Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain...Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.展开更多
In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order...In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.展开更多
An explicit procedure for transforming one bipartite entangled state into another via local operations and classical communication （LOCC） is presented. Our procedure is much simper than the previous ones in the sens...An explicit procedure for transforming one bipartite entangled state into another via local operations and classical communication （LOCC） is presented. Our procedure is much simper than the previous ones in the sense that, it only involves two steps and the explicit expression of local general measurement used in the procedure can be obtained by solving a set of linear equations. Furthermore, this procedure is still applicable in high dimensional case.展开更多
Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic sol...Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.展开更多
In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improv...In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.展开更多
We study the differential equations w2＋ R（z）（w（k））2 = Q（z）, where R（z）, Q（z） are nonzero rationalfunctions. We prove （1） if the differential equation w2 ＋R（z）（w＇）2= Q（z）, where R（z）, Q（z） ar...We study the differential equations w2＋ R（z）（w（k））2 = Q（z）, where R（z）, Q（z） are nonzero rationalfunctions. We prove （1） if the differential equation w2 ＋R（z）（w＇）2= Q（z）, where R（z）, Q（z） are nonzero rational functions, admits a transcendental meromorphic solution f, then Q= C （constant）, the multiplicities of the zeros of R（z） are no greater than 2 and f（z） = √C cos α（z）, where α（z） is a primitive of 1 such that √C cos α（z） is a transcendental meromorphic function. （2） if the differential equation w2 ＋ R（z）（w（k））2 = Q（z）, where k ≥ 2 is an integer and R, Q are nonzero rational functions, admits a transcendental meromorphic solution f, then k is an odd integer, Q ≡ C （constant）, It（z） ≡ A （constant） and f（z） = √C cos（az ＋ b）, where a2k = A1/A.展开更多
In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）...In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.展开更多
Applying Nevanlinna theory of the value distribution of meromorphic functions,the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of ...Applying Nevanlinna theory of the value distribution of meromorphic functions,the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of complex differential-difference equations.Specifically speaking, the estimates about counting function and proximity function of meromorphic solutions to systems of complex differential-difference equations can be given.展开更多
Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f,...Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f, then all meromorphic solutions f satisfy λ(f) = λ(f) = δ(f) = max{β, (n + k)/k},except at most one exceptional meromorphic solution f0.展开更多
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized complex algebraic differential equations and obtain some results.
文摘In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.
基金supported by National Natural Science Foundation of China under Grant No.10404039
文摘An explicit procedure for transforming one bipartite entangled state into another via local operations and classical communication （LOCC） is presented. Our procedure is much simper than the previous ones in the sense that, it only involves two steps and the explicit expression of local general measurement used in the procedure can be obtained by solving a set of linear equations. Furthermore, this procedure is still applicable in high dimensional case.
基金supported by National Natural Science Foundation of China (Grant No. 10871076)
文摘Abstract In this paper, we study the order of the growth and exponents of convergence of zeros and poles of meromorphic solutions of some linear and nonlinear difference equations which have admissible meromorphic solutions of finite order.
基金This research is supported by the Research Foundation of Doctor Points of China （No. 20060422049） and the National Natural Science Foundation of China （No. 10371065）.
文摘In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.
基金supported by National Natural Science Foundation of China(Grant Nos.10871011 and 11271179)
文摘We study the differential equations w2＋ R（z）（w（k））2 = Q（z）, where R（z）, Q（z） are nonzero rationalfunctions. We prove （1） if the differential equation w2 ＋R（z）（w＇）2= Q（z）, where R（z）, Q（z） are nonzero rational functions, admits a transcendental meromorphic solution f, then Q= C （constant）, the multiplicities of the zeros of R（z） are no greater than 2 and f（z） = √C cos α（z）, where α（z） is a primitive of 1 such that √C cos α（z） is a transcendental meromorphic function. （2） if the differential equation w2 ＋ R（z）（w（k））2 = Q（z）, where k ≥ 2 is an integer and R, Q are nonzero rational functions, admits a transcendental meromorphic solution f, then k is an odd integer, Q ≡ C （constant）, It（z） ≡ A （constant） and f（z） = √C cos（az ＋ b）, where a2k = A1/A.
文摘In this paper, we investigate the growth of meromorphic solutions of higher order linear differential equation f^（k） ＋Ak-1 （z）e^Pk-1^（z） f^（k-1） ＋…＋A1 （z）e^P1（z） f′ ＋Ao（z）e^Po（z） f = 0 （k ≤ 2）, where Pj（z） （j = 0, 1,..., k - 1） are nonconstant polynomials such that deg Pj = n （j = 0, 1,..., k - 1） and Aj（z）（≠ 0） （j = 0, 1,..., k - 1） are meromorphic functions with order p（Aj） 〈 n （j = 0, 1,..., k - 1）.
文摘Applying Nevanlinna theory of the value distribution of meromorphic functions,the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of complex differential-difference equations.Specifically speaking, the estimates about counting function and proximity function of meromorphic solutions to systems of complex differential-difference equations can be given.
文摘Suppose that B is a rational function having a pole at co of order n ＞ 0 and that H 0 is a meromorphic function satisfying o(H) =β (n+ k)/k. If the differential equation f(k) + Bf =H(z) has a meromorphic solution f, then all meromorphic solutions f satisfy λ(f) = λ(f) = δ(f) = max{β, (n + k)/k},except at most one exceptional meromorphic solution f0.
