First,an explicit representation A(2)T,S=(GA+E)^-1G of the outer invers A(2)T,S for a matrix A∈Cm×n with the prescribed range T and null space S is derived,which is simpler than A(2)T,S=(GA+E)^-1G-V(UV)-2UG prop...First,an explicit representation A(2)T,S=(GA+E)^-1G of the outer invers A(2)T,S for a matrix A∈Cm×n with the prescribed range T and null space S is derived,which is simpler than A(2)T,S=(GA+E)^-1G-V(UV)-2UG proposed by Ji in 2005.Next,a new algorithm for computing the outer inverse A(2)T,S based on the improved representation A(2)T,S=(GA+E)^-1G through elementary operations on an appropriate partitioned matrix GAInIn0 is proposed and investigated.Then,the computational complexity of the introduced algorithm is also analyzed in detail.Finally,two numerical examples are shown to illustrate that this method is correct.展开更多
It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainder...It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainders are also explicitly represented as a fixed number of interpolation nodes approaching infinitely to the point at which the derivative is evaluated. This implies that complete explicit formulas for local Lagrangian numerical differentiation can be obtained.展开更多
The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth so...The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented.展开更多
Necessary and sufficient conditions for the regularity and q-regularity of (0,1,…,m-2,m)interpolation on the zeros of (1-x2)P_(n-2)￣(α,β)(x) (α,β>-1) in a manageable form are established,where P_(n-2)￣(α,β...Necessary and sufficient conditions for the regularity and q-regularity of (0,1,…,m-2,m)interpolation on the zeros of (1-x2)P_(n-2)￣(α,β)(x) (α,β>-1) in a manageable form are established,where P_(n-2)￣(α,β)(x) stands for the (n-2)th Jacobi polynomial. Meanwhile, the explicit representation of the fundamental polynomials, when they exist, is given. Moreover, we show that under a mild assumption if the problem of (0,1,…,m-2,m) interpolation has an infinity of solutions then the general form of the solutions is fo(x)+Cf(x) with an arbitrary constant C.展开更多
As a distinguished female poet,Emily Dickinson is considered to write many love poems in her life time.This paper attempts to understand the burning love through the implicit and explicit representation in her love po...As a distinguished female poet,Emily Dickinson is considered to write many love poems in her life time.This paper attempts to understand the burning love through the implicit and explicit representation in her love poems.Through the use of the binary opposition and the bold description of the sexual affairs between lovers,the yearning for love is represented in her poems.Whether it is implicit or explicit description,the inequality between the male and the female is fully represented through Dickinson’s love poems.The female not only suffered the emotional repression in a love relationship,but also is reduced to the subordinate social status in every aspects of the Victorian society.展开更多
基金The National Natural Science Foundation of China(No.11771076).
文摘First,an explicit representation A(2)T,S=(GA+E)^-1G of the outer invers A(2)T,S for a matrix A∈Cm×n with the prescribed range T and null space S is derived,which is simpler than A(2)T,S=(GA+E)^-1G-V(UV)-2UG proposed by Ji in 2005.Next,a new algorithm for computing the outer inverse A(2)T,S based on the improved representation A(2)T,S=(GA+E)^-1G through elementary operations on an appropriate partitioned matrix GAInIn0 is proposed and investigated.Then,the computational complexity of the introduced algorithm is also analyzed in detail.Finally,two numerical examples are shown to illustrate that this method is correct.
基金supported in part by the National Natural Science Foundation of China(Grant No.10471128)
文摘It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainders are also explicitly represented as a fixed number of interpolation nodes approaching infinitely to the point at which the derivative is evaluated. This implies that complete explicit formulas for local Lagrangian numerical differentiation can be obtained.
基金Supported by the National Natural Science Foundation of China under Grant No.11461022the Major Natural Science Foundation of Yunnan Province under Grant No.2014FA037
文摘The generalized nonlinear Schrdinger equation with parabolic law nonlinearity is studied by using the factorization technique and the method of dynamical systems.From a dynamic point of view,the existence of smooth solitary wave,kink and anti-kink wave is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given.Also,all possible explicit exact parametric representations of the waves are presented.
文摘Necessary and sufficient conditions for the regularity and q-regularity of (0,1,…,m-2,m)interpolation on the zeros of (1-x2)P_(n-2)￣(α,β)(x) (α,β>-1) in a manageable form are established,where P_(n-2)￣(α,β)(x) stands for the (n-2)th Jacobi polynomial. Meanwhile, the explicit representation of the fundamental polynomials, when they exist, is given. Moreover, we show that under a mild assumption if the problem of (0,1,…,m-2,m) interpolation has an infinity of solutions then the general form of the solutions is fo(x)+Cf(x) with an arbitrary constant C.
文摘As a distinguished female poet,Emily Dickinson is considered to write many love poems in her life time.This paper attempts to understand the burning love through the implicit and explicit representation in her love poems.Through the use of the binary opposition and the bold description of the sexual affairs between lovers,the yearning for love is represented in her poems.Whether it is implicit or explicit description,the inequality between the male and the female is fully represented through Dickinson’s love poems.The female not only suffered the emotional repression in a love relationship,but also is reduced to the subordinate social status in every aspects of the Victorian society.
