带两个服务等级的三台机最优在线算法

研究了带服务等级约束的三台平行机在线排序问题.每台机器和每个工件的服务等级为1或者2,工件只能在等级不高于它的机器上加工,即等级为1的工件只能在等级为1的机器上加工,等级为2的工件可在所有机器上加工.每个工件的加工时间为一个单位,目标是极小化所有工件的总完工时间.考虑两种情形:当一台机器等级为1,两台机器等级为2时,给出了竞争比为17/14的最优在线算法;当两台机器等级为1,一台机器等级为2时,给出了竞争比为43/36的最优在线算法.     

Homeomorphs and amallamorphs of the Petersen graph

Let P be the Petersen graph. The main results of this paper are the discovery of infinite families of chromatically equivalent pairs of P homeomorphs and the discovery of infinite families of flow equivalent pairs of P amallamorphs. In particular, three families of P homeomorphs with 8 parameters, five families with 7 parameters and many families with fewer parameters are obtained. Also one family of P amallamorphs with 9 parameters, three families with 7 parameters, seven families with 6 parameters and many families with fewer parameters are obtained.     

变厚度圆薄板非对称非线性弯曲问题

首先将直角坐标系中的横向变厚度薄板的大挠度方程,转化到极坐标系中的变厚度圆薄板的非对称大挠度方程·　此方程和极坐标系中径向、切向两个平衡方程联立求解·　将物理方程和中面应变非线性变形方程,代入3个平衡方程,可得用3个变形位移表示的3个非对称非线性方程·　用Fourier级数表示的解代入基本方程,获得相应的基本方程·　在周边夹紧边界条件下,用修正迭代法求解·　作为算例,研究了余弦形式载荷作用下的问题,还给出了载荷与挠度的特征曲线,曲线依据变厚度参数变化而变化,其结果和物理概念完全吻合·     

多元整系数多项式因式分解的一种理论和算法

本文将ｔ（ｔ是大于２的整数）元整系数多项式看成为系数为ｔ－２元整系数多项式的二元多项式，建立了多元整系数多项式因式分解的一种新理论，进而得到了分解多元整系数多项式的一个有力的算法。     

Spectrality of a class of self-affine measures with decomposable digit sets

The self-affine measure associated with an expanding matrix and a finite digit set is uniquely determined by the self-affine identity with equal weight.The spectral and non-spectral problems on the selfaffine measures have some surprising connections with a number of areas in mathematics,and have been received much attention in recent years.In the present paper,we shall determine the spectrality and non-spectrality of a class of self-affine measures with decomposable digit sets.We present a method to deal with such case,and clarify the spectrality and non-spectrality of a class of self-affine measures by applying this method.     

损伤粘弹性力学的广义变分原理及应用

从粘弹性材料的Boltzmann迭加原理和带空洞材料的线弹性本构关系出发,提出了一种损伤粘弹性材料具有广义力场的本构模型．应用变积方法得到了以卷积形式表示的泛函,并建立了损伤粘弹性固体的广义变分原理和广义势能原理．把它们应用于带损伤的粘弹性Timoshenko梁,得到了Timoshenko梁的统一的运动微分方程、初始条件和边界条件． 这些广义变分原理为近似求解带损伤的粘弹性问题提供了一条途径．     

带人工雨线的拉索在风激励下的响应

通过在风洞中对一具有可调动力特性、雨线位置和风向角的带人工雨线的拉索模型进行了试验,研究了拉索的风雨激振特性.试验结果和其他研究人员的结果进行了仔细对比,得到了一些新的结论,澄清了过去的一些模糊认识.结果表明,带人工雨线的水平索在风向为零时的响应可以用Den Hartog驰振机制来解释,而风向不为零时,拉索表现为限速振动或限速和驰振的混合型振动.     

Arithmetical and specular self-reference

Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference into an idealized model of self-recognition and the conception(s) of self based on that capacity.     

Balanced contributions for TU games with awards and applications

Calleja et al. [Calleja, P., Borm, P., Hendrickx, R., 2005. Multi-issue allocation situations. European Journal of Operational Research 164, 730–747] introduced multi-issue allocation situations with awards. In this paper, we extend the classical model of cooperative games with transferable utility to the cooperative games with transferable utility and awards. We define a run-to-the-bank rule for cooperative games with transferable utility and awards and characterise it in terms of a property of balanced contributions. We apply our main result to bankruptcy problems and multi-issue allocation situations with awards.     

M/G/1一般减量服务单重休假排队系统的随机分解

本文讨论了M/G/1型一般减量服务单重休假排队模型,运用结构分析法得到稳态队长和服务时间的随机分解的母函数和拉式变换,并给出稳态分布成立的条件及其概率含义．     

模糊正则文法的逼近性

为了扩大现有研究的应用范围,基于max-min型模糊正则文法引入了max-*型模糊正则文法(其中*为特定t-模)的概念,讨论了max-*型模糊正则文法可以通过max-min型模糊正则文法在任意给定的逼近精度来逼近.研究表明,当t-模*满足一定的条件时,max-*型模糊正则文法与max-min型模糊正则文法在生成模糊语言能力方面是等价的.     

Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty

We discuss adaptive sparse grid algorithms for stochastic differential equations with a particular focus on applications to electromagnetic scattering by structures with holes of uncertain size, location, and quantity. Stochastic collocation (SC) methods are used in combination with an adaptive sparse grid approach based on nested Gauss-Patterson grids. As an error estimator we demonstrate how the nested structure allows an effective error estimation through Richardson extrapolation. This is shown to allow excellent error estimation and it also provides an efficient means by which to estimate the solution at the next level of the refinement. We introduce an adaptive approach for the computation of problems with discrete random variables and demonstrate its efficiency for scattering problems with a random number of holes. The results are compared with results based on Monte Carlo methods and with Stroud based integration, confirming the accuracy and efficiency of the proposed techniques.     

居民消费的习惯形成与实际经济周期模型的求解分析——一个基于三部门RBC模型的研究

结合H-P滤波法和King,Plosser&.Robelo(1987)的研究,探讨了一个求解引入居民消费的习惯形成和存在稳态趋势增长的RBC模型的对数线性化方法,并利用该方法求解引入习惯形成和政府支出冲击的三部门RBC模型来分析中国1979-2009年间宏观经济波动.研究表明:这个方法求解本文模型的预测结果与中国的特征事实较一致;与NHG方法求解的预测结果相比较,二者存在明显的差异;对中国经济的解释力要强于NHG方法求解的预测结果.     

考虑耗散效应的金属杆受扰动后的非线性动力学现象分析

研究在周期外载荷作用及Neumann边界条件下,考虑Peierls-Nabarro效应的有限长一维金属杆的运动,以位移表达杆的控制方程,是受扰动的类sine-Gordon方程．利用空间四阶精度,时间二阶精度的有限差分格式模拟系统的动力响应．对于一定特征尺寸及物理性质的金属杆,研究了初始呼吸子及周期载荷幅值对杆动力行为的影响,结果显示了4种典型的动力行为:与空间位置无关的简谐运动、单波的简谐运动、单波的准周期运动和单空间模态的时间混沌运动．通过Poincaré截面和功率谱确定系统的运动特征．     

半环中带算子的L-模糊h-理想

The notions of M-hemirings and L-fuzzy left h-ideals with operators in M-hemirings are introduced,and some properties are investigated.Given an L-fuzzy left h-ideal with operators,a new L-fuzzy left h-ideal with operators is established. Using a collection of left M-h-ideals,L-fuzzy left h-ideais with operators are con- structed.Moreover,the concept of M-Notherian M-hemiring is introduced and its characterization is given.     

Two-derivative Runge-Kutta methods with optimal phase properties

In this work, we consider two-derivative Runge-Kutta methods for the numerical integration of first-order differential equations with oscillatory solution. We construct methods with constant coefficients and special properties as minimum phase-lag and amplification errors with three and four stages. All methods constructed have fifth algebraic order. We also present methods with variable coefficients with zero phase-lag and amplification errors. In order to examine the efficiency of the new methods, we use four well-known oscillatory test problems.     

A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem

Continuous Galerkin formulations are appealing due to their low computational cost, whereas discontinuous Galerkin formulation facilitate adaptative mesh refinement and are more accurate in regions with jumps of physical parameters. Since many electromagnetic problems involve materials with different physical properties, this last point is very important. For this reason, in this article we have developed a combined cG-dG formulation for Maxwell’s problem that allows arbitrary finite element spaces with functions continuous in patches of finite elements and discontinuous on the interfaces of these patches. In particular, the second formulation we propose comes from a novel continuous Galerkin formulation that reduces the amount of stabilization introduced in the numerical system. In all cases, we have performed stability and convergence analyses of the methods. The outcome of this work is a new approach that keeps the low CPU cost of recent nodal continuous formulations with the ability to deal with coefficient jumps and adaptivity of discontinuous ones. All these methods have been tested using a problem with singular solution and another one with different materials, in order to prove that in fact the resulting formulations can properly deal with these problems.     

Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B. Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian spheres and pseudo-hyperbolic spaces with arbitrary codimension and arbitrary index. Consequently, we achieve the complete classification of spatial surfaces with parallel mean curvature vector in all pseudo-Riemannian space forms. As an immediate by-product, we obtain the complete classifications of spatial surfaces with parallel mean curvature vector in arbitrary Lorentzian space forms.      

一种资源投入不确定情形下的合作博弈形式及收益分配策略

首先,将经典合作博弈进行扩展,提出了一类模糊联盟合作博弈的通用形式,涵盖常见三种模糊联盟合作博弈,即多线性扩展博弈、比例模糊博弈与Choquet积分模糊博弈.比例模糊博弈、Choquet积分模糊博弈的Shapley值均可以作为一种特定形式下模糊联盟合作博弈的收益分配策略,但是对于多线性扩展博弈的Shapley值一直关注较少,因此利用经典Shapley值构造出多线性扩展博弈的Shapley值,以此作为一种收益分配策略.最后,通过实例分析了常见三类模糊联盟合作博弈的形式及其对应的分配策略,分析收益最大的模糊联盟合作对策形式及最优分配策略,为不确定情形下的合作问题提供了一定的收益分配依据.     

Diagonalization of tensors with circulant structure

The concepts of tensors with diagonal and circulant structure are defined and a framework is developed for the analysis of such tensors. It is shown a tensor of arbitrary order, which is circulant with respect to two particular modes, can be diagonalized in those modes by discrete Fourier transforms. This property can be used in the efficient solution of linear systems involving contractive products of tensors with circulant structure. Tensors with circulant structure occur in models for image blurring with periodic boundary conditions. It is shown that the new framework can be applied to such problems.