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On Schwarzian Triangle Functions, Automorphic Forms and a Generalization of Ramanujan’s Triple Differential Equations
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作者 Li Chien SHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第11期1648-1662,共15页
Let G be the group of the fractional linear transformations generated by T(τ)=τ + λ, S(τ)=(τ cos π/n + sin π/n)/(-τ sin π/n + cos π/n);where λ=2(cos π/m + cos π/n)/sin π/n;m, n is a pair of... Let G be the group of the fractional linear transformations generated by T(τ)=τ + λ, S(τ)=(τ cos π/n + sin π/n)/(-τ sin π/n + cos π/n);where λ=2(cos π/m + cos π/n)/sin π/n;m, n is a pair of integers with either n ≥ 2, m ≥ 3 or n ≥ 3, m ≥ 2; τ lies in the upper half plane H.A fundamental set of functions f0, fi and f∞ automorphic with respect to G will be constructed from the conformal mapping of the fundamental domain of G. We derive an analogue of Ramanujan's triple differential equations associated with the group G and establish the connection of f0, fi and f∞ with a family of hypergeometric functions. 展开更多
关键词 Hypergeometric function Schwarzian triangle function Jacobi theta functions Ramanu-jan's triple differential equations
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Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem 被引量:1
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作者 Zeyu Liu Tiecheng Xia Jinbo Wang 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第3期161-176,共16页
We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bif... We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms. 展开更多
关键词 CHAOS fractional two-dimensional triangle function combination discrete chaotic map image encryption Menezes-Vanstone elliptic curve cryptosystem
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ON THE SCATTERING OF ARBITRARY SHAPE MICROSTRIP PATCH 被引量:1
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作者 HeXiulian GongShuxi LiuQizhong 《Journal of Electronics(China)》 2004年第5期432-436,共5页
In this letter, discrete complex image method is employed to compute the Green's functions in the spatial domain, which improves the speed of evaluating the impedance matrix.The triangle vector basis function--RWG... In this letter, discrete complex image method is employed to compute the Green's functions in the spatial domain, which improves the speed of evaluating the impedance matrix.The triangle vector basis function--RWG, is used to simulate the current distribution in order to compute the scattering properties of arbitrary shape microstrip patch without the staircase approximation. The numerical result shows the validity of the proposed method. 展开更多
关键词 Green's function Discrete complex image method triangle vector basis function SCATTERING
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