Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the i...Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA : L(H) -L(H) X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L(2-H H), and gave a g6neralisation of Stampflli theorem.展开更多
The equations of motion of a bubble, expanding adiabatically through an incompressible viscous fluid, are deduced when the centre of the bubble moves in a vertical plane in the presence of gravitational acceleration, ...The equations of motion of a bubble, expanding adiabatically through an incompressible viscous fluid, are deduced when the centre of the bubble moves in a vertical plane in the presence of gravitational acceleration, acting vertically downwards. The non-linear equations of motion obtained are solved numerically for different values of the various parameters of the problem. The path traced by the centre of the bubble and velocity of the centre, the change of radius R with time, and the influence of the buoyancy force, which is experienced by the expanding bubble for different values of the gravitational acceleration on these quantities, are investigated. The radius R(t) of the bubble is found to vary periodically with time when the acceleration due to gravity is small. But when the acceleration due to gravity increases, this periodicity in the value of R(t) with t is lost. The influence of viscosity in determining the periodicity of the bubble motion is also investigated.展开更多
A snake algorithm has been known that it has a strong point in extracting the exact contour of an object. But it is apt to be influenced by scattered edges around the control points. Since the shape of a moving object...A snake algorithm has been known that it has a strong point in extracting the exact contour of an object. But it is apt to be influenced by scattered edges around the control points. Since the shape of a moving object in 2D image changes a lot due to its rotation and translation in the 3D space, the conventional algorithm that takes into account slowly moving objects cannot provide an appropriate solution. To utilize the advantages of the snake algorithm while minimizing the drawbacks, this paper proposes the area variation based color snake algorithm for moving object tracking. The proposed algorithm includes a new energy term which is used for preserving the shape of an object between two consecutive images. The proposed one can also segment precisely interesting objects on complex image since it is based on color information. Experiment results show that the proposed algorithm is very effective in various environments.展开更多
In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out...In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.展开更多
Let L be a one-to-one operator of type w having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k C N. In this paper, the authors introduce the Hardy space HPL(Rn) with p ∈(0, ...Let L be a one-to-one operator of type w having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k C N. In this paper, the authors introduce the Hardy space HPL(Rn) with p ∈(0, 1] associated with L in terms of square functions defined via {e-t2kL}t〉O and establish their molecular and generalized square function characterizations. Typical examples of such operators include the 2k-order divergence form homogeneous elliptic operator L1 with complex bounded measurable coefficients and the 2k-order Schr6dinger type operator L2 := (-△)k + Vk, where A is the Laplacian and 0≤V C Llkoc(Rn). Moreover, as an application, for i E {1, 2}, the authors prove that the associated Riesz transform Vk(Li-1/2) p n HP(Rn) for @ (n/(n + k), 1] and establish the Riesz transform characterizations is bounded from HLI(IR ) to p of HPL1(]Rn) for p C (rn/(n + kr), 1] if {e-tL1 }t〉o satisfies the Lr - L2 k-off-diagonal estimates with r C (1, 2]. These results when k := I and L := L1 are known.展开更多
The existence of classical solutions to a stationary simplified quantum energytransport model for semiconductor devices in 1-dimensional space is proved.The model consists of a nonlinear elliptic third-order equation ...The existence of classical solutions to a stationary simplified quantum energytransport model for semiconductor devices in 1-dimensional space is proved.The model consists of a nonlinear elliptic third-order equation for the electron density,including a temperature derivative,an elliptic nonlinear heat equation for the electron temperature,and the Poisson equation for the electric potential.The proof is based on an exponential variable transformation and the Leray-Schauder fixed-point theorem.展开更多
This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or the Onofri inequality for brevity. In dimension two this inequality plays a role similar to that of the Sobolev inequality in higher dimens...This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or the Onofri inequality for brevity. In dimension two this inequality plays a role similar to that of the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, the authors state several elementary remarks.Various new results are also proved in this paper. A proof of the inequality is given by using mass transportation methods(in the radial case), consistently with similar results for Sobolev inequalities. The authors investigate how duality can be used to improve the Onofri inequality, in connection with the logarithmic Hardy-Littlewood-Sobolev inequality.In the framework of fast diffusion equations, it is established that the inequality is an entropy-entropy production inequality, which provides an integral remainder term. Finally,a proof of the inequality based on rigidity methods is given and a related nonlinear flow is introduced.展开更多
文摘Let H be a separable infinite dimensional complex Hilbert space, and L(H) the algebra of all bounded linear operators on 3-t'. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA : L(H) -L(H) X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L(2-H H), and gave a g6neralisation of Stampflli theorem.
文摘The equations of motion of a bubble, expanding adiabatically through an incompressible viscous fluid, are deduced when the centre of the bubble moves in a vertical plane in the presence of gravitational acceleration, acting vertically downwards. The non-linear equations of motion obtained are solved numerically for different values of the various parameters of the problem. The path traced by the centre of the bubble and velocity of the centre, the change of radius R with time, and the influence of the buoyancy force, which is experienced by the expanding bubble for different values of the gravitational acceleration on these quantities, are investigated. The radius R(t) of the bubble is found to vary periodically with time when the acceleration due to gravity is small. But when the acceleration due to gravity increases, this periodicity in the value of R(t) with t is lost. The influence of viscosity in determining the periodicity of the bubble motion is also investigated.
文摘A snake algorithm has been known that it has a strong point in extracting the exact contour of an object. But it is apt to be influenced by scattered edges around the control points. Since the shape of a moving object in 2D image changes a lot due to its rotation and translation in the 3D space, the conventional algorithm that takes into account slowly moving objects cannot provide an appropriate solution. To utilize the advantages of the snake algorithm while minimizing the drawbacks, this paper proposes the area variation based color snake algorithm for moving object tracking. The proposed algorithm includes a new energy term which is used for preserving the shape of an object between two consecutive images. The proposed one can also segment precisely interesting objects on complex image since it is based on color information. Experiment results show that the proposed algorithm is very effective in various environments.
基金supported by National Natural Science Foundation of China(Grant Nos. 10931001,10901076 and 11171345)Shanghai Leading Academic Discipline Project(Grant No.J50101)supported by the Key Laboratory of Mathematics and Complex System(Beijing Normal University),Ministry of Education,China
文摘In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.
基金supported by National Natural Science Foundation of China (Grant No.11171027)Program for Changjiang Scholars and Innovative Research Team in University of China
文摘Let L be a one-to-one operator of type w having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k C N. In this paper, the authors introduce the Hardy space HPL(Rn) with p ∈(0, 1] associated with L in terms of square functions defined via {e-t2kL}t〉O and establish their molecular and generalized square function characterizations. Typical examples of such operators include the 2k-order divergence form homogeneous elliptic operator L1 with complex bounded measurable coefficients and the 2k-order Schr6dinger type operator L2 := (-△)k + Vk, where A is the Laplacian and 0≤V C Llkoc(Rn). Moreover, as an application, for i E {1, 2}, the authors prove that the associated Riesz transform Vk(Li-1/2) p n HP(Rn) for @ (n/(n + k), 1] and establish the Riesz transform characterizations is bounded from HLI(IR ) to p of HPL1(]Rn) for p C (rn/(n + kr), 1] if {e-tL1 }t〉o satisfies the Lr - L2 k-off-diagonal estimates with r C (1, 2]. These results when k := I and L := L1 are known.
基金the Vital Science Research Foundation of Henan Province Education Department(No.12A110024)
文摘The existence of classical solutions to a stationary simplified quantum energytransport model for semiconductor devices in 1-dimensional space is proved.The model consists of a nonlinear elliptic third-order equation for the electron density,including a temperature derivative,an elliptic nonlinear heat equation for the electron temperature,and the Poisson equation for the electric potential.The proof is based on an exponential variable transformation and the Leray-Schauder fixed-point theorem.
基金supported by the Projects STAB and Kibord of the French National Research Agency(ANR)the Project No NAP of the French National Research Agency(ANR)the ECOS Project(No.C11E07)
文摘This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or the Onofri inequality for brevity. In dimension two this inequality plays a role similar to that of the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, the authors state several elementary remarks.Various new results are also proved in this paper. A proof of the inequality is given by using mass transportation methods(in the radial case), consistently with similar results for Sobolev inequalities. The authors investigate how duality can be used to improve the Onofri inequality, in connection with the logarithmic Hardy-Littlewood-Sobolev inequality.In the framework of fast diffusion equations, it is established that the inequality is an entropy-entropy production inequality, which provides an integral remainder term. Finally,a proof of the inequality based on rigidity methods is given and a related nonlinear flow is introduced.