In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based o...In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based on the theorems.展开更多
In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent...In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary.展开更多
Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f...Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z +c) and forward differences △c^n f(z), n ∈ N^+.展开更多
In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lo...In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved.展开更多
We prove that a Cl-generic volume-preserving dynamical system (diffeomor- phism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in ...We prove that a Cl-generic volume-preserving dynamical system (diffeomor- phism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27], we prove that the Cl-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system (diffeomorphism or flow) is Anosov.展开更多
In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ(a, b, c) = (ab, ac, a). Let Wp be the p-th occurrence of w and Gp(ω) be ...In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ(a, b, c) = (ab, ac, a). Let Wp be the p-th occurrence of w and Gp(ω) be the gap between Wp and Wp+l. We introduce a notion of kernel for each factor w, and then give the decomposition of the factor w with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper: for each factor w, the gap sequence {Gp(ω)}p≥1 is the Tribonacci sequence over the alphabet {G1 (ω), G2(ω), G4(ω)}, and the expressions of gaps are determined completely. As an application, for each factor w and p C ∈N, we determine the position of Wp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.展开更多
In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switc...In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function (SLF) method with Finsler's Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.展开更多
In this paper,we study the di erence equation a1(z)f(z+1)+a0(z)f(z)=0;where a1(z)and a0(z)are entire functions of nite order.Under some conditions,we obtain some properties,such as xed points,zeros etc.,of the di eren...In this paper,we study the di erence equation a1(z)f(z+1)+a0(z)f(z)=0;where a1(z)and a0(z)are entire functions of nite order.Under some conditions,we obtain some properties,such as xed points,zeros etc.,of the di erences and forward di erences of meromorphic solutions of the above equation.展开更多
The problem of non-fragile dynamic output feedback H∞control for a class of uncertain switched systems with time-varying delay is discussed.Firstly,the form of non-fragile dynamic output feedback H∞controller is giv...The problem of non-fragile dynamic output feedback H∞control for a class of uncertain switched systems with time-varying delay is discussed.Firstly,the form of non-fragile dynamic output feedback H∞controller is given.Under the condition that the upper bound of time delay and the upper bound of delay derivative are limited simultaneously,Lyapunov functional and its corresponding switching rules are constructed by using single Lyapunov function method and convex combination technique;Secondly,we use the inequality lemma to scale the derived Lyapunov functional in order to eliminate the time-varying delay term in the inequality,and then introduce the J-function to obtain a nonlinear matrix inequality that satisfies the H∞performance indexγ,we also employ Schur complement lemma to transform the nonlinear matrix inequality into set of linear matrix inequalities consisting of two linear matrix inequalities,a sufficient condition for the existence of a non-fragile dynamic output feedback H∞controller and satisfying the H∞performance indexγis concluded for a class of uncertain switching systems with variable time delay;Finally,a switched system composed of two subsystems is considered and the effectiveness and practicability of the theorem are illustrated by numerical simulation with LMI toolbox.展开更多
Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials a...Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials are constructed in [5, 6]. The Strebel rays [3] and the eventually distance minimizing rays [9] are important in Teichmüller spaces and moduli spaces, respectively. Motivated by the study of [3, 9], two special kinds of Strebel rays in the real hyper-elliptic subspace of Teichmüller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article.展开更多
In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equations F(Z)N+pN-1(F)=0,where n ≥ 2 and small functions as proposed by Yang than 1. Pn-1(f) is a di...In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equations F(Z)N+pN-1(F)=0,where n ≥ 2 and small functions as proposed by Yang than 1. Pn-1(f) is a difference polynomial of degree at most n - 1 in f with coefficients. Moreover, we give two examples to show that one conjecture and Laine [2] does not hold in general if the hyper-order of f(z) is no less展开更多
In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz estimate that was originally introduced in [5].
The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT(X) is proved. Then, the notion of angles between two g...The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmuller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.展开更多
In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E...In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E and F,yet obtain the same results for Theorems E and F.We also weaken the condition(1.4)of Theorems C and D.展开更多
Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study of bifurcation. In addition to generating regular oscillations, such ...Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study of bifurcation. In addition to generating regular oscillations, such a modified model can be used to reproduce the burst discharges similar to those recorded in experiments and to describe two new types of oscillatory phenomena. By means of a fast/slow dynamical analysis, we explore the bifurcation and transition mechanisms associated with two types of bursters due to changes in the interaction of two slow variables with different timescales.展开更多
In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality(see[1,4])of meromorphic functions to algebroid functions.
In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 <...In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 < t_1, t_2 < min{α, k}, and 1 < p ≤ τ_1 :=(n+α-2t_1)/( n-α), 1 < q ≤ τ_2 :=(n+α-2 t_2)/( n-α).We first establish the equivalence of classical and weak solutions between PDE system(0.1)and the following integral equations(IE) system{u(x) =∫_( R^n) G_α(x, ξ)v^q(ξ)/|η|t^2 dξ v(x) =∫_(R^n) G_α(x, ξ)(u^p(ξ))/|η|^(t_1) dξ,(0.2)where Gα(x, ξ) =(c n,α)/(|x-ξ|^(n-α))is the Green's function of(-?)^(α/2) in R^n. Then, by the method of moving planes in the integral forms, in the critical case p = τ_1 and q = τ_2, we prove that each pair of nonnegative solutions(u, v) of(0.1) is radially symmetric and monotone decreasing about the origin in R^k and some point z0 in R^(n-k). In the subcritical case (n-t_1)/(p+1)+(n-t_2)/(q+1)> n-α,1 < p ≤ τ_1 and 1 < q ≤ τ_2, we derive the nonexistence of nontrivial nonnegative solutions for(0.1).展开更多
Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random...Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.展开更多
Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation betw...Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.展开更多
In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients....In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.展开更多
文摘In this paper, we investigate normal families of meromorphic functions, prove some theorems of normal families sharing a holomorphic function, and give a counterex- ample to the converse of the Bloch principle based on the theorems.
文摘In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary.
基金supported by the Natural Science Foundation of Guangdong Province in China(2016A030310106)the National Natural Science Foundation of China(11801110,11771090,11761035,11871260)the Foundation of Guangzhou Civil Aviation College(17X0419)
文摘Let c be a nonzero constant and f(z) be a transcendental meromorphic function of finite order. Under some conditions, we study the relationships between the exponent of convergence of fixed points of f(z), its shift f(z +c) and forward differences △c^n f(z), n ∈ N^+.
基金supported by the National Natural Science Foundation of China(10871016)
文摘In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved.
基金partially supported by National Funds through FCT-"Fundacao para a Ciencia e a Tecnologia",(PEst-OE/MAT/UI0212/2011)supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry,ICT&Future Planning(No.2014R1A1A1A05002124)supported by National Natural Science Foundation of China(No.11301018 and 11371046)
文摘We prove that a Cl-generic volume-preserving dynamical system (diffeomor- phism or flow) has the shadowing property or is expansive or has the weak specification property if and only if it is Anosov. Finally, as in [10, 27], we prove that the Cl-robustness, within the volume-preserving context, of the expansiveness property and the weak specifica- tion property, imply that the dynamical system (diffeomorphism or flow) is Anosov.
基金supported by grants from the National Science Foundation of China(114310071127122311371210)
文摘In this paper, we investigate the factor properties and gap sequence of the Tri- bonacci sequence, the fixed point of the substitution σ(a, b, c) = (ab, ac, a). Let Wp be the p-th occurrence of w and Gp(ω) be the gap between Wp and Wp+l. We introduce a notion of kernel for each factor w, and then give the decomposition of the factor w with respect to its kernel. Using the kernel and the decomposition, we prove the main result of this paper: for each factor w, the gap sequence {Gp(ω)}p≥1 is the Tribonacci sequence over the alphabet {G1 (ω), G2(ω), G4(ω)}, and the expressions of gaps are determined completely. As an application, for each factor w and p C ∈N, we determine the position of Wp. Finally we introduce a notion of spectrum for studying some typical combinatorial properties, such as power, overlap and separate of factors.
基金This work was supported by Doctorate Foundation of Shenyang Normal University of China (No. 054-554405-01)
文摘In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function (SLF) method with Finsler's Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.
基金National Natural Science Foundation of China(11801110,11771090,11761035,11871260).
文摘In this paper,we study the di erence equation a1(z)f(z+1)+a0(z)f(z)=0;where a1(z)and a0(z)are entire functions of nite order.Under some conditions,we obtain some properties,such as xed points,zeros etc.,of the di erences and forward di erences of meromorphic solutions of the above equation.
基金science basic research program of the education department of Liaoning Province(No.LJC202002).
文摘The problem of non-fragile dynamic output feedback H∞control for a class of uncertain switched systems with time-varying delay is discussed.Firstly,the form of non-fragile dynamic output feedback H∞controller is given.Under the condition that the upper bound of time delay and the upper bound of delay derivative are limited simultaneously,Lyapunov functional and its corresponding switching rules are constructed by using single Lyapunov function method and convex combination technique;Secondly,we use the inequality lemma to scale the derived Lyapunov functional in order to eliminate the time-varying delay term in the inequality,and then introduce the J-function to obtain a nonlinear matrix inequality that satisfies the H∞performance indexγ,we also employ Schur complement lemma to transform the nonlinear matrix inequality into set of linear matrix inequalities consisting of two linear matrix inequalities,a sufficient condition for the existence of a non-fragile dynamic output feedback H∞controller and satisfying the H∞performance indexγis concluded for a class of uncertain switching systems with variable time delay;Finally,a switched system composed of two subsystems is considered and the effectiveness and practicability of the theorem are illustrated by numerical simulation with LMI toolbox.
文摘Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials are constructed in [5, 6]. The Strebel rays [3] and the eventually distance minimizing rays [9] are important in Teichmüller spaces and moduli spaces, respectively. Motivated by the study of [3, 9], two special kinds of Strebel rays in the real hyper-elliptic subspace of Teichmüller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article.
基金supported by the NNSF of China(11171013,11371225,11201014)the YWF-14-SXXY-008 of Beihang Universitythe Fundamental Research Funds for the Central University
文摘In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equations F(Z)N+pN-1(F)=0,where n ≥ 2 and small functions as proposed by Yang than 1. Pn-1(f) is a difference polynomial of degree at most n - 1 in f with coefficients. Moreover, we give two examples to show that one conjecture and Laine [2] does not hold in general if the hyper-order of f(z) is no less
基金supported by the NSF of China (10801015, 10901012)
文摘In this article, we give a simple proof on the energy scattering for the Hartree equations using the interaction Morawetz estimate that was originally introduced in [5].
基金supported by National Natural Science Foundation of China(11371045,11301248)
文摘The geometry of Teichmuller metric in an asymptotic Teichmuller space is studled in this article. First, a binary infinitesimal form of Teichmuller metric on AT(X) is proved. Then, the notion of angles between two geodesic curves in the asymptotic Teichmuller space AT(X) is introduced. The existence of such angles is proved and the explicit formula is obtained. As an application, a sufficient condition for non-uniqueness geodesics in AT(X) is obtained.
基金This work is supported by the National Natural Science Foundation of China(11771090,11871260,11761035,11801093,11801110).
文摘In this paper,we mainly apply a new,asymptotic method to investigate the growth of meromorphic solutions of linear higher order difference equations and differential equations.We delete the condition(1.6)of Theorems E and F,yet obtain the same results for Theorems E and F.We also weaken the condition(1.4)of Theorems C and D.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11372017,11572084 and 11472061the Natural Science Foundation for the Higher Education Institutions of Anhui Province under Grant No KJ2016SD54+1 种基金the Fundamental Research Funds for the Central Universitiesthe Distinguished Young Professor Program of Donghua University under Grant No 16D210404
文摘Some new elements are introduced into a mathematical model of intracellular calcium oscillations, which make it particularly suitable for the study of bifurcation. In addition to generating regular oscillations, such a modified model can be used to reproduce the burst discharges similar to those recorded in experiments and to describe two new types of oscillatory phenomena. By means of a fast/slow dynamical analysis, we explore the bifurcation and transition mechanisms associated with two types of bursters due to changes in the interaction of two slow variables with different timescales.
基金supported by National Natural Science Foundation of China(1047104810771011)the Fundamental Research Funds for the Central Universities
文摘In this paper,we investigate the growth relations between algebroid functions and their derivatives,and extend famous C.Chang inequality(see[1,4])of meromorphic functions to algebroid functions.
基金supported by the NNSF of China(11371056)partly supported by the NNSF of China(11501021)+1 种基金the China Postdoctoral Science Foundation(2013M540057)partly supported by Scientific Research Fund of Jiangxi Provincial Education Department(GJJ160797)
文摘In this paper, we are concerned with the following Hardy-Sobolev type system{(-?)^(α/2) u(x) =v^q(x)/|y|^(t_2) (-?)α/2 v(x) =u^p(x)/|y|^(t_1),x =(y, z) ∈(R ~k\{0}) × R^(n-k),(0.1)where 0 < α < n, 0 < t_1, t_2 < min{α, k}, and 1 < p ≤ τ_1 :=(n+α-2t_1)/( n-α), 1 < q ≤ τ_2 :=(n+α-2 t_2)/( n-α).We first establish the equivalence of classical and weak solutions between PDE system(0.1)and the following integral equations(IE) system{u(x) =∫_( R^n) G_α(x, ξ)v^q(ξ)/|η|t^2 dξ v(x) =∫_(R^n) G_α(x, ξ)(u^p(ξ))/|η|^(t_1) dξ,(0.2)where Gα(x, ξ) =(c n,α)/(|x-ξ|^(n-α))is the Green's function of(-?)^(α/2) in R^n. Then, by the method of moving planes in the integral forms, in the critical case p = τ_1 and q = τ_2, we prove that each pair of nonnegative solutions(u, v) of(0.1) is radially symmetric and monotone decreasing about the origin in R^k and some point z0 in R^(n-k). In the subcritical case (n-t_1)/(p+1)+(n-t_2)/(q+1)> n-α,1 < p ≤ τ_1 and 1 < q ≤ τ_2, we derive the nonexistence of nontrivial nonnegative solutions for(0.1).
基金Project supported by the National Natural Science Foundation of China(Grant No.61273015)
文摘Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.
基金supported by the National Natural Science Foundation of China(Grants 11372017,11272024,and 11371046)the General Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant NJZY14130)
文摘Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.
基金supported by the National Natural Science Foundation of China(11371225)National Natural Science Foundation of Guangdong Province(2016A030313686)
文摘In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.