In this paper, we observe the generalized Harmonic numbers H<sub>n,k,r</sub> (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers H<sub>n,k,r&...In this paper, we observe the generalized Harmonic numbers H<sub>n,k,r</sub> (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers H<sub>n,k,r</sub> (α,β) with Changhee sequences, Daehee sequences, Degenerate Changhee-Genoocchi sequences, Two kinds of degenerate Stirling numbers. Using Riordan arrays, we explore interesting relations between these polynomials, Apostol Bernoulli sequences, Apostol Euler sequences, Apostol Genoocchi sequences.展开更多
In this paper, some Wgh inequalities for univalent harmonic analytic functions defined by Wright's generalized hypergeometric (Wgh) functions to be in certain classes are observed and proved. Some consequent resul...In this paper, some Wgh inequalities for univalent harmonic analytic functions defined by Wright's generalized hypergeometric (Wgh) functions to be in certain classes are observed and proved. Some consequent results are also discussed.展开更多
The potential-harmonic and generalized Laguerre function method (PHGLF) was modified into the correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF). The eigenenergies for 21S, 31S ...The potential-harmonic and generalized Laguerre function method (PHGLF) was modified into the correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF). The eigenenergies for 21S, 31S and 41S states of helium-like systems from the CFPHGLF are much more accurate than those from the previous PHGLF, but the eigenenergy for the 11S is not as good as that from the PHGLF method. The results indicate that the electron-nucleus cusp plays more important role than the electron-electron cusp and the cluster structure for the loosely bound excited states, and that the electron-electron cusp is absolutely essential for the tightly bound ground state.展开更多
The hyperspherical-harmonic (HH) method is a wonderful tool for directly solving the Schrǒdinger equation of atoms with two or more electrons.However, the HH degeneracy grows dramatically with the global angular mome...The hyperspherical-harmonic (HH) method is a wonderful tool for directly solving the Schrǒdinger equation of atoms with two or more electrons.However, the HH degeneracy grows dramatically with the global angular momentum, which prevents展开更多
Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact...Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).展开更多
采用基于赝势平面波基组的密度泛函理论方法,对具有黄铜矿结构的6种Cu XY2(X=Ga,In; Y=S,Se,Te)晶体的构型、电子结构、线性及二阶非线性光学性质进行了研究.结果表明,6种Cu XY2均为直接带隙半导体,具有相似的能带结构.当X原子相同时,随...采用基于赝势平面波基组的密度泛函理论方法,对具有黄铜矿结构的6种Cu XY2(X=Ga,In; Y=S,Se,Te)晶体的构型、电子结构、线性及二阶非线性光学性质进行了研究.结果表明,6种Cu XY2均为直接带隙半导体,具有相似的能带结构.当X原子相同时,随着Y原子按S→Se→Te依次改变时,体系的静态介电常数、静态折射率和静态倍频系数(d36)依次递增.在占据带中,位于价带顶附近的能带对体系倍频效应影响最为显著,该系列化合物的能带主要成分为Cu的3d轨道和Y原子价层p轨道;对于空能带,对倍频系数影响较大的是以X原子价层p轨道为主要成分的能带. 6种晶体中,Cu In Se2晶体具有较高的光电导率并对太阳光具有较好的吸收性能.综合考虑体系的双折射率和倍频效应等因素,Cu Ga S2和Cu Ga Se22种晶体在二阶非线性光学领域具有潜在的应用价值.展开更多
文摘In this paper, we observe the generalized Harmonic numbers H<sub>n,k,r</sub> (α,β). Using generating function, we investigate some new identities involving generalized Harmonic numbers H<sub>n,k,r</sub> (α,β) with Changhee sequences, Daehee sequences, Degenerate Changhee-Genoocchi sequences, Two kinds of degenerate Stirling numbers. Using Riordan arrays, we explore interesting relations between these polynomials, Apostol Bernoulli sequences, Apostol Euler sequences, Apostol Genoocchi sequences.
文摘In this paper, some Wgh inequalities for univalent harmonic analytic functions defined by Wright's generalized hypergeometric (Wgh) functions to be in certain classes are observed and proved. Some consequent results are also discussed.
基金Project supported by the National Natural Science Foundation of China
文摘The potential-harmonic and generalized Laguerre function method (PHGLF) was modified into the correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF). The eigenenergies for 21S, 31S and 41S states of helium-like systems from the CFPHGLF are much more accurate than those from the previous PHGLF, but the eigenenergy for the 11S is not as good as that from the PHGLF method. The results indicate that the electron-nucleus cusp plays more important role than the electron-electron cusp and the cluster structure for the loosely bound excited states, and that the electron-electron cusp is absolutely essential for the tightly bound ground state.
基金Project supported by the National Natural Science Foundation of China.
文摘The hyperspherical-harmonic (HH) method is a wonderful tool for directly solving the Schrǒdinger equation of atoms with two or more electrons.However, the HH degeneracy grows dramatically with the global angular momentum, which prevents
文摘Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).
文摘采用基于赝势平面波基组的密度泛函理论方法,对具有黄铜矿结构的6种Cu XY2(X=Ga,In; Y=S,Se,Te)晶体的构型、电子结构、线性及二阶非线性光学性质进行了研究.结果表明,6种Cu XY2均为直接带隙半导体,具有相似的能带结构.当X原子相同时,随着Y原子按S→Se→Te依次改变时,体系的静态介电常数、静态折射率和静态倍频系数(d36)依次递增.在占据带中,位于价带顶附近的能带对体系倍频效应影响最为显著,该系列化合物的能带主要成分为Cu的3d轨道和Y原子价层p轨道;对于空能带,对倍频系数影响较大的是以X原子价层p轨道为主要成分的能带. 6种晶体中,Cu In Se2晶体具有较高的光电导率并对太阳光具有较好的吸收性能.综合考虑体系的双折射率和倍频效应等因素,Cu Ga S2和Cu Ga Se22种晶体在二阶非线性光学领域具有潜在的应用价值.
