Thisarticleisconcernedwiththeasymptoticbehaviorofthetwo-dimensionalinviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time- decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined with bilinear estimates and interpolation inequalities for handling the nonlinearity.

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers have been studied, and several integer sequences related to them have been introduced. In the article other types of Sheffer polynomials are considered, by introducing two sets of Euler-type polynomials.

The use of Euler polynomials and Euler numbers allows us to construct a quadrature rule similar to the well-known Euler--MacLaurin quadrature formula, using Euler (instead of Bernoulli) numbers, and even (instead of odd) order derivatives of a given function evaluated at the extrema of the considered interval. An expression of the remainder term and numerical examples are also given. © 2001, Heldermann Verlag. All rights reserved.

Ever more organizations, both private and public, are placing a greater importance on employee engagement as a means of generating better organizational climate and higher levels of performance. Actually, employee engagement is part of the strategic management of high performance organization, which pay always more attention to human resource initiatives. Moreover, forms of involvement in the decision processes make more motivating and more satisfying the activity for employees, as they create the conditions for greater inspiration and, in turn, contribute to their well-being.

The paper deals with de la Vallee Poussin type interpolation on the square at tensor product Chebyshev zeros of the first kind. The approximation is studied in the space of locally continuous functions with possible algebraic singularities on the boundary, equipped with weighted uniform norms. In particular, simple necessary and sufficient conditions are proved for the uniform boundedness of the related Lebesgue constants. Error estimates in some Sobolev-type spaces are also given.

In the present paper, we propose a numerical method for the simultaneous approximation of the finite Hilbert and Hadamard transforms of a given function f, supposing to know only the samples of f at equidistant points. As reference interval we consider [-1,1] and as approximation tool we use iterated Boolean sums of Bernstein polynomials, also known as generalized Bernstein polynomials. Pointwise estimates of the errors are proved, and some numerical tests are given to show the performance of the procedures and the theoretical results.

We revisit a method introduced by Tartar for proving global well-posedness of a semilinear hyperbolic system with null quadratic source in one space dimension. A remarkable point is that, since no dispersion effect is available for 1D hyperbolic systems, Tartar's approach is entirely based on spatial localization and finite speed of propagation.