查询词典 reciprocal equation

By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.

利用一个新的辅助椭圆方程将求解非线性发展方程精确解的问题转化为一个代数方程组进行求解，与已有的辅助椭圆方程法的主要不同是，应用这一新的辅助椭圆方程后降低了平衡次数，减少了所得的代数方程组的个数和方程的项数，从而大大地简化了代数方程组的求解。

Combined KdV equation; Generalized KdV equation; Reduction-order method; Auxiliary differential equation technique; Solitarywave solutions; Periodic solutions; Solitons; Algebraic travelling wave solutions; Physical structures

基础科学，数学，数学分析KdV-mKdV方程；广义KdV方程；降阶法；辅助微分方程；孤波解；周期解；孤子解；代数行波解；物理结构

By means of variable substitution, it is found that the differential equation of motion is a Bessel equation. Based on the equation, responses of elastic displacement, velocity, acceleration of skip and cable tension close to sheave were deduced.

通过变量代换，发现箕斗运动微分方程是可求解的Bessel方程，从而得到了装载过程中箕斗的弹性位移、速度、加速度和天轮处钢丝绳的张力的解析表达式。

ABSTRACT For an infinite soft ferromagnetic elastic crack material, the controlling equation for the plane problem is derived based on the linear theory of Pao and Yeh. Then it is reduced to a biharmonic equation combined with a harmonic equation.

对处于面内磁场中的含穿透裂纹无限大软铁磁弹性体，本文基于Pao和Yeh的磁弹性耦合线性化理论，通过推导，把问题的控制方程表示成一个重调和方程和一个调和方程，而得到问题的复势解。

By transforming the interlace series type linear differential equation with coefficient containing binomial coefficients and arrangement number into the linear differential equation of successive integral,the theory and method for solving this kind of equation are determined.

通过把系数含有二项式系数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并通过实例介绍了它的应用。

The binomial deliverability equation can only be used to describe the high velocity non-Darcy filtering flow. For low permeability fracturing gas wells, due to low permeable property and high flow conductivity of the formation, the filtering flow laws of the formation are different from those before fracturing, and binomial deliverability equation can not be used for the flow condition of gas wells, therefore, new equation is needed.

二项式产能方程只能描述高速非达西渗流，对于低渗压裂气井，地层的低渗透性和裂缝的高导流能力使得其渗流规律已经和压裂前大不一样，二项式产能方程已无法描述气井的生产状况，必须建立新的方程。

Double angle formula can transform the circular function equation to a biquadratic algebraic equation,and the analysis solution can be solved by extract equation directly.

用倍角公式可将该三角函数方程转化成一个四次代数方程，然后用求根公式直接求出解析解。

Moreover, it makes the coefficient matrix of centralized IPM's linear correction equation a block diagonal bordered matrix, which can be decomposed into the constraints equation on internal variables of independent sub-areas and coupled constraints equation. During each IPM iteration, internal variables and coupled variables are solved distributedly; thus distributed algorithm of multi-area ORPF is implemented.

在此基础上，论文将该线性方程分解为相互独立的子区域内部约束方程和复制节点的耦合约束方程，在每次内点法迭代中分布分块求解内部变量和耦合变量，从而实现多区域无功优化的分布式计算。

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

对结构声辐射的边界积分方程的内部形式与外部形式进行了详细的推导，给出了角点系数的计算方法与边界积分方程的形式，在此基础上，分析了奇异积分产生的原理及其对数值计算的重要性，提出了一种计算奇异积分的非等参(来源：Ae8a8BC论文网www.abclunwen.com)单元的变换方法，该方法给Helmholtz 声学边界积分方程中的弱奇异积分与Cauchy 奇异积分的计算以及编程提供了极大便利。

From the ionization constant and electrical neutral principle of weak acid solution, we can draw out chemical balance equation of acid radical ion of acid salt, electric charge conservation equation and supplies conservation equation.

根据弱酸的电离常数和溶液的电中性原理等，可导出其酸式酸根离子的化学平衡式、电荷守恒式和物料守恒式，判断酸式酸根离子所引起的溶液酸碱性及其强弱，从而得出定量判据

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。