Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or...Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or a transcendental singularity） of f if there exists a curve Г ： [0, 1） → C such that limt→1 F（t） = ∞ and limt→1（f o Г）（t） = a. In this paper we find relations between the asymptotic values of f, 9 and f o 9, relations between critical points of f, 9 and f o 9 and also in the case when the two functions f and 9 are semi-conjugated with another entire function.展开更多
In this paper, the concepts of regularity and strong regularity of general. linear methods are introduced. We investigate the conditions which guarantee that general linear methods preserve asymptotic values of the sy...In this paper, the concepts of regularity and strong regularity of general. linear methods are introduced. We investigate the conditions which guarantee that general linear methods preserve asymptotic values of the systems of ordinary differential equations. This work extends the existed results of Runge-Kutta methods and linear multistep methods.展开更多
Let the numbers be defined by , where and are the exponential complete Bell polynomials. In this paper, by means of the methods of Riordan arrays, we establish general identities involving the numbers , binomial coeff...Let the numbers be defined by , where and are the exponential complete Bell polynomials. In this paper, by means of the methods of Riordan arrays, we establish general identities involving the numbers , binomial coefficients and inverse of binomial coefficients. From these identities, we deduce some identities involving binomial coefficients, Harmonic numbers and the Euler sum identities. Furthermore, we obtain the asymptotic values of some summations associated with the numbers by Darboux’s method.展开更多
In this paper, we investigate some analytic properties for a class of holomorphic matrix- valued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in t...In this paper, we investigate some analytic properties for a class of holomorphic matrix- valued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on C^2×2 and Julia set of one dimensional complex dynamic system.展开更多
基金This paper is a main talk on the held in Nanjing, P. R. China, July, 2004.
文摘Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or a transcendental singularity） of f if there exists a curve Г ： [0, 1） → C such that limt→1 F（t） = ∞ and limt→1（f o Г）（t） = a. In this paper we find relations between the asymptotic values of f, 9 and f o 9, relations between critical points of f, 9 and f o 9 and also in the case when the two functions f and 9 are semi-conjugated with another entire function.
文摘In this paper, the concepts of regularity and strong regularity of general. linear methods are introduced. We investigate the conditions which guarantee that general linear methods preserve asymptotic values of the systems of ordinary differential equations. This work extends the existed results of Runge-Kutta methods and linear multistep methods.
文摘Let the numbers be defined by , where and are the exponential complete Bell polynomials. In this paper, by means of the methods of Riordan arrays, we establish general identities involving the numbers , binomial coefficients and inverse of binomial coefficients. From these identities, we deduce some identities involving binomial coefficients, Harmonic numbers and the Euler sum identities. Furthermore, we obtain the asymptotic values of some summations associated with the numbers by Darboux’s method.
基金Supported by National Natural Science Foundation of China(Grant Nos.11571049,11271215,61370195 and 11101048)Beijing Natural Science Foundation(Grant No.4132060)
文摘In this paper, we investigate some analytic properties for a class of holomorphic matrix- valued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on C^2×2 and Julia set of one dimensional complex dynamic system.
