Multicommodity Flow Problem with Variable Arcs Capacities

The problem of maximizing the sum of the flows of all commodities in a network where the capacities of some arcs can be increased by integer numbers within a fixed budget is solved in this paper. Benders' technique is used to decompose the problem. Then Rosen's primal partitioning and non-linear duality theory are used to solve the subproblems generated by the Benders' decomposition. An application of a multicommodity network to the defence problem is mentioned.     

Stochastic Asymptotic Stability of Nowak-May Model with Variable Diffusion Rates

We consider a stochastically perturbed Nowak-May model of virus dynamics within a host. We prove the global existence of unique strong solution. Using the Lyapunov method, we found sufficient conditions for the stochastic asymptotic stability of equilibrium solutions of this model.     

Central Configurations of the 5-Body Problem with Equal Masses in Three-Space

Central configurations with axial symmetry in the 5-body problem with equal masses in three-space are enumerated. It is shown that only two of the configurations have a unique symmetry axis. Symbolic computation techniques are used because the proof involves very tedious computations. Bibliography: 15 titles.     

一个可变保费巨灾风险模型的局部破产概率

考虑极端风险的情况,建立了巨灾风险模型,得到了保险公司破产概率的局部结果.预期有巨灾索赔发生的时候,模型会对保险费率做出相应的调整以减少损失.还提出一个网络马氏骨架框架下的回归型索赔相依的风险模型,该模型不仅在精算领域有很大的理论和应用价值,在网络,金融,生物,排队论等其他领域也将有广泛的应用.     

Anisotropic Elliptic Nonlinear Obstacle Problem with Weighted Variable Exponent

In this paper, we are concerned with a show the existence of a entropy solution to the obstacle problem associated with the equation of the type :$\begin{cases}Au+g(x,u,∇u) = f & {\rm in} & Ω \\ u=0 & {\rm on} & ∂Ω \end{cases}$where $\Omega$ is a bounded open subset of $\;\mathbb{R}^{N}$, $N\geq 2$, $A\,$ is an operator of Leray-Lions type acting from $\; W_{0}^{1,\overrightarrow{p}(.)} (\Omega,\ \overrightarrow{w}(.))\;$ into its dual $\; W_{0}^{-1,\overrightarrow{p}'(.)} (\Omega,\ \overrightarrow{w}^*(.))$ and $\,L^1\,-\,$deta. The nonlinear term $\;g\,$: $\Omega\times \mathbb{R}\times \mathbb{R}^{N}\longrightarrow \mathbb{R} $ satisfying only some growth condition.     

恶化率与工件无关的线性加工时间调度问题

讨论恶化率与工件无关的线性加工时间调度问题 .对于工件间具有平行链约束 ,目标函数为极小化最大完工时间的单机问题 ,分别就链不允许中断和链允许中断两种情况给出了最优算法 .对于工件间没有优先约束 ,目标函数为极小化完工时间和的平行机问题 ,证明了工件按基本加工时间不减排列可以得到最优调度 .     

Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients

We establish conditions for the unique solvability of a boundary-value problem for a weakly nonlinear hyperbolic equation of order 2n, n > (3p + 1)/2, with coefficients dependent on the space coordinates and data given on the entire boundary of a cylindric domain . The investigation of this problem is connected with the problem of small denominators.     

具时滞的半线性抛物问题

基于C.C.Travis和G.F.Webb等人对时滞问题的研究,作者曾在[5]中对一类被称为带正时滞臂的时滞抛物型问题进行了讨论。本文在[5]的基础上继续讨论此类问题。对于抽象时滞问题,在非线性项满足局部Lip连续(甚至对某些变元仅仅是H?lder连续)及一定的增长性限制的条件下,我们对非线性项作了较精细的估计,用半群方法得到了解的存在性和唯一性。进一步,对带零时滞臂的抛物型问题,我们先用上面的结果建立逼近方程,用紧性方法在较弱的条件下也得到了解的存在性。 其次,我们将所得到的抽象结果应用于二阶时滞抛物型     

柔性工期下的资源受限项目调度双目标优化研究

在项目调度过程中,活动工期应根据项目截止工期以及资源供给情况进行合理设置,而在传统的资源受限项目调度问题(RCPSP)中,活动的工期往往是已知且固定的,这在一定程度上限制了项目调度的灵活性。多模式下的项目调度方式虽然弥补了这一缺点,但其提供的工期-资源组合种类固定且有限,并不一定能保证包含最优的工期-资源组合。本文将活动工期作为项目调度问题的决策变量,允许其在一定范围内取值。这种柔性工期调度方式虽然增加了项目调度难度,但提高了项目调度灵活性,同时可以起到压缩项目完工时间的作用。为验证柔性工期调度方式对项目工期和成本的影响,本文建立了工期-成本双目标权衡优化模型,设计了两阶段嵌套算法(NSGAⅡ-RS)对其求解,实验证明,柔性工期调度策略是一种鲁棒性较好的项目完工时间压缩策略。     

Stefan Problem with Change Density Upon Change of Phase (I)

In this paper, we establish the existence of one-dimensional classical solution of one-phase problem and its continuous dependence. In addition, we prove that if ε → 0, the free boundary X(t) withdraws and solution converges to the solution of classical Stefan problem. The two-phase problem wiU be discussed in the coming paper.     

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本文考虑离散时间风险模型$U_n=(U_{n-1}+Y_n)(1+r_n)-X_n$,$n=1,2,\cdots$, 其中$U_0=x>0$为保险公司的初始准备金,$r_n$为在第$n$个时刻的利率, $Y_n$为到时刻$n$为止的总保费收入,$X_n$为到时刻$n$为止的所支付的全部索赔,$U_n$表示保险公司在时刻$n$的盈余. 当$Y_n$和$r_n$满足某些温和条件时,我们得到了在\, $x\to\infty$时,有限时间破产概率$\psi(x,N)=\pr\big(\min\limits_{0\leq n\leqN}U_n<0|U_0=x\big)$关于$N\geq1$的一致渐近的关系式\,$\psi(x,N)\sim\tsm_{k=1}^{N}\ol{F}_X((1+r_1)\cdots(1+r_n)x)$,其中$\ol{F}_X(x)$是$X_1$的尾分布.     

A Finite Horizon Production Model with Variable Production Rates and Constant Demand Rate

In this paper we present a finite horizon single product single machine production problem. Demand rate and all the cost patterns do not change over time. However, end of horizon effects may require production rate adjustments at the beginning of each cycle. It is found that no such adjustments are required. The machine should be operated either at minimum speed (i.e. production rate = demand rate; shortage is not allowed), avoiding the buildup of any inventory, or at maximum speed, building up maximum inventories that are controlled by the optimal production lot size.     

A Problem with Nonlocal Conditions for Partial Differential Equations with Variable Coefficients

We establish conditions for the unique solvability of a problem for partial differential equations with coefficients dependent on variables t and x in a rectangular domain with nonlocal two-point conditions with respect to t and local boundary conditions with respect to x. We prove metric statements related to lower bounds of small denominators appearing in the course of solution of the problem.     

一类变工时的单机排序问题

提出了一类可变加工时间的单台机器排序问题,着重考虑如下的目标函数：最小化工件排序长度、完工时间之和误工工件数等等,且用受束的等规模划分问题证明了可变加工时间的单台机器排序问题是ＮＰ－完全的。     

一类带有变指数算子的非局部问题解的存在性

The purpose of this paper is to investigate a nonlocal Dirichlet problem with(p(x),q(x))-Laplacian-like operator originated from a capillary phenomena.Using the variational methods and the critical point theory,we establish the existence of infinitely many weak solutions for this problem.     

替代价格可变的两产品库存问题研究

从销售商的角度出发,研究了可变替代价格下的两产品库存问题.假设随机需求服从均匀分布,得到了一些有益的结论,并通过数值计算说明了各参数的变化对最优订货量和替代价格的影响.     

引入随机利率的养老保险破产问题

考虑带随机利率，负索赔是随机变量的复合二项养老保险模型。通过引入调节系数，得出破产概率的上界。进一步分析了破产前盈余分布和破产持续时间概率，并获得了递推公式。     

基于变长度染色体混沌遗传算法的专用交通道优化

大型运动会要求主办方在规定时间内将相关人员从运动员村运送至指定比赛场馆.基于大城市日趋严重的交通拥堵,为满足运送时间的要求,通常在城市公共交通网络中设置专用交通道.但专用交通道的设置会对城市公共交通产生影响,最小化其对城市公共交通影响是专用交通道优化问题的关键.针对此类问题,在给出了改进的混合整数规划模型的基础上,提出了基于问题特性的变长度染色体混沌遗传算法,包括变长度染色体编码、混沌个体初始化、交叉操作、变异操作、适应度函数的计算和不可行解的惩罚、修复策略等.最后,以经典算例和随机生成算例对算法有效性进行了验证.