Sustainability in bankruptcy problems

This paper focuses on a new property for bankruptcy rules, calledsustainability, which requires that the agents with small enough claims be fully reimbursed. We show that the constrained equal-awards rule is the only rule that satisfies path independence and sustainability. Exploiting duality relations, we also provide a characterization of the constrained equal-losses rule, as the only one that satisfies composition and independence of residual claims (the dual property of sustainability).     

N = 4 Supersymmetric (Dyonic) Hypermultiplets in String Theory

In four-dimensional N = 4 supersymmetric gauge theory, we obtain an exact metric on the moduli space of quantum vacua and analyze the spectra of BPS states in weak as well as in strong coupling regions. Identifying the hypermultiplet of the dyonic state as a string stretched between D₃-brane probe and a 7-brane, we demonstrate that the two hypermultiplets, which become massless at two singularities in supersymmetric theory, correspond to open strings beginning on the D₃-brane and ending on the respective 7-brane.     

Cyclic networks with general blocking and starvation

We introducegeneral starvation and consider cyclic networks withgeneral blocking and starvation (GBS). The mechanism of general blocking allows the server to process a limited number of jobs when the buffer downstream is full, and that of general starvation allows the server to perform a limited number of services in anticipation of jobs that are yet to arrive. The two main goals of this paper are to investigate how the throughput of cyclic GBS networks is affected by varying (1) the total number of jobsJ, and (2) the buffer allocationk=(k₁..., k_m) subject to a fixed total buffer capacityK=k ₁ +... + k_m. In particular, we obtain sufficient conditions for the throughput to be symmetric inJ and to be maximized whenJ=K/2. We also show that the equal buffer allocation is optimal under the two regimes of light or heavy usage. In order to establish these results, we obtain several intermediate structural properties of the throughput, using duality, reversibility, and concavity, which are of independent interest.Research supported in part by NSF Grant No. ECS-8919818.     

球约束凸二次规划的一个新算法

首先利用Lagrange对偶 ,将球约束凸二次规划问题转化为无约束优化问题 ,然后运用单纯形法求解无约束优化问题 ,从而获得原问题的最优解     

A note on an SOR-like method for augmented systems

Golub et al. (2001, BIT, 41, 71–85) gave a generalizedsuccessive over-relaxation method for the augmented systems.In this paper, the connection between the SOR-like method andthe preconditioned conjugate gradient (PCG) method for the augmentedsystems is investigated. It is shown that the PCG method isat least as accurate (fast) as the SOR-like method. Numericalexamples demonstrate that the PCG method is much faster thanthe SOR-like method.     

Invex-convexlike functions and duality

We define a class of invex-convexlike functions, which contains all convex, pseudoconvex, invex, and convexlike functions, and prove that the Kuhn-Tucker sufficient optimality condition and the Wolfe duality hold for problems involving such functions. Applications in control theory are given.The author is grateful to Professor W. Stadler and the referees for many valuable remarks and suggestions, which have enabled him to improve considerably the paper.     

精确搜索下的非线性共轭梯度法

该文提出一种无约束优化非线性共轭梯度法，证明了精确线性 搜索下的全局收敛性。当目标函数为一致凸函数时，证明了算法具有线性收敛速度。数值实验表明算法对于求解实际问题是有效的。     

一类不可微规划的高阶对称对偶性

本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 .     

On the Existence of Focal Points near Closed Geodesics on Surfaces

We establish some criteria for the existence or nonexistence of focal points near closed geodesics on surfaces. These criteria are in terms of the curvature of the manifold along the closed geodesic and the average values of the partial derivatives of the curvature in the direction perpendicular to the geodesic. Our criteria lead to a new family of examples of surfaces with no focal points. We also show that if S is a compact surface with no focal points and an inequality relating the curvature of the surface to the curvature of the horocycles holds, then the horocycles (considered as curves in S) are uniformly C ^2+Lipschitz.     

一类二层凸规划的对偶二层规划

本文讨论上层目标函数以下层子系统目标函数的最优值作为反馈的一类二层凸规划的对偶规划问题 ,在构成函数满足凸连续可微等条件的假设下 ,建立了二层凸规划的 Lagrange对偶二层规划 ,并证明了基本对偶定理 .