A mathematical model and two-stage heuristic for hot rolling scheduling in compact strip production

This paper addresses a new hot rolling scheduling problem from the compact strip production process, which is the mainstream production technology that is used worldwide for sheet strips. The problem is modeled as a combination of two coupled sub-problems. One sub-problem is a sheet strip assignment problem that assigns sheet strips to rolling turns with the constraints of safe values of different gauge levels, and the other is a sheet strip sequencing problem that decides the rolling sequence for all of the sheet strips in a rolling turn to form a particular parabolic shape in thickness. To solve this hot rolling scheduling problem, we present a novel approach that consists of a sheet strip assignment heuristic and a sheet strip sequencing heuristic. The sheet strip assignment heuristic minimizes the number of virtual sheet strips by generating rolling turns according to the ordered sheet strips with maximum gauge level and their safe values. The sheet strip sequencing heuristic minimizes the average change of the thickness of adjacent sheet strips by arranging a certain number of duplicate sheet strips to the increasing stage of a rolling turn. Extensive experiments based on both synthetic and real-world instances from a compact strip production process show the effectiveness of the proposed two-stage heuristic in solving the hot rolling scheduling problem.     

Using genetic algorithm for dynamic and multiple criteria web-site optimizations

In today’s competitive electronic marketplace, companies try to create long-lasting relations with their online customers. Log files and registration forms generate millions of online transactions. Companies use new techniques to “mine” these data and establish optimal online storefronts to maximize their web presence. Several criteria, such as minimization of download time, maximization of web-site visualization and product association level, can be used for the optimization of virtual storefronts. This paper introduces a genetic algorithm, to be used in a model-driven decision-support system for web-site optimizations. The algorithm ensures multiple criteria web-site optimizations, and the genetic search provides dynamic and timely solutions independent of the number of objects to be arranged.     

云环境下面向复杂资源需求的虚拟机能效部署研究

针对云环境下在线虚拟机部署这一矢量装箱问题进行了研究,提出了多维空间划分模型和在线虚拟机能效部署算法OEEVMP。多维空间划分模型可以引导虚拟机部署,避免多维资源的不均衡利用;基于此模型,提出的OEEVMP算法在物理机运行数量局部最优和全局最优之间取得均衡,从而提高虚拟机部署能效。通过仿真实验,将OEEVMP算法与MFFD算法进行了对比,实验结果验证了所提算法的可行性和有效性。最后,对控制模型的两个参数进行了分析,给出了最佳的参数组合。     

Progressive transmission of subdivision surfaces

Triangle meshes are a standard representation for surface geometry in computer graphics and virtual reality applications. To achieve high realism of the modeled objects, the meshes typically consist of a very large number of faces. For broadcasting virtual environments over low-bandwidth data connections like the Internet it is highly important to develop efficient algorithms which enable the progressive transmission of such large meshes. In this paper we introduce a special representation for storing and transmitting meshes with subdivision connectivity which allows random access to the detail information. We present algorithms for the decomposition and the reconstruction of subdivision surfaces. With this technique, the receiver can reconstruct smooth approximations of the original surface from a rather small amount of data received.     

Counting systems and the First Hilbert problem

The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) with different accuracies. The traditional and the new approaches are compared and discussed.     

On Zipf’s law and rank distributions in linguistics and semiotics

A number of formulas of linguistic statistics are refined. The notions of real and virtual cardinality of a sign are introduced. We show that a formula refining Zipf’s law for the occurrence frequencies in frequency dictionaries can be extended to arbitrary sign objects, i.e., semiotic systems.     

基于MVR-E技术的虚拟社区交流引擎的设计与实现

通过对多媒体及多用户虚拟现实技术结构的分析和研究,就如何在FlashCommunication Application Server环境下开发虚拟社区交流引擎,通过组件方式在互联网上建立虚拟现实站点,并就如何实现虚拟环境下何实现虚拟现实的三维显示、场景更替、对象行走以及各对象之间如何实现消息传递,给出了相应的解决方案.     

A finite-element approach in order to avoid ill-conditioning in thin-sheet problems in frequency domain—Application to magneto-quasistatics

In this work, a new thin-sheet approach in the finite-element method is derived. The focus is on the condition number of the system matrix, namely, to keep this measure preferably independent of the thickness of the sheet. Constant sheet elements are used for the tangential variation in the sheet. However, the information about the discontinuity in normal direction is incorporated into the basis functions of the volume elements that are connected to the sheet elements. The determination of the normal variation can be reduced to a 1D problem which can be solved analytically. No double layers or global asymptotic expansions are required. The advantages with respect to the condition number of the system matrix are shown for a magneto-quasistatic test scenario.     

Mixed-integer programming models for nesting problems

Several industrial problems involve placing objects into a container without overlap, with the goal of minimizing a certain objective function. These problems arise in many industrial fields such as apparel manufacturing, sheet metal layout, shoe manufacturing, VLSI layout, furniture layout, etc., and are known by a variety of names: layout, packing, nesting, loading, placement, marker making, etc. When the 2-dimensional objects to be packed are non-rectangular the problem is known as the nesting problem. The nesting problem is strongly NP-hard. Furthermore, the geometrical aspects of this problem make it really hard to solve in practice. In this paper we describe a Mixed-Integer Programming (MIP) model for the nesting problem based on an earlier proposal of Daniels, Li and Milenkovic, and analyze it computationally. We also introduce a new MIP model for a subproblem arising in the construction of nesting solutions, called the multiple containment problem, and show its potentials in finding improved solutions.     

Virtual manifolds and localization

In this paper, we explore the virtual technique that is very useful in studying the moduli problem from a differential geometric point of view. We introduce a class of new objects ＂virtual manifolds/orbifolds＇, on which we develop the integration theory. In particular, the virtual localization formula is obtained.     

Mixed Integer Models for Branched Sheet Metal Products

A new technique for forming sheet metal makes it possible to construct branched sheet metal products out of one piece of sheet metal. Since the number of potential ways to produce one and the same component increases exponentially with every additional branch, appropriate tools for handling the large number of possibilities are necessary. In this paper we give a Mixed Integer Program that models the different ways of producing branched profiles and show how to incorporate manufacturing constraints into the model. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Boolean duals of virtual groups

The purpose of this paper is to formulate the notion of virtual group and that of a homomorphism between two in such a way that no null sets are involved. That is, we replace the point set by the measure algebra of Borel sets modulo null sets, and the various functions involved must be described by objects associated to these measure algebras, such as σ-homomorphisms. In the process it is necessary to redefine functions satisfying algebraic identities almost everywhere to get new ones satisfying the identities in a stricter sense. Similar refinements on quasiinvariance of measures are also required.     

An optimising approach to alternative clustering schemes

Clustering objects into groups is usually done using a statistical heuristic or an optimisation. The method depends on the size of the problem and its purpose. There may exist a number of partitions which do not differ significantly but some of which may be preferable (or equally good) when aspects of the problem not formally contained in the model are considered in the interpretation of the result. To decide between a number of good partitions they must first be enumerated and this may be done by using a number of different heuristics. In this paper an alternative method is described which uses an integer linear programming model having the number and size distribution of groups as objectives and the criteria for group membership as constraints. The model is applied to three problems each having a different measure of dissimilarity between objects and so different membership criteria. In each case a number of optimal solutions are found and expressed in two parts: a core of groups, the membership of which does not change, and the remaining objects which augment the core. The core is found to contain over three quarters of the objects and so provides a stable base for cluster definition.     

A quasilinearization approach to heat transfer in MHD visco-elastic fluid flow

The paper deals with the study of the flow of an incompressible electrically conducting visco-elastic fluid referred to as Walter’s liquid B over a porous non-isothermal stretching sheet using quasilinearization technique adopting a numerical approach. The sheet is assumed to stretch uni-directionally and the fluid above the sheet is at rest if there were no stretching. The temperature profiles are obtained numerically and these are displayed through graphs for diverse values of Prandtl number, visco-elastic parameter, magnetic parameter, source/sink parameter, wall temperature parameter and wall heat flux parameter. The results are compared with those available in literature obtained through analytical procedures and are seen to be in good agreement.     

General constructions of biquandles and their symmetries

Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including what we refer as the holomorph biquandle of a quandle. These constructions give a wealth of solutions of the Yang-Baxter equation. We also show that for nice quandle coverings a biquandle structure on the base can be lifted to a biquandle structure on the covering. In the second half of the paper, we determine automorphism groups of these biquandles in terms of associated quandles showing elegant relationships between the symmetries of the underlying structures.     

The eye and the fist: Optimizing search and interdiction

Interdiction operations involving search, identification, and interception of suspected objects are of great interest and high operational importance to military and naval forces as well as nation’s coast guards and border patrols. The interdiction scenario discussed in this paper includes an area of interest with multiple neutral and hostile objects moving through this area, and an interdiction force, consisting of an airborne sensor and an intercepting surface vessel or ground vehicle, whose objectives are to search, identify, track, and intercept hostile objects within a given time frame. The main contributions of this paper are addressing both airborne sensor and surface vessel simultaneously, developing a stochastic dynamic-programming model for optimizing their employment, and deriving operational insight. In addition, the search and identification process of the airborne sensor addresses both physical (appearance) and behavioral (movement pattern) signatures of a potentially hostile object. As the model is computationally intractable for real-world scenarios, we propose a simple heuristic policy, which is shown, using a bounding technique, to be quite effective. Based on a numerical case study of maritime interdiction operations, which includes several representative scenarios, we show that the expected number of intercepted hostile objects, following the heuristic decision policy, is at least 60% of the number of hostile objects intercepted following an optimal decision policy.     

On virtual pathwidth of virtual graphs of a virtual link

The geometric representation of a knot is not too dissimilar from a graph and this interaction has helped mathematicians to solve many problems. In this paper, we apply graph theory tools to study the classification of virtual knots and links. We define virtual planar graphs and compute virtual path width of an associated graph of a virtual link. We show that the virtual path width of an associated graph is equal to the virtual bridge number of a pseudo prime knot.     

Fixed point indices in locally convex spaces

The primary objective of this paper is to show that semicomplex structures may be employed to define a local fixed point index on the category whose objects are all finite unions of compact, convex subsets of locally convex topological vector spaces and whose morphisms are all continuous maps between its objects. This is established via the use of the lc1 spaces introduced by Lefschetz to generalize absolute neighborhood retracts.     

On the approximation of unstable parametric minimal surfaces

We prove optimal convergence results for discrete approximations to (possibly unstable) minimal surfaces. This appears to be the first class of results of this type for geometric objects solving a highly non-linear geometric variational problem. We introduce a number of new techniques which we expect will be of use in other geometric problems. The theoretical approximation results are confirmed by numerical test computations.     

基于模糊层次分析的虚拟企业风险评价

在分析虚拟企业风险评价应该考虑的主要因素的基础上,建立了一套适用于虚拟企业风险评价的指标体系,提出了一种基于模糊集合理论与层次分析法相结合的虚拟企业风险评价方法。在多专家指标权重评价的基础上,运用模糊D elph i法对上层准则形成一系列的权重集合,得到三角模糊数表示的准则“重要性”评价。结合以模糊语言变量表示的备选方案偏好等级的“满意度”和下层指标的模糊权重,通过分层结合,得到虚拟企业风险的模糊评分,最后采用重心法和Chang Jing-rong的双系数法对所有方案的三角模糊数进行排序,得到虚拟企业方案综合选择的优先顺序。实例说明了虚拟企业风险评价的具体过程。