查询词典 kernel of integral equation

The bilinear form of BBM equation has known, so we can similiarly get the bilinear form of associated DGH equation, then we can get the bilinear form of DGH equation and 1-soliton by a approciate method.

BBM方程的双线性已知，通过恰当的设法可以类似得到关联DGH方程的双线性形式，即得到了DGH方程的双线性形式，并由此得到了DGH方程的1—孤子解。

This paper, considers conservative equation with periodic boundary value problem, and construct a difference scheme, Uses the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, proves that the scheme converges uniformly to the solution of differential equation with order one.

研究守恒型奇振动方程的周期边界问题，构造一个差分格式，利用分解解的奇性项的方法，结合问题的渐近展开，证明所构造的差分格式为一阶一致收敛。

It is a global convergence method, so it can avoid the drawback of the Newton method. The main idea is to perturb the TV-norm functional term of the Euler-Lagrange equation so large that it can be solved by the Newton method when the observed image is an initial value, and we regard this equation as an auxiliary equation.

它的主要思想是将Euler-Lagrange方程中TV-范数做一个足够大的扰动，得到一个能用以观测图像z为初值的牛顿法求解的辅助方程，通过构造同伦方程将辅助方程和Euler-Lagrange方程联系起来。

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。

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。

It's bell can reach over a meter in diameter.

它的身体最大可以达到直径1米多。

Now they are overdue and I shall have to pay a fine.

现在他们过期了，我不得不付罚款。