Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair...Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.展开更多
In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circle with respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.
Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact ...Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.展开更多
This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas fo...This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.展开更多
On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting
Let f ∈ C[0,1] , and Bn(f,x) be the n-th Bernstein polynomial associated with function f. In 1967, the limit of iterates for Bn(f,x) was given by Kelisky and Rivlin. After this, Many mathematicians studied and genera...Let f ∈ C[0,1] , and Bn(f,x) be the n-th Bernstein polynomial associated with function f. In 1967, the limit of iterates for Bn(f,x) was given by Kelisky and Rivlin. After this, Many mathematicians studied and generalized this result. But anyway, all these discussions are only for univariate case. In this paper, the main contribution is that the limit of iterates for Bernstein polynomial defined on a triangle is given completely.展开更多
The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such op...The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.展开更多
We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz ...We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.展开更多
Describes the representation of moment generating function for the S-lambda type random variables. Higher order asymptotic formula for generalized Feller operators; Regular n-r order moment for the random variables.
Let q 〉 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C(a, q) in quarter intervals, and obtain a sharp asymptotic formula for it.
The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, ...The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula.展开更多
The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8) by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value f...The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8) by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value formula for this study.展开更多
The main purpose of this paper is to use the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums, and give some interesting mean v...The main purpose of this paper is to use the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.展开更多
Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface d...Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(3)=Q(y)z.We can get a power-saving result for a class of special quadratic forms and improve on some previous work.展开更多
The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums, and to give a sharper mean value formula.
Let a(n) be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A(x) =∑n≤xa(n).In this paper, we establish an asymptotic formula of tile fourth power mome...Let a(n) be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A(x) =∑n≤xa(n).In this paper, we establish an asymptotic formula of tile fourth power moment of A(x) and prove that ∫1^TA^4(x)dx=3/64κπ^4s4;2(a^~)T^2κ+O(T^2a-δ4+t) with δ4 = 1/8, which improves the previous result.展开更多
Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic beh...Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic behavior of D_(s)(x):=∑m^(2)+n^(2)≤xS(M,n)and obtain an asymptotic formula by using the elementary method.展开更多
The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the...The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the two-term exponential sums,and give several interesting identities and asymptotic formulae for them.展开更多
基金Supported by the Natural Science Foundation of China(12071487,11671404)the Natural Science Foundation of Anhui Province(2208085MA06)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049,KJ2021A0060)Hunan Provincial Innovation Foundation for Postgraduate(CX20200146)。
文摘Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
文摘In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circle with respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.
文摘Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.
文摘This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.
基金Project support by the State Education Commission of the People’s Republic of China
文摘On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting
基金Supported by National Education Committee Foundation and NSF
文摘Let f ∈ C[0,1] , and Bn(f,x) be the n-th Bernstein polynomial associated with function f. In 1967, the limit of iterates for Bn(f,x) was given by Kelisky and Rivlin. After this, Many mathematicians studied and generalized this result. But anyway, all these discussions are only for univariate case. In this paper, the main contribution is that the limit of iterates for Bernstein polynomial defined on a triangle is given completely.
文摘The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.
文摘We consider the inverse spectral problem for a singular Sturm-Liouville operator with Coulomb potential. In this paper, we give an asymptotic formula and some properties for this problem by using methods of Trubowitz and Poschel.
基金the Natural Science Foundation of Hubei Province.
文摘Describes the representation of moment generating function for the S-lambda type random variables. Higher order asymptotic formula for generalized Feller operators; Regular n-r order moment for the random variables.
基金supported by China Postdoctoral Science Foundation funded project (20080430202)the N.S.F.(10671155) of P.R.China
文摘Let q 〉 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C(a, q) in quarter intervals, and obtain a sharp asymptotic formula for it.
基金supported by the Doctorate Foundation of Xi'an Jiaotong University
文摘The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula.
文摘The main purpose of this paper is to study the mean value properties of the character sums over the interval [1,p/8) by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value formula for this study.
基金Supported by National Natural Science Foundation of China (Grant No. 10671155) and Northwest University Innovation Fund (Grant No. 08YZZ30) The authors express their gratitude to the referee for his very helpful and detailed comments.
文摘The main purpose of this paper is to use the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.
基金supported by the National Natural Science Foundation of China(Grant No.11971476).
文摘Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface defined by u^(3)=Q(y)z.We can get a power-saving result for a class of special quadratic forms and improve on some previous work.
基金This work is supported by the National Natural Science Foundation of P. R. China
文摘The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums, and to give a sharper mean value formula.
文摘Let a(n) be the Fourier coefficients of a holomorphic cusp form of weight κ = 2n ≥ 12 for the full modular group and A(x) =∑n≤xa(n).In this paper, we establish an asymptotic formula of tile fourth power moment of A(x) and prove that ∫1^TA^4(x)dx=3/64κπ^4s4;2(a^~)T^2κ+O(T^2a-δ4+t) with δ4 = 1/8, which improves the previous result.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11971476)。
文摘Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic behavior of D_(s)(x):=∑m^(2)+n^(2)≤xS(M,n)and obtain an asymptotic formula by using the elementary method.
基金Supported by NSF(Grant Nos.11771351 and 11826205)
文摘The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the two-term exponential sums,and give several interesting identities and asymptotic formulae for them.