Dynamic data structures for fat objects and their applications

We present several efficient dynamic data structures for point-enclosure queries, involving convex fat objects in or . Our planar structures are actually fitted for a more general class of objects – (β,δ)-covered objects – which are not necessarily convex, see definition below. These structures are more efficient than alternative known structures, because they exploit the fatness of the objects. We then apply these structures to obtain efficient solutions to two problems: (i) finding a perfect containment matching between a set of points and a set of convex fat objects, and (ii) finding a piercing set for a collection of convex fat objects, whose size is optimal up to some constant factor.     

Effects of multiple blade interaction on the containment of blade fragments during a rotor failure

A finite element analysis is used to study the impact and the containment aspects of rotor blade fragments that are produced during a aircraft jet engine rotor failure. The impact and containment studies are performed on a ring-type containment structure and various fragment types are considered in this study. For each type of fragment, the ring thickness is varied incrementally and the ring response, residual kinetic energy level of the fragments, magnitude of impact forces and the overall containment or failure are determined. First, only a single fragment is considered and the rotor is assumed to contain no other blades. Next, the remaining blades are introduced and the effects of multiple collisions with the other blades on the containment are analyzed. The explicit, nonlinear finite element code Dyna3d is used for the numerical computations in this study and the results are compared with the experimental results performed on a T58 rotor at the spin facility of the Naval Air Propulsion Test Center.     

Covering shadows with a smaller volume

For n?2 a construction is given for convex bodies K and L in Rn such that the orthogonal projection Lu onto the subspace u^⊥ contains a translate of Ku for every direction u, while the volumes of K and L satisfy Vn(K)>Vn(L).A more general construction is then given for n-dimensional convex bodies K and L such that each orthogonal projection Lξ onto a k-dimensional subspace ξ contains a translate of Kξ, while the mth intrinsic volumes of K and L satisfy Vm(K)>Vm(L) for all m>k.For each k=1,…,n, we then define the collection Cn,k to be the closure (under the Hausdorff topology) of all Blaschke combinations of suitably defined cylinder sets (prisms).It is subsequently shown that, if L∈Cn,k, and if the orthogonal projection Lξ contains a translate of Kξ for every k-dimensional subspace ξ of Rn, then Vn(K)?Vn(L).The families Cn,k, called k-cylinder bodies of Rn, form a strictly increasing chain

Cn,1⊂Cn,2⊂?⊂Cn,n−1⊂Cn,n,     

依零测度的Fuzzy集运算

给出了Fuzzy集合依零测度的包含,依零测度的相等。依零测度的并．交,补运算等。并补充地研究了这些基本运算,获得了若干好的性质。Fuzzy集依零测度的基本运算比标准fuzzy集合论的相应运算更有人情味,更为接近人的智能机理。有望在智能信息处理和软计算领域取得好的应用。     

核电站安全壳缺陷检测系统研究设计

借助于可平稳移动于垂直墙面的负压吸附式爬壁机器人平台,将两台分辨率不同的摄像机固定于机器人前端支架上。通过两组相互独立的无线通信网络,分别实现控制爬壁机器人移动和回传摄像机所拍摄到的安全壳外壁视频信息。无线回传的视频信息在本地上位机监控平台上经过前期处理后进行实时播放显示,同时视频处理软件中的缺陷检测算法模块在后台进行图像缺陷检测,检测到缺陷后,软件平台发送停止信号给机器人,同时视频流切换到高清摄像机进行高清照片拍摄,并将包含缺陷信息的高清照片发送至缺陷测量模块,利用在缺陷测量模块中所开发的测量工具进行安全壳外壁缺陷测量,最终测量所得到的缺陷参数会存入后台数据库进行存储管理,方便后期浏览历史数据,监测安全壳外壁缺陷的动态变化情况。     

Coefficient Quantization in Banach Spaces

Let (e _i ) be a dictionary for a separable infinite-dimensional Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c ₀. We also show that, for every ε>0, the unit ball of every separable infinite-dimensional Banach space X contains a dictionary (x _i ) such that the additive group generated by (x _i ) is (3+ε)⁻¹-separated and 1/3-dense in X.      

Optimal scaling of balls and polyhedra

The concern is with solving as linear or convex quadratic programs special cases of the optimal containment and meet problems. The optimal containment or meet problem is that of finding the smallest scale of a set for which some translation contains a set or meets each element in a collection of sets, respectively. These sets are unions or intersections of cells where a cell is either a closed polyhedral convex set or a closed solid ball.This work was supported in part by the Department of Energy Contract DE-AC03-76-SF00326, PA No. DE-AT-03-76ER72018; National Science Foundation Grants MCS79-03145 and SOC78-16811; and the Army Research Office—Durham, Contract DAAG-29-78-G-0026.     

面向词计算的模糊约束重译

对词计算第三步模糊约束重译进行了研究.指出了候选词汇对应的模糊子集和结果约束中的模糊子集之间的贴近度和包容度在获取可信重译结果中的重要性.给出了分离算子的概念并设计了一个满足要求的分离算子.在此基础上定义了包容度的概念并给出了重译指数的计算公式.提出了一种基于重译指数计算的模糊约束重译方法.最后用实例说明了该方法的有效性.     

Extended <Emphasis Type="Italic">B</Emphasis>-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity

The purpose of this paper is to study the extended well-posedness in the sense of Bednarczuk for set-valued vector optimization. This notion of well-posedness can be interpreted as some sort of well-posedness under perturbation in terms of Hausdorff set-convergence. To investigate the extended B-well-posedness, we generalize property (H) due to Miglierina and Molho to the set-valued and perturbed case. Under a convexity assumption, we show that the extended B-well-posedness is closely related to property (H). This work was supported by the Scientific Research Foundation of CUIT (CRF200704), the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the Doctoral Program of Higher Education (20060610005).     

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.