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
This paper obtains a group of necessary and sufficient conditions which guarantee a closed linear operator A to be the complete infinitesimal generator of an analytic semigroup of growth order α.
By meas of the Nevanlinna theory of the value distribution of meromorphic functions, this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution...By meas of the Nevanlinna theory of the value distribution of meromorphic functions, this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution is determined if the order are sufficiently large.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
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 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
In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（...In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.展开更多
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, 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.
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 the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sig...Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.展开更多
Titanium-doped ordered mesoporous alumina with specific structural properties has been prepared by the evaporation induced self-assembly sol-gel method. The results show that the doped titanium helps to stabilize the ...Titanium-doped ordered mesoporous alumina with specific structural properties has been prepared by the evaporation induced self-assembly sol-gel method. The results show that the doped titanium helps to stabilize the ordered mesoporous alumina material without influencing the ordered mesoporosity. The textural properties of the obtained sample are related to the amount of doped titanium. When the molar ratio of aluminum to titanium （n（Al）/n（Ti）） is controlled as 10.2, the titanium-doped ordered mesoporous alumina exhibits high surface area （up to 218 m^2 g^-1）, large pore volume （0.42 cm^3 g^-1） and narrow pore diameter （6.1 nm） after treating at 900 ℃, showing high thermal stability. Moreover, the obtained sample calcined at 900 ℃ still maintains ordered mesoporous structure and exhibits high thermal stability.展开更多
In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental ent...In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental entire function with ρ（A）〈1/2.Suppose that k≥2 and f（k）＋A（z）f=0 has a solution f with λ（f）〈ρ（A）,and suppose that A1=A＋h,where h≡0 is an entire function with ρ（h）〈ρ（A）.Then g（k）＋A1（z）g=0 does not have a solution g with λ（g）〈∞.展开更多
In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function...In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of in the right half-plane are obtained.展开更多
In this paper, we investigate the properties of solutions of some linear difference equations with meromorphic coefficients, and obtain some estimates on growth and value distribution of these meromorphic solutions.
The effects of minor Zn(0.2 at%,0.4 at%,0.6 at%) on the microstructures and mechanical properties of Mg-1.4 Gd-1.2 Y-0.15 Zr(at%) alloys were systematically explored.Results reveal that increasing Zn content leads to ...The effects of minor Zn(0.2 at%,0.4 at%,0.6 at%) on the microstructures and mechanical properties of Mg-1.4 Gd-1.2 Y-0.15 Zr(at%) alloys were systematically explored.Results reveal that increasing Zn content leads to the increase of the intergranular phases and the change of their composition from Mg24(Gd,Y)5 phase and(Mg,Zn)3(Gd,Y) phase to 18 R-LPSO phase and(Mg,Zn)3(Gd,Y) phase.Mg24(Gd,Y)5 phase is body-centered cubic structure and shares the same lattice constant with Mg24Y5 while(Mg,Zn)3(Gd,Y)phase is face-centered cubic structure with lattice constant of 0.72 nm,slightly lower than Mg3Gd.18RLPSO structure is identified to be monoclinic with c-axis not strictly vertical to the bottom surface but93.5°.The growth patterns of intergranular phases change from the divorced growth to coupled growth as compositions change.Moreover,the mechanical performance improves with Zn rising,ascribed to the decrease of brittle phases at grain boundaries and the increase of LPSO structure phases.展开更多
A mathematical expression of the crystal growth rate during crystallization of the amorphous alloys was derived from the micromechanism of crystallization newly developed by the authors. Thus, the satisfactory explana...A mathematical expression of the crystal growth rate during crystallization of the amorphous alloys was derived from the micromechanism of crystallization newly developed by the authors. Thus, the satisfactory explanation of the experimental results obtained by Nunogaki et al., Heimendahl et al. and the authors might be found. It seems also to be modelled with the expression for the crystal growth and the crystal size influenced by time during the crystallization of amorphous Ni-P alloy foil at in situ heating. Based on the expression, the factors influencing the crystal growth rate, such as temperature, time and microstructure of amorphous alloys have been discussed.展开更多
In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes...In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.展开更多
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
New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aimin...New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process（NHPP） corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.展开更多
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This paper obtains a group of necessary and sufficient conditions which guarantee a closed linear operator A to be the complete infinitesimal generator of an analytic semigroup of growth order α.
基金the National Natural Science Foundation of China(10471065)the Natural Science Foundation of Guangdong Province(04010474)
文摘By meas of the Nevanlinna theory of the value distribution of meromorphic functions, this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution is determined if the order are sufficiently large.
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.
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.
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 National Natural Science Foundation of China(Grant Nos.1130123211171119)the Natural Science Foundation of Jiangxi Province(Grant No.20132BAB211009)
文摘In this paper, we consider the growth of solutions of some homogeneous and non- homogeneous higher order differential equations. It is proved that under some conditions for entire functions F, Aji and polynomials Pj（z）, Oj（z） （j = 0, 1,..., k - 1; i = 1, 2） with degree n ≥ 1, the equation f（k） ＋ （Ak-l,1 （z）e pk-l（z） ＋Ak-1,2 （z）eQk-l（z））f（x-1） ＋...＋ （A0,1 （z）eP0（z） ＋ A0,2（z）eQ0（z））f = F, where k ≥ 2, satisfies the properties： When F ≡ 0, all the non-zero solu- tions are of infinite order; when F ≠ 0, there exists at most one exceptional solution f0 with finite order, and all other solutions satisfy -λ（f） = A（f） = σ（f） = ∞.
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 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 the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.
基金the financial support from the National Natural Science Foundation of China(No.51103024)Joint Research Program of Fuzhou University(No.DH-700)
文摘Titanium-doped ordered mesoporous alumina with specific structural properties has been prepared by the evaporation induced self-assembly sol-gel method. The results show that the doped titanium helps to stabilize the ordered mesoporous alumina material without influencing the ordered mesoporosity. The textural properties of the obtained sample are related to the amount of doped titanium. When the molar ratio of aluminum to titanium （n（Al）/n（Ti）） is controlled as 10.2, the titanium-doped ordered mesoporous alumina exhibits high surface area （up to 218 m^2 g^-1）, large pore volume （0.42 cm^3 g^-1） and narrow pore diameter （6.1 nm） after treating at 900 ℃, showing high thermal stability. Moreover, the obtained sample calcined at 900 ℃ still maintains ordered mesoporous structure and exhibits high thermal stability.
基金Supported by the National Natural Science Foundation of China (Grant No. 11171080)Foundation of Scienceand Technology Department of Guizhou Province (Grant No. [2010] 07)
文摘In this paper,we shall use Nevanlinna theory of meromorphic functions to investigate the complex oscillation theory of solutions of some higher order linear differential equation.Suppose that A is a transcendental entire function with ρ（A）〈1/2.Suppose that k≥2 and f（k）＋A（z）f=0 has a solution f with λ（f）〈ρ（A）,and suppose that A1=A＋h,where h≡0 is an entire function with ρ（h）〈ρ（A）.Then g（k）＋A1（z）g=0 does not have a solution g with λ（g）〈∞.
基金supported by the National Natural Science Foundation of China(1110109611201083)+1 种基金Guangdong Natural Science Foundation(S2012010010376)the Startup Foundation for Doctors of Guangdong University of Technology(083063)
文摘In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of in the right half-plane are obtained.
基金The NSF(11661044,11201195) of Chinathe NSF(20132BAB201008) of Jiangxi Province
文摘In this paper, we investigate the properties of solutions of some linear difference equations with meromorphic coefficients, and obtain some estimates on growth and value distribution of these meromorphic solutions.
基金supported by the National Basic Research Program of China(2013CB632202)the Natural Science Foundation of China(51501015,51871195,51874062).
文摘The effects of minor Zn(0.2 at%,0.4 at%,0.6 at%) on the microstructures and mechanical properties of Mg-1.4 Gd-1.2 Y-0.15 Zr(at%) alloys were systematically explored.Results reveal that increasing Zn content leads to the increase of the intergranular phases and the change of their composition from Mg24(Gd,Y)5 phase and(Mg,Zn)3(Gd,Y) phase to 18 R-LPSO phase and(Mg,Zn)3(Gd,Y) phase.Mg24(Gd,Y)5 phase is body-centered cubic structure and shares the same lattice constant with Mg24Y5 while(Mg,Zn)3(Gd,Y)phase is face-centered cubic structure with lattice constant of 0.72 nm,slightly lower than Mg3Gd.18RLPSO structure is identified to be monoclinic with c-axis not strictly vertical to the bottom surface but93.5°.The growth patterns of intergranular phases change from the divorced growth to coupled growth as compositions change.Moreover,the mechanical performance improves with Zn rising,ascribed to the decrease of brittle phases at grain boundaries and the increase of LPSO structure phases.
文摘A mathematical expression of the crystal growth rate during crystallization of the amorphous alloys was derived from the micromechanism of crystallization newly developed by the authors. Thus, the satisfactory explanation of the experimental results obtained by Nunogaki et al., Heimendahl et al. and the authors might be found. It seems also to be modelled with the expression for the crystal growth and the crystal size influenced by time during the crystallization of amorphous Ni-P alloy foil at in situ heating. Based on the expression, the factors influencing the crystal growth rate, such as temperature, time and microstructure of amorphous alloys have been discussed.
文摘In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.
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 Sustentation Program of National Ministries and Commissions of China (Grant No. 51319030302 and Grant No. 9140A19030506KG0166)
文摘New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process（NHPP） corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.
