Convexifiability of continuous and discrete nonnegative quadratic programs for gap-free duality

In this paper we show that a convexifiability property of nonconvex quadratic programs with nonnegative variables and quadratic constraints guarantees zero duality gap between the quadratic programs and their semi-Lagrangian duals. More importantly, we establish that this convexifiability is hidden in classes of nonnegative homogeneous quadratic programs and discrete quadratic programs, such as mixed integer quadratic programs, revealing zero duality gaps. As an application, we prove that robust counterparts of uncertain mixed integer quadratic programs with objective data uncertainty enjoy zero duality gaps under suitable conditions. Various sufficient conditions for convexifiability are also given.     

Optimal production-inventory policy for the multi-period fixed proportions co-production system

Consider the multi-period production-inventory problem where a manufacturer purchases and processes a raw material into two products in fixed proportions when facing uncertain demands. In each period, the manufacturer first reviews the on-hand inventories of the products and then decides the purchase/processing quantity of the raw material. After processing the raw material into the end products, the demands of the two products are realized and satisfied by the available inventories. Any leftover inventories are carried to the next period while the unsatisfied demands are backordered. By proving the concavity and submodularity of the expected profit-to-go function, we establish that the one-dimensional produce-up-to policy is optimal. We also study the case where the raw material is seasonal and the manufacturer has only one chance to purchase. Modeling it as a dynamic program, we establish that the one-dimensional produce-down-to policy is optimal. Finally, we conduct numerical studies to examine the impacts of supply-demand balance and price fluctuation on the optimal policy, and derive managerial insights from the analytical findings.     

Designing a two-echelon distribution network under demand uncertainty

This paper proposes a comprehensive methodology for the stochastic multi-period two-echelon distribution network design problem (2E-DDP) where product flows to ship-to-points are directed from an upper layer of primary warehouses to distribution platforms (DPs) before being transported to the ship-to-points. A temporal hierarchy characterizes the design level dealing with DP location and capacity decisions, as well as the operational level involving transportation decisions as origin-destination flows. These design decisions must be calibrated to minimize the expected distribution cost associated with the two-echelon transportation schema on this network under stochastic demand. We consider a multi-period planning horizon where demand varies dynamically from one planning period to the next. Thus, the design of the two-echelon distribution network under uncertain customer demand gives rise to a complex multi-stage decisional problem. Given the strategic structure of the problem, we introduce alternative modeling approaches based on two-stage stochastic programming with recourse. We solve the resulting models using a Benders decomposition approach. The size of the scenario set is tuned using the sample average approximation (SAA) approach. Then, a scenario-based evaluation procedure is introduced to post-evaluate the design solutions obtained. We conduct extensive computational experiments based on several types of instances to validate the proposed models and assess the efficiency of the solution approaches. The evaluation of the quality of the stochastic solution underlines the impact of uncertainty in the two-echelon distribution network design problem (2E-DDP).     

Technical change and the von Neumann coefficient of uniform expansion

We study technical change for multi-product technologies to examine its effect on economic growth for 27 OECD (Organization for Economic Cooperation and Development) countries during 1951–2014. We review the Malmquist index and reexamine von Neumann’s model of an expanding economy. We estimate the coefficient of uniform expansion via DEA (Data Envelopment Analysis) and use it to measure technical change via a Solow residual and an alternative von Neumann technical change index which equals the difference between the growth rates of the slowest growing output and the fastest growing input. We also exploit a property of constant returns to scale in order to examine technical change of the average technology. During 2005–2014 the Solow residual shows relatively fast technical change. In contrast, the Malmquist, average technology and alternative von Neumann technical change indexes show negative or stagnant technical change.     

考虑后悔规避与匹配意愿的直觉模糊双边匹配方法

针对直觉模糊偏好信息的双边匹配问题,提出一种考虑匹配主体后悔规避心理行为和匹配意愿的双边匹配方法。首先,将双边主体的直觉模糊偏好信息转化为效用值;然后,依据后悔理论的思想,通过一方主体将另一方主体进行两两比较计算每个主体的后悔值和欣喜值,进而计算每个主体的总体后悔欣喜值,构建匹配满意度计算规则,建立双边匹配多目标优化模型,通过分析现有匹配意愿系数确定方法的不足,给出一种新的匹配意愿系数确定方法,在此基础上,考虑双边主体的匹配意愿,采用线性加权法将多目标优化模型转化为单目标规划模型进行求解,获得双边匹配结果;最后,通过一个算例验证了提出方法的可行性和有效性。     

ON THE CAUCHY PROBLEM FOR A SINGULAR INTEGRODIFFERENTIAL EQUATION

The authors establish the existence and uniqueness of global solutions to the Cauchy problem for the third-order Benjamin-Ono equation by the so-called continuation method.     

多媒体计算机辅助高分子物理教学的研究与实践

通过对课程的定位,教学资料的规范化、系列化、系统化和多媒体化,MCAI课件和计算机模拟软件的制作,网络的利用,以及多种媒体的组合教学,对多方位的多媒体计算机辅助高分子物理教学进行了研究与实践;为培养基础扎实、知识面宽、能力强、素质高的人才提供了一种切实有效的教学方案;并将课程建设推上了一个新台阶。     

Asymptotic vulnerability of positional voting rules to coalitional manipulation

Voting rule performances are sometimes evaluated according to their respective resistances to allow profitable misrepresentation of individual preferences. This seems to be a hard task when scoring systems with possibly non integer weights are involved. In this paper, it is shown how one can still obtain asymptotic results in these settings. Our analysis for three-candidate elections provides a characterization of unstable voting situations at which a positional voting rule is manipulable by some coalition not larger than an arbitrary proportion of the electorate. This allows us to address a conjecture by Pritchard and Wilson (2007). That is, under the Impartial Anonymous Culture (IAC), the plurality rule asymptotically minimizes the vulnerability to coalitional manipulation when the size of the manipulating coalition is unrestricted. This later result is no longer valid when only manipulation by small coalitions is considered: now, the Borda rule tends to outperform other rules. Furthermore, the vulnerability of a positional voting rule to coalitional manipulation is not affected by increasing the size of the manipulating coalition from 0.5 to 1.     

光纤陀螺捷联式惯导系统初始对准方法研究

对光纤陀螺（FOG）的零偏重复性、零偏随时间变化规律的重复性进行了实骀研究。根据FOG零偏重复性好和零偏随时间变化规律的重复性好等特点，采用最小二乘估计和Kaiman滤波估计方法，提出、设计实现了一个有效实用的FOG捷联式惯导系统（SINS）初始对准方法，并与转位式初始对准方法的对准结果进行了比较，得到了精度相当的结果。     

Stability of a three-species symbiosis model with delays

In this paper, a three-species symbiosis Lotka–Volterra model with discrete delays is considered. The local stability of positive equilibrium is investigated through constructing a proper Lyapunov function. A detailed and explicit procedure of obtaining sufficient conditions for local stability of the positive equilibrium of the system along with an estimate size of allowable delay is provided.