In this paper, we investigate the surfaces of revolution under the condition FIl（G） = k（G ＋ C）, where r11 is one of the Christoffel-like operators, G is the Gauss map of the surface, k is a non-constant function ...In this paper, we investigate the surfaces of revolution under the condition FIl（G） = k（G ＋ C）, where r11 is one of the Christoffel-like operators, G is the Gauss map of the surface, k is a non-constant function and C is a constant vector in Minkowski 3-space.展开更多
The notion of finite-type open set condition is defined to calculate the Hausdorff dimensions of the sections of some self-similar sets, such as the dimension of intersection of the Koch curve and the line x=α with ...The notion of finite-type open set condition is defined to calculate the Hausdorff dimensions of the sections of some self-similar sets, such as the dimension of intersection of the Koch curve and the line x=α with α∈ Q.展开更多
This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic ini...This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.展开更多
Let {X(t), ≥ 0} be Brownian motion on Sierpinski gasket.The Hausdorff and packingdimensions of the image of a compact set are studied. The uniform Hausdorff and packingdimensions of the inverse image are also discus...Let {X(t), ≥ 0} be Brownian motion on Sierpinski gasket.The Hausdorff and packingdimensions of the image of a compact set are studied. The uniform Hausdorff and packingdimensions of the inverse image are also discussed.展开更多
The abhors determine the Hausdoar and Bouligand dimensions of a class of recurrent setsby usillg elemelltare mathods and, as a corollaly, give a new proof of a conjecture by Dekkingwhich has been proved by Bedford by ...The abhors determine the Hausdoar and Bouligand dimensions of a class of recurrent setsby usillg elemelltare mathods and, as a corollaly, give a new proof of a conjecture by Dekkingwhich has been proved by Bedford by using the ergodic techniques.展开更多
This paper studies the Hausdorff dimensions, the Hausdorff measures of generalized Moranfrontals and the convergence of the Fourier series of functions defined on some generalizedMoran fractals. A general formula is g...This paper studies the Hausdorff dimensions, the Hausdorff measures of generalized Moranfrontals and the convergence of the Fourier series of functions defined on some generalizedMoran fractals. A general formula is given for the calculatinn of the Hausdorff dimensions ofgeneralized Moran fractals and it is proved that their Hausdorff measures are finite positivenumbers under some conditions. In addition, the authors define an orthonormal system offunctions defilled on generalized Moran s-sets (gMs) and discuss the convergence of the Fourierseries, with respect to of each function f(x) E L1(gMs, Hs).展开更多
This paper defines the upper capacity densities of the subsets of R￣n, gets uniform lower bound of the upper capacity densities for -almost all points of the Hausdorff s-sets or the analytic sets with Hausdorff dimen...This paper defines the upper capacity densities of the subsets of R￣n, gets uniform lower bound of the upper capacity densities for -almost all points of the Hausdorff s-sets or the analytic sets with Hausdorff dimension s in R￣n which improves the results of Wen Zhiying and Zhang Yiping's paper in [1].展开更多
文摘In this paper, we investigate the surfaces of revolution under the condition FIl（G） = k（G ＋ C）, where r11 is one of the Christoffel-like operators, G is the Gauss map of the surface, k is a non-constant function and C is a constant vector in Minkowski 3-space.
基金Project supported by the National Natural Science Foundation of China (No. 10301029, No. 10241003, No. 10671180, No. 10626003)the Morningside Center of Mathematics, Beijing, China.
文摘The notion of finite-type open set condition is defined to calculate the Hausdorff dimensions of the sections of some self-similar sets, such as the dimension of intersection of the Koch curve and the line x=α with α∈ Q.
基金This research is supported by the National Natural Science Foundation of China(Grant 10271034).
文摘This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.
文摘Let {X(t), ≥ 0} be Brownian motion on Sierpinski gasket.The Hausdorff and packingdimensions of the image of a compact set are studied. The uniform Hausdorff and packingdimensions of the inverse image are also discussed.
文摘The abhors determine the Hausdoar and Bouligand dimensions of a class of recurrent setsby usillg elemelltare mathods and, as a corollaly, give a new proof of a conjecture by Dekkingwhich has been proved by Bedford by using the ergodic techniques.
文摘This paper studies the Hausdorff dimensions, the Hausdorff measures of generalized Moranfrontals and the convergence of the Fourier series of functions defined on some generalizedMoran fractals. A general formula is given for the calculatinn of the Hausdorff dimensions ofgeneralized Moran fractals and it is proved that their Hausdorff measures are finite positivenumbers under some conditions. In addition, the authors define an orthonormal system offunctions defilled on generalized Moran s-sets (gMs) and discuss the convergence of the Fourierseries, with respect to of each function f(x) E L1(gMs, Hs).
文摘This paper defines the upper capacity densities of the subsets of R￣n, gets uniform lower bound of the upper capacity densities for -almost all points of the Hausdorff s-sets or the analytic sets with Hausdorff dimension s in R￣n which improves the results of Wen Zhiying and Zhang Yiping's paper in [1].
