基于广义超椭球模型的结构非概率可靠性指标

非概率凸集合模型仅需获知结构不确定性的范围或界限来度量结构可靠性,因而适用于小样本不确定性结构工程问题.针对广义超椭球模型,对其非概率可靠性度量问题进行了研究.首先,提出了基于广义超椭球模型的简单非概率可靠性指标,定义为结构功能函数的均值与离差之比,并讨论了该可靠性指标的不一致性问题.其次,为克服上述不一致性问题,提出了一种比例因子非概率可靠性指标,定义为不确定域向外扩大或向内收缩时,失效面与不确定域接触的最小比例因子.最后,通过3个工程算例分析验证了所提非概率可靠性指标的有效性和可行性.     

椭球不确定集下具有消费的投资组合鲁棒优化模型

针对含有不确定参数的优化问题,鲁棒优化作为一种有效的优化手段引起了人们的普遍关注。本文主要介绍了CVaR风险投资纽合模型,并在模型中加入消费,将椭球不确定集下鲁棒优化应用到该模型中,这不仅解决了该模型由于参数的不确定性所造成的缺陷,而且也比较符合实际情况。     

一般凸体Dvoretzky定理(英文)

将关于中心对称凸体的低维椭球截面的Ｄｖｏｒｅｔｚｋｙ的著名定理推广到了一般凸体上．     

E-凸Fuzzy集和E-反凸Fuzzy集

研究了广义凸Fuzzy集和广义反凸Fuzzy集以及它们的性质。通过将凸Fuzzy集和E-凸集相结合,提出了一种新的广义凸Fuzzy集———E-凸Fuzzy集,使得凸Fuzzy集成为它的特例,并对E-凸Fuzzy集的性质进行了初步研究。然后,类似地,通过将反凸Fuzzy集和E-凸集相结合,提出了一种新的广义反凸Fuzzy集———E-反凸Fuzzy集,使得反凸Fuzzy集成为它的特例,并对E-反凸Fuzzy集的性质进行了初步研究。     

具有椭球等高分布误差的半参数回归模型参数的Bayes估计

本文给出了具有椭球等高分布误差的半参数回归模型中参数的Ｂａｙｅｓ估计．     

凸约束广义线性回归模型的参数估计及算法

本文将从实际评估工作中提练出来的一种评估模型推广至因变量未知且带有一般性凸约束条件的广义线性模型,证明了模型解的存在唯一性,并从解的几何背景出发,提出了基于凸集间交互投影的参数最小二乘估计的有效算法.结合模型的特点,引入EM算法给出了参数的极大似然估计.模型的提出丰富了线性模型的结构框架,算法的给出为参数估计提供了行之有效的计算方法.     

凸体的对偶迷向常数与LYZ椭球

研究了凸体处于对偶迷向位置时的解析特征,并建立了凸体对偶迷向常数的新的下界;其次,证明了关于原点中心对称凸体的LYZ椭球与John椭球相等的充要条件;最后,举例具体计算了几个凸多边形的LYZ椭球和John椭球,以进一步认清两者的差别.     

凸体的p次径向平均体的几个性质

本文证明了凸体的p次径向平均体的线性不变性和椭球的p次径向平均体仍是椭球,并且获得了p次径向平均体相应于Blaschke-Santaló不等式的一个反向不等式．     

连续化方法求解约束凸规划问题

1．引言大型规划问题数值求解一直是计算数学工作者感兴趣的课题之一．针对大型约束规划问题,1991年李兴斯山提出凝聚函数法,该方法用光滑的凝聚函数逼近非光滑的极大值函数,从而把多个约束函数转化为带参数的单个光滑函数约束,从而降低了问题的规模．近年来,K3］研究了凸规划问题的凝聚函数法的收敛性,在目标函数强凸性及对一般凸规划研究了收敛性质．向讨论了可行解集有界的线性规划问题的凝聚函数求解算法并证明了收效性定理．上述文章均预先把凝聚参数取得充分小,然后对固定参数的单约束近似问题进行求解．一般地,凝聚参数取得…     

参数集值变分不等式的解映射的有界性和连续性

本文借助于非空闭凸集序列的外极限集和极大单调集值映射的外极限研究了参数集值变分不等式的集值解映射的有界性和外半连续性．     

Global stability analysis and permanence for an HIV-1 dynamics model with distributed delays

This paper mainly investigates the global asymptotic stabilities of two HIV dynamics models with two distributed intracellular delays incorporating Beddington-DeAngelis functional response infection rate. An eclipse stage of infected cells (i.e. latently infected cells), not yet producing virus, is included in our models. For the first model, it is proven that if the basic reproduction number $R_0$ is less than unity, then the infection-free equilibrium is globally asymptotically stable, and if $R_0 $ is greater than unity, then the infected equilibrium is globally asymptotically stable. We also obtain that the disease is always present when $R_0 $ is greater than unity by using a permanence theorem for infinite dimensional systems. What is more, a n-stage-structured HIV model with two distributed intracellular delays, which is the extensions to the first model, is developed and analyzed. We also prove the global asymptotical stabilities of two equilibria by constructing suitable Lyapunov functionals.     

二维水平地震作用下斜交构件多层结构的地震反应

本文针对由斜交构件组成的多层结构,考虑任意角度输入二维水平地运动,采用多种不同的恢复力特性曲线模型,提供了弹性与弹塑性地震反应的计算方法,并据此编制了相应的计算机程序.文内通过一座十层建筑结构的算例,分析了一维与二维地震波输入以及不同的地震波输入角度对各构件地震反应的影响,并讨论了弹性与弹塑性地震反应的差异,提出了一些有参考价值的结论.     

A NEW INVERSION METHOD OF TIME-LAPSE SEISMIC

Time-Lapse Seismic improves oil recovery ratio by dynamic reservoir monitoring. Because of the large number of seismic explorations in the process of time-lapse seismic inversion, traditional methods need plenty of inversion calculations which cost high computational works. The method is therefore inefficient. In this paper, in order to reduce the repeating computations in traditional, a new time-lapse seismic inversion method is put forward. Firstly a homotopy-regularization method is proposed for the first time inversion. Secondly, with the first time inversion results as the initial value of following model, a model of the second time inversion is rebuilt by analyzing the characters of time-lapse seismic and localized inversion method is designed by using the model. Finally, through simulation, the comparison between traditional method and the new scheme is given. Our simulation results show that the new scheme could save the algorithm computations greatly.     

具有免疫应答和吸收效应的病毒感染模型分析

研究了具有免疫应答和吸收效应的病毒动力学模型的动力学行为.通过构造适当的Lyapunov泛函,使用LaSalle不变性原理,证明了基本再生数、CTL免疫再生数、抗体免疫再生数、CTL免疫竞争再生数和抗体免疫竞争再生数决定了模型的全局性态.若基本再生数小于等于1,病毒在体内清除.若基本再生数大于1,正解在满足条件max{...     

A modified Leslie–Gower predator–prey model with ratio‐dependent functional response and alternative food for the predator

In this work, a modified Leslie–Gower predator–prey model is analyzed, considering an alternative food for the predator and a ratio‐dependent functional response to express the species interaction. The system is well defined in the entire first quadrant except at the origin ( 0 , 0 ) . Given the importance of the origin ( 0 , 0 ) as it represents the extinction of both populations, it is convenient to provide a continuous extension of the system to the origin. By changing variables and a time rescaling, we obtain a polynomial differential equations system, which is topologically equivalent to the original one, obtaining that the non‐hyperbolic equilibrium point ( 0 , 0 ) in the new system is a repellor for all parameter values. Therefore, our novel model presents a remarkable difference with other models using ratio‐dependent functional response. We establish conditions on the parameter values for the existence of up to two positive equilibrium points; when this happen, one of them is always a hyperbolic saddle point, and the other can be either an attractor or a repellor surrounded by at least one limit cycle. We also show the existence of a separatrix curve dividing the behavior of the trajectories in the phase plane. Moreover, we establish parameter sets for which a homoclinic curve exits, and we show the existence of saddle‐node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation, and homoclinic bifurcation. An important feature in this model is that the prey population can go to extinction; meanwhile, population of predators can survive because of the consumption of alternative food in the absence of prey. In addition, the prey population can attain their carrying capacity level when predators go to extinction. We demonstrate that the solutions are non‐negatives and bounded (dissipativity and permanence of population in many other works). Furthermore, some simulations to reinforce our mathematical results are shown, and we further discuss their ecological meanings. Copyright © 2017 John Wiley & Sons, Ltd.     

A hybrid hypercube – Genetic algorithm approach for deploying many emergency response mobile units in an urban network

Emergency response services are critical for modern societies. This paper presents a model and a heuristic solution for the optimal deployment of many emergency response units in an urban transportation network and an application for transit mobile repair units (TMRU) in the city of Athens, Greece. The model considers the stochastic nature of such services, suggesting that a unit may be already engaged, when an incident occurs. The proposed model integrates a queuing model (the hypercube model), a location model and a metaheuristic optimization algorithm (genetic algorithm) for obtaining appropriate unit locations in a two-step approach. In the first step, the service area is partitioned into sub-areas (called superdistricts) while, in parallel, necessary number of units is determined for each superdistrict. An approximate solution to the symmetric hypercube model with spatially homogeneous demand is developed. A Genetic Algorithm is combined with the approximate hypercube model for obtaining best superdistricts and associated unit numbers. With both of the above requirements defined in step one, the second step proceeds in the optimal deployment of units within each superdistrict.     

An inequality model for solving interval dynamic response of structures with uncertain-but-bounded parameters

In this paper, we look into the dynamic response of structures with uncertain-but-bounded parameters. A new inequality model for determining the interval dynamic response is presented. First we propose an interval dynamic response solution theorem. An inequality model which is a mathematics programming problem is suggested by the presented theorem. Using the central difference method, we substitute the differential items of the inequality model by difference items. By solving them, the interval dynamic response can be obtained. Two examples are used to illustrate the feasibility and the efficiency of the model.     

一类具免疫应答和非线性感染函数的时滞HIV-1感染模型的全局稳定性

考虑到HIV-1感染过程中免疫反应和非线性感染函数,建立了一类具有三个分布时滞的HIV-1感染动力学模型.得到了关于病毒感染的基本再生数R0和CTLs免疫反应的基本再生数R1 ＜R0.通过构造Lyapunov泛函证明了系统具有阈值动力学性质,即当R0≤1时,系统存在全局渐近稳定的无感染平衡点;当R1≤1＜R0时,系统出...     

Optimization Design of Holding Poles Based on the Response Surface Methodology and the Improved Arithmetic Optimization Algorithm北大核心CSCD

抱杆优化设计需要耗费大量有限元分析计算时间,难以确定可行域.该文采用响应面法(response surface method,RSM)来模拟抱杆结构的真实响应,提出了改进的算术优化算法(improved arithmetic optimization algorithm,IAOA)对抱杆结构进行优化设计.将分数阶积分引入算术优化算法(arithmetic optimization algorithm,AOA),改善了算法的开发能力.采用拉丁超立方抽样,选取抱杆结构杆件截面试验样本,利用最小二乘法对样本点进行分析,构建了抱杆结构应力和位移关于杆件截面尺寸的二阶响应面代理模型.建立以抱杆质量最小化为优化目标,许用应力和位移为约束条件的优化模型,采用IAOA对其进行求解.结果表明:二阶响应面模型能够准确预测抱杆结构的响应值,IAOA的求解精度得到显著提升,代理模型可大幅降低有限元分析所需的计算代价,优化后抱杆结构质量减轻了8.2%.联合使用RSM和IAOA可有效求解大型空间杆系结构的优化设计问题.