In this paper the pseudo -primeness of meromorphic functions of infinite order is dissoussed in detail and quite a few result are obtained, which are improvments of that of Ozawa.
Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there ex...Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0)<e, the solution of the heat flow with initial value u0 must blow up in finite time. We also present a sufficient condition which ensures that any global solutions subconverge to harmonic maps as t→∞.展开更多
A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derive...A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.展开更多
The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the...The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.展开更多
It is proved that in Taub's and Kar's plane-symmetric spacetime,a future directed null geodesic emanating from a point"p"will enter the chronological future of"p".Physically,this implies th...It is proved that in Taub's and Kar's plane-symmetric spacetime,a future directed null geodesic emanating from a point"p"will enter the chronological future of"p".Physically,this implies that the light signal from a movie projector with its back to the screen will finally come back to the screen and form a movie which looks exactly the same as the true one.展开更多
In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f(z) be transcendental mero-morphic in the finite plane and k b...In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f(z) be transcendental mero-morphic in the finite plane and k be a positive integer. If ε is an arbitrary positive numberand a and b are two distinct finite complex numbers, then we have T(r,f)<(1+1/k)N (r,1/f)+(1+1/k)N (r,1/(f^(k)-1)) -N (r,1/(f(k+1))+εT(r,f)+S(r,f)and δ(a,f^(k))+δ(b,f^(k))≤1+1/(2k+1).展开更多
1 Introduction It is known that the stability of control systems is very important. So far, the absolute stability of nonlinear ordinary control systems has been widely studied and many outstanding results have been o...1 Introduction It is known that the stability of control systems is very important. So far, the absolute stability of nonlinear ordinary control systems has been widely studied and many outstanding results have been obtained. However, for the absolute stability of nonlinear control systems with delay, seldom results have been reported. Since the nonlinear control systems with delay are defined on the function space, the absolute stability of it is more difficult and complex than that of nonlinear ordinary control systems. On the other hand, almost all the closed loop control systems are affected by delay. It must be interesting to study the absolute stability of nonlinear control systems with delay. In展开更多
S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length o...S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length of the second fundamental form as a function on this set. Is the image of this function a discrete set of positive numbers?展开更多
Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a, b) of G and by joining each new vertex e* to the end vertices a and b of the edge e cor...Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a, b) of G and by joining each new vertex e* to the end vertices a and b of the edge e corresponding to it. In this paper, we prove that the number of matchings of R(G) is completely determined by the degree sequence of vertices of G.展开更多
The structure of symplectic groups over fields has been determined completely. Several authors discussed symplectic groups over commutative rings, but they made strong restrictions on the underlying rings. In this let...The structure of symplectic groups over fields has been determined completely. Several authors discussed symplectic groups over commutative rings, but they made strong restrictions on the underlying rings. In this letter we start from elementary symplectic matrices and,展开更多
Let R be an arbitrary commutative ring, and n an integer≥3. It is proved for any ideal J of R thatEO<sub>2n</sub>（R, J）=[EO<sub>2n</sub>（R）, EO<sub>2n</sub>（J）]=[EO<sub>...Let R be an arbitrary commutative ring, and n an integer≥3. It is proved for any ideal J of R thatEO<sub>2n</sub>（R, J）=[EO<sub>2n</sub>（R）, EO<sub>2n</sub>（J）]=[EO<sub>2n</sub>（R）, EO<sub>2n</sub>（R, J）]=[EO<sub>2n</sub>（R）, O<sub>2n</sub>（R,J）]=[O<sub>2n</sub>（R）, EO<sub>2n</sub>（R,J）].In particular, EO<sub>2n</sub>（R, J） is a normal subgroupof O<sub>2n</sub>（R）. Furthermore, the problem of normal subgroups of O<sub>2n</sub>（R） has an affirmative solution if and only if aR∩ Ann（2）=α<sup>2</sup> Ann（2） for each a in R. In particular, if 2 is not a zero divisor in R, then the problem of normal subgroups of O<sub>2n</sub>（R） has an affirmative展开更多
In this paper we consider the following equation with polynomials as the coefficients and discuss some properties and the estimation of the number of solutions of (1). It is well known that if n=2, i. e. (1) is a Ricc...In this paper we consider the following equation with polynomials as the coefficients and discuss some properties and the estimation of the number of solutions of (1). It is well known that if n=2, i. e. (1) is a Riccati equation, then it can possess a transcendental meromorphic solution of finite order and a one-parameter family of meromorphic展开更多
By introducing the horosphere coordinate of a unit ball B<sup>n</sup> in C<sup>n</sup> and an integraltransformation formula of functions in such coordidates,the author constructs the heatkerne...By introducing the horosphere coordinate of a unit ball B<sup>n</sup> in C<sup>n</sup> and an integraltransformation formula of functions in such coordidates,the author constructs the heatkernel H<sub>B<sup>n</sup></sub>（z,w,t）of the heat equation associated to the Bergman metric of B<sup>n</sup>.That iswhere c<sub>n</sub> is a well-defined constant and r（z,w）is the geodesic destance of two points zand w of B<sub>n</sub> and t∈ R<sup>+</sup>.Sincethenis the Green function of the topological product space B<sup>m</sup>×B<sup>n</sup>.展开更多
It is known that homogeneous bounded domains are holomorphic isomorphic to N-Siegel domains, in order to compute the holomorphic sectional curvatures of the homogeneous bounded domains, one needs only to compute the h...It is known that homogeneous bounded domains are holomorphic isomorphic to N-Siegel domains, in order to compute the holomorphic sectional curvatures of the homogeneous bounded domains, one needs only to compute the holomorphic展开更多
Let f be an entire function of finite lower order μ and order λ If the zeros of ff'-1 are attracted to q(<+∞) rays,then λmust be finite.Moreover,we have(i)λ≤1/2,when q=1.(ii)The magnitude of acute angle o...Let f be an entire function of finite lower order μ and order λ If the zeros of ff'-1 are attracted to q(<+∞) rays,then λmust be finite.Moreover,we have(i)λ≤1/2,when q=1.(ii)The magnitude of acute angle of these two rays is exactly equal toπ/λ,when q=2 and μ>1 (iii)There are at least two rays such that the magnitude of acute angle between them does not exceed π/λ,when q≥2展开更多
A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,the...A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.展开更多
If f(z) is meromorphic and of finite lower order μ in the plane, then the set of ite deficientfunctions is countable and the total sum of the corresponding deficiencies does not exceedmin{[2μ]+1, max(1,(1/2)2/2μπ)}.
In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we sho...In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we show by using an ana-lytical method that there may exist two or four Hopf bifurcation points separatedat a finite distance from each other;at the same time,a technique for studying theHopf bifurcation value is given.展开更多
文摘In this paper the pseudo -primeness of meromorphic functions of infinite order is dissoussed in detail and quite a few result are obtained, which are improvments of that of Ozawa.
文摘Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0)<e, the solution of the heat flow with initial value u0 must blow up in finite time. We also present a sufficient condition which ensures that any global solutions subconverge to harmonic maps as t→∞.
文摘A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.
文摘The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.
基金supported in part by the Science Fund of the Ministry of Eduction of the People's Republic of China.
文摘It is proved that in Taub's and Kar's plane-symmetric spacetime,a future directed null geodesic emanating from a point"p"will enter the chronological future of"p".Physically,this implies that the light signal from a movie projector with its back to the screen will finally come back to the screen and form a movie which looks exactly the same as the true one.
基金Project partially supported by the National Natural Science Foundation of China.
文摘In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f(z) be transcendental mero-morphic in the finite plane and k be a positive integer. If ε is an arbitrary positive numberand a and b are two distinct finite complex numbers, then we have T(r,f)<(1+1/k)N (r,1/f)+(1+1/k)N (r,1/(f^(k)-1)) -N (r,1/(f(k+1))+εT(r,f)+S(r,f)and δ(a,f^(k))+δ(b,f^(k))≤1+1/(2k+1).
基金Project supported by the National Natural Science Foundation of China.
文摘1 Introduction It is known that the stability of control systems is very important. So far, the absolute stability of nonlinear ordinary control systems has been widely studied and many outstanding results have been obtained. However, for the absolute stability of nonlinear control systems with delay, seldom results have been reported. Since the nonlinear control systems with delay are defined on the function space, the absolute stability of it is more difficult and complex than that of nonlinear ordinary control systems. On the other hand, almost all the closed loop control systems are affected by delay. It must be interesting to study the absolute stability of nonlinear control systems with delay. In
文摘S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length of the second fundamental form as a function on this set. Is the image of this function a discrete set of positive numbers?
文摘Let G be a simple graph. Define R(G) to be the graph obtained from G by adding a new vertex e* corresponding to each edge e = (a, b) of G and by joining each new vertex e* to the end vertices a and b of the edge e corresponding to it. In this paper, we prove that the number of matchings of R(G) is completely determined by the degree sequence of vertices of G.
文摘The structure of symplectic groups over fields has been determined completely. Several authors discussed symplectic groups over commutative rings, but they made strong restrictions on the underlying rings. In this letter we start from elementary symplectic matrices and,
基金Projects supported by the Science Fund of the Chinese Academy of Sciences
文摘Let R be an arbitrary commutative ring, and n an integer≥3. It is proved for any ideal J of R thatEO<sub>2n</sub>（R, J）=[EO<sub>2n</sub>（R）, EO<sub>2n</sub>（J）]=[EO<sub>2n</sub>（R）, EO<sub>2n</sub>（R, J）]=[EO<sub>2n</sub>（R）, O<sub>2n</sub>（R,J）]=[O<sub>2n</sub>（R）, EO<sub>2n</sub>（R,J）].In particular, EO<sub>2n</sub>（R, J） is a normal subgroupof O<sub>2n</sub>（R）. Furthermore, the problem of normal subgroups of O<sub>2n</sub>（R） has an affirmative solution if and only if aR∩ Ann（2）=α<sup>2</sup> Ann（2） for each a in R. In particular, if 2 is not a zero divisor in R, then the problem of normal subgroups of O<sub>2n</sub>（R） has an affirmative
文摘In this paper we consider the following equation with polynomials as the coefficients and discuss some properties and the estimation of the number of solutions of (1). It is well known that if n=2, i. e. (1) is a Riccati equation, then it can possess a transcendental meromorphic solution of finite order and a one-parameter family of meromorphic
文摘By introducing the horosphere coordinate of a unit ball B<sup>n</sup> in C<sup>n</sup> and an integraltransformation formula of functions in such coordidates,the author constructs the heatkernel H<sub>B<sup>n</sup></sub>（z,w,t）of the heat equation associated to the Bergman metric of B<sup>n</sup>.That iswhere c<sub>n</sub> is a well-defined constant and r（z,w）is the geodesic destance of two points zand w of B<sub>n</sub> and t∈ R<sup>+</sup>.Sincethenis the Green function of the topological product space B<sup>m</sup>×B<sup>n</sup>.
文摘It is known that homogeneous bounded domains are holomorphic isomorphic to N-Siegel domains, in order to compute the holomorphic sectional curvatures of the homogeneous bounded domains, one needs only to compute the holomorphic
基金Project supported by the Croucher FoundationTianyuan Foundation+1 种基金partially supported by a U.P.G.C.grantHong Kong
文摘Let f be an entire function of finite lower order μ and order λ If the zeros of ff'-1 are attracted to q(<+∞) rays,then λmust be finite.Moreover,we have(i)λ≤1/2,when q=1.(ii)The magnitude of acute angle of these two rays is exactly equal toπ/λ,when q=2 and μ>1 (iii)There are at least two rays such that the magnitude of acute angle between them does not exceed π/λ,when q≥2
文摘A piston problem of viscous polytropit gas equations is discussed.It is shown that the global solution is bounded uniformly in time if the piston motion is bounded and that if the piston motion is periodic in time,then there exists a periodic solution to the piston problem with the same period.
文摘If f(z) is meromorphic and of finite lower order μ in the plane, then the set of ite deficientfunctions is countable and the total sum of the corresponding deficiencies does not exceedmin{[2μ]+1, max(1,(1/2)2/2μπ)}.
基金Supported by the Chinese National Science Foundation"Tian Yuan"Terms and LNM Institute of Mechanics,Chinese Academy of Sciences
文摘In this paper a mathematical model of chemical systems is investigated.We present the conditions for the existence and local stability of the steady statesand the periodic solution of the Hopf type.Specifically,we show by using an ana-lytical method that there may exist two or four Hopf bifurcation points separatedat a finite distance from each other;at the same time,a technique for studying theHopf bifurcation value is given.
