给出了一类凸模糊集的表示定理。
We investigate the representation theorems of convex fuzzy sets.
综述有关分配格表示定理的某些工作。
It is devoted to summarize some word of representation of distributive lattice.
最后证明了模糊测度空间的正则扩张及表示定理。
The regular extension and representation theorems of fuzzy measure Spaces will be proved.
证明了离散格是一个布尔代数，给出了离散格的表示定理。
It is proved that this lattice is a Boolean algebra, and the representation theory of discretization lattice is given.
研究了序凸集的一些运算性质，得到了紧序凸集的序端点表示定理。
The representation theorem with order-extremal points is obtained for compact order-convex sets.
然后引入拓扑直和的概念，利用它和商空间给出一个归纳极限表示定理。
We introduce the notion of topological direct sum, and get a representative theorem of inductive limit by topological direct sum and quotient space.
本文给出了非对称自变量的线性各向同性标量值和张量值张量函数表示定理的数学证明。
This paper gives a mathematical demonstration of the representation theorems for linear, isotropic scalar - and tensor-valued tensor functions of an asymmetric argument.
本文作为平稳集值随机过程的表示定理的应用，证明了平稳集值随机过程的遍历性定理。
In this paper, we prove the ergodic theorem of a stationary set valued stochastic process by the representation theorem.
作者提出一组有理数概率下效用函数存在的公理，并证明该公理体系下的效用表示定理。
This paper puts forward a set of axioms and proves the existence and uniqueness of utility function with rational probabilities on the set of axioms.
这些结果说明，KLM赋值结构为证明有限语言下单可表示类后承的表示定理提供了一种充分的通用性方法。
These results reveal that KLM valuation structure provides a sufficient and canonical approach to establish representation theorems for any injective inference relations in finite framework.
在一致性公理体系内，研究了一致风险测度的有关性质并由一致风险测度弱化部分条件后推广出凸性风险测度，并证明了它的表示定理。
In this axiom system, we made a study of the coherent measures of risk and convex measures of risk, which is extended from the coherent measures of risk, and proved its representation theorem.
讨论凸多目标最优化问题的严有效解，建立了拉格朗日乘子定理，并把严有效解表示为一个适当的拉格朗日函数的鞍。
We establish a Lagrange multiplier theorem for strict efficiency in convex settings and express strict points as saddle points of an appropriate Lagrangian function.
从陈子定理可以演绎出描写质点运动的各种表示方式。
Chenzi theorem can be applied to describe the motion of particles in many ways.
证明了一个基于图文法表示机制的遗传算法模式定理，描述了交叉和突变对模式作用的效果。
It proves a schema theorem for genetic algorithms in which representation schema is based on graph grammar. The effect of crossover and mutation on schemata is described.
传统上，定理机器证明常常使用某种逻辑表示，然后再进行推理，这些方法往往缺乏灵活性，且证明过程难以理解。
Traditionally, Mechanical theorem proving often use a logic representation, and then inference, these methods lack of flexibility and the proving processes are difficult to understand.
详细说明：命题逻辑中的推理规则可以用来证明一个已经表示成命题公式的定理，但它还不便于机械化实施。
Propositional logic in the inference rule can be used to prove that a propositional formula has been expressed as the theorem, but it is not easy to implement mechanization.
命题逻辑中的推理规则可以用来证明一个已经表示成命题公式的定理，但它还不便于机械化实施。
Propositional logic in the inference rule can be used to prove that a propositional formula has been expressed as the theorem, but it is not easy to implement mechanization.
对二维晶体的矩阵表示、对称性及其对X射线衍射的系统消光规律进行了研究，得到并证明了二维晶体的矩阵表示的二个定理和二维晶体对X射线衍射的系统消光定理。
The crystallographic problems of two-dimensional crystal, such as the matrix expression, the symmetry and the systematic absence law of the crystal's X-ray diffraction, are studied.
通过五个定理给出三角形“五心”的向量表示方法，并提供证明。
The author gave out the delta the vector representation of "five minds" by means of five theorems. and supplied the proof.
包括不变式产生规则，不变式在计算机中的表示和转换，以及定理证明的部分实现方法。
The generation rules, the notation and the transformation of invariants are described. The method of theorem verification is also included.
运用土力学边坡稳定理论，定量表示了焦炭向高炉中心的坍塌量。 模拟结果与实测结果比较符合，证明此模型是适用的。
The volume of the coke collapsing toward the furnace center was quantified by applying the slope stability theory of soil mechanics.
运用土力学边坡稳定理论，定量表示了焦炭向高炉中心的坍塌量。 模拟结果与实测结果比较符合，证明此模型是适用的。
The volume of the coke collapsing toward the furnace center was quantified by applying the slope stability theory of soil mechanics.
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