查询词典 variational method

In this paper we separate the Hamiltonian into three parts: a spherical symmetry Hamiltonian; a z-component of the angular momentum operator, and a non-spherical symmetric potential as the perturbation operator, and provide a propose method by separating the potential containing squared magnetic field B^2 into two parts spherical symmetric and non-spherical symmetric ones so that the first-order energy correction due to the non-spherical symmetric potential is zero, and the second-order correction due to B^2 can be obtained by a simple variational method.

采用变分法和微扰法相结合的方法，把高强度磁场中氢原子的哈密顿H分为三部分：球对称哈密顿；z分量角动量算符相应部分和非球对称势微扰，并用一种特别规定的分解法将哈密顿H中含磁场平方项的势能分解为球对称与非球对称两部分，且使非球对称部分引起的一级修正能量值为零，并采用一种简便的变分法直接求出B^2对能级的二级修正值。

Making use of field matching method,combining with the variational method,the dispersion equation of the ridge loaded ring plane slow wave structure and small signal gain of this type of TWT are presented in this paper.

脊加载环板行波管是一种频带相对较宽的大功率行波管，本文用场匹配和变分原理相结合的方法，研究了脊加载环板慢波结构的导波特性及这种行波管的小信号、大信号特性，讨论了结构的几何尺寸及电子注参量对慢波的传播特性、小信号增益及注波互作用非线性效应的影响。

The numerical method of the variational principle combined with finite element method is presented in the paper.

文中介绍了运用该变分原理并结合有限元方法进行数值计算的方法。

In Chapter 5, A new variational grid optimization method is presented. The functional used in this method comprises of two parts.

在第五章中，提出并实现了一种新的靠近拉氏网格的网格优化方法。

At present, people usually solve ill-posed problems by variational method anditerative method.

目前，人们通常采用两种途径求解不适定问题：一个是变分法，一个是迭代法。

Traditional sports teaching method,already could not adapt the new times sports curriculum to reform; this article means which through the literature law, the questionnaire investigation law, the cut-and-try method unifies, carries on the comparison to the traditional each sports teaching method, discovered the sports competition teaching method can adapt the new times student sports demand; the competition teaching method is unifies the traditional teaching method in the foundation one new teaching method, proved through the experiment, its teaching effect is good.

一些传统的体育教学思想、教学理念、教学方法、教学模式已经不能够适应现代教学的需要，在此过程中，为提高教学质量，就必须对教学方法进行改革。作为体育教学，如何进一步转变体育教育思想，深化体育教学改革，摆脱旧的传统的教学体系、思想体系和理论模式，逐步形成一个新型的，具有中国特色的教学过程和教材体系，使我国体育教学面向未来社会的需要，跟上21世纪学校体育发展的需要，是本文探讨和研究的问题。

Among used machine learning methods, the gradient descent method is widely used to train various classifiers, such as Back-propagation neural network and linear text classifier. However, the gradient descent method is easily trapped into a local minimum and slowly converges. Thus, this study presents a gradient forecasting search method based on prediction methods to enhance the performance of the gradient descent method in order to develop a more efficient and precise machine learning method for Web mining.However, a prediction method with few sample data items and precise forecasting ability is a key issue to the gradient forecasting search method. Applying statistic-based prediction methods to implement GFSM is unsuitable because they require a large number of data items to model a prediction model. In the contrast with statistic-based prediction methods, GM(1,1) grey prediction model does not need a large number of data items to build a prediction model, and it has low computational load. However, the original GM(1,1) grey prediction model uses a mathematical hypothesis and approximation to transform a continuous differential equation into a discrete difference equation in order to model a forecasting model.

其中梯度法是一个最常被使用来实现机器学习的方法之一，然而梯度法具有学习速度慢以及容易陷入局部最佳解的缺点，因此，本研究提出一个梯度预测搜寻法则(gradient forecasting search method， GFSM)来改善传统梯度法的缺点，用来提升一些以梯度学习法则为基础的分类器在资讯探勘上的效率与正确性；而一个所需资料量少、计算复杂度低且精确的预测模型是梯度预测搜寻法能否有效进行最佳解搜寻之关键因素，传统统计为基础之预测方法的缺点是需要较大量的数据进行预测，因此计算复杂度高，灰色预测模型具有建模资料少且计算复杂度低等优点，然而灰色预测理论以连续之微分方程式为基础，并且透过一些数学上的假设与近似，将连续之微分方程式转换成离散之差分方程式来对离散型资料进行建模及预测，这样的作法不尽合理，且缺乏数学理论上的完备性，因为在转换过程中已经造成建模上的误差，且建模过程仅考虑相邻的两个资料点关系，无法正确反应数列未来的变化趋势。

A mixed method of conjugate gradient method and steepest descent method ;2. The Modified Steepest Descent Method──Best Point in Steepest Descent method;3. This paper presents the mathematical model for the optimization of heterogeneous components, and the method using sensitivity analysis and steepest descent method to optimize material properties, the component is then identified.

阐述了非均质材料零件设计优化的数学模型，并采用灵敏度分析以及最速下降法对其各个材料区域的材料性能进行设计优化，得到最佳材料性能参数后，再从非均质材料数据库中找到相应的工程材料，合成满足设计要求的非均质材料零件该方法为设计者提供了切实可行的非均质材料零件的材料设计方

By using accelerating Aitken method in iterative method of nonlinear equations, a new modified method is given. The method is applied to modified Newton method, thereby a new method is developed, which is faster and stable. Also, its algorithm is given. Numerical results show that the new method is very efficient.

通过对非线性方程组的迭代法引入Aitken加速技术，设计了一种非线性方程组的迭代解法的加速方法；将该方法与M步Newton法相结合，得到一种收敛速度快而且计算稳定的方法，并给出了具体算法；数值结果表明了新算法是有效的。

On the design of algorithms, a novel exact hierarchical delay analysis method for general circuits is proposed; based on the sensitization theorem for sequential circuits, an exact minimizing clocking method is proposed; based on Boolean process, a waveform simulation method considering interconnecting delay for logic circuit and a parallel waveform simulation method are proposed; a new method that transforms bit-level waveform polynomial to word-level polynomial model is proposed; a multiple valued synthesis algorithm based on multiple valued Boolean process and a wire-centered delay synthesis policy are proposed, in which timing planning, floorplanning, wire planning and optimal clock skew in early design are considered; a two-layers channel routing method for minimizing crosstalk under grid mode is proposed; based on the transition numbers theorems for waveform polynomial, a new method for generation of test with noise effects is proposed.

算法设计方面，提出了一种精确的通用电路层次化延时分析方法；基于时序电路的敏化定理提出时序电路最小时钟周期精确确定方法；提出基于Boolean过程论的考虑互连延迟的逻辑电路波形模拟方法，在分析了波形模拟适合并行化基础上，进一步提出一种并行波形模拟算法；提出一种将位级电路波形多项式描述转化成字级多项式描述的新方法；提出一种基于多值Boolean过程的多值电路综合算法以及一种将前期设计定时规划、前期设计的布局规划和线网结构化方法及低偏移的时钟分配等技术相结合的面向互连延时的综合策略；提出一种串绕最小化的网格模式下的双层通道布线方法；从波形多项式描述跳变数的定理出发提出了一种考虑噪声效应的测试生成新方法。

Summary In copyright infringement cases,if the alleged infringer uses or even plagiarizes the copyrighted works or parts thereof,which causes no substantially adverse effect on the normal exploitation of the work,nor does it inflict any substantial damages to the right owner,the de minis doctrine should be applied to exempt the liabilities of the defendant and seek the balance of interests between the right owner and the general public embodied by the copyright law.

在侵犯著作权案件中，如果被控侵权行为人虽未经著作权人的同意，使用甚至抄袭了受著作权保护的作品或作品的片段，但若情节轻微，未对该作品的正常使用产生任何实质不利的影响，亦未对权利人的权利造成实质性的损害，则应适用&不计琐细原则&，免除行为人的责任，以寻求在权利人利益与著作权法所体现的社会公共利益之间的平衡。

This new product will become our best seller.

这个新产品会成为我们最畅销的产品。