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.     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

Applications of Parameterizations of Oblique Duals of a Frame Sequence

Two parameterizations of oblique duals of a given frame sequence are applied to show that the sum of a frame sequence and one of its oblique duals may not be a frame sequence, and that type II dual is locally (and globally) optimal in some sense and that the excesses of the frame sequence and its oblique duals are the same. Other observations on the duals of a frame sequence are included also.     

高超声速飞行器纵向动力系统平衡态集的拓扑结构研究

以高超声速飞行器纵向运动的空气动力学模型和结构动力学模型为依据,采用数值分析的方法,研究了高超声速飞行器动力系统平衡点集的拓扑结构.首先根据高超声速飞行器在巡航阶段的飞行边界的限制条件得到在给定的飞行高度和马赫数下的平衡点集,由此近似估算出了高超声速飞行器的飞行包线.然后根据得到的平衡点集,分别研究了高超声速飞行器的迎角、升降舵偏角和发动机的燃料当量比与飞行马赫数和高度的关系,并进行了数值拟合,在此基础上分别描绘了以上三个拟合关系式的曲面关系图。     

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.     

Admissibility of estimators of the probability of unobserved outcomes

The problem of estimating the probability of unobserved outcomes or, as it is sometimes called, the conditional probability of a new species, is studied. Good's estimator, which is essentially the same as Robbins' estimator, namely the number of singleton species observed divided by the sample size, is studied from a decision theory point of view. The results obtained are as follows: (1) When the total number of different species is assumed bounded by some known number, Good's and Robbins' estimators are inadmissible for squared error loss. (2) If the number of different species can be infinite, Good's and Robbins' estimators are admissible for squared error loss. (3) Whereas Robbins' estimator is a UMVUE for theunconditional probability of a new species obtained in one extra sample point, Robbins' estimator is not a uniformly minimum mean squared error unbiased estimator of the conditional probability of a new species. This answers a question raised by Robbins. (4) It is shown that for Robbins' model and squared error loss, there are admissible Bayes estimators which do not depend only on a minimal sufficient statistic. A discussion of interpretations and significance of the results is offered. Research supported by NSF Grant DMS-88-22622.     

大学生职业生涯发展的决定因素的相关研究

本文利用探索性因素分析方法提出了一个可以用作为甄别大学生涯发展的决定因素的诊断工具,以期帮助职业生涯咨询、指导人员对个体的有关职业生涯态度、职业生涯倾向性有一个基本的了解;同时利用这个工具可以提高个体对职业生涯的认知水平,帮助个体更好地进行职业生涯规划。     

Groups of Automorphisms of Tournaments

By the Holland Representation Theorem, every lattice ordered group (l-group) is isomorphic to a subalgebra of the l-group of automorphisms of a chain. Since weakly associative lattice groups (wal-groups) and tournaments are non-transitive generalizations of l-groups and chains, respectively, the problem concerning the possibility of representation of wal-groups by automorphisms of tournaments arises. In the paper we describe the class of wal-groups isomorphic to wal-groups of automorphisms of tournament and show some of its properties.     

高科技企业健康度评价研究

高科技企业的生存和健康发展越来越受到各级政府的广泛关注。章以模糊数学和层次分析理论为指导构建了高科技企业健康度评价的指标体系和评价模型，评价过程不仅考虑了影响健康度的所有因素，而且保留了各级评价的全部信息。实例采用典型的高科技企业指标数据，评价结果直观地反映了高科技企业的实际情况。     

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。     

On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations

This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda＇s results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

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。     

k个矩阵的核子空间的和的维数

利用齐次线性方程组的解的表达式及分块矩阵的一个秩等式,得出了k个矩阵的核子空间的和的维数的一个公式,它推广了维数公式.并给出了这个公式的几个应用.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Asymptotics of families of solutions of nonlinear difference equations

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.     

Existence of periodic points of endomorphisms of a circle

A theorem of Block and Franke is improved on the existence of periodic points for a map of a circle to itself and a proof which seems more understandable is given. Project supported by the National Natural Science Foundation of China (Grant No. 19531070).