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Let X be a reflexive Banach space with both X and X locally uniformly convex. D is a bounded, open, convex subset of X. T∶D→X is a pseudo-monotone operator; C∶D→X is a compact or strongly continuous operator.

何震设X是自反Banach空间且X和X均为局部一致凸空间，D是X的开、有界、凸子集， T∶D→X是伪单调算子(pseudo-monotone)， C∶D→X是紧算子或全连续算子。

Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space.

王娴 ，何震Xu和Norr已经证明了建立在一致凸Banach空间的一个非空有界闭凸子集上的渐进非扩张映射的三步迭代的收敛定理问题。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

My kingdom is bounded only by the world , for I am not an Italian, or a Frenchman, or a Hindu, or an American, or a Spaniard--I am a cosmopolite

因为我既不是意大利人也不是法国人，不是印度人也不是美国人，也不是什么西班牙人，我是一个宇宙人。

My kingdom is bounded only by the world, for I am not an Italian, or a Frenchman, or a Hindu, or an am erican, or a Spaniard--I am a cosmopolite

因为我既不是意大利人也不是法国人，不是印度人也不是美国人，也不是什么西班牙人，我是一个宇宙人。

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。

By setting symmetric orbit traps (in particular, by using more complex bounded sets, such as chaotic attractors, as orbit traps), visually fascinating images with cyclic or dihedral symmetry can be created in this way.

通过设置具有对称性的轨迹井(同时也把轨迹井推广到更加复杂的有界集上，如混沌吸引子)，生成具有循环群对称性的彩色图像。

A solid bounded by a cylindrical surface and two parallel planes.

由一个圆柱形侧表面和两个平行平面限定而成的立体形状。

This invention relates to a gas phase reagent dispensing apparatus comprising a cylindrically shaped vessel including a floor and an interior volume bounded by interior wall and floor surfaces.

本发明涉及一种包括圆柱形器皿的气相反应物分配装置，圆柱形器皿包括底板以及由内壁和底板面限界的内部体积。

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。