An iterative rounding 2-approximation algorithm for the k-partial vertex cover problem

We study a generalization of the vertex cover problem. For a given graph with weights on the vertices and an integer k, we aim to find a subset of the vertices with minimum total weight, so that at least k edges in the graph are covered. The problem is called the k-partial vertex cover problem. There are some 2-approximation algorithms for the problem. In the paper we do not improve on the approximation ratios of the previous algorithms, but we derive an iterative rounding algorithm. We present our technique in two algorithms. The first is an iterative rounding algorithm and gives a （2 ＋ Q/OPT ）-approximation for the k-partial vertex cover problem where Q is the largest finite weight in the problem definition and OPT is the optimal value for the instance. The second algorithm uses the first as a subroutine and achieves an approximation ratio of 2.     

A robust counterpart approach to the bi-objective emergency medical service design problem

The paper presents a bi-objective robust program to design a cost-responsiveness efficient emergency medical services (EMS) system under uncertainty. The proposed model simultaneously determines the location of EMS stations, the assignment of demand areas to EMS stations, and the number of EMS vehicles at each station to balance cost and responsiveness. We develop a robust counterpart approach to cope with the uncertain parameters in the EMS system. Extensive numerical studies are performed to demonstrate the benefits of our robust optimization approach.     

The numerical stability of barycentric Lagrange interpolation

The Lagrange representation of the interpolating polynomialcan be rewritten in two more computationally attractive forms:a modified Lagrange form and a barycentric form. We give anerror analysis of the evaluation of the interpolating polynomialusing these two forms. The modified Lagrange formula is shownto be backward stable. The barycentric formula has a less favourableerror analysis, but is forward stable for any set of interpolatingpoints with a small Lebesgue constant. Therefore the barycentricformula can be significantly less accurate than the modifiedLagrange formula only for a poor choice of interpolating points.This analysis provides further weight to the argument of Berrutand Trefethen that barycentric Lagrange interpolation shouldbe the polynomial interpolation method of choice.     

多路径下应急资源调度的非线性混合整数规划模型

本文通过对地震、瘟疫、恐怖袭击等灾害发生的特点与调运应急资源的机理进行分析,兼顾已发生地点的需求和其它地点潜在发生事故的可能性,建立非线性混合整数规划模型。从资源调运过程中的多路径以及不同的路径由于所受到不确定性的干扰和阻碍,往往引起随机的调运效率降低等情况进行考虑,最小化资源救助点到不同资源需求点的时间总量,同时对于已出事点与潜在出事点,利用发生概率作为权重进行轻重区别,由此使研究更贴近实际应用。最后给出算例对模型进行分析求解,验证了模型的可行性。     

“舍割”摆中共轭点的妙用

文章介绍了利用共轭点可以测量等值摆长、重力加速度、周期和转动惯量等。     

An Exact Solution Method for Reliability Optimization in Complex Systems

Systems reliability plays an important role in systems design, operation and management. Systems reliability can be improved by adding redundant components or increasing the reliability levels of subsystems. Determination of the optimal amount of redundancy and reliability levels among various subsystems under limited resource constraints leads to a mixed-integer nonlinear programming problem. The continuous relaxation of this problem in a complex system is a nonconvex nonseparable optimization problem with certain monotone properties. In this paper, we propose a convexification method to solve this class of continuous relaxation problems. Combined with a branch-and-bound method, our solution scheme provides an efficient way to find an exact optimal solution to integer reliability optimization in complex systems. This research was partially supported by the Research Grants Council of Hong Kong, grants CUHK4056/98E, CUHK4214/01E and 2050252, and the National Natural Science Foundation of China under Grants 79970107 and 10271073.     

Internal hydraulic analysis of impeller rounding in centrifugal pumps as turbines

The use of pumps as turbines in different applications has been gaining importance in the recent years, but the subject of hydraulic optimization still remains an open research problem. One of these optimization techniques that include rounding of the sharp edges at the impeller periphery (or turbine inlet) has shown tendencies of performance enhancement.In order to understand the effect of this hydraulic optimization, the paper introduces an analytical model in the pump as turbine control volume and brings out the functionalities of the internal variables classified under control variables consisting of the system loss coefficient and exit relative flow direction and under dependent variables consisting of net tangential flow velocity, net head and efficiency.The paper studies the effects of impeller rounding on a combination of radial flow and mixed flow pumps as turbines using experimental data. The impeller rounding is seen to have positive impact on the overall efficiency in different operating regions with an improvement in the range of 1-3%. The behaviour of the two control variables have been elaborately studied in which it is found that the system loss coefficient has reduced drastically due to rounding effects, while the extent of changes to the exit relative flow direction seems to be limited in comparison. The reasons for changes to these control variables have been physically interpreted and attributed to the behaviour of the wake zone at the turbine inlet and circulation within the impeller control volume.The larger picture of impeller rounding has been discussed in comparison with performance prediction models in pumps as turbines. The possible limitations of the analytical model as well as the test setup are also presented. The paper concludes that the impeller rounding technique is very important for performance optimization and recommends its application on all pump as turbine projects. It also recommends the standardization of the rounding effects over wide range of pump shapes including axial pumps.     

Performance enhancements for GROMACS nonbonded interactions on BlueGene

Several improvements to the previously optimized GROMACS BlueGene inner loops that evaluate nonbonded interactions in molecular dynamics simulations are presented. The new improvements yielded an 11% decrease in running time for both PME and other kinds of GROMACS simulations that use nonbonded table look-ups. Some other GROMACS simulations will show a small gain.     

测量结果及其不确定度的修约方法

基于国家计量技术规范和实际应用情况,文章提出,为了保证修约值最接近原始数值、修约方法规范统一、易于操作,测量不确定度应统一取成两位有效位数,并据此来修约测量结果.