Inverse spectral problems for differential pencils on the half-line with turning points

The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points is studied. We establish properties of the spectral characteristics, give a formulation of the inverse problem, prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem.     

Isolated spectral points of a linear relation

Monatshefte für Mathematik - We characterize the isolated points of the spectrum, the poles of the resolvent and the Riesz points of a bounded and closed linear relation on a Banach space. The...     

不动点集为孤立点的可换对合

在该文中作者决定了向量空间S_3((Z_2)^3)。就协边而言,作者利用此结果和“((Z_2)^k,q)流形丛”协边的正合序列,得到了((Z_2)^3,M^3)的固定孤立点集的所有协边类。     

On the isolated points of the surjective spectrum of a bounded operator

For a bounded operator acting on a complex Banach space, we show that if is not surjective, then is an isolated point of the surjective spectrum of if and only if , where is the quasinilpotent part of and is the analytic core for . Moreover, we study the operators for which . We show that for each of these operators , there exists a finite set consisting of Riesz points for such that and is connected, and derive some consequences.

     

Isolated singularities of polyharmonic inequalities

We study nonnegative classical solutions u of the polyharmonic inequality

     

On generalized equilibrium points

Generalizations of the usual definition of saddle point and equilibrium point are introduced in this paper. The existence of these points is shown to be related to a class of functions that we call perturbed convex functions. First and second order conditions regarding the existence of these points are also proved.     

真拟弱几乎周期点和拟正则点

T为紧致度量空间X上的连续映射,M（X）为X上所有Borel概率测度.设x∈X,记Mx（T）为概率测度序列{1n∑n 1i=0δTi（x）}在M（X）中的极限点的集合,其中δx表示支撑集是{x}的点测度.记W（T）和QW（T）分别为T的弱几乎周期点和拟弱几乎周期点集.本文证明,如果（X,T）非平凡且满足specifcation性质,则存在x,y∈QW（T）／W（T）（称为真拟弱几乎周期点）,分别满足μ∈Mx（T）,x∈Supp（μ）和ν∈My（T）,y∈/Supp（ν）,回答了周作领等提出的公开问题.Mx（T）在弱拓扑中是紧致连通集,所以,要么是单点集,要么是不可数集.如果x∈QW（T）／W（T）,则Mx（T）是不可数集.一个自然的问题是,怎么刻画M x（T）是单点集的点x（这时x称为拟正则点）.本文给出M x（T）是单点集的充要条件.     

Detecting discontinuity points from spectral data with the quotient-difference (qd) algorithm

This paper introduces a new technique for the localization of discontinuity points from spectral data. Through this work, we will be able to detect discontinuity points of a 2π-periodic piecewise smooth function from its Fourier coefficients. This could be useful in detecting edges and reducing the effects of the Gibbs phenomenon which appears near discontinuities and affects signal restitution. Our approach consists in moving from a discontinuity point detection problem to a pole detection problem, then adapting the quotient-difference (qd) algorithm in order to detect those discontinuity points.     

Density of the set of positive proper minimal points in the set of minimal points

One of the important problems of vector optimization concerns the density of the set of positive proper minimal points in the set of minimal points. We use the concepts of dentable point and approximating cones to derive sufficient conditions guaranteeing that the set of minimal points is contained in the closure of the set of positive proper minimal points. The result can be applied to obtain a density result for the unit ball in 1 ^p , 1<p<+, which does not follow from any other well-known density theorem.The author would like to thank Professor W. T. Fu for helpful comments. Moreover, the author is grateful to Professor H. P. Benson and the referees for valuable remarks and suggestions concerning a previous draft of this paper.     

Weierstrass points on cyclic covers of the projective line

We are interested in cyclic covers of the projective line which are totally ramified at all of their branch points. We begin with curves given by an equation of the form , where is a polynomial of degree . Under a mild hypothesis, it is easy to see that all of the branch points must be Weierstrass points. Our main problem is to find the total Weierstrass weight of these points, . We obtain a lower bound for , which we show is exact if and are relatively prime. As a fraction of the total Weierstrass weight of all points on the curve, we get the following particularly nice asymptotic formula (as well as an interesting exact formula):

where is the genus of the curve. In the case that (cyclic trigonal curves), we are able to show in most cases that for sufficiently large primes , the branch points and the non-branch Weierstrass points remain distinct modulo .

     

图的分数因子与孤立韧度

图G的孤立韧度定义为I(G)=min{｜S｜/i(G-S)∶SV(G),i(G-S)≥2},若G不是完全图.否则令I(G)=∞.本文给出了图的分数k因子与图的分数[a,b]因子的存在性与图的孤立韧度的关系.证明了,若δ(G)≥k且I(G)≥k,则G有分数k因子;若δ(G)≥I(G)≥a-1 a/b,则图G有分数[a,b]因子,其中a相似文献   

Fixed points of asymptotic contractions

Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies

     

Accelerated spectral approximation

A systematic development of higher order spectral analysis, introduced by Dellwo and Friedman, is undertaken in the framework of an appropriate product space. Accelerated analogues of Osborn's results about spectral approximation are presented. Numerical examples are given by considering an integral operator.

     

正态分布在学生学习成绩评估中的应用

本文将正态分布应用于学生学习成绩评估中，将原始分数转换为标准分数后，各科的分数方可比较或相加，从而改变了将原始分数直接相加比较的那种不够科学也不甚合理的传统做法。     

区间映射的链回归点的可链点集

主要讨论区间映射的链回归点的可链点集与链等价集的关系,证明了:若区间映射的拓扑熵是零,则它的链回归点的可链点集与链等价集相等.此外还得到了区间映射有正拓扑熵的几个等价条件.     

Admissible points of a convex polyhedron

In this paper, we present several new properties of the admissible points of a convex polyhedron. These properties can be classified into two categories. One category concerns the characterization and generation of these points. The other category concerns the circumstances under which these points are efficient solutions for linear multiple-objective programs with nonnegative criteria matrices. To illustrate some of the potential utility of these properties, we describe their application to two practical problems. These problems are the linear multiple-objective problem with interval coefficients and the problem of optimizing over the efficient set.This research was supported, in part, by the Center for Econometrics and Decision Sciences, University of Florida, Gainesville, Florida.     

Boundedness results for periodic points on algebraic varieties

We give some conditions under which the periods of a self map of an algebraic variety are bounded.     

On the compactly locally uniformly rotund points of Orlicz spaces

In this paper, locally uniformly rotund points and compactly locally uniformly rotund points are introduced. Moreover, criteria for compactly locally uniformly rotund points in Orlicz spaces are given.     

A note on semicentral idempotents

In this note we answer the question raised by Han et al. in [3 Han, J., Lee, Y., Park, S. (2014). Semicentral idempotents in a ring. J. Korean Math. Soc. 51(3):463–472, MR3206399.[Crossref], [Web of Science ®] , [Google Scholar]] whether an idempotent isomorphic to a semicentral idempotent is itself semicentral. We show that rings with this property are precisely the Dedekind-finite rings. An application to module theory is given.