(p,Y)-算子框架的稳定性

In this paper we study the stability of（p,Y）-operator frames.We firstly discuss the relations between p-Bessel sequences（or p-frames） and（p,Y）-operator Bessel sequences（or（p,Y）-operator frames）.Through defining a new union,we prove that adding some elements to a given（p,Y）-operator frame,the resulted sequence will be still a（p,Y）-operator frame.We obtain a necessary and sufficient condition for a sequence of compound operators to be a（p,Y）operator frame.Lastly,we show that（p,Y）-operator frames for X are stable under some small perturbations.     

Dependence Between Order Statistics in Samples from Finite Population and its Application to Ranked Set Sampling

Let X1, X2,..., Xm, Y1, Y2,..., Yn be a simple random sample without replacement from a finite population and let X(1) X(2) ... X(m) and Y(1) Y(2) ... Y(n) be the order statistics of X1, X2,..., Xm and Y1, Y2,..., Yn, respectively. It is shown that the joint distribution of X(i) and X(j) is positively likelihood ratio dependent and Y(j) is negatively regression dependent on X(i). Using these results, it is shown that when samples are drawn without replacement from a finite population, the relative precision of the ranked set sampling estimator of the population mean, relative to the simple random sample estimator with the same number of units quantified, is bounded below by 1.     

Identification of some real interpolation spaces

We interrelate the real interpolation spaces associated with the couples , and , proving among others the identities

for all .

     

一些同余问题的例外集合

利用特征和与指数和的估计,研究了一些同余问题的例外集合.具体来说,设p为充分大的素数,集合Y■Zp,正整数N相似文献   

论附属于某种连续映像的不等式及其在纤维空间中的应用

<正> §1. 设 X,Y 为拓扑空间,又设 f:X→Y 为连续映像.J.H.C.Whitehead 证明 X,Y 为 CW 丛而 f 能导出基本群及上同调群间的同模对应时,f 为同伦对等映像.映像 f 是否存在,不仅与 X,Y 的基本群及上同调群的构造有关,而与 X,Y 内在的几何结构有密切的关系.连续照像 f 导出 X,Y 之间上同调群的准同模对应 f,那末 f 能与某些准同模对应相交换,由此 J.H.C.Whitehead 指出正则准同模的观念.由[4]可知正则同模论供应我们许多同伦不变量,它们是直接可以计算的东西,并且对于 X,Y 间连续映像的分类问题,应该有密切的关系.     

Unconditional ideals of finite rank operators

Let X be a Banach space. We give characterizations of when is a u-ideal in for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when is a u-ideal in for every Banach space Y, when is a u-ideal in for every Banach space Y, and when is a u-ideal in for every Banach space Y.     

半鞅序列积分误差的极限过程的收敛定理

Jacod, Jakubowski和M\'emin讨论了与单个独立增量过程$X$的误差过程$^n\!X =X_t-X_{[nt]/n}$相关的积分误差过程$Y^n(X)$和$Z^{n,p}(X)$, 研究了半鞅序列$\{(nY^n(X),nZ^{n,p}(X))\}_{n\ge 1}$的极限定理. 记半鞅序列$\{(nY^n(X),nZ^{n,p}(X))\}_{n\ge1}$的极限过程为$(Y(X),Z^p(X))$, Jacod等给出了其极限过程$(Y(X)$, $Z^p(X))$的表达式. 本文将研究半鞅序列$\{X^n\}_{n\ge1}$积分误差的极限过程$Y(X^n)$和$Z^{p}(X^n)$的收敛定理, 主要研究半鞅序列$\{(X^n,Y(X^n),Z^p(X^n))\}_{n\ge1}$的依分布弱收敛和依分布稳定收敛.     

二阶线性矩阵微分系统的振动性

本文研究了矩阵微分系统（P（t）Y′）′＋Q（t）Y＝0，t∈［t0，∞）．其中P，Q和Y是n×n实连续矩阵函数，且P（t）和Q（t）是对称的．P（t）是正定矩阵（P（t）＞0，t∈［t0，∞））．利用推广的Riccati变换，得到了系统（1）振动的若干新判据．所得结果改进了Erbe，Kong和Ruan的相应结果．     

On subtransversality

Summary Let (X, A) and (Y, B) be pairs of manifolds. By means of a «completed» bijet bundle over the blow-up of X along A we give simple geometric interpretations of the notion of subtransversality of a smooth map f: (X, A)(Y, B) along A.     

Tubenumgebungen Steinscher Räume

Let X be a complex space and YX a closed analytic subspace. If Y is Stein then for every compact subset KY one can find arbitrarily small Stein open neighbourhoods of K in X.     

Erratum to: Foliations associated to harmonic maps on some complex two ball quotients

Science China Mathematics - In [Y, p. 1146, l. 35], it is stated that “P?#T2 has a two-fold cover that is T2”. This is a mistake. As a result, [Y, Theorem 4.2] should be corrected...     

Estimation of optimality for multidimensional control systems

Consider a class of functionsY, U on a multidimensional domainA, satisfying a differential equationY=h(x, Y, U) and given restrictions on values. We seek good lower bounds for a multiple integral over such a class. For givenY, U, such lower bounds allow one to estimate the closeness of the integral to its infimum.This research was performed under a Faculty Research Fellowship at Western Michigan University, Kalamazoo, Michigan.     

Quasi-Uniform Extensions for Prescribed Traces of Sections of Entourages

Let (X, U) be a quasi-uniform space and Y X be given. An extension of the given space is a quasi-uniformity V on Y such that U is the trace of V on X and X is dense for the topology T induced by V. The paper looks for extensions V such that the collection of all pairs (V X, V (p)) or all triples (V X, V-1 (p), V(p)) is prescribed, where V runs over a (sub)base for V and p Y - X.     

Very Strange Projective Curves

Let Y ? Pⁿ, n ≥ 3, be an integral non-degenerate very strange projective curve, i.e. assume that the general hyperplane section of Y is not in linearly general position; hence we are in characteristic p. Let π: X → Y be the normalization. Set d? deg(Y), g? Pa(X) and L? π* (Oy(1)). Here we prove that d > 2g?2 and in particular h¹(X,L) = 0 and h⁰(X,L) = d+1?g ≥ (d?1)/2 > n+1.     

The Dirichlet energy of mappings from ${\bf B^3}$ into a manifold: density results and gap phenomenon

Weak limits of graphs of smooth maps with equibounded Dirichlet integral give rise to elements of the space . We assume that the 2-homology group of has no torsion and that the Hurewicz homomorphism is injective. Then, in dimension n = 3, we prove that every element T in , which has no singular vertical part, can be approximated weakly in the sense of currents by a sequence of smooth graphs {u _k } with Dirichlet energies converging to the energy of T. We also show that the injectivity hypothesis on the Hurewicz map cannot be removed. We finally show that a similar topological obstruction on the target manifold holds for the approximation problem of the area functional.Received: 9 May 2003, Accepted: 5 June 2003, Published online: 25 February 2004     

Measurable functions and almost continuous functions

I show that if (X, ) is a Radon measure space and Y is a metric space, then a function from X to Y is -measurable iff it is almost continuous (=Lusin measurable). I discuss other cases in which measurable functions are almost continuous.Part of the work of this paper was done during a visit to Japan supported by the United Kingdom Science Research Council and Hokkaido University     

The etale homotopy theory of a geometric fibration

A geometric fibration, f:XY, is a smooth map of schemes which locally on Y admits a smooth, relative compactification. The etale homotopy type of the geometric fibre when completed away from the residue characteristics of Y, , is shown to be weakly homotopy equivalent to the completion of the Hurewicz fibre of the etale homotopy type of f,F(f _et ^r )^{^}. This implies a homotopy sequence for f. A key topological fact is verified in the appendix: for any pointed Hurewicz fibre triple FEB, the action of _l(F) on the homotopy type of various covering spaces of F extends to an action of _l(E).Partially supported by the N.S.F., I.H.E.S., and University of Warwick.     

The relaxed Dirichlet energy of mappings into a manifold

Let be a smooth 1-connected compact oriented manifold without boundary, such that its 2-homology group has no torsion. We characterize in any dimension n the weak lower semicontinuous envelope of the Dirichlet integral of Sobolev maps in .Received: 6 November 2004, Accepted: 15 November 2004, Published online: 22 December 2004     

Groups G2(p) as quotients of (2,3,7;2p)

It is proved that for any prime the group is a quotient of      

ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤p＜∞) AND c0 IN BANACH SPACES

Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1 ＜ p ＜∞). Then there exists a quotient space of X which is asymptotically isometric to lq (1/p 1/q=1). Complementedasymptotically isometric copies of c0 in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0.