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
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
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
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61072147 and 11271008)
文摘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.
文摘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.