查询词典 equivalent equation

In this paper, we will investigate the matrix equation in composition over a complete Brouwerian lattice. First, we give an equivalent condition for the solvability of this equation, i.e. theorem 2.2.3 in this paper: The matrix equation in composition over a complete Brouwerian lattice is solvable iff is the minimal solution of this equation.

本文主要探讨完备Brouwer格上的型矩阵方程，首先给出该类矩阵方程可解的一个等价条件，即本文的定理2.2.3：完备Brouwer格上的型矩阵方程可解的充要条件是是它的解，且是最小解。

A novel method for monitoring the state of transformer windings by identifying parameter of leakage inductance is presented in this paper, using Least Square techniques based on the equivalent equation of transformer leakage inductance. The mathematical model is derived for on-line identification of winding electrical parameter.

以变压器漏电感方程作为绕组参数在线计算的模型，提出了一种利用最小二乘算法进行绕组漏电感参数实时辨识从而实现绕组变形在线监测的方法，推导了用于变压器漏电感参数辨识的方程，针对参数的不可辨识问题提出了解决方案，分析了辨识结果产生误差的原因。

Through creating a differential equation whose oscillation is equivalent to the impulsive equation, or considering the relation between impulsive points and delay, we get some sufficient conditions for the oscillation of the equation.

第二章讨论了二阶自共轭脉冲微分方程，通过建立与之振动性等价的微分方程，或考虑脉冲点与时滞间的关系，我们得出方程振动的一些充分条件。

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。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

By utilizing the expansion expression of equilibrium point of the system, the homogeneous equation s solution was obtained, and then the nonlinear differential equation was equivalent to its nonlinear Volterra's integral equation of the second kind by the constant variation method.

首先将系统在平衡点附近进行展开，求得其齐次方程的解，然后利用常数变易法将非线性微分方程变为等价的第二类非线性Volterra积分方程。

Secondly, for a more general matrix equation in composition, we obtain another equivalent condition for the solvability of this equation and give an equivalent characterization to the solution set of the equation.

第二， 对于一般情况下的型矩阵方程，本文给出其可解的另一个等价条件，同时对其解集作了一个等价性描述。

In the second part, the theory of numerical simulation is introduced, including description of body configuration, elastic-plastic large deformation constitutive equation and finite element formula. It is followed by the derivation of equation from the basic theory of elastic-plastic deformation. The solution to temperature field, thermal stress, thermal strain, equivalent effective stress and equivalent strain is achieved then. In addition, we exposit the relation between machine load and thermal load in coupling analysis.

介绍了物体的构形及其描述，弹塑性大变形的本构方程、有限元列式；并进一步论述了弹塑性变形的基本理论，推导了弹塑性方程组；阐述了温度场的求解、热应力及热应变的理论概要，说明了等效应力与等效应变，并进一步阐明了在热力耦合分析中，机械负荷与温度负荷之间的关系；此外，还简介了Marc AutoForge程序结构的特点。

We can lead out the equivalent border integral equation by Green the second equation,dividing the inner border in the liquid into a series strip of awls shell or cylindrical shell ,and solve border integral equation along different segment of border, then lead out border integral equation.

由Green第二恒等式导出等价的边界积分方程，将液体内边界分成一系列锥壳或柱壳状条，对边界积分方程进行分段积分，导出边界元格式方程。

Nonlinear partial differential dynamic equations of bending vibration of a tilting stepped drive shaft with two supports were built under non-inertia movement coordinate system by theorem of the motion of mass center and Heaviside function. According to the condition of equal displacement in an adjoining plane of the shaft, an equivalent shaft and its equation were obtained. A motion equation of the equivalent shaft was obtained by method of Galerkin. An approximate steady-state solution of the main resonance was obtained by method of multiple scales. The influence factors, motion stability, amplitude jump of main resonance of a stepped drive shaft and so on were analyzed.

用质心运动定理、Heaviside函数建立了非惯性系下倾料两端支承阶梯传动轴的非线性弯曲振动偏微分动力学方程，并根据相邻轴段的衔接面处位移相等的条件，得到阶梯轴的当量轴及其动力学方程；用Galerkin法得到当量轴的弯曲运动方程，用多尺度法求得稳态下当量轴的主共振的一次近似定常解，分析了影响阶梯传动轴主共振的因素、运动稳定性、振幅突变性等。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。