查询词典 equivalent 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。

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。

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。

Chapter 2 is devoted to study of exact solutions of the nonlinear evolution equations. Using solutions of a Bernoulli equation instead of tanh in tanh-function method we find some more general solutions of the KdV-Burgers-Kuramoto equation , and by using the nonlinear telegraph equation we show that there are many different choices on its balancing number m and the power n of the nonlinear term in Bernoulli equation by which we can recover the previously known solutions and also can derive new square root type solitary wave solutions. Exact solitary wave solutions for a surface wave equation are obtained by means of the homogeneous balance method. We also present an approach for constructing the solitary wave solutions and non-solitary wave solutions of the nonlinear evolution equations by using the homogeneous balance method directly, which is also used to find the steady state solutions, solitary wave solutions and the non-solitary wave solutions of the 2+1 dimensional dispersive long wave equations. The soliton-like solutions of the BLMP equation and the 2+1 dimensional breaking soliton equation are found by use of the symbolic-computation-based Method.

第二章中研究了非线性发展方程的精确解：用双曲正切函数法中的双曲正切函数换为Bernoulli方程的解的方法而给出KdV-Burgers-Kuramoto方程的精确解并用非线性电波方程为例说明了平衡数m和Bernoulli方程中非线性项的次数n有着多种选择的可能，它不但使我们能找到已知解而且也能找出新的根式孤立波解；用齐次平衡法给出一个曲面波方程的精确孤立波解，并提出直接用齐次平衡法寻找非线性发展方程的孤立波解、非孤立波解的方法，作为应用给出2+1维色散长波方程组等的定态解、孤立波解、非孤立波解等；用Symbolic-computation-basedMethod获得BLMP方程和2+1维破裂孤子方程的类孤子解；提出sine-Gordon型方程的直接求解方法，并获得sine-Gordon方程、双sine-Gordon方程、sinh-Gordon方程、MKdV-sine-Gordon方程和Born-Infeld方程等的精确孤立波解。

The actinic radiation-curable and cationically polymerizable organic substance is at least one glycidylether of a polyhydric aliphatic, alicyclic or aromatic alcohol having at least three epoxy groups with epoxy equivalent weight between 90 and 800 grams per equivalent, at least one solid or liquid alicyclic epoxide with an epoxy equivalent weight between 90 and 330 grams per equivalent having at least two epoxy groups and monomer purity greater than about 90 % by weight, or at least a solid or liquid epoxycresol novolac or epoxyphenol novolac having epoxy equivalent weight between 130 and 350, or mixtures thereof.

可光化辐射固化并可阳离子聚合的有机物质为至少一种带有至少3个环氧基团环氧当量为90―800克每当量的脂族、脂环族或芳族多元醇的缩水甘油醚，至少一种环氧当量为80―330克每当量带有至少两个环氧基团且单体纯度大于约90wt％的固态或液态脂环环氧化物，或至少一种环氧当量为130―350的固态或液态环氧甲酚线性酚醛清漆或环氧苯酚线性酚醛清漆，或其混合物。

Three classes of equivalent system methods which are used in finding high order flight control systems low order equivalent are studied. The first class methods are the classical frequency domain-based equivalent system methods which recommended by MIL-F-8785C and MIL-STD-1797A. Five longitudinal low order equivalent systems and fourteen lateral ones are discussed in detail and some pieces of advice are given. Also conduct an investigation in the time domain-based equivalent system methods .

研究了求取高增稳飞机的低阶等效系统的几种方法：研究了经典的频域等效系统方法，针对纵向5种、横向14种构型的低阶等效系统进行了拟配实践，并提出一些有益的看法；以频域等效系统方法为基础，提出了时域等效系统新方法；以最小二乘辨识为基础，提出了两种纵向短周期低阶等效系统时域辨识方法(等效延迟时间τ_q参与或不参与)。

The examples show: It is not only scientific and rational approximately, but also as referenced calculational methods of threshold quanlity of increased or emendatory chemical substance in the "Identifecation of major hazard installations "(GB18218-2000) in the future, that appliance respective of TNT equivalent method, gasoline equivalent method, methane equivalent method, methl ethyl ketone peroxide equivalent method and hydrogen sulfide equivalent method for the rhrehold quanlity in the work site and store area of volatile substance, combustible liquid substance, combustible gaseous substance, active chemical substance and poisonous substance. At the same time, Comparing with the death radius method and evaluative method of combustible, volatile, poisonous mojor hazardinstalltions, hazard grading method of hazard degree grading in the chemical factory for the major hazard installations is simplerof operation and more practical of calcutating result, and have some significance on generalizer.

实例验证表明：TNT当量法、汽油当量法、甲烷当量法和过氧化甲乙酮当量法分别对爆炸性物质、易燃液体物质、易燃气体物质和活性化学物质的临界量确定，具有一定的科学性和合理性，可作为《重大危险源辨识》(GB18218-2000)中临界量数值修订和危险物质扩充时进行临界量确定的参考计算方法，同时，化工厂危险程度的重大危险源分级法与易燃、易爆和有毒重大危险源评价法和死亡半径法相比，评估过程简单易行，分级结果符合实际，具有较强的可操作性和一定的推广意义。

In the 2A1 distorted trigonal bipyramid structure ,the single non equivalent Ga atom has the population of 4s 4p ,while the two equivalent Ga atoms have the population of 4s 4p .this compares with a Ga population of 4s 4p in the undistorted D3h structure ,hence the jahn-teller distortion causes depletion of the charge density on the 4s orbital of the non-equivalent Ga atom, and enhancement of charge density on the 4s orbital for the two equivalent atoms .an opposite trend is observed for the 4p orbitals of these Ga atoms .the P population for the two equivalent atoms is 3s 3p .the populations of the other 2B1 state with the edge-capped tetrahedral structure are similar with the exception that all three Ga atoms have similar but not identical populations .

在2A1被变形的三角bipyramid结构，唯一非等效Ga原子有4s 4p的人口，而二个等效Ga原子在未变形的D3h结构有4s 4p 。this的人口和4s相比4p的Ga人口，因此jahn出纳畸变在non-equivalent Ga原子的4s轨道导致电荷密度的取尽，并且电荷密度的改进在4s轨道为二个等效原子。an在趋向对面对这些Ga原子4p轨道被观察。the人口为二个等效原子是另一个2B1状态3s 3p 。the人口与边缘加盖的四面体结构是相似的P 除之外全部三个Ga原子有相似，但不相同人口。

The propose of the research is to insist on the view of applying to solve the various confusion in applying at present when present The Doctrine of Equivalents in China by analyzing dispute in applying of DOE; apply the research method of history analysis and compare synthetically, integrate with the case analysis and draw the conclusion: It is necessary to induct The Doctrine of Equivalents to prevent the tortious people filching the benefit of the inventor and confirm whether the infringed people imitated and copied patent on purpose, it is international tidal current to apply DOE in the processing of patent infringement cognizance, and firstly it must ensure the protecting confine by explaining the claim with compromise explain method, the difference of different extent in patent creation also effect the demarcation of equivalent extension; it should apply the rule of comparing factor one by one rather than comparing the whole equivalent in comparison of equivalents, and needs to be confirmed by increasing the assistant means in the processing of patent infringement cognizance by using Triple Identity Test of Graver; contrast and analyze whether they are equivalent depend on the level of the common technicians in relative domain and it is scientific and reasonable to confirm equivalent time standard by infringement date; in judicial practice of equivalent cognizance, it may use the experiences in Japan for reference to solve the cognizance misunderstanding area of reality in the law and the technology; The superabundance designation that may be understood as a display unfair contract because of neglect and materially misunderstanding should be conditionally applied in current time.

研究目的在于通过分析等同原则在适用上的争议，提出我国适用等同原则时应坚持适用的观点，解决目前在适用中的各种混乱局面；运用历史分析和综合比较的研究方法，结合案例分析；专利侵权认定中引入等同原则是必要的，其实质是防止侵权人窃取发明人的利益，被侵权人是否故意模仿或抄袭专利，不影响等同侵权的判定，运用等同原则判定专利侵权已成为世界性的潮流；适用等同原则首先要对权利要求进行解释以确定保护范围，在解释权利要求时应采取折衷的解释方法，不同专利创造性程度的差异也影响着等同范围的划定；在等同物的比较上，应当适用&逐个要素比较&，而不能适用&整体比较&，在适用&三一致&标准进行侵权认定时，还需要增加辅助手段予以确定；是否构成等同，应当以所属领域普通技术人员的水平来对比分析，以侵权日为等同的时间标准是科学合理的；在等同认定的司法实践中，解决法律事实和技术事实认定上的误区，可以借鉴日本的经验；多余指定可以理解为一个因疏忽大意或重大误解而订立的显失公平的合同，应当在现阶段有条件限制地予以适用。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

Putt your way through 36 fun-filled holes of minigolf on 3D designed courses with elevated greens, bunkers, bridges and water hazards, among other crazy obstacles.

您的推杆方式，通过36个有趣的填孔迷你的三维设计的课程，以提升绿党，掩体，桥梁和水的危害，除其他疯狂的障碍。

Some participles can be used either as attributes or as predicatives.

有些分词既可当定语用，也可当表语用。