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Let Xand Y be different Banach spaces and 〓Lbe a bounded linear operator,thegeneralized condition number 〓and〓ABA=A,B〓L}are studied.

文章讨论了两类广义条件数的几种表达式，研究了这两类广义条件数之间的关系，并将它们用到算子方程的扰动估计中，推广了Demko[IV.1]中的结果。

In general,the convergent sequence and bounded set are concepts only in topological spaces.

收敛序列和有界集一般是拓扑空间中的概念，文章首先引入序列收敛C和L-空间(给出某种序列收敛关系的向量空间)，然后在其中定义有界集。

Rule II Every bounded monotonic sequence has limit.

准则 II 单调有界数列必有极限。

This paper investigates the problem of the best weighted simultaneous approximation to totally bounded sequence s from a set G of generalized polynomials with restricted coefficients in complex normed linear spaces X.

在复赋范线性空间X中考察了具限制系数的广义多项式集G对全有界序列的加权同时逼近问题。

It is proved that when all the ratios of the generic term of a subaddtive sequence to its ordinal number form a lower bounded sequence,the ratio sequence must have limitation .

从这一结果出发证明了，当定义在(0，+∞)上的次可加函数与其自变量之比为有界函数时，次可加函数必存在上下确界函数，并证明了其上下确界函数均为齐次线性函数。

127 Ma. These ages suggest problems in stratigraphic correlation, indicate that there is considerable diachroneity in the timing of volcanism and sedimentation in the Middle and Late Jurassic Yanshan orogen, and cast doubt on the traditional interpretation that the Tiaojishan-Tuchengzi sequence is bounded by regional unconformities dated at ca.

这些测年数据说明以往的地层对比是有问题的，燕山造山带在中、晚侏罗世所发育的火山岩和沉积岩地层是穿时的。

A Banach space X with a unconditional basis {xn} is said to have the property P if, every bounded block basis sequence of {xn} spans a complemented subspace of X.

称一个带无条件基｛xn｝的Banach空间有性质P，如果｛xn｝的每一有界块基序列都张成X的可补子空间。

In this dissertation, the best simultaneous approximation with weight to infinite sequence from simultaneous-suns in complex normed linear space is considered, and in the case when the weight satisfies a certain condition, the characterizations of approximation from a simultaneous-sun and uniqueness of approximation from a RS-set are obtained; moreover, in the case when the weight is free, the characterizations of approximation to a totally bounded sequence from a convex set are established.

本文在复赋范空间中研究了同时太阳集对无限序列的加权同时逼近问题，在权满足一定条件时，通过把所研究问题转化为连续向量值函数空间中相应集对一个上半连续函数的最佳逼近问题，得到了逼近的特征和RS集逼近的唯一性定理，有例表明它们是已有结果的本质推广；在权不受限制时，得到了凸集对全有界序列逼近的特征。

Based on the view that the theorem of closed mested interval is an axiom,this paper deduces the essential limit of monotonic bounded sequence of number and the Dedekind theorem,and proves the general theorem of bull closed nested interval of real number .

以通常所说的闭区间套定理作为公理推出单调有界数列存在极限和Dedekind定理，并且证明了通常所说的实数满闭区间套定理

ORF identification involves scanning each of the six reading frames and determining which one contains a stretch of DNA sequence bounded by a start and stop codon, yet containing no start or stop codons within it; a sequence meeting these conditions could correspond to the actual single product of the gene.

ORF辨认包含检测这六个浏览框架并决议哪一个包括以启动子和终止子为界线的DNA序列而其内部不包孕启动子或密码子，符合这些条件的序列有可能对应一个真正的单一的基因产物。

You have to walk your own alk in this life.

次生中你必须走自己的路。

To start with, the thesis analyses ***ism in terms of the generic masculine words, word order and semantic derogation of women in greater detail.

论文首先从阳性词泛指，词序，词义的贬降等方面对英语中的性别歧视现象进行了详细的分析。