A representation for the velocity and pressure fields in three-dimensional Stokes flow was presented in terms of a biharmonic function A and a harmonic function B.This representation was used to establish a general th...A representation for the velocity and pressure fields in three-dimensional Stokes flow was presented in terms of a biharmonic function A and a harmonic function B.This representation was used to establish a general theorem for the calculation of Stokes flow due to fundamental singularities in a region bounded by a stationary no-slip plane boundary.Collins's theorem for axisymmetric Stokes flow before a rigid plane follows as a special case of the theorem.A few illustrative examples are given to show its usefulness.展开更多
In this paper, using the orthonormal multiresolution analysis（MRA） of L^2（R^s）, we get two important properties of the scaling function with dilation matrix A = MI of L^2 （R^s）. These properties axe chaxacterize...In this paper, using the orthonormal multiresolution analysis（MRA） of L^2（R^s）, we get two important properties of the scaling function with dilation matrix A = MI of L^2 （R^s）. These properties axe chaxacterized by some inequalities and equalities.展开更多
Fourier series is an important mathematical concept. It is well known that we need too much computation to expand the function into Fourier series. The existing literature only pointed that its Fourier series is sine ...Fourier series is an important mathematical concept. It is well known that we need too much computation to expand the function into Fourier series. The existing literature only pointed that its Fourier series is sine series when the function is an odd function and its Fourier series is cosine series when the function is an even function. And on this basis, in this paper, according to the function which satisfies different conditions, we give the different forms of Fourier series and the specific calculation formula of Fourier coefficients, so as to avoid unnecessary calculation. In addition, if a function is defined on [0,a], we can make it have some kind of nature by using the extension method as needed. So we can get the corresponding form of Fourier series.展开更多
文摘A representation for the velocity and pressure fields in three-dimensional Stokes flow was presented in terms of a biharmonic function A and a harmonic function B.This representation was used to establish a general theorem for the calculation of Stokes flow due to fundamental singularities in a region bounded by a stationary no-slip plane boundary.Collins's theorem for axisymmetric Stokes flow before a rigid plane follows as a special case of the theorem.A few illustrative examples are given to show its usefulness.
基金Supported by the Natural Science Foundation of Ningxia Province(NZ0691)
文摘In this paper, using the orthonormal multiresolution analysis（MRA） of L^2（R^s）, we get two important properties of the scaling function with dilation matrix A = MI of L^2 （R^s）. These properties axe chaxacterized by some inequalities and equalities.
文摘Fourier series is an important mathematical concept. It is well known that we need too much computation to expand the function into Fourier series. The existing literature only pointed that its Fourier series is sine series when the function is an odd function and its Fourier series is cosine series when the function is an even function. And on this basis, in this paper, according to the function which satisfies different conditions, we give the different forms of Fourier series and the specific calculation formula of Fourier coefficients, so as to avoid unnecessary calculation. In addition, if a function is defined on [0,a], we can make it have some kind of nature by using the extension method as needed. So we can get the corresponding form of Fourier series.
