Investigation of the isothermal (vapour + liquid) equilibria of aqueous 2-amino-2-methyl-1-propanol (AMP), N-benzylethanolamine,or 3-dimethylamino-1-propanol solutions at several temperatures

The vapour pressures of (2-amino-2-methyl-1-propanol (AMP) + water), (N-benzylethanolamine + water), or (3-dimethylamino-1-propanol + water) binary mixtures, and of pure AMP and 3-dimethylamino-1-propanol components were measured by means of two static devices at temperatures between 283 K and 363 K. The data were correlated with the Antoine equation. From these data, excess Gibbs functions (G^E) were calculated for several constant temperatures and fitted to a fourth-order Redlich–Kister equation using the Barker’s method. The {2-amino-2-methyl-1-propanol (AMP) + water} binary mixture exhibits negative deviations in G^E (at T < 353.15 K) and a sinusoidal shape for G^E for the higher temperatures over the whole composition range. For the aqueous N-benzylethanolamine solution, a S shape is observed for the G^E for all investigated temperatures over the whole composition range. The (3-dimethylamino-1-propanol + water) binary mixture exhibits negative deviations in G^E (at T < 293.15 K), positive deviations in G^E (for 293.15 K < T < 353.15 K) and a sinusoidal shape for G^E for the higher temperatures over the whole composition range.     

Phase equilibrium properties of binary aqueous solutions of benzylamine, 1,2-bis(2-aminoethoxy)ethane,or 2-[2-(dimethylamino)ethoxy]ethanol

The vapour pressures of (benzylamine + water), {1,2-bis(2-aminoethoxy)ethane + water}, or {2-[2-(dimethylamino)ethoxy]ethanol + water} binary mixtures, and pure 2-[2-(dimethylamino)ethoxy]ethanol component were measured by means of two static devices at temperatures between (283.15 and 363.15 (or 323.15)) K. The data were correlated with the Antoine equation. From these data, excess Gibbs functions (G^E) were calculated for several constant temperatures and fitted to a fourth-order Redlich–Kister equation using the Barker’s method. The (benzylamine + water) binary mixture exhibits positive deviations in G^E for (303.15 < T/K < 323.15) and a sinusoidal shape in G^E for T > 323.15 K over the whole composition range. The aqueous 1,2-bis(2-aminoethoxy)ethane or {2-[2-(dimethylamino)ethoxy]ethanol + water} solutions exhibit negative deviations in G^E for all investigated temperatures over the whole composition range.     

The S-Jeribi Essential Spectrum

Ukrainian Mathematical Journal - We study some properties and results on the S-Jeribi essential spectrum of linear bounded operators in a Banach space. In particular, we give some criteria for the...     

Existence and Numerical Solutions of Nonlinear Quadratic Integral Equations Defined on Unbounded Intervals

The first goal of this article is to discuss the existence of solutions of nonlinear quadratic integral equations. These equations are considered in the Banach space L ^p (?₊). The arguments used in the existence proofs are based on Schauder's and Darbo's fixed point theorems. In particular, to apply Schauder's fixed point theorem based method, a special care is devoted to the proof of the L ^p -compactness of the operators associated with our nonlinear quadratic integral equations. The second goal of this work is to study a numerical method for solving nonlinear Volterra integral equations of a fairly general type. Finally, we provide the reader with some examples that illustrate the different results of this work.     

Computation of the spectra of some integral operators and application to the numerical solution of some linear integral equations

In this paper, we present two methods of computing the spectrum of a compact integral operator. The first method is based on an exact matrix representation of the operator. The second method uses a convenient quadrature method to discretisize the integral operator and to provide accurate approximations to the spectrum and the eigenfunctions of this later. Also, we show how our methods can be used in the framework of some stable procedures for the approximation of f^† the normal solution of the minimal L²-norm of the integral equation of the first kind Af = g, which is often an ill-posed equation. These procedures are based on a spectral expansion of the operator A. To finish, we give some numerical examples that illustrate the results of this work.