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Hausdorff Dimension of a Class ofweierstrass functions

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Analysis in Theory and Applications 2020年第4期36卷 482-496页

作者： Huojun Ruan Na Zhang School of Mathematical Sciences Zhejiang UniversityHangzhouZhejiang 310027China

It was proved by Shen that the graph of the classical weierstrass function∑∞n=0λn cos(2πbnx)has Hausdorff dimension 2+logλ/log b,for every integer b≥2 and everyλ∈(1/b,1)[Hausdorff dimension of the graph of the classical weierstrass functions,Math.Z.,289(2018),223-266].In this paper,we prove that the dimension formula holds for every integer b≥3 and everyλ∈2(1/b,1)if we replace the function cos by sin in the definition of weierstrass function.A class of more general functions are also discussed.

关键词： Hausdorff dimension weierstrass function SRB measure.

The Hausdorff dimension of graph of a class of weierstrass functions

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Progress in Natural Science:Materials International 1996年第5期 37-43页

作者：孙道椿文志英 Department of Mathematics Wuhan University Wuhan 430072 China Department of Mathematics Wuhan Unrveristy Wuhan 430072 China Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China

Consider the following type of weierstrass functionswhere . Determine the Hausdorff dimension of graph of the above functions under some weak conditions, which generalizes some known results.

关键词： weierstrass function Hausdorff dimension fractal.

The Fractional Derivatives of a Fractal function

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Acta Mathematica Sinica,English Series 2006年第3期22卷 719-722页

作者： Kui YAO Wei Yi SU Song Ping ZHOU Department of Mathematics Nanjing University and PLA University of Sci-Tech Department of Mathematics Nanjing University Institute of Mathematics Zhejiang Sci-Tech University

The present paper investigates the fractional derivatives of weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Wei... 详细信息

关键词： weierstrass function fractional derivatives dimensions of graphs of functions

ON A CLASS OF BESICOVITCH functionS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION

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Analysis in Theory and Applications 2004年第2期20卷 175-181页

作者： ZhouSongping HeGuolong ZhejiangInstituteofScienceandTechnology ChinaNingboUniversityChina ZhejiangNormalUniversity China

This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ>1. The results show thatis a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions. For the fractional Riemann-Liouvtlle differential operator Du and the fractional integral operator D-v, the results show that if A is sufficiently large, then a necessary and sufficient condition for box dimensionof Graph(D-v(B)), 0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)), 0 < u < 2 - s, to bes + u is also lim.

关键词： weierstrass function Besicovitch function fractal dimension box dimension Hard- mard condition

Single Mode Periodic Wave Trains in Self-Gravitating Dusty Plasma

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Journal of Applied Mathematics and Physics 2023年第11期11卷 3585-3609页

作者： Francis Formusang Ngwabe François Marie Moukam Kakmeni Complex Systems and Theoretical Biology Group Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS) Department of Physics Faculty of Science University of Buea Buea Cameroon

In this paper, we consider the dynamics of modulated waves in an unmagnetized, non-isothermal self-gravitating dusty plasma model. The varying charge on the moving dust, as it moves in and out of regions of differing electron and ion densities (due to changes in the electrostatic potential), will be out of phase with the equilibrium charge. The effect of the dust is to increase the phase velocity of the ion-acoustic (IA) waves i.e. decrease the Landau damping. In the low-amplitude limit and weak damping, we apply the reductive perturbation method on the model that resulted to the complex cubic Ginzburg-Landau (CCGL) equation. From these results, it is observed that, the plasma parameters strongly influence the properties of the solitary wave solution namely, the amplitude and the width. The effects of non-isothermal electrons, gravity, dust charge fluctuations and drifting motion on the ion-acoustic solitary waves are discussed with application in astrophysical contexts. It is also observed that the number of charges residing on the dust grains increases the modulational stability of the plane waves in the plasma, thus, enhancing the generation of modulated waves.

关键词： Ginzburg-Landau Equation weierstrass function Modulated Waves Self-Gravitating Dusty Plasma