查询词典 eigenfunctions

Under the constraints between potentials and eigenfunctions, the Lax systems are nonlinearized to be finite dimensional completely integrable systems in Liouville sense.

在位势与特征函数之间的约束条件下，Lax系统被非线性化成为有限维Liouville完全可积系统。

Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励，通过随机平均法，Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题，其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

The eigenvalues and eigenfunctions of Laplacian with Dirichlet boundary condition on equilateral triangles are derived from one dimensional representation of D3 group.

由D3群一维表示，得到了正三角形上满足Dirichlet边界条件拉普拉斯算子的本征值和本征函数，并讨论了本征函数的对称性。

In this paper we mainly utilize super and sub solution techniques, use comparision principle and construct appropriate supersolution and subsolution by eigenfunctions to discuss two kinds of nonlocal nolinear parabolic systems with homogeneous Dirichlet boundary condition.

两类非线性抛物方程解的整体存在与爆破性质本文主要利用上下解方法，运用比较原理，通过特征函数等构造适当的上下解讨论了两类抛物型方程组解的整体存在与爆破。

They are the deflection w, the rotations of the normal to the undeformed median surface Φx,Φy and the force function F. In the present paper these dependent functions are expressed as generalized double Fourier series with beam eigenfunctions as general terms.

本文中将这四个独立的函数表示为广义傅里叶级数，选用了两个变量分离的梁本征函数之积构成广义傅里叶级数的通项，通过梁本征函数中的待定常数使所选级数预先满足简支、固支或弹性支持边界条件。

Since we get continuous rather than discrete allowed values for E0, the positive-energy eigenfunctions are called continuum eigenfunction

由于对E≥0得到连续的而非分立的允许值，正能量的本征函数叫做连续谱本征函数。

Thus, we get the eigenfunctions and eigenvalues of a class of the singularly perturbed eigenvalue problem with the turning point.

本文研究一类具有转向点的二阶方程在大特征值的情形下的奇摄动特征函数和特征值问题。

A Green function expression and an equivalent generalized Fourier expansion with corresponding Sturm-Liouville eigenfunctions and eigenvalues are given.

给出了用格林函数表示的普遍解和相应的Sturm-Liouville本征函数及本征值。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

Making use of a generalization of Brillouin-Wigner perturbation theory, in this project, we have studied such a division of energy eigenfunctions and properties of eigenfunctions in their perturbative and non-perturbative regions.

本项目利用推广的布里渊-维格纳微扰论研究了本征函数的这种划分，以及微扰与非微扰区的本征函数的性质。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷