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.
The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n,...The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.展开更多
In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions...In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions.展开更多
Let k be an infinite field,A be a finite set of k,and Q∈k[x](with x=(x_(1),...,X_(n))and n≥2)be a noncons taut polynomial.The main goal of this paper is to construct a polynomial P(x)∈k[x]with suitably large partia...Let k be an infinite field,A be a finite set of k,and Q∈k[x](with x=(x_(1),...,X_(n))and n≥2)be a noncons taut polynomial.The main goal of this paper is to construct a polynomial P(x)∈k[x]with suitably large partial degrees in x_(1),...,x_(n-1)such that P and Q axe coprime,and P-aQ is reducible for all a in A.展开更多
At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational inter...At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.展开更多
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.
基金The NSF (61033012,10801023,10911140268 and 10771028) of China
文摘The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.
文摘In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions.
文摘Let k be an infinite field,A be a finite set of k,and Q∈k[x](with x=(x_(1),...,X_(n))and n≥2)be a noncons taut polynomial.The main goal of this paper is to construct a polynomial P(x)∈k[x]with suitably large partial degrees in x_(1),...,x_(n-1)such that P and Q axe coprime,and P-aQ is reducible for all a in A.
基金Supported by Shanghai Natural Science Foundation (Grant No.10ZR1410900)Key Disciplines of Shanghai Mu-nicipality (Grant No.S30104)+1 种基金the Anhui Provincial Natural Science Foundation (Grant No.070416227)Stu-dents’ Innovation Foundation of Hefei University of Technology (Grant No.XS08079)
文摘At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 （0 〈 dl ≤ m） and d2 （0 ≤ d2≤ n）, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.
基金supported by Natural Science Foundation of China(11271289,11502141)the Fundamental Research Funds for the Central Universitiesthe Key Program of NSFC-Guangdong Joint Fund of China(U1135003)
