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GENERALIZED RIEMANN INTEGRAL ON fractal setS

Acta Mathematica Scientia 2017年第5期37卷 1230-1236页

作者：苏峰 Department of Basic Courses Guangzhou Maritime UniversityGuangzhou 510330China

The theory of integration to mathematical analysis is so important that many mathematicians continue to develop new theory to enlarge the class of integrable functions and simplify the Lebesgue theory integration. In this paper, by slight modifying the definition of the Henstock integral which was introduced by Jaroslav Kurzweil and Ralph Henstock, we present a new definition of integral on fractal sets. Furthermore, its integrability has been discussed, and the relationship between differentiation and integral is also established. As an example, the integral of Cantor function on Cantor set is calculated.

关键词： fractal set integral Hausdorff measure s-set

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THE NAGUMO EQUATION ON SELF-SIMILAR fractal setS

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 519-530页

作者： HU JIAXINDepartment of Mathematics, Tsinghua University, Beijing 100084, China. Department of Mathematics Tsinghua University Beijing 100084 China

The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.

关键词： fractal set Spectral dimension Sobolev-type inequality Strong (Weak) solution

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INERTIAL fractal setS FOR DISSIPATIVE ZAKHAROV SYSTEM

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Acta Mathematicae Applicatae Sinica 1997年第3期13卷 279-288页

作者：戴正德郭柏灵 Department of Mathematics Yunnan University Kunming China Institute of Applied Physics and Computational Mathematics Beijing China

[1] has proved that the dissipative Zakharov system has an ε2-weak compact attractor. In this paper, we further show that the dissipative Langmuir waves in plasmas admit an inertial fractal set of (ε2,ε1)-type. We ... 详细信息

关键词： Dissipative Zakharov system fractal set dimension

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HAUSDORFF DIMENSION OF CUTset OF COMPLEX VALUED RADEMACHER SERIES

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Acta Mathematicae Applicatae Sinica 2000年第2期16卷 140-148页

作者：吴敏 Department of Mathematics Hubei University Wuhan China

Cutsets of series form an important class of fractal sets. In this paper, the author obtains the Hausdoff dimension of outset of complex valued Rademacher serise.

关键词： Hausdorff dimension fractal set outset

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