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By some definitions, induced polarization is a lossy type of dielectric polarization with a long time constant.

根据定义，激发极化是一种长时间常量的有损电介质极化。

Physics majors learn the differential and integral calculus in the style of Cauchy and Weierstrass, with ε–δ definitions of continuity and differentiability.

这个定理还是非常有用的，下面就来演示一下。证明存在a，b两个无理数，使 a b 为有理数。是无理数，现在考察数X

Dilatancy is a very important property of geotechnical materials, but now there're different definitions about it in geotechnical engineering.

剪胀是岩土材料一个非常重要的特性，但目前对于剪胀的描述并不统一。

CBFEC emphasizes direct correspondence of concepts in EC with its software architecture for ease of understanding and using; minimal coupling with specific problem structure for easy adaptation it to solve a large number of wholly different problems; interface-centered design for extendibility. To achieve those objects, the problem-solving method of EC is analyzed and the problem-solving procedure of EC is divided into three interactive aspects: population-based stochastic searching mechanism, problem specific information to implicitly guide the stochastic searching, and the observation and control of the computation procedure of EC. Then the key concepts of EC are identified in those three aspects; the normal implementations of those concepts are summarized; the interfaces represents those concepts in software are abstracted; the collaborations of components through those interfaces are designed. CBFEC is implemented on mainstream component software platform COM/DCOM (Component Object Model/Distributed COM from Microsoft), which includes interfaces definitions, commonly using EC components implemented those interfaces, such as Simply EA component, Steady State EA component, EA component, EA component, Population component, Tournament Selection component, Linear Ranking Selection component, Nonlinear Ranking Selection component, Random Number Generator component, etc, and the collaborations of those components through those interfaces.

具体的做法是把演化计算看作是基于组件的软件工程的一个应用领域：首先分析了演化计算求解问题的一般思路和方法，把演化计算问题求解过程分为："设计基于群体的随机搜索机制"、"研究问题的性质并以此隐含地定义算法的搜索方向"和"求解过程的观察与控制"三个部分；然后分别找出各个部分中的关键概念，总结这些概念现有的一般实现方法，抽取其本质，以此结合设计模式来定义组件软件的接口；通过分析演化计算各个概念之间的相互联系来设计组件软件间通过接口的进行交互的方式；最后还在目前一种主流组件软件开发平台COM／DCOM（微软提出的组件对象模型）的基础上实现了常用的演化计算组件，如简单演化算法组件、稳态演化算法组件、演化算法组件、演化算法组件、种群组件、锦标赛选择策略组件、线性排名选择策略组件、非线性排名选择策略组件、随机数发生器组件等等。

The thesis puts forward intensive definitions of three types of relations and their consistency. By building the corresponding model based on graph theory, it studies the consistency property of relations, and brings forward three static consistency validation methods with the assistance of graphic connectivity, directed path, accessibility et al.

论文对这三种类型的关系及其一致性进行了详细定义和研究，通过建立相应的图论模型，借助于图的连通性、有向路、可达性等，研究了各种关系的一致性性质，提出了三种静态一致性的检验方法。

On the fuzzy number valued mapping F:〓→〓, we put forward the definitions ofdirectional derivative, differential, gradient and subdifferential, and with the "cut method" byusing respectively the directional derivative and differential of two crisp functions that aredetermined by F, characterize the directional derivative and differential of F.

对于模糊映射F：〓→〓，提出了方向导数，微分，梯度及次微分的概念，并通过取截集，用由F所完全确定的通常函数的方向导数和微分分别刻划F的方向导数和微分。

Happiness is your soul to be rely on somewhere, but disconsolateness; Happiness is your heart to be gratified mostly, but restlessness; Happiness is your spirit to be pleased, but blues; Happiness is the true feeling from men's innermost heart but definitions and elements people giving.

幸福是你的灵魂有所依托，而非孤独惆怅；幸福是心灵欣慰安详，而非躁动不安；幸福是精神愉悦，而非抑郁寡欢；幸福是"今年欢笑复明年"，而非"雨中寂寥月中愁"。幸福不是定义，不是章节，不是元素，不是感慨，是内心最真实的感觉。

At last the results have been applied to the tracking problem of a class of mechanical systems with discontinuous friction term. Chapter 3 mainly deals with uniformly ultimate boundedness of a class of nonautonomous systems with discontinuous right-hand sides and corresponding perturbed systems (in the sense of Filippov solutions). The definitions of globally uniformly strongly ultimate boundedness and globally uniformly weakly ultimate boundedness of discontinuous systems and the definition of globally equiuniformly strongly ultimate boundedness of corresponding perturbed systems are presented firstly.

首次给出不连续系统全局强一致最终有界、全局弱一致最终有界的定义，以及针对于扰动系统的全局强等度一致最终有界性的定义，并基于非光滑的Lyapunov函数得到了不连续系统全局一致强、弱最终有界的Lyapunov定理和扰动系统全局强等度一致最终有界性的Lyapunov定理。

From information processing to knowledge creation the information processing view, evident in scores of definitions of knowledge management in the trade press and academic texts, has often considered organizational memory of the past as a reliable predictor of the dynamically and discontinuously changing business environment.

从信息处理到知识创造信息加工观点，可见在几十次的定义，知识管理的业界新闻和学术文本经常考虑组织记忆的过去作为一个可靠的预测性，动态连续变化的商业环境。

Climatic gradients were based on data sets from 841 meteorological stations throughout China. Definitions for floristic distributional patterns were based upon the work of Prof. Z. Y. Wu. Most of these floristic distributional patterns were strongly correlated with the geographic gradients in climate, except for cosmopolitan, cultivated and invasive genera. Tropical genera form a large fraction of the total genera (ranging from 0.84% to 94.38% in the regional floras) with the highest proportion in southern Yunnan and Hainan Island. Tropical genera occur predominantly in southern China of 0° N latitude and decreased with increasing latitude, as would be expected. Interestingly, the disjunct Tropical Asia and Tropical America distribution were not restricted to southern latitudes. Temperate genera account for 5.1% to 98.83% of the total genera in regional floras with the highest proportion in the province of Xinjiang. Most of these genera followed geographic gradients in climate as expected (temperate genera conspicuously dominate the landscape at higher latitudes), except the East Asian and North American disjunct distribution, Eastern Asian distribution and Chinese endemic distribution. Generally, most plant genera demonstrated some correlation with climatic and geographic gradients. The most important gradients were those of annual air temperature and precipitation. A small fraction did not demonstrate significantly particular pattern:"Cosmopolitan","East Asian and North American disjunct","Eastern Asian" and "Chinese endemic" distributions. The North Temperate distribution had the highest correlation with mean annual air temperature and precipitation.

结果如下：(1)除世界分布、栽培和入侵成分外，大部分中国种子植物属的地理成分的分布与地理相关密切；(2)热带分布属（泛热带分布、热带亚洲至热带美洲间断分布、旧世界热带分布、热带亚洲至热带大洋洲分布、热带亚洲至热带非洲分布及热带亚洲分布合计）占各地方植物区系的0.84%到94.38%，其最低值出现在中国西北部的新疆和青海地区，最高值出现在中国云南南部和海南；(3)热带分布属在＜北纬30°的地区占优势，除热带亚洲至热带美洲间断分布外，其它热带成分随纬度增加迅速减少；(4)温带分布属（北温带分布、东亚和北美间断分布、旧世界温带分布、温带亚洲分布、地中海区、西亚到中亚分布、中亚分布和东亚分布合计）占各地方植物区系的5.1%至98.83%，其最高值出现在中国西北部的新疆地区，最低值出现在中国云南南部和海南；(5)除东亚和北美间断分布、东亚分布和中国特有分布外，其它温带成分随纬度增加迅速增加；(6)在温带成分中，东亚和北美间断分布及东亚分布属主要出现在中国亚热带到暖温带地区，北温带分布、旧世界温带分布和温带亚洲分布属在中国北部占优势，而地中海区、西亚到中亚分布和中亚分布属则在中国西北部占优势；(7)除世界分布、东亚和北美间断分布、东亚分布和中国特有分布外，所有其他成分都显示了与气候因素密切相关，其中，北温带分布属与年均温和年降雨量最为密切相关。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。