建立了基本二元关系以及偏好关系的对偶理论。
This paper establishes the duality theory of preference relations.
同时，我们还建立了对偶理论及相关的鞍点理论。
Moreover, we develop corresponding duality theory and related saddle point theory.
在PERT技术中运用对偶理论，为敏度分析创造了必要条件。
Prerequisite for dual theory and sensitivity analysis in PERT is set up.
线性规划中对偶理论的一系列定理是针对变量无上界的线性规划的。
In linear programming, a series of theorems of dual theory are adopted to deal with the linear programmings with unbounded variables.
利用包络函数、二级近似概念和对偶理论，提出了一种结构优化的有效解法。
An efficient solution method for structural optimization is proposed by coordinated use of mathematical transformation, two level approximation concepts and dual theory.
运用广义网络流模型和线性规划对偶理论，提出了一种金融产品的套利定价方法。
An arbitrage pricing method for financial products in terms of generalized network model and duality theory of linear program is presented.
根据对偶理论，应用对偶规划精确映射原问题，再按泰勒展式建立对偶问题的二阶近似。
According to the dual theory, the dual programming was used to map the original problem exactly and the second approximation of the dual problem was set up by Taylor's expansion.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
本文针对模糊数的排序问题以及不确定规划中的模糊线性规划及对偶理论进行了较为深入的研究。
In this paper, a more in-depth study was conducted to the scheduling problem of fuzzy Numbers, the fuzzy linear programming of the uncertain programming and its duality theory.
本文首先介绍了耶理的对偶理论，进而应用该理论研究了市场保险、自我保险与自我保障三者的相互作用。
First, this article introduced Yaari's Dual Theory of Choice, and then studied the effect between self-insurance, self-protection and market insurance according to Yaari's Dual Theory of Choice.
本文利用线性规划的对偶理论，研究了交通网络通路影子价格，并据此提出了道路网络规划方案产生的方法。
Using the theory of duality, this paper deals with the shadow price of the transport network and proposes the method of producing transport network planning.
对偶理论是数学规划的理论基础，其中在各种约束条件下对弱对偶定理的研究是对偶理论研究的重要组成部分。
The duality theory is the basic theory for mathematical planning in which the study of weak duality theorem under different controlling conditions is an important part of duality theorem research.
本文还对模糊系数型线性规划的对偶理论进行了研究，并提出和证明了与经典线性规划对偶理论相对应的相关定理。
The fuzzy linear programming duality theory has been also studied in this article; the related theorems corresponding to the duality theorems in classical linear programming were proposed and proved.
对最适化条件、拉格朗日乘数理论以及对偶理论的综合论述，以及在控制、通信、动力系统和资源分配问题上的应用。
Comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Applications drawn from control, communications, power systems, and resource allocation problems.
本文给出了重力式桥墩与明挖基础整体优化设计的数学模型，选择序列线性规划法，并利用线性规划的对偶理论求最优解。
In this paper, a mathematical model for integral optimization design of pier shaft and its foundation is given, and the SLP method and duality theory are applied here to have a optimal solution.
对偶不变性结果是泛函分析空间理论的核心内容。
Duality invariance is the core of the space theory of functional analysis.
同时，电磁波导的辛分析也是构造对偶有限元的理论基础。
Moreover, symplectic analysis for electromagnetic waveguides provides the theoretical basis for constructing dual finite element method (FEM).
框架理论的研究内容主要包括：框架性质的研究、对偶框架性质的研究及框架扰动的研究等。
The research contents of frame theory mainly include: frame characters, dual frame characters, perturbation of frames, etc.
第3章给出无约束极大极小问题的一个对偶算法的收敛理论。
Chapter 3 is devoted to the study of the convergence theory of a dual algorithm for unconstrained minimax problems.
最后验证了电磁对偶的双四维势电磁场理论具有SO(2)电磁对偶性。
Finally, we verified that the doublet four dimensional potential electromagnetic theory has obvious SO (2) duality symmetry.
经典定价理论认为，市场出清价格应确定为市场优化问题的对偶解。
A clearing price is directly obtained from the dual solution of market optimization in standard pricing.
第四节用象似性理论解释对偶、排比和复叠的生成机制。
The fourth part interprets the formation mechanism of antithesis, parallelism and duplication based on the theory of iconicity.
利用对偶规划理论对模型进行了求解。
The dual quadratic programming is applied to solving the optimal model of continuum.
本文从CGE模型的构建过程以及对偶线性规划、影子价格等方面阐述了线性规划理论与方法对古典经济学理论的贡献。
Initiating the construction of CGE model together with its dual linear programming and values traced, the paper expatiates the contribution o.
本文比较了各种保费计算原理的性质，研究期望效用理论、对偶效用理论在保费计算原理中的作用，对传统上保费计算原理的可加性提出了疑问。
The roles of expectative utility and dual utility in premium principle has been studied in this paper by comparing the properties of traditional premium principles.
讨论了抽象对偶系统中的向量值无穷矩阵变换，在一个所涉拓扑线性空间没有任何限制的情况下，得到了无穷矩阵变换理论的一个新结果。
For infinite matrices of linear and some nonlinear mappings between topological vector spares which have not any restriction, we establish a new result of infinite matrix transformations.
对偶极矩作了象观和理论上的描述。
Phenomenological and theoretical interpretation of the dipole moment was discussed in this paper.
对偶极矩作了象观和理论上的描述。
Phenomenological and theoretical interpretation of the dipole moment was discussed in this paper.
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