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If F is a space of functions defined on a domain Ω and ψ is a function taking Ωinto itself, then the composition operator C〓 induced by ψ is defined by C〓: f〓fοψ,〓f∈F. It is obvious that C〓 is a linear operator.

设F是定义在区域Ω上的一个函数空间，φ：Ω→Ω是Ω到自身的一个映射，则可通过函数的复合定义一个线性算子C〓：f→foφ，〓f∈F，称为由φ诱导的复合算子。

Consistency conditions in the development system are defined as concrete graph properties in first-order logic with equality. Some classes of consistency conditions related to object and relation types, processes, styles and applications are defined.

在考察了各种对象的演化特征之后，我们用图重写规则定义了基本演化规则，包括对象、关系的添加和删除，对象、关系类型的修改，以及一些典型的高级演化规则。

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。

To obtain the likelihood function indicating the uncertainty of observed information, noisy data is firstly expressed by a set of data vectors instead of a single vector, and then transferred to probability density curve defined in model space through confidence value defined in data space.

我们将数据向量的概念扩展为数据向量的集合，通过引入数据空间内的信赖度，把数据噪声转移到模型空间的概率密度函数上，即获得了反映数据本身的不确定性的似然函数。

The spherical equivalence of cycloplegic auto-refraction equal or less than -0.5D in either eye is defined as myopia and that equal or higher than +2D is defined as hyperopia.

分析了学龄期儿童的纵向屈光改变情况、近视眼的发病率及其危险因素、儿童视力现状以及一些常见眼病的患病率情况。

Firstly, we defined a series of new concepts as the schemata containment, schemata competence, schemata intersection, and schemata dominance. Then, we defined the GA schema deceptiveness based on primary schemata competence, including complete schema deception, consistent schema deception, sequential schema deception, and basic schema deception.

4系统研究了GA欺骗问题，提出了模式包含、竞争与关联等概念，给出了基于主竞争关系的模式欺骗性与GA欺骗问题的严格定义，包括完全欺骗问题、一致欺骗问题、序列欺骗问题和基本欺骗问题。

In such cases, the default argument defined for the base version of the virtual will be passed to the derived version, which was defined using a different default argument.

在这种情况下，为虚函数的基类版本定义的默认实参将传给派生类定义的版本，而派生类版本是用不同的默认实参定义的。

After analyzing the three major defining standards in the theoretical field, the writer presents the defining standard on the cooperative behavior of cheating insurance money: With the consideration on the influence of the status of the employees in the insurance company on the nature of cooperative crime as the presupposition, firstly the nature of the cooperative crime should be defined according to the criminal nature of the committer, and then to decide whether the committers should be convicted separately by contrasting the degree of the crime legally defined.

有学者提出保险诈骗罪的法定刑应该提高，本文不赞成此观点，认为将本罪的法定刑提高，与刑法的谦抑性原则不符，应该从社会环境、经济体制等方面来寻找解决问题的途径，而不应一味加重刑罚的力度；刑法是整个社会的最后一道防线，在应用这道防线时应当充分考虑到成本和效益的问题。

In this thesis, we defined duality Fuzzy relation in a pointwise Fuzzy set by a set of duality Fuzzy point. Then we defined Fuzzy congruence and Fuzzy rough set in Fuzzy semigroups.

本文把二维模糊点作成的集合定义为一个点态化模糊集上的模糊二元关系，进一步定义模糊同余关系，并通过它又定义点态化模糊集上模糊粗糙子集，并研究了它们的一些性质。

So in the dot-matrix, microcal, for spot color, you must deliberately additional or specify only the rows (for example, in Photoshop with defined spot colors, you can have two situations: If the spot color as a hue applied to the entire image, it is necessary to convert a Duotone image mode, and a Duotone spot color plate application; if the spot color for specific areas of the image, you must create a spot color channel); and in vector drawing environments, if the selection or define a spot color, the color has been to spot color attribute exists, unless you specifically set this spot color property changes or converted to business card printing and membership card making colors (for example, in an additional Iiiustrator and defined a spot color, even if it is referenced to a different data file, or in Illustrator will use that spot color data file with a different vector software open, and so on, this spot color color property does not change).

所以在不背阵画图软件洋，差于专色，务必锐意不天增撤或选举才动（比如：在Photoshop洋增撤和界说专色，可以有两栽景遇：若不兵专色息为一栽色调答用于合座图像，需不兵图像变换为单色调模式，并在其洋一个单色调印版上答用专色；若不兵专色用于图像的特定不天区，则务必成立专色通道）；而在矢量画图境况边，若采取或界说一个专色，则该色不断会以专色的属性活命，除非附带不兵此专色属性保持或变换不败制卡和会员卡制息色（比如：在Iiiustrator洋增撤和界说的一个专色，即使被引用到其他Illustrator数据文件洋或不兵搁置该专色的数据文件用其他矢量软件敞开等，此专色的颜色属性都不会保持）。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。