We consider the following non-linear elliptic equation △u＋ f（x,u）=0,x∈K on fractal domains with zero-Dirichlet boundary conditions, where K is self-similar fractal, △ is the Laplacian defined on K. f（x, t） is...We consider the following non-linear elliptic equation △u＋ f（x,u）=0,x∈K on fractal domains with zero-Dirichlet boundary conditions, where K is self-similar fractal, △ is the Laplacian defined on K. f（x, t） is asymptotically linear as t→ ∞. We get the non-trivial and non-negative solution by using Mountain Pass lemma.展开更多
This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block co...This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.展开更多
The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicat...The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.展开更多
Fractals play an important role in mathematics, aesthetic, science, and engineering. The representative Sierpinski-triangle fractals have been successfully constructed by V-shape molecules in experiments. The molecula...Fractals play an important role in mathematics, aesthetic, science, and engineering. The representative Sierpinski-triangle fractals have been successfully constructed by V-shape molecules in experiments. The molecular Sierpinski triangles formed by molecules with linear backbones have been theoretically predicted but not experimentally discovered. To achieve this goal in the experiment, we used[1,1’;4’,1’’;4’’,1’’’]-quaterphenyl-3,40 0-dicarbonitrile molecules as building blocks and employed cobalt atoms as cements, then successfully obtained metal-organic Sierpinski triangles with an order up to 2 on the Au（111） surface. There are twenty-four types of three-fold coordination nodes formed between the metal atom and organic ligands via coordinate interactions. The coexistence of various nodes is responsible for that the highest order of Sierpinski triangles is limited to 2.展开更多
Various fractal morphologies are obtained by introducing noise reduc-tion, tansential and radial probabilities into DLA (diffusion-limited aggregation)medel. As the noise is reduced, perimeter sites with extremely sm...Various fractal morphologies are obtained by introducing noise reduc-tion, tansential and radial probabilities into DLA (diffusion-limited aggregation)medel. As the noise is reduced, perimeter sites with extremely small values of lo-cal field gradient ar展开更多
The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence...The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.展开更多
基金Supported by the National Natural Science Foundation of China(10025107)
文摘We consider the following non-linear elliptic equation △u＋ f（x,u）=0,x∈K on fractal domains with zero-Dirichlet boundary conditions, where K is self-similar fractal, △ is the Laplacian defined on K. f（x, t） is asymptotically linear as t→ ∞. We get the non-trivial and non-negative solution by using Mountain Pass lemma.
基金supported by the National Natural Science Foundation of China(61171170) the Natural Science Foundation of Anhui Province(1408085QF115)
文摘This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.
文摘The linear relationship between fractal dimensions of a type of generalized Weierstrass functions and the order of their fractional calculus has been proved. The graphs and numerical results given here further indicate the corresponding relationship.
基金supported by the National Natural Science Foundation of China (Nos. 21522301, 21373020, 21403008, 61621061, 21433011, 61271050)the Ministry of Science and Technology (Nos. 2014CB239302 and 2013CB933404)
文摘Fractals play an important role in mathematics, aesthetic, science, and engineering. The representative Sierpinski-triangle fractals have been successfully constructed by V-shape molecules in experiments. The molecular Sierpinski triangles formed by molecules with linear backbones have been theoretically predicted but not experimentally discovered. To achieve this goal in the experiment, we used[1,1’;4’,1’’;4’’,1’’’]-quaterphenyl-3,40 0-dicarbonitrile molecules as building blocks and employed cobalt atoms as cements, then successfully obtained metal-organic Sierpinski triangles with an order up to 2 on the Au（111） surface. There are twenty-four types of three-fold coordination nodes formed between the metal atom and organic ligands via coordinate interactions. The coexistence of various nodes is responsible for that the highest order of Sierpinski triangles is limited to 2.
文摘Various fractal morphologies are obtained by introducing noise reduc-tion, tansential and radial probabilities into DLA (diffusion-limited aggregation)medel. As the noise is reduced, perimeter sites with extremely small values of lo-cal field gradient ar
基金supported by the National Natural Science Foundation of China (No.10871156)the Fund of Xi'an Jiaotong University (No.2009xjtujc30)
文摘The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.
