This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists ...This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients展开更多
We have set up the high pressure device used for single crystal X-ray diffraction, determined the X-ray absorption curve of the device on Nicolet four-circle diffractometer, established the data collection programme o...We have set up the high pressure device used for single crystal X-ray diffraction, determined the X-ray absorption curve of the device on Nicolet four-circle diffractometer, established the data collection programme of a fixed φ scheme, and corrected the offsets of the optical centering of the crystal by using a reflection which is measured in eight different orientations. The mixture ratio of methanol: ethanol: water 16: 3: 1 was used as a pressure medium, high pressure calibration was based on the wavelength shift of the R_1 fluorescence line of ruby, and the pressure of 100 kbar was obtained.展开更多
This article will introduce the general formula of multiple Patterson function(MPF), and deduce therefrom phase structure invariants in reciprocal space that Hauptman and Karle introduced in a different way. By expand...This article will introduce the general formula of multiple Patterson function(MPF), and deduce therefrom phase structure invariants in reciprocal space that Hauptman and Karle introduced in a different way. By expanding the concept of the structure invariant, it may be found that a connection exists between the structure invariants in positive and reciprocal spaces. The phase question of MPF can be merged into the estimation question of phase structure invariants in the probability direct method.This theme will show the general group of Σ relationship without extra magnitudes. It might be one of the methods used in calculating MPF, and it primarily discusses the property of MPF.展开更多
Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact sol...Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.展开更多
基金Supported by Inner Mongolia Natural Science Foundations of China (200408020108).
文摘This paper discusses the approximation by reciprocals of polynomials with positive coefficients in Orlicz spaces and proved that if f（x） ∈ L^＊M[0, 1], changes its sign at most once in （0, 1）, then there exists x0 ∈ （0, 1） and a polynomial Pn∈ Fin（＋） such that ｜｜f（x）-x-x0/Pn（x）｜｜M≤Cω（f,n-1/2）M, where Пn（＋） indicates the set of all polynomials of degree n with positive coefficients
基金Project supported by the National Natural Science Foundation of China.
文摘We have set up the high pressure device used for single crystal X-ray diffraction, determined the X-ray absorption curve of the device on Nicolet four-circle diffractometer, established the data collection programme of a fixed φ scheme, and corrected the offsets of the optical centering of the crystal by using a reflection which is measured in eight different orientations. The mixture ratio of methanol: ethanol: water 16: 3: 1 was used as a pressure medium, high pressure calibration was based on the wavelength shift of the R_1 fluorescence line of ruby, and the pressure of 100 kbar was obtained.
文摘This article will introduce the general formula of multiple Patterson function(MPF), and deduce therefrom phase structure invariants in reciprocal space that Hauptman and Karle introduced in a different way. By expanding the concept of the structure invariant, it may be found that a connection exists between the structure invariants in positive and reciprocal spaces. The phase question of MPF can be merged into the estimation question of phase structure invariants in the probability direct method.This theme will show the general group of Σ relationship without extra magnitudes. It might be one of the methods used in calculating MPF, and it primarily discusses the property of MPF.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11875040 and 12171308)
文摘Reciprocal transformations of the space-time shifted nonlocal short pulse equations are elaborated.Covariance of dependent and independent variables involved in the reciprocal transformations is investigated.Exact solutions of the space-time shifted nonlocal short pulse equations are given in terms of double Wronskians.Realness of independent variables involved in the reciprocal transformations is verified.Dynamics of some obtained solutions are illustrated.
