查询词典 metrically convex subset

Different from the former study,the value region of projective operator in the neural network which they study was a general closed convex subset of n demensional Euclidean space and it wasn't a compact convex set in general,that is,the value region of projective operator was probably unbounded.

与以前研究投影算子的值域一般是n维欧氏空间中的紧凸子集不同，而是n维欧氏空间中未必有界的闭凸子集，同时目标函数也是一般的连续可微函数，未必为凸函数。

Different from the former study, the value region of projective operator in the neural network which they study was a general dosed convex subset of n demensional Euclidean space and it wasn＇ t a compact convex set in general, that is, the value region of projective operator was probably unbounded.

与以前研究投影算子的值域一般是n维欧氏空间中的紧凸子集不同，而是n维欧氏空间中未必有界的闭凸子集，同时目标函数也是一般的连续可微函数，未必为凸函数。

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。

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。

Our purpose is to obtain a new generalized fixed point theorem in a complete metrically convex metric spaces , which generalizes and improves the corresponding result in .

给出了在完备度量凸空间上的一类新的不动点定理，改进了文献[1]中的相应的结论。

Convex body; star body; polar body; inequality; extremum; i—th width integral of convex body; mixed width-integral of convex bodies; mixed chord-integrals of star bodies; affine surface area; mixed affine surface area; mixed projection body; mixed body; L_p-projection body; L_p-centroid body

基础科学，数学，几何、拓扑凸体；星体；极体；不等式；极值；凸体i-次宽度积分；凸体混合宽度积分；星体混合弦长积分；仿射表面积；混合仿射表面积；混合投影体；混合体； L_p-投影体； L_p-质心体

This article outlines the progress of ancient Chinese lenses from the Pre-Qin Period to the Five Dynasties, and discusses mainly two arguments: First, the"yangsui" recorded and narrated in Lun Heng by Wang Chong of Eastern Han Dynasty may be a plano-convex glass lens; secondly, the"four mirrors" recorded and narrated in Tanzi Hua Shu by Tan Qiao of Southern Tang Dynasty may be a plano-convex lens, a biconvex lens, a transparent planeparallel plate and a concave-convex lens respectively, but what kind of tra...

本文概述了中国古代透镜从先秦到五代的发展进程，着重从古代文献和出土文物的研究出发，结合中国古代社会经济发展水平，论证了东汉王充《论衡》中记述的阳燧可能是玻璃平凸透镜；论证了南唐谭峭的《谭子化书》中记述的"四镜"可能是平凸透镜、双凸透镜、平光镜和凹凸透镜。作者认为《谭子化书》"四镜"段可能实际上是对中国古代透镜发展的阶段性总结。

The proposed method has the merit that the numerical characteristics of stochastic temperature field response can be obtained by analyzing the random temperature field just in one time.3. Perturbed numerical algorithm of nonprobabilistic convex set theoretical models on the temperature fieldThe uncertain parameters of physical parameters and initial boundary conditions of heat conduction are described by the convex model. The perturbation formulas of the upper and lower bounds of temperature field response with unknown-but-bounded parameters are given via the combination of matrix perturbation theory and the convex set theory model.4. Numerical analysis for transient temperature field with interval parametersConsidering the uncertainties of the transient heat transfer, the physical parameters and initial boundary conditions are regarded as interval variables.

该方法具有只进行一次随机温度场分析便可以获得其响应的数字特征的优点。3、温度场的非概率凸集合理论模型的摄动数值解法将结构导热的物理参数、温度场的初始和边界条件等不确定性参数以凸模型加以描述，基于矩阵摄动理论和处理不确定问题的凸集合理论模型的结合，导出有界不确定参数瞬态温度场响应所在集合的上、下界摄动计算公式。4、具有区间参数的瞬态温度场数值分析考虑结构瞬态热传导问题的不确定性，将结构各物理参数和温度的初、边值条件均视为区间变量。

One convex set which is Cartesian product of nonregular convex polygons is used instead of the other convex set which is Cartesian product of regular polygons.

采用不规则凸多边形的笛卡儿积构成的凸集代替正多边形的笛卡儿积构成的凸集，前者比后者更紧凑。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48