Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.     

Multiplicity results of nonlinear fractional magnetic Schrödinger equation with steep potential

In this article, we prove the existence and multiplicity of non-trivial solutions for an indefinite fractional elliptic equation with magnetic field and concave–convex nonlinearities. Our multiplicity results are based on studying the decomposition of the Nehari manifold.     

A note on the maximum points of the minimum of quasiconvex functions

The paper deals with the problem of maximizing the minimum of quasiconvex functions over a compact convex set Z. Subsets of Zare given which contain all solutions or at least one solution.     

Multicategory ψ-Learning and Support Vector Machine: Computational Tools

Many margin-based binary classification techniques such as support vector machine (SVM) and ψ-learning deliver high performance. An earlier article proposed a new multicategory ψ-learning methodology that shows great promise in generalization ability. However,ψ-learning is computationally difficult because it requires handling a nonconvex minimization problem. In this article, we propose two computational tools for multicategory ψ-learning. The first one is based on d.c. algorithms and solved by sequential quadratic programming, while the second one uses the outer approximation method, which yields the global minimizer via sequential concave minimization. Numerical examples show the proposed algorithms perform well.     

Feasibility in reverse convex mixed-integer programming

In this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints, where some or all of the variables are integer. In particular, we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility (CF), that is constraints that may affect a feasibility status of the system after some perturbation of the right-hand sides. Furthermore, we will investigate properties of the irreducible infeasible sets and infeasibility sets, showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system, are subsets of the set CF of constraints critical to feasibility.     

Athermal metal-free planar waveguide concave grating demultiplexer

An athermal metal-free planar waveguide concave grating demultiplexer is proposed. We designed the dielectric mirror at the grating facet instead of coating with the metal on the back wall of the grating facet. The transfer-matrix method is introduced to design the dielectric mirror and the reflectance spectral responses of the 2D waveguide structure are simulated using the FDTD software (RSoft, Inc.). To reduce the temperature sensitivity of the device, the three-focal-point method is introduced. We use the design example to show the high-reflectance bandwidth of the dielectric mirror. The fabrication errors are also taken into consideration. By using the numerical model of the scalar diffraction theory, the flat-top spectral responses of the channels are simulated.     

球面镜真空紫外光谱反射率的高精度测量

为了实现对球面镜真空紫外光谱反射率的直接测量,构建了一套真空紫外光谱反射率测试系统。该系统以氟化镁窗口氘灯与Seya-Namioka凹面光栅单色仪产生单色光源,反射式调制器与参考探测器做光学补偿,内径80mm的荧光积分球与精密转台作为接收系统。光学补偿消除单色光源不稳定性,荧光积分球消除了两次测量光斑不同对探测器响应的影响,且减少了系统的能量损失。利用该系统测量了115～180nm球面镜的反射率,测试结果表明测量重复性优于±0.3%;按国际通用不确定度评估规范,对系统进行不确定度分析,相关不确定度小于1.3%。实现了球面镜反射率的高精度测量。     

用激光法测量凹透镜焦距的探究

结合简单的几何原理,根据激光光源的特性提出了一种简便测量凹透镜焦距的新方法.     

On fuzzy multi-valued functions, part 4: Fuzzy economic models

An application to fuzzy economic systems of the fuzzy multi-valued functions theory elaborated by both of us in our previous papers is presented. First, stationary and dynamic fuzzy economic models are defined. Next the optimality of fuzzy trajectories of these models is introduced and investigated.     

Solving Sum of Ratios Fractional Programs via Concave Minimization

This article presents an algorithm for globally solving a sum of ratios fractional programming problem. To solve this problem, the algorithm globally solves an equivalent concave minimization problem via a branch-and-bound search. The main work of the algorithm involves solving a sequence of convex programming problems that differ only in their objective function coefficients. Therefore, to solve efficiently these convex programming problems, an optimal solution to one problem can potentially be used to good advantage as a starting solution to the next problem.