In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almos...In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.展开更多
We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, ...We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.展开更多
Under the frame of the （2＋1）-dimensional zero curvature equation and Tu model, （2＋1）-dimensional Tu hierarchy is obtained. Again by employing a subalgebra of the loop algebra ↑-A2 the integrable coupling system...Under the frame of the （2＋1）-dimensional zero curvature equation and Tu model, （2＋1）-dimensional Tu hierarchy is obtained. Again by employing a subalgebra of the loop algebra ↑-A2 the integrable coupling system of the above hierarchy is presented. Finally, A multi-component integrable hierarchy is obtained by employing a multi-component loop algebra ↑-GM.展开更多
基金The research was supported by the National Nat ural Science Foundation of China(10571164)Specialized Research Fund for the Doctoral Program of Higher Education(20050358052)+1 种基金Guangdong Natural Science Foundation(06301315)the Doctoral Foundation of Zhanjiang Normal University(Z0420)
文摘In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.
基金Supported by the National Nature Science Foundation.
文摘We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.
文摘Under the frame of the （2＋1）-dimensional zero curvature equation and Tu model, （2＋1）-dimensional Tu hierarchy is obtained. Again by employing a subalgebra of the loop algebra ↑-A2 the integrable coupling system of the above hierarchy is presented. Finally, A multi-component integrable hierarchy is obtained by employing a multi-component loop algebra ↑-GM.
