Theorie de nevanlinna p-adique

We study meromorphic functions in all ℂp or in a disc of ℂp. Using some properties of the valuation polygon notion, we show p-adic results perfectly analogous to those of Nevanlinna in the complex case. As an application we prove the p-adic analogue of Malmquist-Yosida Theorem: Let m∈ℕ and R(x.y)∈ℂp(x,y). If the differential equation: (dy/dx)^m=R(x,y), m∈ℕ, has a non rational meromorphic solution in all ℂp, then R(x,y) is a polynomial in y of degree ≤2m.      

Carbamate Formation and Amine Protonation Constants in 2-Amino-1-Butanol–CO<Subscript>2</Subscript>–H<Subscript>2</Subscript>O System and Their Temperature Dependences

The apparent protonation constant of an amino butanol (AB) and its carbamate formation constant in the CO₂–H₂O–AB system were determined at T = 298.15–328.15 K, and at various ionic strengths up to 0.2 mol·L^?1 by potentiometric titration. The Debye–Hückel equation was used to extrapolate the protonation constants to zero ionic strength. The variation of the thermodynamic equilibrium constant for carbamate formation with temperature was modeled according to the relationship of log₁₀ K₁ = 280.91/T ? 0.1105, while the temperature dependency of the amine protonation constant was correlated by log₁₀ K₂ = 1926.53/T + 2.9482. Van’t Hoff type plots of the pK values showed linear relationships indicating that the standard enthalpy changes of reaction are constant over this range of temperatures. Hence, our current findings are crucial for designing efficient unit operations involving separation of CO₂ from natural or flue gases.     

About the p-adic Yosida equation inside a disk

Let K be a complete ultrametric algebraically closed field and let ?(d(0, R^?)) be the field of meromorphic functions inside the disk d(0,R⁻) = {x ∈ K ∣ ∣x∣ < R}. Let ?_b(d(0, R^?)) be the subfield of bounded meromorphic functions inside d(0,R⁻) and let ?_u(d(0, R^?)) = ?(d(0, R^?)) ? ?_b(d(0, R^?)) be the subset of unbounded meromorphic functions inside d(0,R⁻). Initially, we consider the Yosida Equation: , where m ∈ ?^* and F(X) is a rational function of degree d with coefficients in ?_b(d(0, R^?)). We show that, if d ≥ 2m + 1, this equation has no solution in ?_u(d(0, R^?)).Next, we examine solutions of the above equation when F(X) is apolynomial with constant coefficients and show that it has no unbounded analytic functions in d(0,R⁻). Further, we list the only cases when the equation may eventually admit solutions in ?_u(d(0, R^?)). Particularly, the elliptic equation may not.     

Performance of various RANS eddy-viscosity models for turbulent natural convection in tall vertical cavities

The present study is dedicated to the identification of turbulence models that are accurate and numerically economic for computing the natural air-flow and heat transfer by convection in tall cavities with differentially heated vertical walls. The eddy-viscosity models (EVM) are among the simplest to implement and the most economical to treat this problem. This study evaluated the dynamic, thermal and computational performances of twenty EVM turbulence models with one, two or three-equation closure. All the models were first implemented in several in-house codes using the finite volume method. The predictions of the retained models in terms of profiles of velocity, temperature and vertical velocity fluctuations in the cavity have been compared with those of experimental or numerical studies. The obtained results were used to identify the turbulence models that are accurate and numerically economic in predicting natural convection in vertical cavities with a high aspect ratio. The EVM models with three-equation (v2-f and ζ-f) provide the most accurate mean and fluctuating quantities, followed by the k-ε RNG (ReNormalization Group) and k-ω SST (Shear Stress Transport) models. The computing time of these four models is higher than that of the 2L (two-layer) and q-ω models, which provide fairly accurate results especially for the mean heat transfer between the vertical active walls. The other one-equation (Spalart and Allmaras model) and two-equation (k-ε, k-ω and hybrid models) turbulence models tested in this work, have a high computing time and/or predictions that are not sufficiently precise simultaneously for both velocity and temperature fields.     

Comparative study of kinetics isomerization of substituted polyacetylene (Cl,F and I): Ab initio and DFT calculations

Ab initio and DFT methods were used to investigate the interconversions of substituted polyacetylene conformers C₁₀H₆X₆ (X=F, Cl and I) in the vapour phase. The rates of this geometrical isomerization have been calculated and the Arrhenius parameters evaluated. In the case of unsubstituted polyacetylene as the reference, the B3LYP Arrhenius parameters obtained are A₁=2.99 × 10¹⁷ s^–1 and E_a=17.30 kcal mol^–1. The values of the equilibrium constant for the reaction have also been determined at various temperatures between 300 and 500 K and the value of the energies change calculated. The results also suggest that the straightforward kinetics characterizing the majority of substituted polyacetylene isomerizations above 300 K. The isomerization energies are positive and the barrier heights ΔE_barrier are expected to be sensitive for the magnitude of halogens effects. According to geometries features the Cis → Trans isomerization in the gas phase occurs by a rotational mechanism.     

Well posedness and stability result for a thermoelastic laminated Timoshenko beam with distributed delay term

In this work, we consider a linear thermoelastic laminated timoshenko beam with distributed delay, where the heat conduction is given by cattaneoâs law. we establish the well posedness of the system. For stability results, we prove exponential and polynomial stabilities of the system for the cases of equal and nonequal speeds of wave propagation.     

A priori estimates for superlinear and subcritical elliptic equations: the Neumann boundary condition case

We consider here solutions of a nonlinear Neumann elliptic equation Δu +?f (x, u) =?0 in Ω, ?u/?ν =?0 on ?Ω, where Ω is a bounded open smooth domain in ${\mathbb{R}^N, N\geq2}$ and f satisfies super-linear and subcritical growth conditions. We prove that L ^∞?bounds on solutions are equivalent to bounds on their Morse indices.     

Topologically Algebraic Algebras

We show that a locally convex algebra is topologically algebraic if, and only if, it is algebraic.Thanks are offered to Professor M. Oudadess for many remarks which allowed an improvement of the first version of this paper. We are also indebted to Professor A. Mallios for valuable suggestions.     

Size and shape controlled of α-Fe2O3 nanoparticles prepared via sol–gel technique and their photocatalytic activity

Journal of Sol-Gel Science and Technology - Haematite (α-Fe2O3) nanoparticles (NPs) of different sizes and morphologies were prepared from two different iron precursors (iron acetate (A) and...