查询词典 order

By using modern mathematical theory,the ordering axiom is generalized tothe lattice-order axiom,and the continuity axiom is weakened to constructlattice-order decision-making behavior axioms,of which rationality is confirmed.

应用现代数学理论，将Von Neumann-Morgenstern理性行为公理体系中的全序刻划推广为格序刻划，并相应地弱化连续性公理，建立起新的格序决策行为公理体系，研究了该公理体系的合理性。

In this dissertation,Von Numann and Morgenstern Axioms are analyzedagain at first.It is pointed out not only that preference relations are often latticeordered,but also that the transitivity axiom,along with the independence axiomand the continuity axiom is still rational to a high degree,then a new set ofaxioms for lattice-order decision-making behavior is established.At last,relatedsubjects based on lattice in preference theory,utility theory,decision-makingmethods,multiattribute decision-making,and group decision-making are studied.In this way,the lattice-order decision-making theory is framed.Main creativeresults are obtained as follows

本论文重新审视了Von Neumann-Morgenstern理性行为公理体系，对以前学者较少涉及到的连通性公理提出了质疑，指出偏好关系具有格特征，而传递性公理、独立性公理以及连续性公理在很大程度上仍具有合理性，进而创建了格序决策行为公理体系，研究了基于格的偏好理论、效用理论、决策方法、多目标决策以及群决策中的相关问题，初步构建了格序决策理论框架，主要研究成果如下

In this paper,at first we transformed the nonlinear elliptic system of 2m first order equations into the complex form, then by use the results on the Riemann-Hilbert problem for nonlinear elliptic complex equation of first order, the method of continuity, the Schauder fixed-point theorem and the Leray-Schauder theorem, we proved that the modified Riemann-Hilbert boundary value problem for the complex system with some conditions is solvable.

本文先将较一般的多个未知函数的一阶椭圆型实方程组化为复方程组，然后讨论这些复方程组在某些条件下的一些边值问题的可解性。这里所考虑的方程组既包含线性的，也包含非线性的，比广义超解析函数所满足的方程组还要广，又本文主要研究较一般的Riemann-Hilbert边值问题，先给出这种边值问题解的先验估计式，然后用参数开拓法及Leray-Schauder定理证明这种边值问题的可解性结果。

Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

A second-order symmetric fabric tensor is introduced to the model, such as the stiffness of the contact planes, the hardening parameter, the dilatant/ contractant coefficient are made dependent of the orientation of the contact plane in order to capture the inherent and stress induced anisotropic behavior of clay.

在上述考虑微结构的饱和软粘土的弹塑性本构模型的基础上将考虑组构的各向异性的二阶组构张量引入接触面上的刚度、硬化参数、剪胀系数等参数中，由此反映材料引起的各向异性和应力引起的各向异性。

PSO is a population-based optimization algorithm, which mimics the social behavior of animals in a flock. It makes use of individual and group memory to update each particle position allowing global and local search optimization. The objective function considered was the total weight of the structure subjected to stresses, displacements and forces constraints. The effects of the parameters were investigated as well and such combination of tuning parameters promote a better global search behavior avoiding premature convergence while rapidly converging to the optimal solution. Results showed the effectiveness of the proposed method by comparing with ANSYS Design Optimization Tool (zero-order method). The PSO with the tuning parameters makes it an ideal method for offshore wind turbines foundations optimization tasks.(2) A reliability analysis method for pile foundation bearing axial loads based PSOThe performance function of pile foundation's axially bearing capacity sometimes is nonlinear and complex, on the basis of geometric meaning of structural reliability index, an optimum model with PSO for structural reliability analysis under arbitrary random variables was established, The PSO algorithm is very efficient to solve global optimization problemsIts use in structural reliability field presents not only the advantage of its facility of implementation, but also the possibility to obtain the design point and the failure probability with a good accuracy. In addition, PSO is a zero order algorithm, for no derivative is necessary for its implementation.

本文的研究针对桩式海上风机基础结构的特点，在国内外有关研究成果的基础上对海上风机基础结构优化设计理论和可靠度方法一些相关问题进行了较为深入的研究，具体做了以下几个方面的工作：(1)基于粒子群优化的桩式海上风机基础确定性优化设计方法桩式海上风机基础的优化设计是一个复杂的、非线性约束的优化问题，针对传统的基于梯度信息的优化方法在处理非线性问题中易陷入局部最优解的问题，本文将一种耦合惩罚函数的PSO算法引入到海上风机基础结构概念设计中，PSO算法是从群体动物聚集觅食这一活动中受到启发而发展的，该算法利用个体和群体的信息共享不断改进自身的位置从而进行局部和全局最优搜索，本文中以桩和三脚架连接段直径及壁厚为设计变量，以基础总重量作为优化的目标函数，在给定的约束条件下建立了三脚架基础优化数学模型，另外本文还研究了PSO参数变化对结果的影响，协调的参数组合可以避免陷入早熟收敛而能够快速的获得全局的最优解，通过与ANSYS优化模块的计算结果比较验证了该方法的有效性，本方法为海上风机基础的确定性设计提供了一条有效的途径。

The optimal convergence rates in H-1 and L-2 norms are proved, and the convergence order in L-2 norm is one order higher than that in H-1 norm.

并分别给出了解的H-1模和L-2模的最优收敛阶估计， L-2模收敛阶比H-1模收敛阶高一阶。

For example,we have the following simple result:Lei the Taylor series F =has a radius of convergence or 1, where 0 = If F is of order p (For the two cases of the radius of convergence,the meanings of "order"are different.).

如果这级数有级ρ(在收敛半径是∞或1时，"级"的意义不同)，那么在第一种情形。

In order to get the numerical solution, the paper devises a three hierarchic implicit scheme which eliminates the strict restriction of explicit scheme, thus, it can be used in more areas. By using the energy estimation method, the convergence and stability of the difference scheme are proved and the scheme is second order convergence for time and space.

对求解方程构造了一个三层隐式差分格式，消除了显格式的稳定性对计算步长的严格限制，使之适用范围更广，并用能量估计的方法严格证明了差分格式的收敛性与稳定性，该格式对于时间和空间均具有二阶收敛性。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。