两个Fitting类的例子

给出了两个特殊的群类,即R={H|C_H(F(H))≤F(H)}和S={G|1≠K⊿G~((∞)),G~((∞))=KC_(G(∞))(K)},证明了他们都是Fitting类,这两个Fitting类都和单群理论有密切联系.各自都包含了一些很值得注意的群,对每个Fitting类给出了群G属于该Fitting类的一个充要条件.     

连锁类的几个不变性质

给出了连锁类的几个不变性质,得到：在ＣＭ局部环中,广义ＣＭ性是连锁类的不变性质;强广义ＣＭ性是偶连锁类的不变性质;在正则局部环中,余维数ｋ≤３可光滑性是连锁类的不变性质。     

特征为2的奇异二次面上3个类和4个类 -4 结合方案的几何构作

利用特征为 2 的有限域上射影空间,我们构作了一些三个类和 4 个类的结合方案,并计算了它们的参数．     

特征为2的奇异二次面上3个类和4个类结合方案的几何构作

利用特征为２的有限域上射影空间，我们构作了一些三个类和４个类的结合方案，并计算了它们的参数。     

涉及两个n维单形的两类不等式

本文给出了涉及两个 n维单形的两类不等式 ,并得到了两个推论 .     

两个涉及第二类Stirling数的求和规则

本文利用第二类Ｓｔｉｒｌｉｎｇ数给出了两个求和规则，从而重新得到了一些古典组合恒等式的统一证明，并由此给出了一些级数求和的渐近估计。     

涉及两个n维单形的四类不等式

给出了涉及两个n维单形的棱长、体积与外接球半径的四类不等式,从而推广和改进了相关文献的结果.     

基于类内类间距离量级平衡的FCM聚类算法设计

类内距离和类间距离数值量级差异性导致两类距离无法直接融合,进而影响了FCM聚类模型设计。首先,本文全面回顾了经典和改进型的FCM聚类模型,构建了类内距离和类间距离迹的关系模型,分别从类内类间距离的变化不一致性和量级差异性两个方面分析了现有FCM聚类模型的不足;其次,运用高斯核距离替代传统的欧式距离来表征类内类间距离,基于最小化类内紧凑度与类间分离度差的思想,设计了类内类间距离平衡方法,提出了一种改进的FCM聚类目标函数与算法;最后,运用算例说明了本方法的有效性和优越性。     

关于两个n维单形的棱长与体积的两类不等式

给出了联系两个n维单形的棱长与体积的两类不等式,从而推广和改进了相关文献的结果.     

格序群的极小扭类,准素扭类和极扭类

本文给出了格序群的扭类是准素扭类的一个充分必要条件，证明了任一非零扭类至少包含一个极小扭类，从而将文〔１〕和〔２〕中在有限制条件情况下的有关结论推广到无任何限制条件的情形。本文还给出了一个扭类是极扭类的几个充分必要条件，并得到了格序群的极扭类、准素扭类和极小扭类之间的关系。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

白骨化尸体死亡时间的推断

本文分析了15具白骨化尸体标本的股骨汞(Hg),铅(Pb),镉(Cd)元素含量数据,在三年的时间内采集了3次,一共收集到45个数据。首先将这组数据看着纵向数据,利用线性随机效应混合模型、Cox随机混合效应模型进行分析,结果显示,如果对每个白骨化尸体标本建立线性模型,可以精确预测出死亡时间,而且不需要采集铅元素含量数据。混合效应模型的预测效果也很好,最大误差不会超过1个月。其次我们对数据不作任何假设,利用机器学习中随机森林方法分析数据,并利用5折交叉验证方法来判断结果的可靠性,训练集和测试集的NMSE分别为0.1205944,0.5604286,因此可以用训练出的模型来预测死亡时间。     

Modelling and analysis of dynamics of viral infection of cells and of interferon resistance

Interferons are active biomolecules, which help fight viral infections by spreading from infected to uninfected cells and activate effector molecules, which confer resistance from the virus on cells. We propose a new model of dynamics of viral infection, including endocytosis, cell death, production of interferon and development of resistance. The novel element is a specific biologically justified mechanism of interferon action, which results in dynamics different from other infection models. The model reflects conditions prevailing in liquid cultures (ideal mixing), and the absence of cells or virus influx from outside. The basic model is a nonlinear system of five ordinary differential equations. For this variant, it is possible to characterise global behaviour, using a conservation law. Analytic results are supplemented by computational studies. The second variant of the model includes age-of-infection structure of infected cells, which is described by a transport-type partial differential equation for infected cells. The conclusions are: (i) If virus mortality is included, the virus becomes eventually extinct and subpopulations of uninfected and resistant cells are established. (ii) If virus mortality is not included, the dynamics may lead to extinction of uninfected cells. (iii) Switching off the interferon defense results in a decrease of the sum total of uninfected and resistant cells. (iv) Infection-age structure of infected cells may result in stabilisation or destabilisation of the system, depending on detailed assumptions. Our work seems to constitute the first comprehensive mathematical analysis of the cell-virus-interferon system based on biologically plausible hypotheses.     

函数的次微分性质

本文给出了函数的Fenchel次微分、Frechet次微分,Hadamard次微分,Gateaux次微分的一些重要性质,并对函数的性质尤其是凸性给出其次微分刻画。     

碾压混凝土坝施工层面变形分析模型

针对碾压混凝土坝施工层面对大坝变形产生显著影响的问题,深入研究了施工层面的变化性质及规律,提出了层面不同阶段变形的模拟方法,建立了施工层面有厚度和无厚度分析模型,提出的模型能反映层面的弹性变形、衰减蠕变、不可逆变形以及加速蠕变等变形状态．实例分析表明:所提出的碾压混凝土坝施工层面有厚度和无厚度分析模型能较客观地模拟大坝的结构变化形态,尤其是施工层面有厚度分析模型较完整地模拟了层面的渐变规律,其计算结果与原位监测成果吻合较好．同时,提出的方法和建立的分析模型可推广应用于常规混凝土坝,特别是坝基内断层和夹层等变形规律的分析．     

Variational analysis of functions of the roots of polynomials

The Gauss-Lucas Theorem on the roots of polynomials nicely simplifies the computation of the subderivative and regular subdifferential of the abscissa mapping on polynomials (the maximum of the real parts of the roots). This paper extends this approach to more general functions of the roots. By combining the Gauss-Lucas methodology with an analysis of the splitting behavior of the roots, we obtain characterizations of the subderivative and regular subdifferential for these functions as well. In particular, we completely characterize the subderivative and regular subdifferential of the radius mapping (the maximum of the moduli of the roots). The abscissa and radius mappings are important for the study of continuous and discrete time linear dynamical systems. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday. Terry is one of those rare individuals who combine a broad vision, deep insight, and the outstanding writing and lecturing skills crucial for engaging others in his subject. With these qualities he has won universal respect as a founding father of our discipline. We, and the broader mathematical community, owe Terry a great deal. But most of all we are personally thankful to Terry for his friendship and guidance. Research supported in part by the National Science Foundation Grant DMS-0203175. Research supported in part by the Natural Sciences and Engineering Research Council of Canada. Research supported in part by the National Science Foundation Grant DMS-0412049.     

一类柔性臂机器人的稳定性

本文研究了一类柔性臂机器人的控制问题,且柔性臂的弯曲振动与扭转振动的耦合作用表现在边界方程中。本文运用算子谱理论、算子半群理论等,得到系统的主算子生成的C0-半群的具体表示式,并证明了半群的解析性、非紧性及非一致指数稳定性。     

Analytic description of statistics of spectra of quantum graphs

We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008.     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

Location of courts of justice: The making of the new judiciary map of Portugal

Location modeling techniques have been applied to an extremely wide variety of public facilities. However, their application to one of the most ubiquitous public facilities – courts of justice – has been very rare. In this paper, we describe a study promoted by the Ministry of Justice of Portugal to define a proposal for the country's new judiciary map – that is, the spatial organization of the judicial system. The new map aims to promote the efficiency and specialization of the justice system (leading to better and faster court decisions) and to provide a good level of accessibility to courts. We developed two optimization models addressing those goals – a districting model, to determine the borders of new, large judicial districts; and a court location model, to determine the location, type, size, and coverage area of the courts included in each new district. Both models are discrete facility location models and consider hierarchical facilities – generic courts and specialized courts of multiple types. Our study was publicly acknowledged by the Portuguese government as having contributed to the new judiciary map that has since been approved and implemented.