查询词典 function field

The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. The advantage is that the cost function variation is independent of the flow field variation, with the result that the gradient of cost function with respect to arbitrary number of design variables can be determined without the need for additional flow-field evaluations. So each design cycle requires the numerical solution of both the flow and the adjoint equations leading to a computational cost roughly equal to the cost of two flow solutions.

虽然他们的研究成果大多数都可以在公开性文献上看到，但是其中一些具体的细节问题的处理方法却没有透露，比如：伴随方程如何离散求解才能减小最终梯度计算中的误差，使得设计过程有效地进行；伴随方程与流动方程的边界条件是不同的，如何合理地处理伴随方程的边界条件，才能推动设计过程朝着设计目标而发展；在减阻问题中目标函数如何定义，求解梯度的具体数学公式如何推导，如何通过数值方法来实现它们等。

Optimal algorithm of combined nonlinear Hopfield network appears powerful validity in solving nonlinear planning, which includes nonlinear objective function, linear constrains and high-demension of decision-making variants, for its ability of nonlinear parallel computation. It is prominent among optimal algorithms because of its function of simply implement with electrocircuit hardware. Genetic algorithm is expressly suitable for optimal calculation regarding the planning of massive, highly nonlinear, inconsecutively differentiable and multiobjective function as well as objective function without analytical expression. However, it inclines to prematurity, as well as its limitation in ability of partial optimal search. Introducing the optimal algorithm of niche genetic simulated annealing to standard Genetic algorithm, can therefore improve the full-scale or partial search ability of Genetic algorithm effectively. It has a far-flung perspective in the field of systemic planning of water pollution control.

组合式非线性Hopfield网络优化算法所具有的非线性大规模并行计算能力在求解具有非线性目标函数、线性约束条件及高维决策变量的非线性规划问题方面显示出了强大的生命力，它易于电路硬件实现的功能更是在优化算法中独树一帜；遗传算法采用概率搜索技术，不受目标函数与约束条件的限制，特别适合大规模、高度非线性的不连续可微的多峰目标函数及无解析表达式的目标函数的规划问题的优化计算，但其存在容易早熟、局部寻优能力较差等缺点，本文在标准遗传算法中引入小生境技术及模拟退火算法有效地改善遗传算法的全局和局部搜索性能，提高了全局最优解的寻优质量，小生境遗传退火模拟优化算法在水污染控制系统规划中的应用前景极为广阔。

The thesis first recommends the famous fuzzy Gaussian approximation system which is based on the Gaussian membership function, the fuzzy logic of product reasoning and the fuzzy law of weight approach. This thesis is discusses the general fuzzy Gaussian membership function that can approximate the form of triangular, trapezoid and Gaussian function , and its basic form is .The general fuzzy Gaussian membership function is to be generally used in the field of approximation .

模糊逼近是近年来发展比较迅速的一个新兴方向，论文首先给出了模糊理论中著名的基于高斯隶属函数、乘积推理模糊逻辑和重心解模糊法的模糊高斯型万能逼近定理，在此基础上本文进一步给出了可以用来逼近三角形、梯形和高斯形的广义高斯隶属度函数形式，它的基本形式是。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

Properties of efficient portfolios and the efficient frontier to the model are systematically analyzed. Our main results concerning the properties are: every efficient portfolio can be solved by minimizing portfolio risk under a given level of portfolio return or by maximizing portfolio return under a given level of portfolio risk; on the efficient frontier, the risk is a convex and strictly increasing function of the return and the return is a concave and strictly increasing function of the risk; the utility function on the efficient frontier can be expressed as a quasi-concave function of the risk or the return if the investor's utility function is quasi-concave.

从理论上系统地对该模型下的有效投资组合和有效前沿的性质进行了分析，结果表明：每一个有效投资组合可通过在给定期望收益水平的条件下最小化投资组合风险来获得，或者在给定风险水平的条件下最大化期望投资组合收益来获得；在有效前沿上，风险是收益的严格单调递增凸函数，收益是风险的严格单调递增凹函数；当投资者的效用函数是拟凹函数时，则有效前沿上的效用可表达成风险或收益的拟凹函数。

The convex function develeped so many years that convex functionals are now a class of very universal functionals.The kinetic energy in the classical is the most natural convex function.Others like entropy and so on are convex functions.The economic core is closely connected with the convex function.The western economic core question is the optimized question.The optimized theory has something to do with the convex function and the concave function.

凸函数的发展经年已相当完善其应用非常广泛，在古典力学中的动能，就是最自然直接的凸函数，其他如熵……等均是，连经济学的核心都与之有极密切相关，西方经济学的核心问题是最优化问题，最优化理论又与凸函数与凹函数密切相关。

The decreasing conditions of an energy function are investigated by the use of convex function. By utilization of the primal convex function, the conditions are analyzed under which its conjugate function minus a quadratic function is also convex.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

The paper uses precise step to produce the continuity function of water hammer mathematic model, not only gains more precise water hammer pressure function and water hammer wave speed functionbut also founds correct water hammer mathematic modelContinuity EquationMovement EquationAfter ignoring subordinate facts, function (1) and (2) translate into the current applied water hammer pressure function and water hammer wave speed function.

本论文对水击数学模型中的连续性方程重新进行了严谨的推导，不仅得到了更加准确的水击压强和水击波速的计算公式也建立了正确的水击数学模型连续性方程运动方程当忽略次要因素以后，公式(1)和(2)即可转化为当前应用的水击压强计算公式和水击波速计算公式。

In the first session the fans vibration on-line monitoring system is realized with VC language, also compile auto power spectrum density function, cross power spectrum density function, autocorrelation function and cross correlation function etc spectral analysis function to carry through simple offline fault diagnosis.

首先用稳定性强、扩展性好的VC++语言开发了通风机振动在线监测系统，并编写了自功率谱密度函数、互功率谱密度函数、自相关函数和互相关函数等频谱分析函数来进行简单的离线故障诊断。

The production moved off-Broadway to New York City, where she won the Joseph E. Calloway award for her performance, and was profiled in American Theater Magazine as one of ten young theater artists to watch.

生产提出过百老汇的新的纽约市，在那里她赢得了约瑟夫calloway奖，她的表现，并于异型在美国的战区杂志之一， 10战区的青年艺术家观赏。

It's a risk tradeoff, and I believe that adding test support code usually wins.

这是一个风险的权衡，我相信添加测试代码通常会占上风。