This paper establishes the duality theory of preference relations.
建立了基本二元关系以及偏好关系的对偶理论。
Moreover, we develop corresponding duality theory and related saddle point theory.
同时，我们还建立了对偶理论及相关的鞍点理论。
Some new ideas and methods for the application of the duality theory are presented, such as cross convolution, cross cyclical co...
在双重性原理的应用部分，还提出了交叉卷积、交叉循环卷积、借用变换对法等新概念与新方法。
An arbitrage pricing method for financial products in terms of generalized network model and duality theory of linear program is presented.
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。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
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。
Some new ideas and methods for the application of the duality theory are presented, such as cross convolution, cross cyclical convolution and borrowtransform-pair methods.
在双重性原理的应用部分，还提出了交叉卷积、交叉循环卷积、借用变换对法等新概念与新方法。
The papar calls scientits′ attention to that, the wave-particle duality theory established depond on the wavelength being small enough, but the demarcation line is not clear.
指出，虽然波粒二象性成立的前提是波长足够小，但在现有理论中却提不出一条清晰的界线。
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。
Then, by use of multiple carrier system's frequency-sharing property and convex optimization, a subcarrier and power optimal allocation algorithm is proposed based on Lagrangian duality theory.
然后，运用凸优化技术分析了该资源分配问题，并基于拉格朗日对偶法给出了一种子载波和功率最优分配算法。
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.
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。
Comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Applications drawn from control, communications, power systems, and resource allocation problems.
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。
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.
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 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.
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 dual law in lattice theory is introduced and some concepts and properties relative to it are discussed, while generalizing the concept of duality and the idea of the duality principle.
推广了对偶的概念与对偶原理的思想，在格论中引入了对偶律，并讨论了与之相关的一些概念和性质。
Duality invariance is the core of the space theory of functional analysis.
对偶不变性结果是泛函分析空间理论的核心内容。
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.
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。
The duality of social benefit and economic benefit owned by the management of educational theory books decides its unique marketing mode.
教育理论图书经营所特有的社会效益和经济效益双重性，决定了其特有的营销模式。
Finally, we verified that the doublet four dimensional potential electromagnetic theory has obvious SO (2) duality symmetry.
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。
In this paper, the specific resistance of liquid duality natrium Kalium alloy is calculated by using the theory of Ziman - Faber.
采用齐曼-费柏理论计算了不同组分比例下液态二元钠钾合金的电阻率。
The theory of"internet duality of virtuality and reality"holds that virtuality is not only a form of existence, but also an important aspect of human conscience.
网络虚实二重性理论认为，虚拟不仅是事物的一种存在形式，也是人性的重要方面。
The double solutions correspond possibly to the wave-particle duality in quantum theory, and connect the double solution theory of the nonlinear wave mechanics.
双解可能对应于量子理论中的波-粒二象性，联系于非线性波动力学的双重解。
Optical interconnection technique is a kind of theory using photon wave-particle duality phenomenon to achieve the signal transmission and data exchange.
光互连技术是以光的波粒二相性的各种现象实现信号传输和数据交换的理论。
The forming process and active mechanism of the Generalized-Gradient theory can be simplified as it's of the duality structure from high gradient to low gradient in space.
广义梯度推移过程及其作用机理可简约为“高梯度—低梯度二元空间结构”的形成、作用机理及其演化过程。
The value of the administrative formality includes utility-theory, standard-theory and duality-theory in terms of theory, but, by nature, it has both inner and outer values.
行政程序价值在理论上有工具说、本位说和二元说之争，按其属性可分为程序的内在价值和外在价值。
The value of the administrative formality includes utility-theory, standard-theory and duality-theory in terms of theory, but, by nature, it has both inner and outer values.
行政程序价值在理论上有工具说、本位说和二元说之争，按其属性可分为程序的内在价值和外在价值。
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