查询词典 theorems

Chapter 4 establishes the theory of convex fuzzy mappings: The concepts, such as Jensen's inequality, positively homogeneous, infimal convolution, right scalar multiplication and convex hull are introduced. The corresponding theorems are demonstrated by using the parametric representations of fuzzy numbers. In anti-fuzzy number space, the conjugate mapping of convex fuzzy mapping is concerned, and convexities of conjugate set and conjugate mapping of convex fuzzy mapping are proved. The notions of subgradient, subdifferential, differential with respect to convex fuzzy mappings are investigated, which provides the basis of the theory of fuzzy extremum problems.

在第4章中，建立了有关凸模糊映射的理论：建立了关于凸模糊映射的Jensen不等式、模糊正齐次映射、凸模糊映射的下卷积、右数乘和凸包等概念，利用模糊数的参数化表示，给出了相应的定理；在反模糊数空间，对凸模糊映射的共轭也作了探讨，证明了凸模糊映射的共轭集合和共轭映射都是凸的；最后对凸模糊映射的次梯度、次微分和微分等概念进行了研究，为模糊极值理论打下了基础。

In this paper, with the framework of non-equilibrium thermodynamic separation theory, a mathematical model of nonlinear chromatography is established according to the actual chromatography processes based on the three basic theorems, Lagrangian-Eulerian description, continuity axiom and local equilibrium assumption.

本文在梁恒等建立的非平衡热力学分离理论的框架下，以Lagrangian-Eulerian描述、连续性公理和局域平衡假设三大基本法则为基础，建立了一种制备色谱理论模型。

In this paper, the relevant definitions and theorems of function series continuity and function of the carried out a detailed convergence analysis, so that readers of their intrinsic relationship between the more detailed understanding.

本文通过相关定义与定理对函数的连续性及函数项级数的收敛性进行了详细的分析，使读者对它们之间存在的内在关系有更详细的认识。关键词：函数列；函数项级数；连续性；收敛性；一致收敛性

In the proof,sufficient conditions are proved mainly by properties of K function and continuity of Lyapunov function:in necessary proof,we separately structure Lyapunov functions which satisfy the conditions of the theorems, such that the results establish.

在定理的证明中充分性主要利用K类函数严格单调递增和Lyapunov函数的连续性；必要性的证明中，分别构造Lyapunov函数，满足定理的条件，使得定理的结论成立。

The paper states the distinctions between Riemann integral and Lebesgue integral from the aspects of the definition of integral,the continuity of integrable function,the additivity of integral,integral limitation theorems and Newton-Leibnitz formula.

从积分的定义，可积函数的连续性，积分的可加性，积分极限定理，牛顿-莱布尼兹公式五个方面阐述了黎曼积分与勒贝格积分的区别。

For a better understanding of the proofs several theorems of convex analysis are recalled in the first part.

为了更好地理解证明，在第一部分回顾了凸分析的一些定理。

Certain topics which might properly not be regarded as part of "convex analysis",such as fixed-point theorems,have been omitted,not because they lack charm or applications,but because they would have required technical developments somewhat outside the mainstream of the rest of the book.

某些主题可能没有被视为是"凸分析"的组成部分，例如省略了定点定理，并不是因为它们缺乏吸引力或应用，而是由于它们所需要的技术发展有点超出这本书的主流。

We proposed and proved three theorems through which the theoretical formula of cosine transform spectrum of gravity anomalies of the point mass and the vertical rectangular-cylinder was deduced in order to obtain the general equation of gravity anomalies.

为获得重力异常余弦变换谱的通式，提出并证明了3个定理；利用它们推导了点质量和直立矩形柱体的重力异常余弦变换谱理论公式，同时给出了重力异常余弦变换谱通式。

We proposed and proved three theorems through which the theoretical formula of cosine transform spectrum of gravity anomalies of the point mass and the vertical rectangularcylinder was deduced in order to obtain the general equation of gravity anomalies.

为获得重力异常余弦变换谱的通式，提出并证明了3个定理；利用它们推导了点质量和直立矩形柱体的重力异常余弦变换谱理论公式，同时给出了重力异常余弦变换谱通式。

A number of properties of countable topological space were given systematically, such as its countability, separability, compactness and connectedness, including their proofs on the basis of the nature of topological space, real number space and corresponding theorems.

摘要在可数补拓扑空间的拓扑性质的研究基础上，系统的给出了可数补拓扑空间的可数性，分离性，紧致性，连通性等性质，并给予证明。

The father that if work,mad father, love annoys, disposition is too indrawn the be short ofing that the father of Mu Ne, resign oneself to adversity causes father easily to love is broken; Communicate time effectively between father and son, Mu Zizhi to be less than a hour on average to wait a moment every week, it is the cause that causes the child to become addiction.

如工作狂的父亲、爱愤怒的父亲、性格过于内向木讷、逆来顺受的父亲都易造成父爱的缺失；父子、母子之间的有效沟通时间每周平均小于一小时等等，都是造成孩子成瘾的原因。

These are vandal proof and they come with a locking mechanism.

这是野蛮的证据，他们来到了锁机制。