A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this p...A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.展开更多
In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,a...In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.展开更多
Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).
For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-verte...For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-vertex-vertex join G_1* G_2.Then,describe the Laplacian matrix of the graph G_1 * G_2 and use generalized inverse of the Laplacian matrix to get formulas for resistance distance and Kirchhoff index.Through the obtained formulas,the resistance distance of any pairs of vertices and Kirchhoff index of the join graph can be computed.展开更多
Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the ...Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the n× n matrix whose (i,j) th entry is N - i-1 (x j) . This paper presents a computation formula for det V - n(x 1, ...,x n) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications.展开更多
In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponentia...In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponential sums, and give an exact computational formuiu for it.展开更多
The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q ...The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q （a positive odd number）, and give an exact computational formula for it.展开更多
文摘A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.
文摘In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.
文摘Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).
基金National Natural Science Foundation of China(No.11361033)
文摘For some complicated graphs obtained by graph operations,it is very difficult to compute resistance distance and Kirchhoff index.Define a new graph operation,and obtain a class of new join graphs:the subdivision-vertex-vertex join G_1* G_2.Then,describe the Laplacian matrix of the graph G_1 * G_2 and use generalized inverse of the Laplacian matrix to get formulas for resistance distance and Kirchhoff index.Through the obtained formulas,the resistance distance of any pairs of vertices and Kirchhoff index of the join graph can be computed.
文摘Suppose that x is a complex number and i is a non negative integer. Define N - i(x)=|x| i if i is even and N - i(x)=x|x| i-1 if i is odd. Let V - n(x 1, ...,x n) denote the n× n matrix whose (i,j) th entry is N - i-1 (x j) . This paper presents a computation formula for det V - n(x 1, ...,x n) , which can be considered as a generalized that of Vandermonde determinant, and some its important theoretical applications.
基金supported by the National Natural Science Foundation of China(Nos.11371291,11471258)the Graduate Independent Innovation Fund of Northwest University(No.YZZ13071)
文摘In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponential sums, and give an exact computational formuiu for it.
基金Supported by the NSF of China(Grant No.11771351)
文摘The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q （a positive odd number）, and give an exact computational formula for it.
