查询词典 exponential equation

In chapter four,at first,we investigate classification theory of the positive homogeneous p-Laplacian equation ,the main method is Prufer's transformation,and then we discuss the nontrivial solution for associated nonhomogeneous equation by making use of Leray-Schauder degree.

接着研究了非齐次方程的可解性。在第四章中，我们首先是建立了正齐次p-Laplacian 方程的分类理论，主要利用Prufer 变换。再应用Leray-Schauder 度理论证明非齐次方程的可解性。

Some new solutions of an auxiliary ordinary differential equation are obtained, which were neglected by Sirendaoreji etc. in auxiliary equation method.

得到了一个辅助微分方程的一些新解，这些解在Sirendaoreji等的辅助方程方法中没有给出。

Global asymptotic stability of a class of nonlinear rational difference equation s was studied by means of setting up an auxiliary equation,so that a sufficient condition was obtained.

运用建立辅助方程的方法研究一类非线性有理差分方程正平衡点的全局渐近稳定性，得到一个充分条件。

By utilizing the auxiliary ordinary differential equation and its solutions, the first kind and second kind of KdV equation with variable coefficients were investigated by means of the extended tanh-function method, and abundant new exact solitary wave solutions were obtained under certain conditions.

利用该方程及其解，采用改进的tanh函数展开法研究了第1类和第2类变系数KdV方程，获得了在一定条件下的若干新精确孤波解。

Moreover, existence of analytic solutions for a linear iterative equation with variable coefficients is given by reducing to an auxiliary equation and using Schauder's fixed point theorem.

此外，本章还使用Schauder不动点定理，通过建立辅助方程，研究了变系数的线性型迭代方程解析解的存在性。

Moreover, existence of analytic solutions for a linear iterative equation with variable coefficients is given by reducing to an auxiliary equation and using Schauders fixed point theorem.

此外，、本章还使用Sehauder不动点定理，通过建立辅助方程，研究了变系数的线性型迭代方程解析解的存在性。

Firstly, using strategy of introducing associated auxiliary equation to a givenpartial differential equation without admitting Lagrangian, we make the extendedequations possess a variational principle. Based on this, the concepts of extendedconservation law and extended symmetry to given partial differential equationare put forwarded.

首先，我们给出了引入伴随方程扩充原方程的策略，使给定偏微分方程的扩充方程组具有对应泛函，即称为Lagrange系统的方法，以此为基础提出了作为偏微分方程传统守恒律和对称概念的一种推广—偏微分方程扩充对称和扩充守恒律的概念；其次，先给出以得到的Lagrange系统为基础，利用N？

Rational Difference Equation; Global Attractively; Global Asymptotical Stability; Subsequence; Auxiliary equation

基础科学，数学，数学分析有理差分方程；全局吸引性；全局渐近稳定性；半环；辅助方程

Although the Preissman scheme of KP equation is multisymplectic, it took too efforts to realize, Hence we elimate the auxiliary variable by a trivial computation and obtained the multisymplectic forty-five points scheme of KP equation. And then, we test this forty-five points scheme on soliton and solitary waves over long time intervals, the numerical results shows the propagation and interact of soliton and solitary waves.

但是在实际的数值实验中，由于需要计算共轭动量的值，Preissman格式需要占用的计算内存比较大，计算时间比较长，因此我们在数值格式中消去共轭动量，最后得到与多辛Preissman格式等价的一个多辛45点格式，我们用这个格式进行了数值实验，数值实验结果很好地显示了孤立子和孤立波的传播与碰撞。

Firstly, based on natural gradient and nonlinear principal component analysis, a matrix equation is obtained by block recursive updating,and then the matrix equation is solved using QR factorization and back substitution to obtain the optimal separating matrix.

此外，结合自然梯度和非线性主分量分析提出了一种块递归的盲源分离方法，构造出按块递归更新的矩阵方程，然后用QR分解和回代法求解该矩阵方程得到最优分离矩阵。

Pradeep Indulkar, a senior official at the Maharashtra state Home Ministry say 101 human were killed and 287 injured.

马哈拉施特拉邦内政部高级官员Pradeep Indulkar称，有101人在冲突中丧生，287人受伤。

Mark Frei, a senior vice president of West, says 80% of West's homeagents have some college education, compared with 30% of those whowork in office-based call centers.

Frei说，该公司80%在家办公的人员都拥有本科学位，而在公司电话中心工作的人中只有30%拥有本科学位。