集值度量广义逆的存在性

设X,Y为Banach空间,T∈L(X,Y)为从X到Y的线性算子,D(T),N(T),R(T)分别为T的定义域,核空间与值域,使用算子T的自身性质,给出T具有集值度量广义逆T和R(T)D(T)的充分必要条件.     

关于线性算子的右有界拟线性内逆

对于从线性空间到赋范线性空间的线性算子T引入右有界拟线性内逆的概念.在算子值域的闭包R(T)为切比雪夫子空间的条件下,给出右度量内逆的表示.证得:如果算子的值域R(T)非闭且闭包R(T)为切比雪夫的,则必存在不同的右有界拟线性内逆.     

Banach空间中度量广义逆的乘积扰动

设X,Y为自反严格凸Banach空间.记A∈B(X,Y)为具有闭值域R(A)的有界线性算子,有界线性算子T=EAF∈B(X,Y)为A的乘积扰动.本文研究了有界线性算子A的Moore-Penrose度量广义逆的乘积扰动.在值域R(A)为α阶一致强唯一和零空间N(A)为β阶一致强唯一的条件下.给出了‖T~M-A~M‖的上界估计,作为应用,我们在L~p空间上讨论了Moore-Penrose度量广义逆的乘积扰动.     

Banach空间中集值度量广义逆齐性单值选择的判据

本文研究了Banach空间(X,‖·‖),(Y,‖·‖)上具有闭值域的稠定闭算子T:X→Y的(集值)度量广义逆.在限定X为自反的、Y为一般的Banach空间且算子值域R(T)为空间Y中Chebyshev子空间时,证明了算子T具有非空闭凸集值的度量广义逆的存在性,运用Banach空间中广义正交分解定理,得出算子T的集值度量广义逆具有唯一齐性单值选择,并且该单值选择恰为赋等价严格凸范数的空间Xr=(X,‖·‖_r)上算子T的Moore-Penrose度量广义逆.特别地,将抽象的Banach空间X与Y具体化为有限维Banach空间l₁ⁿ=(Rn,‖·‖₁)(即n维空间Rn赋l₁范数)与有限维Hilbert空间(即m维欧式空间l₂^m=(Rm,‖·‖₂),亦即m维空间赋l₂范数),线性算子T可具体表示为m×n阶矩阵A,得到了从n维空间l₁ⁿ到m维空间l     

Banach空间中线性算子的(集值)度量广义逆的表示及应用

在Banach空间Y无自反和从Banach空间X到Y的线性算子T无闭值域和稠定的假定下,利用Banach空间几何方法证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,建立了该度量广义逆的存在性、唯一性和等价表达式,并给出了此表达式的一个应用示例．所得的部分结果本质地拓广王玉文和潘少荣在Banach空间Y自反,从X到Y的线性算子T为闭值域和稠定的假定下的近期相应结果．     

Banach空间中线性算子方程的约束极值解

设X,Y与Z为Banach空间L∈L(X,Z),T∈L(X,Y)为线性算子.运用线性算子的度量广义逆概念,在L(x)=y的极值解集合中,给出T(x)=h的约束极值解的精确刻画.     

Banach空间的逼近紧性与度量投影算子的连续性及其应用

首先给出赋范线性空间中的非空集合C的逼近紧性的等价描述. 如所周知, 如果C是Banach空间X中的一个逼近紧的半Chebyshev闭集, 那么由X到C的度量投影算子π_c是连续的. 当X是中点局部一致凸的Banach 空间, 利用Banach空间几何的技巧证得: C的逼近紧性对投影算子π_c的连续性也是必要的. 利用这个一般结论给出: 当T是由逼近紧且严格凸的Banach空间$X$到中点局部一致凸Banach空间Y的有界线性算子时, T有连续的Morse-Penrose度量广义逆T⁺$的充分必要条件.     

Banach空间中线性算子的(集值)度量广义逆及其齐性单值选择

为研究Banach空间中不适定线性算子方程的最佳逼近解,Nashed在文[1]中引入了Banach空问中线性算子T的(集值)度量广义逆T的概念,并提出“求解线性算子的(集值)度量广义逆的具有良好性质的单值选择是值得研究”的公开问题.本文首先证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,给出了该度量广义逆的等价表达式,并利用Banach空间的再赋范方法,给出其有界齐性的单值选择,部分地解决了Nashed所提出的公开问题.     

闭算子的线性斜投影广义逆的新扰动

讨论Banach空间中无界闭算子的线性斜投影广义逆的稳定性问题,利用T有界及广义Neumann引理给出了新的扰动定理.     

Banach空间中不适定线性算子方程的最佳逼近解

设X,Y为Banach空间,T为从X到Y的线性算子.T的值域R(T)≠Y且为逼近紧子空间,T的零空间N(T)≠{θ}.证得不适定算子方程Tx=y的最佳逼近解对任意y∈Y均存在的充分必要条件是N(T)为X的迫近子空间.     

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.     

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.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

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。     

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.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

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.