Triple color images encryption algorithm based on scrambling and the reality-preserving fractional discrete cosine transform

An image encryption algorithm to secure three color images simultaneously by combining scrambling with the reality-preserving fractional discrete cosine transform (RPFrDCT) is proposed. The three color images to be encrypted are converted to their indexed formats by extracting their color maps, which can be considered as the three components of a color image. These three components are affected each other by scrambling the interims obtained from vertically and horizontally combining the three indexed formats with the help of the chaos-based cyclic shift. The three scrambled components are separately transformed with the RPFrDCT, in which the generating sequences are determined by the Chirikov standard chaotic map. Arnold transform is used to further enhance the security. Due to the inherent properties of the chaotic maps, the cipher keys are highly sensitive. Additionally, the cipher image is a single color image instead of three color ones, and is convenient for display, storage and transmission due to the reality property of RPFrDCT. Numerical simulations are performed to show the validity of the proposed algorithm.     

Image quality assessment in multiband DCT domain based on SSIM

The performance of image quality assessment method based on SSIM (structural similarity) is better than the PSNR (peak signal to noise ratio), but the assessment effects of SSIM is poor for seriously blurred image, therefore, the model that combined HVS (human visual sensitivity) and SSIM was established. The basic idea is based on the human eye's sensitivity to different frequency distortion image, the image is two-dimensional discrete cosine transform frequency component into low, mid, high-frequency component, to obtain the frequency component of light, contrast and structural information, using Pearson coefficient for weight and sum processing to the sub-image according to frequency bands of different sensitive degree, finally, get the sharpness of the image. Through nonlinear regression analysis of objective assessment and DMOS, experiments showed that this method was closer to human perception than SSIM and GSSIM for serious blurred distortion image. At the same time, compared to conventional algorithm MAE (mean absolute error), MSE (mean square error) and PSNR, this model was more consistent with human visual characteristics.     

Controllability for a class of second-order evolution differential inclusions without compactness

In this paper, we discuss the existence and controllability for a class of second-order evolution differential inclusions without compactness in Banach spaces. By applying the technique of weak topology and Glicksberg–Ky Fan fixed point theorem, we prove our main results without the hypotheses of compactness on the operator generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Further, we extend our study to existence and controllability of second-order evolution differential inclusions with nonlocal conditions and impulses. Finally, an example is given for the illustration of the obtained theoretical results.     

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

The efficiency of noninteger n‐generalized exponential type orbitals (NGETO) r^n*?1 e with hyperbolic cosine (HC) cosh (βr^μ) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree‐Fock‐Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z ≤ 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree‐Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double‐zeta functions. All the nonlinear parameters are fully optimized. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Net information measures for modified Yukawa and Hulthén potentials

The dimensional analyses of the position and momentum variances‐based quantum mechanical Heisenberg uncertainty measure, as well as the entropic information measures given by the Shannon information entropy sum and the product of Fisher information measures are carried out for two widely used nonrelativistic isotropic exponential‐cosine screened Coulomb potentials generated by multiplying the superpositions of (i) Yukawa‐like, ?Z(e^?μr/r), and (ii) Hulthén‐like, ?Zμ(1/(e^μr ? 1)), potentials by cos(bμr) followed by addition of the term a/r², where a and b ≥ 0, μ are the screening parameters and Z, in case of atoms, denotes the nuclear charge. Under the spherical symmetry, all the information measures considered are shown to be independent of the scaling of the set [μ, Z] at a fixed value of μ/Z, a, and b and the other parameters defining the superpositions of the potentials. Numerical results are presented, which support the validity of the scaling properties. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The completeness of the sines and cosines in the space of integrable functions

The paper addresses the completeness of sines and cosines with non-integer indices in the space of Lebesgue-integrable functions. The criteria for the variation from the integer value have been found such that sine and cosine systems are complete.     

具有反铁磁相互作用的双铁磁链中的非线性激发

采用双子格模型和相干态表示,研究了链与链之间存在反铁磁相互作用的双铁磁链系统中的非线性激发的性质,得到了孤子的宽度,能量及有效质量。结果表明在不同情况下的各向异性双铁磁链中可以激发拓扑性孤子或非拓性孤子或非拓生反孤子。     

POLYNOMIALLY BOUNDED COSINE FUNCTIONS

We characterize polynomial growth of cosine functions in terms of the resolvent of its generator and give a necessary and sufficient condition for a cosine function with an infinitesimal generator which is polynomially bounded.     

General solutions to a class of time fractional partial differential equations

A class of time fractional partial differential equations is considered, which in- cludes a time fractional diffusion equation, a time fractional reaction-diffusion equation, a time fractional advection-diffusion equation, and their corresponding integer-order partial differential equations. The fundamental solutions to the Cauchy problem in a whole-space domain and the signaling problem in a half-space domain are obtained by using Fourier- Laplace transforms and their inverse transforms. The appropriate structures of the Green functions are provided. On the other hand, the solutions in the form of a series to the initial and boundary value problems in a bounded-space domain are derived by the sine- Laplace or cosine-Laplace transforms. Two examples are presented to show applications of the present technique.     

Algebraic Bethe Ansatz for the Osp(1|2) Model with Reflecting Boundaries

In the framework of graded quantum inverse scattering method, we obtain the eigenvalues and the eigenvectors of the Osp(l|2) model with reflecting boundary conditions in FBF background. The corresponding Bathe ansatz equations are obtained.