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extremum condition
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  极值条件
     We explain the economical meaning of all kinds of parameters,and analyze the extremum condition of the long-run cost function under constant factor production elasticity and factor price.
     并对长期成本函数的重要参数给出了新的经济解释,分析了在投入要素的产量弹性和价格保持不变的前提下长期成本函数的极值条件,得出了企业最大长期成本出现的充要条件是各种生产要素等量投入。
短句来源
     In this paper, the theorem of Rayleigh quotient is introduced at first, then by use of it, a new rigorous proof for an unconstrained extremum condition is given.
     本文首先介绍Rayleigh商定理,然后利用Rayleigh商定理给出无约束极值条件新的严格证明。
短句来源
     With the method, sub-pixel position of low-light-level strips central point is extracted by Hessian matrix algorithm according to second-order derivative extremum condition of strips image gray scale, which is used for considering two- dimensional variation of stripe intensity profile. Noises during image processing will be eliminated by three feature constraints such as continuity constraint, direction constraint and stripes spacing constraint.
     该方法根据光条图像灰度的二阶方向导数极值条件,利用Hessian矩阵算法提取弱光条中心点的亚像素位置,通过连续性约束、方向约束和光条间距约束等特征约束条件去除图像处理过程中出现的噪声点。
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     Iterative functionals are constructed based on variation methods combined with Lagrangian multiplier methods,and iterative formulae for solving vibration equations are given after the Lagrangian multiplier is determined by functional extremum condition.
     结合变分法与拉氏乘子法,构造含拉氏乘子的迭代泛函,由泛函极值条件确定拉氏乘子给出求解振动方程的迭代格式。
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  “extremum condition”译为未确定词的双语例句
     Based on ideal deformation theory, the authors developed a finite element inverse approach for sheet metal forming process simulation. The formulation of finite element equation is derived by the relative extremum condition of the global plastic work of the deforming body.
     依据理想形变理论 ,研究开发了冲压成形过程模拟的有限元逆算法 ,根据变形体的整体塑性功取相对极值的条件 ,导出了逆算法有限元方程。
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  extremum condition
For the unmodified and chill-modified eutectic microstructures it seems probable that the basic equation is applicable but that the extremum condition is not.
      
The present measurements fit the extremum condition of the Hunt and Jackson theory of eutectic growth.
      
We reject the extremum condition with respect to one of the order parameters in spin glass models.
      
We show that it is possible to introduce an expansion at fixed magnetization amplitude in the inverse of lattice coordination number if the direction is selected by an extremum condition.
      
When the extremum condition in the thermodynamical potential is imposed, a family of Bogoliubov transformations that give us a planckian spectrum is found, even in "pathological" cases such as the minimally coupled scalar field.
      
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Recently, there present many works to discuss the phase transition-like behaviour of the polaron in polar crystals. However, all these works didn't consider the incorporate effect of the temperature and electron-phonon Frohlich Coupling constant r. In this paper, starting from the Bogolyubov inequality for the free energy, we discuss this incorporate effect on the phase transition-like behaviour of the polaron.The Hamiltonian of a system consisting of the electrons and phonons is shown as (2.1) in the text....

Recently, there present many works to discuss the phase transition-like behaviour of the polaron in polar crystals. However, all these works didn't consider the incorporate effect of the temperature and electron-phonon Frohlich Coupling constant r. In this paper, starting from the Bogolyubov inequality for the free energy, we discuss this incorporate effect on the phase transition-like behaviour of the polaron.The Hamiltonian of a system consisting of the electrons and phonons is shown as (2.1) in the text. And assume that the Bogolyubov ineqality between the real free energy F(H) and the model free energy Fmod(H) also holds for the polaron. The Bogolyubov ineqality has the form (2.4) in the text. In this representation, H can be regarded as the sum of H0 and a perturbed term (H-H0). H0 is represented [by (2.8) which is called the model Hamiltonian. In the course of calculation, we introduce two unitary transformations 171 and U2. Then, applying these transformations to (2.4), we finally obtain the expression (2.27) from which the free energy can be determinded. Lagrange multiplier u in (2.27) has the meaning of the translation velocity of the polaron. The effective mass of the polaron and the mean numbers of phonons N in the cloud around the electron are, respectively, represented by (3.5) and (3.6). The expectation value of the polaron energy with respect to the ground state |0> at the different temperature is expressed by (3.4).From the extremum condition we can futher de-termine the parameters A, ε and λ. Then, inserting these parameters just determined into (3.4), (3.5) and (3.6), we can obtain the ground state energy, the mean phonon numbers and the effective mass. Fig.1 shows the α dependence of the ground state energy when the temperature is smaller than a certain critical value Tc. From this figure, one can see that the ground state energy is linearly dependent on α until the point αc, and then, it is approximately proportional to α2. There are two branches for each curves. One corresponds to small α and has the same rules as that obtained by Lee-Low-Pines approximation. The other begins at the point αc and corresponds to the results of the strong coupling approximation.The crroes-point αc of the two branches is the phase transition point. At the critical point the polaron state changes from a nearly-free-type state to a self-trapped one. In addition, there is also another branch which is represented in the dotted line. This branch corresponds to unstable solution. Fig. 2 and Fig.3 show how the mean phonon numbers and the effective mass vary with the coupling constant α. From these two figures the characteristic feature of the phase transition is most conspicuous. Both the mean phonon numbers and the effective mass have an abrupt change at the point αc.Reversely, when the temperature is larger than Tc, as shown in Fig.5, the rule of the ground state energy variating with α is the same for different temperatures. When α<αc, the ground state energy is equal to zero. As soon, as α arrives at αc, the ground state energy abruptly jumps to a certain value, then, it varies approximately with α2. This means that there only exists free electron state for α<αc, and polaron state for α>αc.αc is the phase transition point. For the different temperature, the phase transition point αc is different. If we plot the phase transition point αc as a function of the temperature T, as shown in Fjg. 8, the curve's shape is very intresting. There is a λ-like point on this (kT, αc) diagram. The temperature corresponding to this Y point is called the critical temperature Tc. The calculation indicates that this λ point is approximately (0.98 hω0, 6). Above the criticaltemperature Tc, a approximately varies with T1/2. on the contrary, when T

本文将电子的动量和位置的线性组合作为算符,应用了Bogolyubov不等式,并对哈密顿量进行两次么正变换,对电子-声子耦合常数α的整个区域和温度的尽可能广泛范围计算了体极化子的基态能量,有效质量及电子周围的平均声子数。发现对应一定的温度,当α超过一定值α时,极化子将发生相变。并且本文还找到了一个临界温度T_c,当温度大于T_c与温度小于T_c时其相变行为是不同的。

The unconstrained extremum conditions are the important parts of optimization theory, and have certain significance in the theory and practice. The optimality conditions for constrained problems become a logical extension of the conditions for unconstrained problems. One strategy for solving a constrained problem is to solve a sequence of unconstrained problems. In this paper, the theorem of Rayleigh quotient is introduced at first, then by use of it, a new rigorous proof for an unconstrained extremum condition...

The unconstrained extremum conditions are the important parts of optimization theory, and have certain significance in the theory and practice. The optimality conditions for constrained problems become a logical extension of the conditions for unconstrained problems. One strategy for solving a constrained problem is to solve a sequence of unconstrained problems. In this paper, the theorem of Rayleigh quotient is introduced at first, then by use of it, a new rigorous proof for an unconstrained extremum condition is given. This proof is more concise than the old one, and it has considerably practical value in learning and grasping the optimization theory for those readers who are not familiar with the theory of limit of sequence.

无约束极值条件是最优化理论的重要组成部分,在理论上和实践上都有重要意义,约束问题的最优性条件是它的逻辑推广,解约束最优化问题的一种策略是解一系列无约束问题。本文首先介绍Rayleigh商定理,然后利用Rayleigh商定理给出无约束极值条件新的严格证明。这种方法比已有证法更简明,对那些不熟悉序列极限理论的读者,在学习和掌握最优化理论方面,有一定的实际意义。

Based on ideal deformation theory, the authors developed a finite element inverse approach for sheet metal forming process simulation. The formulation of finite element equation is derived by the relative extremum condition of the global plastic work of the deforming body. Iterative algorithms are proposed to determine the initial guess of the inverse approach and the shape of the work piece relevant to given blank shape. Applying the FE inverse approach, the authors predict the blank shape of sheet metal...

Based on ideal deformation theory, the authors developed a finite element inverse approach for sheet metal forming process simulation. The formulation of finite element equation is derived by the relative extremum condition of the global plastic work of the deforming body. Iterative algorithms are proposed to determine the initial guess of the inverse approach and the shape of the work piece relevant to given blank shape. Applying the FE inverse approach, the authors predict the blank shape of sheet metal forming process, calculate the final shape and the strain distribution for a given blank shape. Numerical simulation shows that FE inverse approach can be used for rapid evaluation of sheet metal forming process design and for the optimization of the process parameters.

依据理想形变理论 ,研究开发了冲压成形过程模拟的有限元逆算法 ,根据变形体的整体塑性功取相对极值的条件 ,导出了逆算法有限元方程。提出了求逆算法初始解以及求解与给定形状的毛坯相对应的冲压件形状的迭代计算方法。采用有限元逆算法预测了与冲压件形状相对应的冲压件毛坯的展开形状 ,根据给定的板坯形状计算了冲压件最终构形及应变分布。分析计算实例表明 ,逆算法可用于对板料成形工艺方案进行快速评价 ,对冲压工艺参数进行优化

 
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