带有积分边值条件的两项分数阶微分方程正解的存在性

主要研究一类带有积分边值条件的两项分数阶微分方程在不同条件下正解的存在性及存在唯一性.利用上下解理论与Schauder不动点定理相结合的方法,得到正解的存在性.利用Banach压缩映像原理,推出正解的存在唯一性.并给出两个例子来说明结果的应用性.     

一类半线性椭圆型方程组的边值问题

利用不动点定理和有关不等式,证明了一类半线性椭圆型方程组存在有界正解.同时研究了正解唯一性的充分条件,并且进行了证明.     

一类带积分边界条件的弹性梁微分方程边值问题正解的存在性和唯一性（英文）

本文主要研究一类带积分边界条件的四阶弹性梁微分方程边值问题正解的存在性和唯一性,通过广义凹算子不动点定理获得边值问题正解的存在性和唯一性,最后给出一个例子.     

三阶非线性奇异边值问题正解的存在唯一性

用混合单调方法研究了三阶非线性边值问题正解的存在唯一性.定理的证明非常自然而且完善了现有的结论.     

带扰动和参数的三阶边值正解的存在唯一性

利用广义凹算子的不动点定理讨论了一类带扰动和参数的三阶两点边值问题,给出这类边值问题正解的存在唯一性.     

有界洞型区域内双调和方程边值问题的可解性

这篇文章利用不动点定理证明了有界洞型区域内双调和方程边值问题正解的存在性及唯一性.并对解的不存在情形进行了研究.     

二阶带时标的非线性奇异动力方程的m点边值问题的正解

研究二阶带时标的非线性奇异动力方程m点边值问题的正解,利用锥上的混合单调不动点定理,得到了正解的存在性和唯一性.本文中方程的非线性项可能是奇异的.并举例说明相应的结果.     

分数阶p-Laplacian边值问题正解的存在唯一性

运用Schauder不动点定理和上下解方法研究了一类分数阶p-Laplacian边值问题正解的存在性和唯一性,并给出了唯一解的迭代序列.     

经由和型算子方法下共形分数阶微分方程正解的唯一性和迭代序列

本文研究了一类共形分数阶微分方程两点边值问题,通过利用定义在锥上的一类和型算子不定点定理,获得了微分方程正解存在唯一性,并构造一个迭代序列逼近唯一正解.最后,通过两个例子验证了本文获得的主要结论.     

一类具Pucci算子的椭圆方程解的存在唯一性(英文)

本文研究一类具Pucci算子的完全非线性椭圆方程边值问题.在一些假设下,利用不动点定理和上、下解方法,证明了问题正解的存在唯一性.     

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．     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

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.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

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。     

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.     

On the R-Order of Convergence of a Family of Methods for Simultaneous Extraction of Part of All Roots of Algebraic Polynomials

This note deals with the R-order of convergence of Weierstrass-Durand-Kerner-Dochev type single-step methods for the simultaneous determination of only a part of all roots of algebraic polynomials.     

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.