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A new fractional two-dimensional quadric polynomial discrete chaotic map (2D-QPDM) with the discrete fractional difference is proposed. Afterwards, the new dynamical behaviors are observed, so that the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits of the proposed map are given, respectively. The new discrete fractional map is exploited into color image encryption algorithm and it is illustrated with several examples. The proposed image encryption algorithm is analyzed in six aspects which indicates that the proposed algorithm is superior to other known algorithms as a conclusion. [ABSTRACT FROM AUTHOR]

In this paper, a novel fractional quantum logistic map (FQLM) based on fractional difference is proposed and image encryption algorithm based on it are exploited. First, the FQLM is proposed and its dynamical behaviors are observed with bifurcation diagram, phase portraits and largest Lyapunov exponent plots. After that, the ECC is utilized to cover up the encryption keys and the FQLM is used for the permutation and diffusion process of image encryption. Finally, the cryptosystem is used in image encryption and the algorithm is analyzed in four respects, showing a distinct advantage of the proposed cryptosystem over some of existing ones. [ABSTRACT FROM AUTHOR]

A new fractional two-dimensional triangle function combination discrete chaotic map (2DTFCDM) with the discrete fractional difference is proposed in this paper. The chaos behaviors are observed through the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits. The proposed map is applied in color image encryption with the secret keys generated by Menezes–Vanstone Elliptic Curve Cryptosystem. The image encryption system is analyzed using six aspects indicating the superiority of the proposed algorithm compared to the other algorithms. [ABSTRACT FROM AUTHOR]

This work clarifies the concept of cell average by pointing out the differences between cell average and cell centroid value, which are averaged cell-centered value and pointwise cell-centered value, respectively. Interpolation based on cell averages is constructed and high order QUICK-like numerical scheme is designed for such interpolation. A new approach of error analysis is introduced in this work, which is similar to Taylor's expansion. [ABSTRACT FROM AUTHOR]

A series of norbornane-based HIV-1 protease (PR) inhibitors are designed theoretically to displace the tetrahedrally coordinated internal water molecule that bridges inhibitor to flaps via hydrogen bonds. These designed inhibitors use the norbornenone oxygen atom to mimic this structural water molecule and contain diols to interact with the carboxylate oxygens of catalytic aspartates. The binding free energies were estimated by modified linear interaction energy approach [Zoete H, Michielin O, Karplus M, J Comput Aided Mol Des17:861, 2003], in which the binding free energy is written as a linear combination of the electrostatic interaction energy between PR and the ligand, Eelec, the van der Waals interaction energy between PR and the ligand, EvdW, and the difference of the solvation free energies of the complex, the receptor, and the isolated ligand, ΔGsolv. The equation obtained in previous work [Da W. Zhang, Philip Lin Huang, Sylvia Lee-Huang, John Z. H. Zhang, J Theor Comput Chem7:485, 2008] is applied directly to calculate the binding free energy of designed norbornane-based HIV-1 PR inhibitors. [ABSTRACT FROM AUTHOR]