A new nonlocal model for the restoration of textured images

In this paper, we focus on the mathematical and numerical study of a new nonlocal reaction-diffusion system for image denoising. This model is motivated by involving the decomposition approach of $H^{-1}$ norm suggested by Meyer [25] which is more appropriate to represent the oscillatory patterns and small details in the textured image. Based on Schaeffer''s fixed point theorem, we prove the existence and uniqueness of solution of the proposed model. To illustrate the efficiency and effectiveness of our model, we test the denoising experimental results as well we compare with some existing models in the literature.     

On the class of almost L-weakly and almost M-weakly compact operators

In this paper, we introduce and study new concepts of almost L-weakly and almost M-weakly compact operators.     

A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant

In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI) defined on a uniform criss-cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan’s iterated version and we illustrate the theoretical results by some numerical examples.     

Second degree classical forms

A form (linear functional) u is called regular if there exists a sequence of polynomials {P_n}_n≥0, deg P_n = n which is orthogonal with respect to u. Such a form is said to be of second degree if there are polynomials B and C such that the Stieltjes function satisfies a relation of the form BS²(u) + CS(u) + D = 0.Classical forms correspond to classical orthogonal polynomials: sequences of polynomials whose derivatives also form an orthogonal sequence. In this paper, the authors determine all the classical forms which are of second degree. They show that Hermite, Laguerre and Bessel forms are not of second degree. Only Jacobi forms which satisfy a certain condition possess this property.     

Synthesis and structure determination of a new layered zincophosphate: [H2N2C6H16]0.5[Zn2(PO4)(HPO4)(H2O)]·H2O

The synthesis and crystal structure of a new microporous zincophosphate are described. [H₂N₂C₆H₁₆]_0.5[Zn₂(PO₄)(HPO₄)(H₂O)]·H₂O crystallizes in the triclinic space group P1¯ with a = 8.822(4), b = 9.236(4), c = 8.451(3) Å, = 67.19(3), = 91.32(3), = 111.10(3)°, V = 586.7(4) ų and Z = 2. This new material consists of infinite two-dimensional anionic layers alternated with planes containing organic diprotonated templates, N, N, N, N-tetramethylethylenediamine [H₂N₂C₆H₁₆]²⁺ molecules. The framework structure is built up of ZnO₄, ZnO₃OH₂, PO₄, and PO₃OH tetrahedra, linked through oxygen vertices. The presence of terminal OH₂ and OH groups, leads to an open structure containing four- and eight-rings. The organic molecules are interconnected to the framework through hydrogen bonds.     

Synthesis and X-ray structure of p-tolyl phenylthioglyoxylate

The title compound (C₁₅H₁₂O₂S) is triclinic witha=7.077(10),b=8.825(2),c=11.068(2) Å, =106.66(3)^o, Z=2, and space group P. The significant structural features lies in the two carbonyl groups of the thioglyoxylate which are oriented antiperiplanar to each other [–168.2(2)^o]. The central C(8)–C(9) bond is 1.553(3) Å. The phenyl rings are twisted with respect to the carbonyl groups. Short contacts are present between S and O(1) [2.652(2) Å] and also between S and O(2) [2.758(2) Å].     

Relative Gorenstein Dimensions

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C have been subject of several works as interesting extensions of (Gorenstein) homological dimensions. In this paper, we extend to the noncommutative case the concepts of G _C -projective module and dimension, weakening the condition of C being semidualizing as well. We prove that indeed they share the principal properties of the classical ones and relate this new dimension with the classical Gorenstein projective dimension of a module. The dual concepts of G _C -injective modules and dimension are also treated. Finally, we show some interesting interactions between the class of G _C -projective modules and the Bass class associated to C on one side, and the class of G\({_{C^{\vee}}}\) -injective modules (C ^∨ = Hom _R (C, E) where E is an injective cogenerator in R-Mod) and the Auslander class associated to C in the other.     

Continued Fractions and Transcendence of Formal Power Series Over a Finite Field

The aim of this paper was to establish a new transcendence criterion for a class of quasi-periodic continued fractions of formal power series over a finite field depending only on the length of specific blocks appearing in the sequence of partial quotients.     

Spectral discretization of a model for organic pollution in waters

We are interested in a mixed reaction diffusion system describing the organic pollution in stream‐waters. In this work, we propose a mixed‐variational formulation and recall its well‐posedness. Next, we consider a spectral discretization of this problem and establish nearly optimal error estimates. Numerical experiments confirm the interest of this approach. Copyright © 2016 John Wiley & Sons, Ltd.