Banach空间一阶非线性微分方程终值问题解的存在性

在Fréchet空间中利用推广的Tychonov不动点定理研究了Banach空间中一阶非线性微分方程终值问题解的存在性.     

关于Banach空间隐式常微分方程的解的存在性

讨论了 Ｂａｎａｃｈ 空间中隐式常微分方程 Ｆ（ｔ,ｘ,ｘ′） ＝ ０, ｘ（ｔ０ ） ＝ ｘ０ , ｘ′（ｔ０） ＝ ｙ０ 的解的存在性,其中, Ｆ 的定义域可含无穷远点     

Ascoli-Arzela定理的一个推广及应用

给出了无穷区间上一类抽象连续函数族相对紧性判断的一个充分必要条件，并应用它获得了抽象空间上一阶微分方程的终值问题和Ｆｒｅｄｈｏｌｍ型积分方程解的存在性。     

无穷区间上两类抽象无界函数族相对紧的判定及其应用

给出了无穷区间上抽象无界连续函数族和抽象无界可微函数族相对紧性判定的充要条件,并应用它获得了无穷区间上二阶微分方程两点边值问题无界解的存在性.     

Banach空间中一阶非线性脉冲微分方程终值问题解的存在性

利用分段估计法和Mnch不动点定理,研究Banach空间中一阶非线性脉冲微分方程终值问题,在较宽松的条件下建立了新的存在性定理,本质上改进和推广了某些已知的结果.     

近似超紧空间的相对可乘性

利用广义Zadeh型函数讨论近似超紧性的相对可乘性问题,使得文[1]与[3]的一些结果是本文的推论。     

Banach空间一阶微分方程终值问题的解

本文利用新的比较结果和半序理论研究Ｂａｎａｃｈ空间中一阶非线性微分方程终值问题的最小解和最大解的存在性,改进和推广了某些已知结果．     

Banach空间二阶积分-微分方程终值问题极值解

利用新的比较定理和半序理论,研究Banach空间二阶非线性积分-微分方程终值问题最小解和最大解的存在性,获得了新的结果.     

L-拓扑空间的相对S*-紧性

在L-拓扑空间中引入相对S*-紧性的概念,得到了它的一些性质,如它是L-好的推广,对子集遗传,被连续的广义Zadeh型函数所保持。此外,给出了相对S*-紧性的网式刻画。     

L-拓扑空间的相对Sβ-紧性

在L-拓扑空间中引入相对Sβ-紧性的概念,得到了它的一些性质,如它是L-好的推广,对闭子集遗传,被连续的广义Zadeh型函数所保持.此外,给出了相对Sβ-紧性的网式刻画.     

Cubature Formulas of a Nonalgebraic Degree of Precision

We deal with cubature formulas that are exact for polynomials and also for polynomials multiplied by r, where r is the Euclidean distance to the origin. A general lower bound for the number of nodes for a specified degree of precision is given. This bound is improved for centrally symmetric integrals. A set of constraints (consistency conditions) is introduced for the construction of fully symmetric formulas. For one dimension and arbitrary degree, it is shown that the lower bound is sharp for centrally symmetric integrals. For higher dimensions, as an illustration, cubature formulas are only constructed for low degrees. March 6, 2000. Date revised: April 30, 2001. Date accepted: May 31, 2001.     

Correlation decay and the absence of zeros property of partition functions

Absence of (complex) zeros property is at the heart of the interpolation method developed by Barvinok for designing deterministic approximation algorithms for various graph counting and related problems. An earlier method used for the same problem is one based on the correlation decay property. Remarkably, the classes of graphs for which the two methods apply often coincide or nearly coincide. In this article we show that this is not a coincidence. We establish that if the interpolation method is valid for a family of graphs, then this family exhibits a form of the correlation decay property which is asymptotic strong spatial mixing at superlogarithmic distances. Our proof is based on a certain graph polynomial representation of the associated partition function. This representation is at the heart of the design of the polynomial time algorithms underlying the interpolation method itself. We conjecture that our result holds for all, and not just amenable graphs. Indeed this conjecture was recently confirmed by Regts. See the body of the article for details.     

Brauer代数的中心维数问题

Brauer代数B_n(t)是一种在表示论,数学物理中重要的带一个参数t的有限维代数.当t取普通值时它们的结构已经了解得比较清楚,例如,不可约表示分类.当t取某些特殊值时有关它们还仍有些问题未探明.本文讨论任意参数时Brauer代数的中心的维数问题.主要结论是当t取某些特殊值时,Brauer代数中心的维数必定大于或等于t取普通值时它们的维数.     

Matrix correction of a dual pair of improper linear programming problems

A matrix is sought that solves a given dual pair of systems of linear algebraic equations. Necessary and sufficient conditions for the existence of solutions to this problem are obtained, and the form of the solutions is found. The form of the solution with the minimal Euclidean norm is indicated. Conditions for this solution to be a rank one matrix are examined. On the basis of these results, an analysis is performed for the following two problems: modifying the coefficient matrix for a dual pair of linear programs (which can be improper) to ensure the existence of given solutions for these programs, and modifying the coefficient matrix for a dual pair of improper linear programs to minimize its Euclidean norm. Necessary and sufficient conditions for the solvability of the first problem are given, and the form of its solutions is described. For the second problem, a method for the reduction to a nonlinear constrained minimization problem is indicated, necessary conditions for the existence of solutions are found, and the form of solutions is described. Numerical results are presented.     

Stability analysis of set trajectories for families of impulsive equations

In this paper, for a family of impulsive equations, a heterogeneous matrix-valued Lyapunov-like function is considered, the comparison principle is formulated, and stability conditions for the set of stationary solutions are established. In addition, for a class of impulsive equations with uncertain parameters the monotone iterative technique for constructing a set of solutions is adapted.     

Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems

The determination of solutions of the Jacobi partial differential equations (PDEs) for finite-dimensional Poisson systems is considered. In particular, a novel procedure for the construction of solution families is developed. Such a procedure is based on the use of time reparametrizations preserving the existence of a Poisson structure. As a result, a method which is valid for arbitrary values of the dimension and the rank of the Poisson structure under consideration is obtained. In this article two main families of time reparametrizations of this kind are characterized. In addition, these results lead to a novel application which is also developed, namely the global and constructive determination of the Darboux canonical form for Poisson systems of arbitrary dimension and rank two, thus improving the local result provided by Darboux' theorem for such a case.     

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.     

The properties of solutions of a class of isoperimetric problems of stability optimization

A class of isoperimetric problems of stability optimization is considered. These arise, for example, when maximizing the Euler force in the destabilization of a column (rod) of varying cross-section and given volume (Lagrange's problem). It is well known that an extremum which depends on the form of the boundary conditions can be achieved for both simple and double eigenvalues. A class of problems is identified for which a global maximum is found at a simple eigenvalue. The possibility of achieving a local extremum for the first (simple) eigenvalue at stationary points is analysed qualitatively in terms of the parameter values and the form of the boundary conditions.     

Some Remarks on Equivalence of Moduli of Smoothness

The present paper investigates polynomials for which the inverse inequality for moduli of smoothness holds. The technique for approach is different from the previous works for splines and is elegantly organized.