• ETRI Journal
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• v.38 no.6
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• pp.1135-1144
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• 2016

Fractal antenna arrays are geometry-based thinned arrays having multiband applications. The major challenge of these arrays is their large number of elements at higher expansion factors. This article presents the thinning of fractal antenna arrays while maintaining an appropriate balance between the side lobe level and beam width by using various quantized fractal distribution functions. A 2D square fractal antenna array and 3DSierpinski gasket antenna array are considered in this article to validate the proposed distribution functions. Nearly one third of the antenna elements are thinned in each successive iteration except in the case of a one-count distribution function. The proposed technique can simplify practical implementation and exhibits better performance for various parameters such as the side lobe level, side lobe angle, and half power beam width than fully populated fractal antenna arrays.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.157-163
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• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.

• Bulletin of the Korean Chemical Society
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• v.26 no.11
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• pp.1723-1727
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• 2005

A generalized fractional diffusion equation (FDE) is presented, which describes the time-evolution of the spatial distribution of a particle performing continuous time random walk (CTRW) on a fractal lattice. For a case corresponding to the CTRW with waiting time distribution that behaves as $\psi(t) \sim (t) ^{-(\alpha+1)}$, the FDE is solved to give analytic expressions for the Green’s function and the mean squared displacement (MSD). In agreement with the previous work of Blumen et al. [Phys. Rev. Lett. 1984, 53, 1301], the time-dependence of MSD is found to be given as < $r^2(t)$ > ~ $t ^{2\alpha/dw}$, where $d_w$ is the walk dimension of the given fractal. A Monte-Carlo simulation is also performed to evaluate the range of applicability of the proposed FDE.