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Let f be defined for all nonnegative x, and suppose that it is continuous, strictly increasing and bounded on its domain.

令f定义在一切非负的x 上，并在定义域内连续、严格递增和有界。

According to Liouville's theorem , any bounded complex analytic function defined on the whole complex plane is constant.

如上所述，实或复解析函数均在实变量的意义上无穷可微。

However,in this paper,it is first introduced sequential convergence C and L*- space which is a vector space giving some relation:xmCx between sequences and points in it,then the bounded set is defined in vector space.

设C为一序列收敛关系，T是由C确定的拓扑，B是由C确定的有界集族，则有B=BT(C，并进一步从L*-空间构造了包囿拓扑向量空间。

Fuzzy sequentially compact set in fuzzy normed space was defined and the relations between fuzzy sequentially compact set and fuzzy total bounded set were studied some properties of topolisical space were generalized to fuzzy topolisical linear space.

在模糊赋范空间中给出了列紧集的概念，并对于模糊列紧集与模糊全有界集之间的关系作了进一步的研究，使得与分明的情况基本上协调起来。

The box ratio property is simply defined as the width to height ratio of the region bounding box.

这个盒子比财产是简单的定义宽高比的区域范围盒子。

Highway subgrade Highway subgrade may be defined as the supporting structure on which pavement and its special undercourses rest .in cut sections ,the subgrade is the original soil lying below the special layers designated as base and subbase material .in fill section ,the subgrade is constructed over the native ground and consists of imported material form nearby roadway cuts or from bowwow pits.

公路路基公路路基可界定为支撑结构对路面和特殊undercourses休息。在削减部分，路基是原来的地势低于土壤的特殊层指定为基础和基层材料。填补节中，路基建造的本地地面，由进口物质形式附近的巷道削减或从bowwow坑。

And the process of hardware design, programme of application software and procedure of square brackets are defined.

介绍SINUMERIK840D在铣床中的应用，详细说明了硬件设计过程，应用软件的编制以及程序方框图。

Water-deficient is a key factor to restrict agricultural production and economic development in the region. In order to improving the infrastructure conditions of agricultural production as soon as possible, inducting farmers to develop non-pollution vegetable and economic crops, helping farmers to increase income in planting and breeding, and facilitating sustainable development of agricultural production, according to Year 2002 Project Guide Rural of Mini-type Water Commonweal Establishment Construction and some relative requirements, local government has defined to construct rainwater-collection model project in Tianhui brae after analyzing and reasoning.

水资源缺乏是制约该区域农业生产和经济发展的关键因素，为改善丘陵灌区农业生产条件，引导农户发展无公害蔬菜和经济作物，在种植和养殖业上帮助农户增收，促进农业生产的可持续发展，根据2002 年度农村小型水利公益设施建设项目指南和相关要求，经过认真研究，科学分析论证，确定在天回山丘陵区实施集雨节水灌溉示范项目。

Intimately bound up in the religious teaching of Brahminism was the division of society into rigidly defined castes.

密切在宗教教学Brahminism是社会分工的硬性规定纳入种姓。

At first the typical die and mould components and their standard processing technique,and the types of facilities were defined.Then the integer programming model of the facility planning was established and the branch and bound method was used to give a solution to the model cases.

定义了模具典型零件、设备类及模具典型零件标准工艺；建立了设备资源规划的整数规划数学模型；采用分枝—定界法对给定实例进行求解；计算结果证明了模型的有效性及实用性。

The statistical analysis of this large set of mutations has led us to propose a diagnostic strategy that should help with the molecular work-up of optic neuropathies.

这一大系列基因突变的统计学分析引导我们提出一个诊断策略，可以帮助我们对视神经病变进行分子学的诊断检查。

The results show that the pipe grouting changes the mechanical parameters of surrounding rocks to achieve the security of engineering objectives by reinforcing surrounding rocks and bolcking the water.

研究表明：小导管注浆一方面改变了围岩的力学参数，另一方面利用浆液的固结特性可以实现堵水和加固围岩的工程目标，使隧道在开挖过程中的安全得到保障。