Pm‖Cmax问题的算法AKK的一个改进的最坏情况性能比

本文考虑的是平行机排序问题Pm‖Cmax.对此问题Knuth和Kleitman给出了一个近似算法AKK,Graham证明了此算法的最坏情况性能比不大于1＋1-1/m/1＋｜k/m｜,而且当k≡0（modm）时这个界是紧的.在本文中我们给出了此算法的一个改进的最坏情况性能比： 1＋max{1-1/m/1＋k1＋1/m,1-1/m-k2/1＋k1},其中k1和k2为非负整数且k1m＋k2=k.本文证明了当k2≠0时,它好于Graham的结果,同时我们给出了两个实例说明这个界是紧的.     

具有优先权和准备时间的自由作业时间表问题

研究具有优先权和准备时间的自由作业时间表问题 ,在稠密时间表的情况下 ,给出一种启发式算法 ,猜想该算法的紧界是 2 -2 /( m +1 ) ,其中 m是机器台数 .对于只有两台机器的情况 ,即当 m =2 时 ,证明该算法的最坏性能比是 4/3 ,并通过实例证明上界是紧的 .     

工件带到达时间的两阶段柔性流水作业的近似算法

研究了工件带到时间的两阶段柔性流水作业的排序问题,基于求解流水作业和平行机问题的算法思想,提出两个相应的近似算法H(R)和H(MR(?)),证明了这两个算法的最坏情况性能比分别为3-1/m和2/5-1/m,讨论了界的紧性,并利用数值模拟以分析算法与最优值的近似性能比.     

极小化加权完工时间和的Flowshop问题的算法

本文讨论了极小化加权完工时间和的Flowshop问题.我们给出了一个最坏情况误差界为m的启发式算法,对于m=2的情况,如果工件具有一致权因子,即pi相似文献   

Flow shop排序问题Fm／prmu／∑^WjCj的一个启发式算式

本文给出了Flow shop排序问题Fm/prmu/∑^WjCj的一个启发式算式，其最坏情况的界为m，且是紧界。     

带机器准备时间的平行机在线与半在线排序

本文研究带机器准备时间的m台平行机系统在线和半在线排序问题.对在线排序问题,我们证明了LS算法的最坏情况界为2-1/m.对已知工件加工时间递减,已知总加工时间和已知工件最大加工时间三个半在线模型,我们分析了它们的下界和所给算法的最坏情况界.对其中两台机情形均得到了最好近似算怯。     

有两个服务等级的平行机排序问题

对有两个服务等级的平行机排序问题的m台机情形,证明了修正的MF算法的最坏情况界不超过4/3 (1/2)~k,其中k是算法中预先给定的迭代次数.而已有的算法仅为2-1/(m-1),从而大大改进了已有文献中的结果.     

带约束的平行机排序的一个近似算法

讨论有资源约束和有机器准备时间的平行机排序问题,资源约束为每个机器至多可加工k个工件,在极小化makespan的上给出了一个匹配算法,证明其最坏情况最紧界是2-m^-1,并进一步给出了它的两个带参数的最坏情况界。     

复合并行机F''''2|m1≥2,m2=1|Cmax排序问题的归并算法研究

在文献[1]中,已经证明了排序问题F2|m1≥2,m2=1|Cmax是NP完全问题,没有好算法.本文提出了复合并行机F'2|m1≥2,m2=1|Cmax排序问题的一个启发式算法--归并算法,并证明了该算法在最坏情况下的性能比(Performance Ratio)是2m-1/m,且优于文献[2]中算法.     

可转包两台流水作业机排序的近似算法

研究可转包的两台流水作业机排序问题, 目标是极小化最大完工时间和总外包费用之和. 首先给出最坏情况界为2的近似算法, 接着对工件满足有序化约束的情形给出最坏情况界为\frac{3}{2}的改进算法, 以上算法界均为紧界.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by