In this paper, we investigate the growth and the fixed points of solutions and their 1st, 2nd derivatives of second order non-homogeneous linear differential equation and obtain the estimation of the order and the exp...In this paper, we investigate the growth and the fixed points of solutions and their 1st, 2nd derivatives of second order non-homogeneous linear differential equation and obtain the estimation of the order and the exponent of convergence of fixed points of solutions of the above equations.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equat...Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equations.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
In this paper, we shall utilize Nevanlinna value distribution theory and normality theory to study the solvability of a certain type of functional-differential equations. We also consider the solutions of some nonline...In this paper, we shall utilize Nevanlinna value distribution theory and normality theory to study the solvability of a certain type of functional-differential equations. We also consider the solutions of some nonlinear differential equations.展开更多
Objective To investigate therelationships between serum concentration of insulin -like growth factor - I (IGF-I) and left ventricular function as well as coronary collateral circulation in patients with coronary arter...Objective To investigate therelationships between serum concentration of insulin -like growth factor - I (IGF-I) and left ventricular function as well as coronary collateral circulation in patients with coronary artery disease (CAD) . Methods In 41 patients with CAD and 15 control subjects without CAD, the concentrations of serum IGF - I were measured using radioimmunoassay. The relationships between the concentration of serum IGF - I and Leaman coronary artery score, Rentrop grade of coronary collateral circulation, left ventricular ejection fraction (LVEF) as well as left ventricular wall motion Cortina score were assessed. Results 1. There was no significant difference in the mean level of serum IGF -I between the CAD group and the control group (107. 92±44.74 ng/ml vs 113.05 ±33. 65 ng/ml, P> 0. 05), but the IGF - I concentrations in the subgroup with collateral circulation were significantly greater than that in the control group (147. 33 ±29. 92 ng/ml vs 113. 05±33. 65 ng/ml, P < 0. 01) or in the subgroup without collateral circulation (147. 33 ±29. 92 ng/ml vs 80. 01±29. 75 ng/ml , P < 0. 01). 2. The serum concentration of IGF -I had no significant correlation to the Leaman coronary artery score. 3. The serum level of IGF -I had significantly positive correlation to both LVEF ( r = 0. 45, P < 0. 001) and the Rentrop grade of coronary collateral circulation ( r = 0. 74, P < 0. 001), and was negatively related to the left ventricular wall motion Cortina score (r = -0. 53, P < 0. 001). 4. The Leaman coronary artery score had no significant correlation to the Rentrop grade of coronary collateral circulation. 5. The Leaman coronary artery score was related to neither the LVEF nor the Cortina score in the whole CAD group. In the subgroup without coronary collateral circulation, however, the Leaman score had significantly negative correlation to LVEF ( r = - 0. 46, P < 0. 05) and positive correlation to the Cortina score (r = 0. 47, P < 0. 05) . Conclusions The serum concentration of IGF -I was associated with both left ventricular function and coronary collateral circulation in patients with CAD. IGF -I may play a role in promoting coronary collateral circulation and in protecting left ventricular function in patients with coronary artery disease.展开更多
In this paper, we study the growth of solutions of higher order differential equation with meromorphic coefficients, and find some conditions which guarantee that its every nontrivial solution is of infinite order.
In this paper, we investigate the growth of solutions of the differential equations f^((k))+ A_(k-1)(z)f^((k-1))+ ··· + A_0(z)f = 0, where A_j(z)(j = 0, ···, k-1) are entire functions.Whe...In this paper, we investigate the growth of solutions of the differential equations f^((k))+ A_(k-1)(z)f^((k-1))+ ··· + A_0(z)f = 0, where A_j(z)(j = 0, ···, k-1) are entire functions.When there exists some coefficient A_s(z)(s ∈ {1, ···, k-1}) being a nonzero solution of f''+P(z)f = 0, where P(z) is a polynomial with degree n(≥ 1) and A_0(z) satisfies σ(A_0) ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.展开更多
In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results ar...In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results are improved and generalized. More precisely,some results of the growth order of solutions of system of differential equations to difference equations are extended.展开更多
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations...We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.展开更多
Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient funct...Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f(w).展开更多
文摘In this paper, we investigate the growth and the fixed points of solutions and their 1st, 2nd derivatives of second order non-homogeneous linear differential equation and obtain the estimation of the order and the exponent of convergence of fixed points of solutions of the above equations.
基金supported by the Natural Science Foundation of China (10471065)the Natural Science Foundation of Guangdong Province (04010474)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equations.
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 the National Natural Science Foundation of China (11171184)the Scientific ResearchFoundation of CAUC,China (2011QD10X)
文摘In this paper, we shall utilize Nevanlinna value distribution theory and normality theory to study the solvability of a certain type of functional-differential equations. We also consider the solutions of some nonlinear differential equations.
文摘Objective To investigate therelationships between serum concentration of insulin -like growth factor - I (IGF-I) and left ventricular function as well as coronary collateral circulation in patients with coronary artery disease (CAD) . Methods In 41 patients with CAD and 15 control subjects without CAD, the concentrations of serum IGF - I were measured using radioimmunoassay. The relationships between the concentration of serum IGF - I and Leaman coronary artery score, Rentrop grade of coronary collateral circulation, left ventricular ejection fraction (LVEF) as well as left ventricular wall motion Cortina score were assessed. Results 1. There was no significant difference in the mean level of serum IGF -I between the CAD group and the control group (107. 92±44.74 ng/ml vs 113.05 ±33. 65 ng/ml, P> 0. 05), but the IGF - I concentrations in the subgroup with collateral circulation were significantly greater than that in the control group (147. 33 ±29. 92 ng/ml vs 113. 05±33. 65 ng/ml, P < 0. 01) or in the subgroup without collateral circulation (147. 33 ±29. 92 ng/ml vs 80. 01±29. 75 ng/ml , P < 0. 01). 2. The serum concentration of IGF -I had no significant correlation to the Leaman coronary artery score. 3. The serum level of IGF -I had significantly positive correlation to both LVEF ( r = 0. 45, P < 0. 001) and the Rentrop grade of coronary collateral circulation ( r = 0. 74, P < 0. 001), and was negatively related to the left ventricular wall motion Cortina score (r = -0. 53, P < 0. 001). 4. The Leaman coronary artery score had no significant correlation to the Rentrop grade of coronary collateral circulation. 5. The Leaman coronary artery score was related to neither the LVEF nor the Cortina score in the whole CAD group. In the subgroup without coronary collateral circulation, however, the Leaman score had significantly negative correlation to LVEF ( r = - 0. 46, P < 0. 05) and positive correlation to the Cortina score (r = 0. 47, P < 0. 05) . Conclusions The serum concentration of IGF -I was associated with both left ventricular function and coronary collateral circulation in patients with CAD. IGF -I may play a role in promoting coronary collateral circulation and in protecting left ventricular function in patients with coronary artery disease.
基金The NSF(11201195)of Chinathe NSF(20132BAB201008)of Jiangxi Province
文摘In this paper, we study the growth of solutions of higher order differential equation with meromorphic coefficients, and find some conditions which guarantee that its every nontrivial solution is of infinite order.
基金Supported by the National Natural Science Foundation of China(11201195)Supported by the Natural Science Foundation of Jiangxi Province(20122BAB201012,20132BAB201008)
文摘In this paper, we investigate the growth of solutions of the differential equations f^((k))+ A_(k-1)(z)f^((k-1))+ ··· + A_0(z)f = 0, where A_j(z)(j = 0, ···, k-1) are entire functions.When there exists some coefficient A_s(z)(s ∈ {1, ···, k-1}) being a nonzero solution of f''+P(z)f = 0, where P(z) is a polynomial with degree n(≥ 1) and A_0(z) satisfies σ(A_0) ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.
基金Project Supported by the fundamental research funds for the Central Universities project of China(No.11614801)Combining with the project of Guangdong Province production(No.2011A090200044)
文摘In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results are improved and generalized. More precisely,some results of the growth order of solutions of system of differential equations to difference equations are extended.
基金supported by the Natural Science Foundationof China (10471065)the Natural Science Foundation of Guangdong Province (N04010474)
文摘We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations.
文摘Under suitable conditions on {X-n}, the author obtains the important results: it is almost sure that the random integral function f(w) = Sigma (infinity)(n=0) X(n)z(n) (of finite positive order) has no deficient function, and any direction is a Borel direction (without finite exceptional value) of f(w).
