模型.假定系统是可修的,逐次故障后的维修时间构成随机递增的几何过程,系统工作时间构成随机递增的几何过程,在修理工休假时间为定长的情况下,分别选取系统的总工作时间T和故障维修次数N为更换策略,以长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式,通过最大化目标函数来获取系统最优的更换策略T*和N*.并在一定条件下给出了策略N比策略T优的充分条件.最后,通过数值例子验证了方法的有效性.     

随机DEA期望值模型的一些性质

为判别决策单元在随机DEA期望值模型下的随机有效性,首次提出了随机期望无效、随机期望弱有效、随机期望有效以及随机期望超有效的概念．并给出了三个命题用于判别不同显著性水平下随机期望效率与期望效率的关系．在此基础上,得到了两个重要的性质：（1）当期望效率保持不变时,随机期望效率为显著性水平的增函数;（2）当显著性水平保持不变时,随机期望效率为期望效率的增函数．最后,利用随机模拟和一个算例对上述结论进行了验证．     

折现率离散时间风险模型下最大赤字问题

在引入折现率的条件下研究离散时间风险模型,运用递推方法和全概率公式,得到了破产前盈余,破产后赤字以及它们的联合分布所满足的微分积分方程,作为推论得到了破产概率所满足的微积分方程并得出结论.     

A partially penalty immersed interface finite element method for anisotropic elliptic interface problems

In this article, we develop a partially penalty immersed interface finite element (PIFE) method for a kind of anisotropy diffusion models governed by the elliptic interface problems with discontinuous tensor‐coefficients. This method is based on linear immersed interface finite elements (IIFE) and applies the discontinuous Galerkin formulation around the interface. We add two penalty terms to the general IIFE formulation along the sides intersected with the interface. The flux jump condition is weakly enforced on the smooth interface. By proving that the piecewise linear function on an interface element is uniquely determined by its values at the three vertices under some conditions, we construct the finite element spaces. Therefore, a PIFE procedure is proposed, which is based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. Then we prove the consistency and the solvability of the procedure. Theoretical analysis and numerical experiments show that the PIFE solution possesses optimal‐order error estimates in the energy norm and norm.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1984–2028, 2014     

遗传算法求解约束非线性规划及Matlab实现

对于约束非线性规划问题,传统的方法:可行方向法、惩罚函数法计算烦琐且精度不高.用新兴的遗传算法来解决约束非线性规划,核心是惩罚函数的构造.以前的惩罚函数遗传算法有的精度较低,有的过于复杂.本文在两个定义的基础上构造了新的惩罚函数,并在新的惩罚函数的基础上,提出了一种解决约束非线性最优化问题的方法.通过两个例子应用Matlab说明了这个算法的可行性.     

CGEMA and VGAP: a Colour Graphics Editor for Multiple Alignment using a Variable GAP penalty. Application to the muscarinic acetylcholine receptor

Summary Today, more than 40 protein amino acid (AA) sequences of membrane receptors coupled to guanine nucleotide binding proteins (G-proteins) are available. For those working in the field of medicinal chemistry, these sequences present a new type of information that should be taken into consideration. To make maximal use of sequence data it is essential to be able to compare different protein sequences in a similar way to that used for small molecules. A prerequisite, however, is the availability of a processing environment that enables one to handle sequences in an easy way, both by hand and by computer. In order to meet these ends, the package CGEMA (Colour Graphics Editor for Multiple Alignment) was developed in our laboratory. The programme uses a user-definable colour coding for the different AAs. Sequences can be aligned by hand or by computer, using VGAP, and both approaches can be combined. VGAP is a novel in-house written alignment programme with a variable gap penalty that also handles consecutive alignments using one sequence as a probe. In addition, secondary structure prediction tools are available.From the 20 protein sequences, available for the muscarinic acetylcholine receptor, 13 different sequences were selected, covering the subtypes m1 to m5. By comparing the sequences, two major groups are revealed that correspond to those found by considering the transducing system coupled to the various receptor subtypes. Different parts of the protein sequences are identified as characterizing the subtype and binding the ligands, respectively.     

Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation

In this paper, we present a power penalty function approach to the linear complementarity problem arising from pricing American options. The problem is first reformulated as a variational inequality problem; the resulting variational inequality problem is then transformed into a nonlinear parabolic partial differential equation (PDE) by adding a power penalty term. It is shown that the solution to the penalized equation converges to that of the variational inequality problem with an arbitrary order. This arbitrary-order convergence rate allows us to achieve the required accuracy of the solution with a small penalty parameter. A numerical scheme for solving the penalized nonlinear PDE is also proposed. Numerical results are given to illustrate the theoretical findings and to show the effectiveness and usefulness of the method. This work was partially supported by a research grant from the University of Western Australia and the Research Grant Council of Hong Kong, Grants PolyU BQ475 and PolyU BQ493.     

带常利率的Erlang(2)风险模型的罚金折现期望函数

The purpose of this paper is to consider the expected value of a discounted penalty due at ruin in the Erlang（2） risk process under constant interest force. An integro-differential equation satisfied by the expected value and a second-order differential equation for the Laplace transform of the expected value are derived. In addition, the paper will present the recursive algorithm for the joint distribution of the surplus immediately before ruin and the deficit at ruin. Finally, by the differential equation, the defective renewal equation and the explicit expression for the expected value are given in the interest-free case.     

目标约束下的投资选择

根据 Markowitz投资组合理论和传统的期望效用理论 ,在效用函数相同的情况下 ,所有的理性投资者都将采用相同的最优投资策略 .但在现实中 ,不同的投资者往往采用不同的投资策略 ,依据传统理论只能认为他们并不都是理性投资者 .本文引入了目标约束后 ,说明了由于不同的投资者具有不同的目标约束 ,所以用传统的期望效用理论无法解释的看似非理性的行为其实却是理性的最优选择 .     

参数的E Bayes估计法及其应用

提出了参数的一种估计方法—— E Bayes估计法 ,对寿命服从指数分布的产品 ,在失效率的先验分布为 Gamma分布时 ,给出了失效率的 E Bayes估计和多层 Bayes估计 ,并在此基础上给出了失效率和可靠度的 E Bayes估计的性质 .结合实际问题进行了计算 ,结果表明提出的 E Bayes估计法可行且便于应用 .