上有界的

Suppose that f is a real-valued ω〓-lower semicontinuous function defined on a ω〓closed bounded subset A〓 of the dual E〓 of a locally convex space E, which is bounded below on A〓, and suppose every ω〓 closed convex subset of C〓≡ω〓-clcoA〓 is the ω〓closed convex hull of its w〓-β-exposed points.

假设X是一个局部凸空间，X〓是其对偶。A〓是X〓上的ω〓有界闭子集，f是A〓上的ω〓-下半连续实值函数且在A〓上下有界。

Based on the concepts of bounded operator, positive bounded operator and possible bounded operator their connections are discussed such that the contents are deeper.

在有界算子，肯定有界算子以及可能有界算子这些概念的基础上，进一步讨论它们之间的联系，使得关于这方面的内容更全面深刻。

A discussion is made of the continuously sufficient and necessary conditions of the bounded variation fon the closed interval in the paper.

讨论了有界变差数 f在闭区间上连续的充要条件以及函数 f在闭区间上有有界变差的充要条件。

In the third chapter, we use the tool of Carleson measure, charactering the bounded and compact of weighted composition operator on Bergman space on strongly pseudoconvex domains, these results generalized the results of G.

在第三章，利用Carleson测度这一工具，刻划了有界强拟凸域上Bergman空间上加权复合算子的有界性及紧性。

On the other hand, Let M~n be an z-dimensional complete noncompactoriented submanifold with finite total curvature in an-dimensional simplyconnected space form F~ of constant curvature c. In this thesis, we provethat if M satisfies one of the following: n≥3, c=0 and integral from n=M H~n＜∞;n≥5, c=-1 and H＜1-2/n~(1/2); n≥3, c=1 and H is bounded, where Hdenotes the mean curvature of M. then the dimension of the space of L~2 harmonic1-forms on M is finite.

本文还证明：若具常曲率c的完备单连通空间型F~中具有有限全曲率的n维完备非紧可定向子流形M满足下面条件之一：n≥3，c=0且integral from n=M H~n＜∞；n≥5，c=-1且H＜1-2/n~(1/2；n≥3，c=1且H有界的，则M上L~2调和1-形式空间的维数是有限的，这里H为M的平均曲率。

The representation of sequences is very helpful for the research of their linear complexity,so this paper we first research trace representation of periodic sequences,and the trace representation of a New Generalized Cyclotomic Sequence of order two of length pq is given,then for 2~mp~n period binary sequences,where p is an odd prime and 2 is a primitive root modulo p~2,we present a relation-ship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity and have the upper bound and lower bound of the value k, finally we discuss the k-error linear complexity of legendre sequences,also have the upper bound and lower bound of the value k,and discusses the situation where the linear complexity drop again for some Legendre sequences.

序列的表达形式对于其线性复杂度的研究是十分有帮助的，本文我们首先研究的是周期序列的迹表示，给出了2阶pq长度的扩展分圆序列的迹表示，然后讨论了周期为2~mp~n(m≥2)序列的线性复杂度与使得线性复杂度变小的最小的k值的关系，给出了k值的上界和下界，这里p为奇素数，2是模p~2的本原根，并通过例子讨论了其线性复杂度的稳定性，最后对Legendre序列k-错线性复杂度进行了分析，也给出了k值的上界和下界，并对某些Legendre序列讨论了线性复杂度再次下降的情况。

It is shown that an exponentially bounded integrated bisemigroups can be considered as the integration of a strongly continuous bisemigroup of bounded linear operators in some subspace of a Banach space with stronger norm topology,and also as the restriction of a strongly continuous bisemigroup of bounded linear operators in a bigger space with weaker norm topology.

证明了Banach空间x上的指数有界积分双半群可以作为x的某个子空间上具有较强范数拓扑下的有界线性算子强连续双半群的积分，同时也可作为较大空间上具有较弱范数拓扑下的有界线性算子强连续双半群积分的限制。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

We introduce convex,and in particular semidefinite,optimization methods,duality and complexity theory to shed new light to this relation for the single stock problem, given moments of the prices of the underlying assets,we show that we can find best possible bounds on option prices with general payoff funcations efficiently,either algorithmically(solving a semidefinite optimization problem)or in closed form, conversely,given observable option prices,we provide best possible bounds on moments of the prices of the underlying assets,as well as on the prices of the other options on the same asset by sovling linear optimization problems for options that are affected by multiple stocks either directly(the payoff of the option depends on multiple stocks)or indirectly(we have information on correlations between stock prices),we find on-optimal bounds using convex optimization methods,however,we show that it is NP-hard to find best possible bounds in multiple dimensions,we extend our results to incorporate transactions costs,this paper,in theory and practice can provide a reference to researchers and designers about Chinese financial derivative products,the full text is divided into six chapters as follows: ChapterⅠ:Papers on the background and significance of the subjects on a number of option pricing models as well as their advantages and shortcomings of the model and describes the status of research and writing papers and the main contents of the basic idea.

相应地，给定期权价格，也能够出标的资产瞬时价格的最有可能的最好的界。还有通过解决一个线性最优化问题，根据同一标的资产的其他期权的价格来找到这个期权的界值，对于期权受到多种股票价格直接影响(期权的收益依赖于多种股票)或者间接影响(我们有股票之间联系的有用信息)，如果使用凸规划方法我们就会发现没有最优的界，也能够证明对于多维情形确实是很难找到最优的最有可能的界值，最后将这一结论推广到考虑交易成本的情况。本文在理论和实践上给我国金融衍生产品研究者和设计者提供一定的参考。全文共分为六章，具体安排如下：第一章：阐述论文的选题背景和意义，介绍期权定价的一些模型以及这些模型的优点与缺点，并介绍国内外研究的现状以及论文的写作基本思路与主要内容。

By this equality,we prove that the amplitude of a compact DG module M over a cohomologically bounded DG algebra A is just the sum of the amplitude of A and the projective dimension of M.

对于一个同调有界的连通DG代数上的紧的DG模，我们由此等式可得其振幅与DO代数的振幅的差恰是它的投射维数。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。