警车配置及巡逻方案研究

以警车的配置与巡逻方案为研究对象,建立了一套警车巡逻模型,并提出巡逻效果显著度及隐藏性的评价标准,分别针对警车初始位置配置与巡逻方案的制定,提出警车配置优化选址的贪婪算法与基于多Agent的警车巡逻方案设计方法,给出了不同情景下的配置及巡逻方案:①在只考虑警车选址配置的情况下,配置19辆警车可以使全市路网警车覆盖率达到92.8%;②在顾及巡逻效果显著性与隐藏性的情况下,配置25辆警车使全市路网在整个巡逻过程中平均警车覆盖率达到90.9%;③在配置10辆警车的情况下,使得全市路网在整个巡逻过程中平均警车覆盖率达到61.5%.     

长期投资者的战略资产配置选择

在股票期望收益率服从一个均值回复过程的假设下,推导出具有幂效用函数的投资者的资产配置函数,着重分析了投资期限对投资者资产配置结果的影响,发现长期投资者比短期投资者在股票上配置更大的资产比例.虽然不同投资期限的投资者具有相同的短视配置,但是战略配置随着投资期限的增大而增大.     

信息不对称约束下用水许可证拍卖制度设计

用水许可证制度是实施水资源统一管理的重要措施之一。行政配置中配置主体之间存在信息不对称，导致配置效率低，也存在“寻租”的可能。本文首先分析了信息不对称约束下的取用水许可证配置效率问题，然后引入拍卖理论，建立了信息不对称约束下的取用水许可证拍卖模型。属于多物品拍卖问题，本文给出了最优拍卖制度设计，实现取水许可证的高效配置，为取用水许可证的高效配置市场化方式提供借鉴作用。     

武器装备动态配置中的风险决策分析

从武器装备配置决策的风险性出发 ,探讨了在武器装备配置中费用—效益的关系 ,建立了武器装备静态与动态配置过程最佳方案确定的数学模型 .通过方案的评估择优使得我们能够科学的优化资金流向 ,为决策者在实施武器装备配置决策时提供较有力的科学依据 .     

NSGA-II算法在农业水保措施配置优化中的应用

农业水保措施的配置要考虑其生态效益和经济效益.不同水保措施组合方案有其相应的生态和经济效益,如何配置使综合效益最佳是一个最优化问题.分析了农业水保措施配置最优化需要考虑的两个目标,并将其公式化,建立了水保措施配置优化模型,并应用NSGA-II多目标遗传算法求解该模型.最后,以甘肃天水市罗玉沟流域的水保措施配置为例,进行了初步应用.结果表明,采用NSGA-II算法在水保措施配置优化模型求解时,计算效率较高,优化结果稳定,具有一定的应用价值.     

关于两点边值问题配置解的组合方法

目前,在用组合校正方法提高两点边值问题配置解的精度方面,已有一些工作。例如,Manabu Sakai考虑了三次样条配置解而采用两种不同投影的组合;黄友谦考虑了三次样条配置解同差分解的组合;林群,刘嘉荃给出了配置解的外推方法。本文基于上述工作的思想,提出一种新的组合方法。即通过对三次样条配置解和二次样条配置解进     

基于粗集模糊物元的项目组合配置战略贴近度研究

战略导向下的项目组合配置问题是企业进行多项目管理时需要解决的重要问题,对企业战略目标最大化的实现起到关键作用。论文在研究项目与项目关系的视角下,以项目组合配置方案和企业战略关系为出发点,提出了项目组合配置战略贴近度概念,构建了项目组合配置模糊物元模型,并以战略贴近度值的大小为度量标准,对项目组合配置方案与企业战略吻合程度进行分析,为企业项目组合管理提供决策依据。     

土地资源的可拓性及优化配置系统结构模型

本文应用可拓学的理论和方法，对土地资源的特征及优化配置原理进行分析，设计了优化配置系统结构模型，为土地资源的优化配置和合理利用提供了一种新的科学方法。     

基于人口老龄化的中国医疗卫生人员配置充分性测度——贝叶斯时空演化分析实证

基于2010-2018年省级数据,用贝叶斯时空模型分析中国老龄化与医疗卫生人员配置的时空演化特征,并构建了基于老龄化的医疗卫生人员配置水平充分性和增长充分性测度指数进行分析。研究结果表明:中国老龄化和医疗卫生人员的空间分布格局不同,局部变化趋势各异;基于老龄化的医疗卫生人员配置水平充分性西北部优于东南部,老龄化程度越高的地区医疗卫生人员配置水平越显不足;医疗卫生人员配置增长充分性西部优于东部,老龄化增长越强的地区医疗卫生人员配置增长的充分性越低;基于老龄化的医疗卫生人员配置充分性将各地区分为四个层次:水平充分性和增长充分性兼具的省份占26%,水平充分、增长不足的省份占22%,水平不足、增长充分的省份占39%,水平和增长双重不足的省份占13%。基于上述结论提出了基于老龄化时空演化特征进行医疗卫生资源均衡、充分配置的相关建议。     

时滞积-微分方程配置解的多重校正

本文讨论线性Volterra时滞积一微分方程的连续分片多项式样条配置方法．在适当条件下,获得了配置解的导数在结点集上成立的精细误差展开式．以此为基础,给出了配置解的多重校正格式．     

Indirect methods of collocation: Trefftz‐Herrera collocation

A nonstandard collocation method (TH‐collocation) is presented, where collocation is used to construct specialized weighting functions instead of the solution itself, as it is usual, so that in this sense it is an indirect method. TH‐collocation is shown to be as accurate as standard collocation, but computationally far more efficient. The present article is the first of a series devoted to explore thoroughly collocation methods. The following classification of collocation methods is introduced: direct‐nonoverlapping; indirect‐nonoverlapping; direct‐overlapping; and indirect‐overlapping. Most of the effort reported in the literature has gone to direct‐nonoverlapping methods. The procedure presented in this article falls into the indirect‐nonoverlapping category and it is based on Trefftz‐Herrera formulation. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 709–738, 1999     

Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

We analyse collocation methods for nonlinear homogeneous Volterra—Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and give conditions for such existence and uniqueness in some cases. Finally, we illustrate these methods with an example of a collocation problem and give some examples of collocation problems that do not fit in the cases studied previously.     

Superconvergence of the iterated collocation methods for Hammerstein equations

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].     

Numerical solution of calcium-mediated dendritic branch model

The standard algorithms for spatial discretizations of calcium-mediated dendritic branch models via finite difference methods are quite accurate, but they are also extremely slow. To improve computational efficiency we apply spatial discretization using a spectral collocation method. Simulations using the spectral collocation method are compared to the finite difference approach using a model for calcium-mediated restructuring with spine pruning. We find that the spectral collocation method is about fifteen times more efficient to achieve similar accuracy than the finite difference approach even though spectral collocation requires more steps.     

双比例延迟微分方程配置法的可达阶

近几十年来,随着延迟微分方程广泛应用于变最测试、信号传递、机械化工、生命科学及经济管理系统等实际中,人们对此类方程的数值计算要求越来越高．     

On orthogonal collocation by the zeros of orthogonal 0-interpolants

The orthogonal collocation method is quite prominent among the collocation methods that determine approximate solutions of boundary value problems. This method involves Gaussian knots as collocation points and, in general, has fourth order convergence. Here, we discuss a similar method in which the knots are based on pre-assigned and free zeros of polynomials that arise in orthogonal 0-interpolants. Some numerical results demonstrate an advantage of the proposed collocation points over the Gaussian knots. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability of collocation methods for delay differential equations with vanishing delays

We analyze the asymptotic stability of collocation solutions in spaces of globally continuous piecewise polynomials on uniform meshes for linear delay differential equations with vanishing proportional delay qt (0<q<1) (pantograph DDEs). It is shown that if the collocation points are such that the analogous collocation solution for ODEs is A-stable, then this asymptotic behaviour is inherited by the collocation solution for the pantograph DDE.     

Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations

Summary. We prove numerical stability of a class of piecewise polynomial collocation methods on nonuniform meshes for computing asymptotically stable and unstable periodic solutions of the linear delay differential equation by a (periodic) boundary value approach. This equation arises, e.g., in the study of the numerical stability of collocation methods for computing periodic solutions of nonlinear delay equations. We obtain convergence results for the standard collocation algorithm and for two variants. In particular, estimates of the difference between the collocation solution and the true solution are derived. For the standard collocation scheme the convergence results are “unconditional”, that is, they do not require mesh-ratio restrictions. Numerical results that support the theoretical findings are also given. Received June 9, 2000 / Revised version received December 14, 2000 / Published online October 17, 2001     

Piecewise spectral collocation method for system of Volterra integral equations

The main purpose of this paper is to investigate the piecewise spectral collocation method for system of Volterra integral equations. The provided convergence analysis shows that the presented method performs better than global spectral collocation method and piecewise polynomial collocation method. Numerical experiments are carried out to confirm these theoretical results.     

Superconvergence of collocation methods for a class of weakly singular Volterra integral equations

We discuss the application of spline collocation methods to a certain class of weakly singular Volterra integral equations. It will be shown that, by a special choice of the collocation parameters, superconvergence properties can be obtained if the exact solution satisfies certain conditions. This is in contrast with the theory of collocation methods for Abel type equations. Several numerical examples are given which illustrate the theoretical results.