A novel chaotic image encryption scheme using DNA sequence operations

In this paper, we propose a novel image encryption scheme based on DNA (Deoxyribonucleic acid) sequence operations and chaotic system. Firstly, we perform bitwise exclusive OR operation on the pixels of the plain image using the pseudorandom sequences produced by the spatiotemporal chaos system, i.e., CML (coupled map lattice). Secondly, a DNA matrix is obtained by encoding the confused image using a kind of DNA encoding rule. Then we generate the new initial conditions of the CML according to this DNA matrix and the previous initial conditions, which can make the encryption result closely depend on every pixel of the plain image. Thirdly, the rows and columns of the DNA matrix are permuted. Then, the permuted DNA matrix is confused once again. At last, after decoding the confused DNA matrix using a kind of DNA decoding rule, we obtain the ciphered image. Experimental results and theoretical analysis show that the scheme is able to resist various attacks, so it has extraordinarily high security.     

Size‐guided multi‐seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size‐guided multi‐seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest‐energy configurations of the cluster with n − 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.     

Index transforms with Weber-type kernels

New index transforms with Weber-type kernels, consisting of products of Bessel functions of the first and second kind, are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The results are applied to solve a boundary value problem on the wedge for a fourth-order partial differential equation.     

Dependence of electronic and optical properties of multilayer SiC and GeC on stacking sequence and external electric field

The electronic and optical properties of different stacked multilayer SiC and GeC are investigated with and without external electric field (EEF). The band gaps of multilayer SiC and GeC are found smaller than that of monolayer SiC and GeC due to the interlayer coupling effect. When EEF is applied, the direct band gaps (ΔK–M) of multilayer SiC and direct band gaps (ΔK–K) of multilayer GeC all turn to indirect band gaps (ΔK–G) as the band at the G point drops dramatically toward zero. The imaginary part ε₂(ω)s of multilayer SiC and GeC show that new absorption peaks between 2–5 eV appear when the polarized direction is perpendicular to the layer plane, and new absorption peaks in infrared region appear as the EEF is higher than a certain point when the polarized direction is parallel to the layer plane. Our calculations reveal that different stacking sequences and EEF can provide a wide tunable band structures and optical properties for multilayer SiC and GeC.     

Is bismuth subsalicylate an effective nontoxic catalyst for plga synthesis?

Poly(d,l ‐lactide‐co‐glycolide) (PLGA) copolyesters are commonly used in biomedical applications. Researches were carried out on nontoxic or low‐toxic catalysts that are enough efficient to provide short polymerization times, adequate microstructure chains and similar properties than the commercial PLGA materials. In this study, PLGA were synthesized by ring‐opening copolymerization (ROP) using three different catalysts. Stannous octoate is the first catalyst we used, as it is very efficient, even its toxicity is still on debate. Two others low‐toxic catalysts [zinc lactate and bismuth subsalicylate (BiSS)] were also evaluated. The comparison of these ROP was realized in terms of kinetics and control of the polymerization. Then, the influence of the catalyst on the PLGA microstructure chains is reported. Finally, abiotic hydrolytic degradation rate is studied. Results described in this article show that BiSS is one very attractive catalyst to produce low toxic PLGA for biomedical applications. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1130–1138     

Strong approximation for ρ-mixing sequences

We establish strong invariance principles for sums of stationary ρ-mixing random variables with finite and infinite second moments under weaker mixing rates.Some earlier results are improved.As applications,some results of the law of the iterated logarithm with finite and infinite variance are obtained,also a conjecture raised by Shao in 1993 is solved.     

A general poisson approximation theorem

We study the rate of convergence in a limit theorem due to Kabanov-Liptser-Shiryayev. We show how the probabilities P(N _t= k) can be computed from the compensator, when it is deterministic.     

Hidden Markov models revealing the stress field underlying the earthquake generation

The application of the hidden Markov models (HMMs) is attempted for revealing key features for the earthquake generation which are not accessible to direct observation. Considering that the states of the HMM correspond to levels of the stress field, our objective is to identify these states. The observations are considered after grouping earthquake magnitudes and the cases of different number of states are examined. The problems of HMMs theory are solved and the ensuing HMMs are compared on the basis of Akaike and Bayesian information criteria. A new insight on the evaluation of future seismic hazard is given by calculating the mean number of steps for the first visit to a particular state, along with the respective variance. We further calculate an estimator of the mean number of steps for the first visit to a particular state and we construct its confidence interval. Additionally, a second approach to the problem is followed by assuming a different determination of observations. The HMMs applied to both approaches, contribute significantly to seismic hazard assessment via revealing the number of the stress levels as well as the way in which these levels are associated with certain earthquake occurrence.     

A generalization of the Leibnitz rule of successive differentiation

This note generalizes the well-known Leibnitz rule of successive differentiation for the product of two functions to a similar result for the product of three functions.