abelian equation

abelian equation的基本解释

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阿贝耳方程

与abelian equation相关的网络例句 [注：此内容来源于网络，仅供参考]

In chapter three,we have derived a generalized dual London equation for the Abelian "electric" field A_μfrom the effective dual Abelian-Higgs model.The approximative result and the numerical simulation result as well as their figs were shown via solving the dual Abelian-Higgs model with different methods.Hereby the vortex solution of the chromo-electric field and the vortex energy density were also discussed.Finally,we have studied the dual Abelian-Higgs model with additional vacuum constant,and have unpuzzled the vacuum constant corresponding to the bag model.When the quark sources is introduced, the vacuum constant in the MIT bag model is proportional to the quartic of the monopole mass.

利用不同方法求解该方程，给出了该方程的近似结果和数值模拟结果，并分别对两种情形画出图像作了比较，据此还讨论了色电场的涡旋解及能量密度，最后讨论了含有附加真空常数的对偶阿贝尔-黑格斯模型并对应口袋模型给出了附加真空常数的物理解释，引入夸克源之后还预言麻省口袋模型中的真空常数正比于单极质量的四次方。

Arad and Blau proved that an abelian table algebra can be viewed as a group algebra of some abelian group G. Chapter 3 of this paper gives the structural theorem of abelian table algebras by defining a group structure in table basis. Furthermore, the structure of elementary abelian table algebras is discussed using the number of composition series of table algebras.

Arad和Blau证明了abel表代数等价于某个有限生成abel群G的群代数，受此启发本文第3节通过定义表基的一个群结构给出了abel表代数的结构定理，并从合成列数目的角度对初等abel表代数进行了细致刻画。

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。

与abelian equation相关的网络解释 [注：此内容来源于网络，仅供参考]

abelian equation：阿贝耳方程

abelian differential 阿贝耳微分 | abelian equation 阿贝耳方程 | abelian extension 阿贝耳扩张