Real Paley-Wiener type theorems for the Dunkl transform on {\mathcal{S}}'(\mathbb{R}^{d})

We prove real Paley-Wiener type theorems for the Dunkl transform ℱ _D on the space of tempered distributions. Let T∈S′(ℝ ^d ) and Δ _κ the Dunkl Laplacian operator. First, we establish that the support of ℱ _D (T) is included in the Euclidean ball , M>0, if and only if for all R>M we have lim  _n→+∞ R ⁻²ⁿ Δ _κ ⁿ T=0 in S′(ℝ ^d ). Second, we prove that the support of ℱ _D (T) is included in ℝ ^d ∖B(0,M), M>0, if and only if for all R<M, we have lim  _n→+∞ R ²ⁿ  ℱ _D ⁻¹(‖y‖⁻²ⁿ ℱ _D (T))=0 in S′(ℝ ^d ). Finally, we study real Paley-Wiener theorems associated with -slowly increasing function.      

Thermal dehydration of CeP<Subscript>3</Subscript>O<Subscript>9</Subscript>·3H<Subscript>2</Subscript>O by controlled rate thermal analysis

The aim of this work is to highlight the importance of controlling the residual water vapour pressure above the sample as well as the rate of the thermal decomposition during the thermal dehydration of cerium cyclotriphosphate trihydrate CeP₃O₉·3H₂O. For this reason, the dehydration of the titled compound was followed by both techniques: the constant rate thermal analysis at P _H2O = 5 hPa and the conventional TG-DTA in air.     

PROTOCHLOROPHYLL(IDE)630 PHOTOSENSITIZES ACTIVE Ca2+ ACCUMULATION IN MICROSOMAL AND MITOCHONDRIAL FRACTIONS ISOLATED FROM PLANTS

Abstract— White light irradiation of a microsomal fraction from etiolated plants affects their ATP-dependent Ca²⁺ accumulation by inhibiting active uptake and enhancing passive efflux. The succinate-dependent mitochondrial Ca²⁺ accumulation as well is decreased by light. The wavelength dependence of these light effects as well as their low quantum yield suggest non-phototransformable protochloro-phyll(ide) [PChl(ide)] to be the photoreceptor. PChlide has been isolated from corn leaves pretreated with 5-amino levulinic acid. Addition of Pchlide causes photosensitization of an otherwise light insensitive microsomal Ca²⁺ accumulation. The observed light effect may be due to contamination of the mitochondrial as well as the microsomal fractions with PChl(ide)‡ containing particles. Irradiation of the intact tissue leads to the almost complete disappearance of the light effect on the in vitro Ca²⁺ accumulation.     

Delone Sets with Finite Local Complexity: Linear Repetitivity Versus Positivity of Weights

We consider Delone sets with finite local complexity. We characterize the validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this context, we show that linear repetitivity is equivalent to positivity of weights combined with a certain balancedness of the shape of return patterns.     

Third-order laser-field-expansion analysis of the Lorenz–Haken equations

This paper revisits a few aspects of laser-dynamics with a strong-harmonic expansion analysis from which new analytical information, within the intrinsic pulsing regime that characterizes the non-linearly coupled differential Lorenz–Haken equations, is extracted. The analysis is expected to provide clearer insights to the physics involved in the laser-dynamics issue. Carried out to third-order in electric field amplitude, the procedure allows for the derivation of a closed form expression which describes the permanent-oscillation frequency of the unstable periodic state. Comparison between the frequency values evaluated from the literal formula and those obtained through direct numerical simulations shows a realistic fit inside the control parameters space that displays symmetric period-one pulsing solutions.     

Theoretical study of normal and inverse electron demand cycloaddition reactions between cyclohexadiene and 2-aryl-4,6-dinitrobenzotriazole 1-oxides

In this work, we theoretically study Diels-Alder reactions between cyclohexadiene and a series of 2-aryl-4,6-dinitrobenzotriazole 1-oxides (5a-d). Based on various calculation methods such as SCF/6–31G* and DFT/B3LYP with the 6–31G* standard basis set, we discuss the thermodynamic possibility of these reactions. The reactions between a series of 6-nitrobenzotriazole 1-oxides(5aa ₁ -ab ₁ ) and cyclohexadiene are also studied. The text was submitted by the authors in English.     

Finite difference discretization of the Benjamin‐Bona‐Mahony‐Burgers equation

Numerical solutions of the Benjamin‐Bona‐Mahony‐Burgers equation in one space dimension are considered using Crank‐Nicolson‐type finite difference method. Existence of solutions is shown by using the Brower's fixed point theorem. The stability and uniqueness of the corresponding methods are proved by the means of the discrete energy method. The convergence in L^∞‐norm of the difference solution is obtained. A conservative difference scheme is presented for the Benjamin‐Bona‐Mahony equation. Some numerical experiments have been conducted in order to validate the theoretical results.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

The hydrodynamic and thermal characterization of a yield stress fluid in stirred tanks equipped with simple helical ribbons with two stages

The objective of this paper is to characterize the hydrodynamic and thermal behaviors of yield stress fluids within a cylindrical agitated vessel equipped with simple helical ribbon stirrers (SHR) (one and two-stages) by means of the numerical simulation approach. For this purpose, a computational fluid dynamic simulation using the 3D finite volume technique has been carried out to solve the continuity, momentum and thermal energy equations. In this study, we have analyzed the Oldroyd and Reynolds numbers effects on the hydrodynamic and thermal behaviors for the two mentioned stirrers types. In addition, the influence of the impeller width and its clearance from the vessel wall on the velocity and thermal fields has been investigated. Velocity and thermal fields’ visualization has been presented in different (r–z) and (r–θ) planes. Moreover, the power constant and Nusselt number are correlated by a relationship relating the physical properties and the geometric ratios defining the SHR.     

Ab initio study of heterojunction discontinuities in the ZnO/Cu2O system

Solar cells based on transparent conductive oxides such as ZnO/Cu₂O constitute a very advanced way to build high-performance cells. In this work, we are interested in the characterization of the interface through nanoscale modeling based on ab initio approaches (density functional theory, local density approximation, and pseudopotential). This work aims to build a supercell containing a heterojunction ZnO/Cu₂O and study the structural properties and the discontinuity of the valence band (band offset) from a semiconducting to another phase. We build a zinc oxide in the wurtzite structure along [0001] on which we place the copper oxide in the hexagonal (CdI₂-type) structure. We choose the method of Van de Walle and Martin to calculate the energy offset. This approach fits well the density functional theory. Our calculation of the band offset gives a value that corresponds to other experimental and theoretical values.