平面图形的形心在旋转体体积计算中的应用

本文讨论平面图形绕平面内的直线旋转的旋转体体积与被旋转的平面图形的形心的关系.当被旋转的平面图形的内部与旋转轴没有交点时,得到了用被旋转的平面图形的面积以及被旋转的平面图形的形心到旋转轴的距离表示的旋转体体积公式.     

维数不同的相关量之间的微积分关系

维数不同的相关量之间的微积分关系王金贵（北京电力高等专科学校１０００４４）我们可能都留意过，圆的面积的导数等于圆的周长，即，球的体积的导数等于球的表面积，即．反过来，当然有圆的周长的积分等于圆的面积，即．球的表面积的积分等于球的体积，即．事实上，不仅...     

一个命题的中间点的渐近性

关于中值定理的中间点的渐近性的讨论已得到大量有趣的结果,对于某些经典命题的中间点的渐近性的讨论也是十分有趣的课题,本文给出了数学分析中的一个经典命题的中间点的一个渐近性的刻画.     

赋权图的圆染色与区间染色

赋权图的区间染色的定义与赋权图的圆染色的定义非常类型,唯一的区别就是将Ｇ的顶点对应圆周上的孤换为Ｇ的顶点对应区间上的子区间,讨论了赋权的圆染色与区染色的关系。     

李群表示论和Schubert条件

本文将Grassmann流形上的Schubert子簇所满足的经典的Schubert条件推广到一般的复半单李群G的广义旗流形.利用复半单李群的表示理论,我们首先在李群的权空间上引入自然的Ehresman偏序.这一偏序可以导出李群的最高权表示的权系、Weyl群及其陪集空间上的Ehresman偏序.然后我们对一般的复表示定义了相应的射影空间,Grassmann流形和旗流形.这使得能够像经典的情形一样来分析广义旗流形的Schubert子簇满足的Schubert条件.在讨论中,我们还给出了李群G的Weyl群及其陪集空间中的Bruhat-Chevalley偏序的简单判别条件.我们的结果应用到例外群,给出了Fulton提出的关于例外群的Schubert分析的问题的部分回答.     

可引进群运算的两类平面图

在某些文献中,我们常常看到图论与代数的概念及方法的密切联系和交错应用。例如,不久前,Babai等人即考虑了有敏锐的边可迁置换群的有向图,得到了关于这种图的最大外度数的估计的一些定理。而Bertram则反过来借助于图论的概念及方法,给出了关于有限群的某些数值(如非交换群中两两可换的一组元素的最大个数,等等)的大小的估计。 本文也将讨论群与图之间的联系。我们将使某些平面图的顶点与某些置换群的元素相对应,使顶点的序列与群元素的乘积相对应,然后通过对群的性质的研究,发现相应的平面图的顶点度数的一些规律,并据此解决     

关于线性偏微分方程的Cauchy问题的唯一性

<正> Cauchy问题的唯一性是偏微分方程的基本问题之一.经典的Cauchy-Kowalewski定理断言,解析方程或方程组的解析解是唯一的.1901年,Holmgren证明了,线性的解析方程或方程组的光滑解的唯一性.在取消关于系数的解析性的假设这个方向上的第一个结果是由Carleman在1939年给出的,他证明了两个自变量的相应结果,其中假设方程的主部的系数是实的,以及特征根是单重的,因而特征根的虚部如果不恒为零则总不为零.     

动态中国银行网络系统传染性风险研究

银行网络系统的传染性风险是目前国内外研究的重要问题,但是目前针对银行网络系统传染的风险研究均考虑的是静态的网络结构及网络上银行的资产负债也均为静态,忽视了动态的网络结构及银行动态的资产负债的演化.文章首先构建动态演化的银行网络系统,其包括网络结构的动态演化与银行节点的资产负债的动态演化;然后根据中国的实际数据,构建动态演化的中国银行网络系统,进一步研究中国银行网络系统的传染的演化规律,为中央银行制定政策提供决策依据.     

ω_(aδ)~ω∪bω_δ形图簇的伴随分解及其补图的色等价性

研究图的伴随分解及其补图的色等价性.采用伴随多项式的性质讨论图的伴随分解式,通过图的伴随分解式确定其补图的色性.证明了形图簇的伴随多项式的分解定理,从上述定理得到了这类图簇的补图的色等价性.结论通过图的伴随分解研究其补图的色等价性,是有效的途径与方法,从图的伴随分解式容易看出其补图的色等价图的结构规律.     

一个自入射Koszul代数的Hochschild同调与循环同调

代数的Hochschild同调群与其对应的Gabriel箭图的循环圈有着紧密的联系.本文基于Furuya构造的一个四点自入射Koszul代数的极小投射双模分解,用组合的方法计算了该代数的Hochschild同调空间的维数,并用循环圈的语言给出该代数的Hochschild同调空间的一组k-基.进一步,当基础域k的特征为零时,我们也得到了该代数的循环同调群的维数.     

A multivariate adaptive regression splines cutting plane approach for solving a two-stage stochastic programming fleet assignment model

The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an airline timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize profit. While costs associated with assigning a particular fleet type to a leg are easy to estimate, the revenues are based upon demand, which is realized close to departure. The uncertainty in demand makes it challenging to assign the right type of aircraft to each flight leg based on forecasts taken six to twelve weeks prior to departure. Therefore, in this paper, a two-stage stochastic programming framework has been developed to model the uncertainty in demand, along with the Boeing concept of demand driven dispatch to reallocate aircraft closer to the departure of the aircraft. Traditionally, two-stage stochastic programming problems are solved using the L-shaped method. Due to the slow convergence of the L-shaped method, a novel multivariate adaptive regression splines cutting plane method has been developed. The results obtained from our approach are compared to that of the L-shaped method, and the value of demand-driven dispatch is estimated.     

数学建模视角下的教育量化研究

以对人教A版高中必修教材使用顺序研究的技术路线为例,即从概念到变量—从变量到数据—从数据到模型—从模型到计算结果—从计算结果到揭示、解释教育规律的模式,说明数学建模是量化研究的核心,量化研究的本质就是通过建立数学模型以达到解决相关教育问题的目的.     

Modelling the role of cell-cell adhesion in the growth and development of carcinomas

In this paper, a mathematical model is presented to describe the evolution of an avascular solid tumour in response to an externally-supplied nutrient. The growth of the tumour depends on the balance between expansive forces caused by cell proliferation and cell-cell adhesion forces which exist to maintain the tumour's compactness. Cell-cell adhesion is incorporated into the model using the Gibbs-Thomson relation which relates the change in nutrient concentration across the tumour boundary to the local curvature, this energy being used to preserve the cell-cell adhesion forces.

Our analysis focuses on the existence and uniqueness of steady, radially-symmetric solutions to the model, and also their stability to time-dependent and asymmetric perturbations. In particular, our analysis suggests that if the energy needed to preserve the bonds of adhesion is large then the radially-symmetric configuration is stable with respect to all asymmetric perturbations, and the tumour maintains a radially-symmetric structure—this corresponds to the growth of a benign tumour. As the energy needed to maintain the tumour's compactness diminishes so the number of modes to which the underlying radially-symmetric solution is unstable increases—this corresponds to the invasive growth of a carcinoma. The strength of the cell-cell bonds of adhesion may at some stage provide clinicians with a useful index of the invasive potential of a tumour.     

Interaction of intelligent and autonomous systems – part II: realization of cognitive technical systems

In this study, the application of a meta-modelling technique to structure complex environments is demonstrated with two examples. A special situation-operator model developed to model the human-machine-interaction is applied to automated supervision within the HMI context and to realize flexible and situated interaction of autonomous systems. A concept to automated monitoring of human operators is introduced to illustrate the structuring of complex environments as the first example. In the second example, this modelling technique is applied to a mobile robot to autonomously build and update a mental model of the interaction with the environment as an example of a cognitive technical system.     

基于集对分析的地区经济发展水平综合评价研究——以环渤海地区为例

地区经济发展水平问题是一个复杂的系统问题,运用集对分析同一度概念的综合评价方法,以环渤海地区为例,对其五个省市经济发展情况进行了综合评价、排序及分析,为环渤海地区经济发展提供借鉴和参考.     

基于模糊聚类分析的教师课堂教学质量评价

用模糊聚类的方法对教师的课堂教学进行分类分析,选取合适的相似系数,建立模糊相似矩阵,用直接聚类法进行分类,它不能实现我们传统意义的名次排序,但它很好的实现了量化评价和质性评价的结合,实现了评价的诊断功能,为信息反馈提供了依据,充分发挥了评价的导向和激励功能.     

A local convergence property of primal-dual methods for nonlinear programming

We prove a new local convergence property of some primal-dual methods for solving nonlinear optimization problems. We consider a standard interior point approach, for which the complementarity conditions of the original primal-dual system are perturbed by a parameter driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed system and by applying the fraction to the boundary rule to maintain strict feasibility of the iterates with respect to the nonnegativity constraints. The analysis of the rate of convergence is carried out by considering an arbitrary sequence of perturbation parameters converging to zero. We first show that, once an iterate belongs to a neighbourhood of convergence of the Newton method applied to the original system, then the whole sequence of iterates converges to the solution. In addition, if the perturbation parameters converge to zero with a rate of convergence at most superlinear, then the sequence of iterates becomes asymptotically tangent to the central trajectory in a natural way. We give an example showing that this property can be false when the perturbation parameter goes to zero quadratically.      

Providing operational analysis to a peace support operation: the Kosovo experience

The Operational Analysis (OA) Branch of the HQ ARRC deployed into Kosovo concurrently with the withdrawal of Serbian forces. The authors, all members of the Operational Analysis Branch, were responsible for providing general scientific, and more specifically Operational Research, advice to General Jackson, Commander of the Kosovo Force. This paper outlines the work done by OA Branch leading up to, and during the challenging period from the first deployment of troops into Kosovo in June 1999 to October 1999. The work of the branch was in two major sections; the first, support to returning Kosovo to normality and the second, to monitor the compliance of the Kosovo Liberation Army (UCK) with the undertaking to demilitarise. OA Branch provided not only the military with work to quantify the return to normality, but also worked with and provided data to aid agencies. The work ranged from assessments of damage to the infrastructure of Kosovo, particularly the housing, through to the monitoring of crime. The population estimates produced by the branch corrected the emotive image being produced in the media, and became the subject of an international press conference. OA Branch's weekly Compliance Monitoring report was the authoritative document for checking on the progress of the UCK towards demilitarisation; this coupled with work on trends in violence were regularly briefed to the KFOR Commander.     

A methodology for conducting interdisciplinary social research

The Vienna Circle idea that science is an interdisciplinary enterprise leads to the question of how the knowledge of the natural sciences can be used to further understanding in the social sciences. Analysis of the practice of social research shows there is no easy answer to this question. Ideologies colour the use of exact knowledge in social research methods; even in the natural sciences ideological misunderstandings seem inevitable in research practice. The concept of strangification is introduced to describe this situation and to give a framework for a methodology to handle this problem of scientific regression. It is applied to the problem how the mathematical theory of complexity can be used in the social sciences to understand complex social phenomena.     

Mathematical programming modeling of the Response Time Variability Problem

The Response Time Variability Problem (RTVP) is a scheduling problem that has recently been defined in the literature. The RTVP has a broad range of real-life applications from manufacturing to services and information technology. A previous study developed a position exchange heuristic to apply to initial sequences for the RTVP, and a MILP (Mixed Integer Linear Programming) to obtain optimal solutions with a practical limit of 25 units to be scheduled. This paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality. The contribution of this paper is 4-fold: (i) larger instances can be solved to optimality by the off the shelf standard software; (ii) the new optimal solutions of the RTVP can be used to compare the results of heuristic procedures; (iii) the importance of modeling is demonstrated, as well as the huge impact that reformulation, redundant constraints and the elimination of symmetries have on the efficiency of MILPs is clearly established; finally (iv) a challenge to develop a customized optimization algorithm to rival the MILP solution efficiency for the RTVP is put forward.