Electronic transitions of fluorene, dibenzofuran, carbazole, and dibenzothiophene: From the onset of absorption to the ionization threshold

A comparative study of the electronic transitions of fluorene and its hetero-analogues dibenzofuran, carbazole, and dibenzothiophene was performed in a wide energy range. Gas phase, crystal phase, and linear dichroism electronic transmittance spectra were measured with synchrotron radiation. Electronic transitions to excited singlet states were predicted with time-dependent density functional theory, TD-B3LYP/6-31+G(d,p). Based on the experimental and theoretical results, symmetry assignments of electronic transitions in the vacuum and near-UV region are suggested. The correspondence between excited states in these molecules, similarities, and differences between their electronic spectra are discussed.     

Chaos based multiple image encryption using multiple canonical transforms

We propose a new method for multiple image encryption using linear canonical transforms and chaotic maps. Three linear canonical transforms and three chaotic maps are used in the proposed technique. The three linear canonical transforms that have been used are the fractional Fourier transform, the extended fractional Fourier transform and the Fresnel transform. The three chaotic maps that have been used are the tent map, the Kaplan-Yorke map and the Ikeda map. These chaotic maps are used to generate the random phase masks and these random phase masks are known as chaotic random phase masks. The mean square error and the signal to noise ratio have been calculated. Robustness of the proposed technique to blind decryption has been evaluated. Optical implementation of the technique has been proposed. Experimental and simulations results are presented to verify the validity of the proposed technique.     

Escape dynamics in collinear atomic-like three mass point systems

The present paper studies the escape mechanism in collinear three point mass systems with small-range-repulsive/large-range-attractive pairwise interaction. Specifically, we focus on the asymptotic behaviour for systems with non-negative total energy.On the zero energy level set there are two distinct asymptotic states, called 1+1+1escape configurations, where all the three separations infinitely increase as t→∞. We show that 1+1+1 escapes are improbable by proving that the set of initial conditions leading to such asymptotic configurations has zero Lebesgue measure. When the outer mass points are of the same kind we deduce the existence of a heteroclinic orbit connecting the 1+1+1 escape configurations. We further prove that this orbit is stable under parameter perturbation.In the positive energies’ case, we show that the set of initial conditions leading to 1+1+1 escape configurations has positive Lebesgue measure.     

RECOVERY BASED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATION IN 2D

We design and numerically validate a recovery based linear finite element method for solving the biharmonic equation.The main idea is to replace the gradient operator▽on linear finite element space by G(▽)in the weak formulation of the biharmonic equation,where G is the recovery operator which recovers the piecewise constant function into the linear finite element space.By operator G,Laplace operator△is replaced by▽·G(▽).Furthermore,the boundary condition on normal derivative▽u-n is treated by the boundary penalty method.The explicit matrix expression of the proposed method is also introduced.Numerical examples on the uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed method.     

A Gleason–Kahane–Żelazko theorem for the Dirichlet space

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions.We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane.     

A globally linearly convergent method for pointwise quadratically supportable convex–concave saddle point problems

We study the Proximal Alternating Predictor–Corrector (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle [8] to solve nonsmooth structured convex–concave saddle point problems consisting of the sum of a smooth convex function, a finite collection of nonsmooth convex functions and bilinear terms. We introduce the notion of pointwise quadratic supportability, which is a relaxation of a standard strong convexity assumption and allows us to show that the primal sequence is R-linearly convergent to an optimal solution and the primal-dual sequence is globally Q-linearly convergent. We illustrate the proposed method on total variation denoising problems and on locally adaptive estimation in signal/image deconvolution and denoising with multiresolution statistical constraints.     

Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications

In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc.     

A shadowing lemma for quasi-hyperbolic strings of flows

In this paper we prove a shadowing lemma for pseudo orbits made by quasi-hyperbolic strings. We allow singularities in question and hence, in particular, the quasi-hyperbolic strings are formulated by the rescaled linear Poincaré flow instead of the usual linear Poincaré flow. We also introduce the sectional Poincaré map and rescaled sectional Poincaré map for Lipschitz vector fields on Banach spaces in the article.     

Essential spectra of self-adjoint relations under relatively compact perturbations

This paper is concerned with the stability of essential spectra of self-adjoint relations under relatively compact perturbation in Hilbert spaces. Relationships between relative boundedness and relative compactness of linear relations are established, and some necessary and sufficient conditions of relative compactness and relative boundedness of linear relations are given. It is shown that the essential spectra of self-adjoint relations are invariant under either relatively compact perturbation or a more general perturbation. The results obtained in the present paper generalize the corresponding results for operators to relations, and some of which weaken certain assumptions of the related existing results.