查询词典 adjoint difference equation

In this topic, the dynamic analysis methods for piezoelectric vibrator are studied systematically based on the theoretical model, FEM numerical experimentation and FEM governing equation for given compound-mode vibrator, and some valuable conclusions are obtained. The main work accomplished is summarized as follows: 1.Elaborate the main modeling methods for piezoelectric vibrator and the significance and necessity to study the dynamic characteristics of piezoelectric vibrator which emphasize the urgency of this paper. 2.Take the bending deformation induced by piezoelectric ceramic as example, the energy transfer mechanism of electric energy to mechanical energy are analyzed; the motion and force transfer mechanism are analyzed for the longitudinal-bending vibrator. 3.Based on mode assumption and Hamilton principle, the coupling model of piezoelectric vibrator of linear USM is built; moreover, the equivalent circuit model is obtained and a coupling equation represents the relation between electric parameters and mechanical parameters is derived which provides foundation to match the vibrator and driving circuit. 4.Combine the constitutive equation of piezoelectric ceramic with elastic-dynamical equation, geometric equation in force field and the Maxwell equation in electric field and the corresponding boundary condition equation, the FEM control equation for piezoelectric vibrator of USM to solve dynamic electro-mechanical coupling field is established by employing the principle of virtual displacement. The equation lays the foundation to study the non-linear constitutive equation of piezoelectric ceramic driven by high-power. 5.Define the dynamic indexes of characteristic of vibrator and carry out variable parameters simulation by calculating the model parameters and the electric characteristics of vibrator are simulated according to the equivalent circuit model. By numerical experimentation, the working mode of vibration of vibrator and the shock excitation results of the working frequency band which provides the mode frequency to realize bimodal are analyzed. Detailed calculation of the electro-mechanical coupling field parameters is made by programming the FEM control equation.

本课题从理论模型、有限元数值试验、有限元控制模型等方面以复合振动模式振子为例对超声电机压电振子的动力学特性及其分析方法进行了全面系统地研究，得出了许多有价值的结论，主要概括如下： 1、阐述了目前针对超声电机压电振子的主要建模方法，对压电振子动态特性的研究意义和必要性进行了论述，突出了本文研究内容的迫切性； 2、以压电陶瓷诱发弹性体发生弯曲变形为例，分析了压电陶瓷通过诱发应变来实现机电能量转换的机理；对基于纵弯模式的压电振子的运动及动力传递机理进行了分析； 3、基于模态假定，利用分析动力学的Hamilton原理，建立了面向直线超声电机压电振子的机电耦合动力学模型，并据此建立了压电振子的等效电路模型，导出了电参量与动力学特性参量的耦合方程，为压电振子与驱动电路的匹配提供了依据； 4、从压电陶瓷的本构方程出发，综合力场的弹性动力学方程、几何方程、电场的麦克斯韦方程以及相应的边界条件方程，采用虚位移原理，建立了压电振子动态问题机电耦合场求解的有限元控制方程，为研究其大功率驱动下的非线性本构模型奠定了基础； 5、界定压电振子的动力学特性指标，对压电振子的机电耦合动力学模型参数进行计算及变参数仿真；依据等效电路模型，对压电振子的电学特性进行了仿真分析；通过有限元数值实验，对压电振子工作模态附近的模态振型及工作频率附近的频段进行了激振效果分析，找出了实现模态简并的激振频率；利用有限元控制方程，通过编程计算，对压电振子的力电耦合场参数进行了详细计算，得出了一些有价值的结论。

In this paper,a systematic direct perturbation method of dark solitons is found.Having analyzed the mistakes in earlier works on perturbation method for dark solitonsand essence of the direct perturbation method for bright solitons,we notice that to in-troduce the adjoint solutions of the squared Jost solutions and to prove the completenessare crucial to the problem.Giving up the unnecessary scheme of introducing the adjointoperator in the bright soliton case,we directly find the adjoint solutions by meetingthe demand for the orthogonality that inner product of the squared Jost solutions andits adjoint should be proportional to a δ function in the case of continuous spectra.The corresponding adjoint operator is thus found.Taking into account the reductiontransformation,we find a correct description for the completeness of the squared Jostsolutions and directly verify its validity with explicit expressions of the squared Jostsolutions.

本论文建立了系统的暗孤子直接微扰方法，在对前人关于暗孤子微扰方法的错误以及亮孤子直接微扰方法的本质作了充分的分析后，认识到引入平方Jost解的伴随解和证明完备性是问题的关键，撇开过去亮孤子情况首先引入伴随算子的非必要作法，直接从平方Jost解与其伴随解的内积在连续谱时正比于δ函数这一正交性要求出发，找出了伴随解，同时得出了应有的伴随算子，在考虑到约化变换性后，得到了暗孤子情况的平方Jost解的完备性的正确表述，并在单个暗孤子的情况利用平方Jost解的显式直接验证了它的正确性。

The optimal control law obtained consists of linear analytic functions and a compensation term which is a series sum of the adjoint vectors. The analytic functions can be found by solving a Riccati matrix difference equation and a matrix difference equation. The compensation term can be obtained by a recursion formula that solves adjoint vector equations.

得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成，其解析函数由一次性求解Riccati矩阵差分方程和矩阵差分方程得到，补偿项由求解伴随向量差分方程的递推公式得到。

How to establish the adjoint medel is discussed by using the Gateaux differential of function and the concepts of the adjoint operators in Hibert space. At the same time it is verified that selecting proper finite difference scheme can ensure discrete form remaining the same adjoint r...

文中利用泛函的Gateaux微分和Hilbert空间上伴随算子的概念讨论了连续的伴随模型的建立，并通过选择适当的差分格式离散伴随模型，使其保持连续时的伴随关系，同时给出了水温初始场最优化过程及相应的同化试验数值结果。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程，如矿方程，Klein-Gordon方程，Sine-Gordon方程，及Sinh-Gordon方程的近似，Landau-Ginzburg-Higgs方程，Duffing方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到n+1维空间情形。

Furthermore data assimilation experiments are conducted with MM5 Adjoint-model Assimilation System made by adjoint codes. With a case of heavy rainfall taking place from 00h July 23 to 00h July 24,2002, several numerical simulation experiments of different schemes are performed. The results are as follows. MM5 Adjoint-model Assimilation System not only can improve the initial field effectively and promote the coordination with the model but also can enhance the forecast on the precipitation and other elements. The assimilation of CDW has an improvement on quality of upper wind. The effect of direct numerical simulation with utilizing the CDW to amend the initial field gains the advantage over the one not.

结果表明，MM5伴随模式同化系统能有效改善初始场与模式的协调能力，提高模式对于降水场和其它要素场的预报；使用云导风资料修正初始场后直接模拟的效果比未使用时直接模拟的效果要好，对部分区域的强降水预报精度有一定程度的改善；使用伴随模式同化系统后，加入云导风资料的同化试验对其它要素的改善与直接同化常规资料的效果相比，改善优势不明显，但从各要素的误差来看，对于风场的改善最好。

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

We also give all positive self-adjoint extensions ofsingular differential operators,and all positive self-adjoint operators generated by theproducts of differential expressions 〓,where l is an nth order differentialexpression.The result that each positive self-adjoint operator is not necessarily theform of operator product 〓.This answers an open problem proposed by theauthors recently.

我们也给出了奇型微分算子的所有正自伴扩张形式及乘积微分算式〓所诱导的所有正自伴算子形式，证明〓所诱出的正自伴算子不必须是由算子乘积〓为l所生成的算子）的形式，从而回答了作者新近提出的一个公开问题。

To further investigate the influence of the Internet on the students, a further research is conducted by breaking the students into three groups -frequent Internet users, occasional Internet users and non-internet users. The result indicates that the self-harmony of frequent Internet users shows a sharp difference in terms of school and grade, the self and the unharmony of show a sharp difference in terms of school, grade and sex, and that the self-esteem and the two dimension - the flexibility and rigidity of self-harmony show no difference in terms of school, age and sex; the self-harmony and all dimensions of occasional Internet users show no significant difference, the self-esteem of occasional Internet users show no significant difference in terms of school and grade but show significant difference in terms of sex; the self-harmony and all dimensions of the non-Internet users show no significant difference, the self-esteem of the non-Internet users show no significant difference in terms of grade and sex, and the self-esteem of the non-Internet users show significant difference in terms of school.

为了进一步研究网络对学生的影响，又将学生分为经常上网、偶尔上网、不上网三类分别来研究：经常上网学生自我和谐在学校、年级都存在极显著差异，自我与经验的不和谐在学校、年级、性别存在极显著差异，自尊和自我和谐的灵活性和刻板性两个维度在学校、年龄、性别都没有差异；偶尔上网学生，自我和谐及各维度都不存在显著性差异，自尊在学校和年级不存在显著性差异，在性别上有显著性差异；不上网学生自我和谐及各维度都不存在显著性差异，自尊在年级和性别不存在显著性差异，自尊在学校上有显著性差异。

Establish the steady-state and transient model using the three hydrodynamics equations (Continuity equation, Momentum equation and Energy equation). By comparing different state equation, it selects the BWRS state equation which is considered the most accurate state equation in current natural gas measurement. It calculates compression factor, density and other Thermal parameters based on BWRS state equation. In Numerical solution of the steady-state and transient model, compression factor, friction coefficient and all the other Thermal parameters are recalculated in each small time step to reduce the numerical calculation error.

在稳态模型的建立上，利用流体力学三大方程(连续性方程、运动方程和能量方程)，通过比较不同的状态方程选用了目前被认为最精确的用于天然气计量的BWRS状态方程，并以此方程为基础进行压缩因子、密度等热物性参数的计算；在稳态模型的求解上，选用容易计算，精度较高的标准型龙格—库塔(Runge-Kutta)法进行数值求解，并且在迭代过程的每一小步都重新计算燃气的压缩因子，摩阻系数等所有的计算参数，以减少数值计算的误差。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。