平均跟踪性与双曲线性同胚

本文研究了双曲线性自同胚的平均跟踪性,利用双曲线性映射的性质和压缩映射定理,得到了在有界的Banach空间上的双曲线性自同胚具有平均跟踪性.另外,证明了在一般的度量空间上的压缩映射也具有平均跟踪性.     

均匀性度量中的密集性偏差与稀疏性偏差

该文根据王元，方开泰［２］的近似偏差（discrepancy）的均匀性准则，定义了理想布点情况下的标准半径，定义了ｍ 维单位子空间Ｃｍ＝［０，１］中两点间的ｆ距离和ｇ距离，由此定义了最大空穴半径和最小空穴半径，提出了均匀性度量的密集性偏差与稀疏性偏差．给出了二维情况 下的计算结果．我们的方法计算量不大，不仅能较好地度量布点的均匀性以及布点在低维投影的均匀性，而且能指导如何调整布点使之尽可能与理想布点接近．     

Fuzzy序列紧性,可数Fuzzy紧性和Fuzzy列紧性

本文引进了Fuzzy序列紧性、可数Fuzzy紧性和Fuzzy列紧性,它们是一般拓扑学中相应概念的“良扩张”(R. Lowen意义下),文中讨论了这些fts的主要性质,以及它们之间的联系。     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

一类二阶非线性差分方程的振动性与渐近性

研究了一类二阶非线性差分方程解的振动性与渐近性,建立了三个新的振动性与渐近性定理,推广和改进了已知的一些结果.     

二阶非线性摄动微分方程解的振动性与渐近性

研究了一类二阶非线性摄动微分方程解的振动性与渐近性,建立了四个新的振动性与渐近性定理,推广和改进了已知的一些结果.     

一类二阶非线性摄动微分方程的振动性与渐近性

研究了一类二阶非线性摄动微分方程解的振动性质和渐近性质,建立了两个新的振动性与渐近性定理,推广和改进了已有的一些结果.     

半群的拟紧性和不可约性

利用算子半群生成元的边界扰动方法,给出了Banach格上C0半群的拟紧性和不可约性的充分条件.并利用该结果对一串联可修复系统的拟紧性和不可约性进行了研究.     

线性距离空间的一致凸性与自反性

本文研究了线性距离空间的一致凸性与自反性，同时对吴从Ｘｉｎ等提出的严格缩条件能否去掉的问题给出了肯定的答案。     

高阶泛函微分方程的振动性和渐近性

本文讨论带有强迫项的时滞型泛函微分方程的振动性和渐近性。对于形如和的方程得到了几个振动及渐近性质的判别准则。本文的结论的证明还修正了R.S.Dahiya在讨论线性方程时出现的错误。     

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。     

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.     

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.     

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。     

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.     

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.     

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。     

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.     

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.