An Adaptive Algorithm for Vector Partitioning

The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part. Here all parameters d, p, n are considered variables. In this paper, we study the adjacency of vertices in the associated partition polytopes. Using our adjacency characterization for these polytopes, we are able to develop an adaptive algorithm for the vector partition problem that runs in time O(q(L)v) and in space O(L), where q is a polynomial function, L is the input size and v is the number of vertices of the associated partition polytope. It is based on an output-sensitive algorithm for enumerating all vertices of the partition polytope. Our adjacency characterization also implies a polynomial upper bound on the combinatorial diameter of partition polytopes. We also establish a partition polytope analogue of the lower bound theorem, indicating that the output-sensitive enumeration algorithm can be far superior to previously known algorithms that run in time polynomial in the size of the worst-case output.     

米散射理论在新型导光板中的应用

根据米散射理论,提出了新型导光板的设计思路,计算并分析了对于一定波长的入射光,不同粒径的微粒的散射特性。总结了随着微粒粒径的变化,散射效率、消光效率与背向散射效率的变化规律,分析了散射过程中的偏振度随粒子粒径几散射角变化的情况,同时模拟计算了多个微粒对同一波长的入射光经过多次散射后的概率统计结果。     

Escape factors in spherically symmetric plasmas

In this paper we present explicit formulas for the escape factors of strong spectral lines in spherical-symmetric plasmas. The plasma does not necessarily have a homogeneous density. The calculations include two new elements: the first incorporates an accurate calculation of the angle-averaged areal density of ions from any internal point to the edge of the sphere. The second is the use of a saddle point method to carry out the integration over the line profile. Approximate expressions for the asymptotic behavior of the escape factor are given for Gaussian, Lorentzian and Holtsmarkian line shapes.     

Polariton emission in GaN microcavities

We present a detailed experimental study aimed at demonstrating the polariton nature of the photoluminescence emission in a bulk GaN microcavity grown on (111) silicon. The comparison of the photoluminescence with coincident reflectivity measurements at different temperatures shows an anticrossing behaviour with a Rabi splitting of the order of 35 meV up to room temperature. Relevant confirmations of the mixing between excitons and photons are found in the analysis of the spectral linewidth and of the time resolved kinetics.     

The method of lines applied to nonlinear nonlocal functional differential equations

This paper discusses nonlinear functional differential equation in a real reflexive Banach space with nonlocal history condition. By using the method of lines, the existence and uniqueness of a strong solution are established. Finally, some applications of the abstract results are presented.     

新型塑料导线直径在线测量系统

本文提出了一种用线阵ＣＣＤ非接触实时测量塑料导线直径的仪器，它有如下特点：（１）采用了对被测目标所发出的烟雾不敏感的光学系统，提高了测量精度；（２）采用工作于脉冲方式的大功率近红外ＬＥＤ做照明光源，其寿命比采用白炽灯作为光源大为增长，同时缩小了体积并有利于抑制可见光的干扰；（３）对电信号采用了两级滤波、直流恢复、自适应阈值二值化等处理技术；（４）采用定标的方法来消除目标位置移动的影响，提高了测量精度，降低了加工装配精度要求。现场使用证明，它能长期可靠地工作，总的测量误差小于±０．０２ｍｍ。     

The diameter of a fuzzy set

In pattern recognition one often wants to measure geometric properties of imprecisely defined subsets of an image. This paper proposes definitions of intrinsic and extrinsic diameter for fuzzy subsets which reduce to the ordinary definitions when the subsets are crisp. We also define height and width for a fuzzy subset and show how they relate to the area (i.e., integral of membership). For convex fuzzy subsets the intrinsic diameter cannot exceed the extrinsic diameter, but it can be smaller. Finally, for piecewise constant convex fuzzy subsets the intrinsic diameter cannot exceed half the fuzzy perimeter, but this need not be true in the nonconvex case.     

Une nouvelle définition des volumes libres dans les liquides non associés: application à la détermination des diamètres moléculaires

Résumé Une étude systématique des volumes libres extrapolés à fluidité nulle a été menée sur une vingtaine de liquides. Une nouvelle équation est proposée pour ce volume libre limite, noté «V.L.L.» et nous la comparons à celle déduite des calculs de l'Hydrodynamique classique; elle permet de déterminer les valeurs de diamètres moléculaires; ces dernières sont en bon accord avec celles obtenues de la viscosité des gaz, de la diffusion Raman ou Rayleigh. En outre, et aux erreurs expérimentales près, les valeurs des diamètres moléculaires sont données pour 10 dérivés du benzène, valeurs qui ne se trouvent pas, à notre connaissance, dans la littérature, exception faite du benzène pur.

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Summary A systematic study of free volumes extrapolated at zero fluidity is executed for 20 liquids. A new equation for this Limit Free Volume (V.L.L.) is proposed and compared with the theoretically calculated free volume; values of molecular diameters are determined and found to be in good agreement with values obtained from gas viscosity, Raman and Rayleigh scattering, respectively. Moreover, within experimental error, values of molecular diameters are found for 10 benzene derivatives which are not, at our knowledge, available in the literature, except for pure benzene.

Avec 1 figure et 3 tableaux     

Analysis of longitudinal multispin orders in strongly coupled spin systems

Longitudinal multispin orders provide an effective way for measurement of scalar couplings and also to probe molecular interactions and dynamics. Analysis of longitudinal orders has been made in strongly coupled AB and ABX spin systems to determine the dependence of strong coupling parameter on these orders. Experimental and simulated spectra of various longitudinal orders are illustrated for these spin systems. This general procedure can be extended to broad range of spin systems to understand the influence of strong coupling on longitudinal orders.     

Curves of positive solutions of boundary value problems on time-scales

Let TR be a time-scale, with a=infT, b=supT. We consider the nonlinear boundary value problem

(2)

(4)

u(a)=u(b)=0,