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Nonlinear flexural wave equation is solved by the Jacobi elliptic function expansion method. Two kinds of exact periodic solutions of the nonlinear equations are obtained, that is, the shock wave solution and the solitary wave solution. The necessary condition for existence of exact periodic solutions, shock solution and solitary solution is discussed, which is consistent with the qualitative analysis.

利用Jacobi椭圆函数展开法,对该非线性方程进行求解,得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解,讨论了这些解存在的必要条件,这与定性分析的结果完全相同。

The Jacobi elliptic function-like solution and trigonometric function solution of variable coefficient KP equation.

获得了变系数KP方程新的类孤波解、类Jacobi椭圆函数解和三角函数解。

In long wave limit, these elliptic function wave patterns may degenerate into single valued localized excitations dromion and multi-lumps.

椭圆函数传播波之间的相互作用是非弹性的,而在长波极限下相应相干孤子激发Dromion,Lumps之间的相互作用可以是弹性的,也可以是非弹性的。

Two novel spherical helical antennas can be designed by projecting the planar equiangular spiral antenna onto the surfaces of hemisphere and partial sphere. Their radiation properties are analyzed by the moment method with curved basic and testing function, and the curves of the VSWR, gain, polarization and pattern vs.

将平面等角螺旋天线投影到半球面和部分球面上,可得到两种新型球面螺旋天线,采用基于曲线基函数的矩量法对其辐射特性进行了分析,给出了天线的驻波、增益、极化及方向图等随频率变化的曲线。

The empirical wavelet coefficients of the error variance in the model are given and shown to be asympototically i.i.d. normal.

首先给出了回归模型的条件方差函数的经验小波系数,然后证明了它们是渐近独立和正态的。

The time correlation function of concentration fluctuation for PSt-DVB having wave vector q is proved to have the form of an exponential decay.

该微粒的浓度涨落时间相关函数在波矢为q时,有指数衰减形式,其衰减速率г=q2Dt。

The thought based on the hyperbola function method is extended,and more explicit and exact solutions are successfully derived,including shock wave type solutions with break point and exponential function type solutions .

在此基础上又对双曲函数法的思想进行了推广,从而获得了其更多的显式精确解,包括间断型激波解和指数函数型解。

To this end, we systematically investigate the some properties of m-band compactly supported orthogonal multiwavelets system related to each type symmetric center filter.

从一个给定的具有对称性质的m带紧支撑正交多尺度函数出发,欲构造也具有对称性质的m带紧支撑正交多小波,可转化为对给定矩阵的对称仿酉扩充问题。

Like Fourier analysis, any function with finite energy can be expanded on the orthonormal wavelet bases.

与Fourier分析方法一样,任意的能量有限函数可以用小波正交基展开。

According to the relation spectrum resolution is inverse proportional to focal distance given a certain incident wavelength and phase number,and the theoretic formula is consistent with reported experimental result.

光谱分辨率是评价衍射微透镜分光特性的主要指标,根据标量衍射理论,给出了多台阶位相型菲涅尔透镜的设计公式,并利用球面波的传输理论推导了微透镜主焦距与光谱分辨率之间的函数关系,得出在入射波长和位相台阶数一定的情况下,光谱分辨率与中心焦距之间呈反比;理论推导的结果与已发表的实验结果一致。

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