Facility location in the presence of forbidden regions,I: Formulation and the case of Euclidean distance with one forbidden circle

A constrained form of the Weber problem is formulated in which no path is permitted to enter a prespecified forbidden region $\text{R}$ of the plane. Using the calculus of variations the shortest path between two points $\text{x}\text{,}\text{y}\text{?}\text{R}$ which does not intersect $\text{R}$ is determined. If $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is unconstrained distance, we denote the shortes distance along a feasible path by $\text{d}\text{(}\text{x}\text{y}\text{)}$. The constrained Weber problem is, then: given points $\text{x}{}_{\mathrm{j}}\text{?}\text{R}$ and positive weights w_j, j = 1,2,…,n, find a point $\text{x}\text{?}\text{R}$ such that

$\text{f(}\text{x}\text{)=}\text{Σ}\text{n}\text{j=1}\text{d(}\text{x}\text{,}\text{x}{}_{\mathrm{j}}\text{)}$

is a minimum.An algorithm is formulated for the solution of this problem when $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is Euclidean distance and $\text{R}$ is a single circular region. Numerical results are presented.     

On a class of dependent Sparre Andersen risk models and a bailout application

In this paper a one-dimensional surplus process is considered with a certain Sparre Andersen type dependence structure under general interclaim times distribution and correlated phase-type claim sizes. The Laplace transform of the time to ruin under such a model is obtained as the solution of a fixed-point problem, under both the zero-delayed and the delayed cases. An efficient algorithm for solving the fixed-point problem is derived together with bounds that illustrate the quality of the approximation. A two-dimensional risk model is analyzed under a bailout type strategy with both fixed and variable costs and a dependence structure of the proposed type. Numerical examples and ideas for future research are presented at the end of the paper.     

含一般模糊弹性约束的广义模糊变量线性规划

建立并讨论了一类含有一般模糊弹性约束的广义模糊变量线性规划问题.首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析.然后选取风险中性的决策者来定义序关系,应用Verdegay模糊线性规划方法将含一般模糊弹性约束的广义模糊变量线性规划转化经典的线性规划问题,简化了原问题的求解.最后通过数值算例进一步说明了该方法的有效性.     

Determination/estimation of an optimal replacement interval under minimal repair

In this paper the problem of estimation of an optimal replacement interval for a system which is minimally repaired at failures is studied. The problem is investigated both under a parametric and a nonparametric form of the failure intensity of the system. It is assumed that observational data from n systems are available. Some asymptotic results are shown. A graphical procedure for determining/estimating an optimal replacement interval is presented. The procedure is particularly valuable for sensitivity analyses, for example with respect to the costs involved.     

Difference systems of sets based on cosets partitions

Difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.     

An optimal co-reinsurance strategy

This article considers a co-reinsurance strategy that (1) protects insurance companies against catastrophic risks; (2) enables insurers to gather sufficient information about the different risk attitudes of reinsurers and diversify their reinsured risks; (3) enables insurers to create better risk-sharing profiles by balancing the risk tolerances of reinsurers; (4) has the benefit of allowing reinsurers to accumulate experience with risks with which they are unfamiliar; (5) reduces the overall direct cost of a reinsurance contract; (6) allows a government to back some insurance products, such as the terrorism insurance programs that were established in many countries after the September 11th terrorist attacks; and (7) reflects the practical reinsurance industry of some countries, such as Iran. Such a co-reinsurance strategy can be fully determined by estimating its parameters whenever three optimal criteria are satisfied and prior information about the unknown parameters is available. Two simulation-based studies have been conducted to demonstrate (1) the practical applications of our findings and (2) the possible impact of any type of dependency between the co-reinsurance’s parameters and the evaluated optimal co-reinsurance strategy.     

The Efect of Queueing Strategy on Network Trafc

In recent years,the transportation system has been faced by increasing challenge in congestion and inefciency,and research in trafc network has become a significant area of interest.In this paper,we introduce a dynamic-information-based(DIB)queueing strategy into network trafc model under the efcient routing strategy.DIB makes a packet with higher priority to be delivered if there are less packets travelling along its path from the current node to the destination.It is found that,compared with the traditional first-in-first-out(FIFO)queueing strategy,DIB can efectively balance the trafc load of the system via delaying packets to be delivered to congested nodes.Although the network capacity has no obvious changes,some other indexes which reflect transportation efciency are efciently improved in the congestion state.Besides,extensive simulation results and discussions are provided to explain the phenomena.The results may provide novel insights for research on trafc systems.     

An ALE finite element method for a coupled Stefan problem and Navier–Stokes equations with free capillary surface

In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.     

Synthesis of a “molecular rope curtain”: Preparation and characterization of a sliding graft copolymer with grafted poly(ethylene glycol) side chains by the “grafting onto” strategy

A sliding graft copolymer (SGC) with poly(ethylene glycol) (PEG) side chains was prepared by ester formation between terminal carboxyl groups of oxidized PEG methyl ether with molecular weight of 2000 (mPEG2000‐COOH) and hydroxyl groups of a polyrotaxane consisting of PEG and cyclodextrins (CDs). Formation of the SGC structure was confirmed by ¹H NMR, attenuated total reflectance Fourier‐transformed infrared, and gel permeation chromatography. The SGC was soluble in good solvents of PEG and insoluble in poor solvents of PEG. Estimation of the number of grafted mPEG chains suggested a “rope‐curtain” like structure, in which an mPEG chain is connected to each CD ring. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011