On Hyperbolic Variational Inequalities of First Order and Some Applications

This paper presents further developments in the study of strong solutions and their coincidence sets to the obstacle problem for linear transport operators. Under natural mild assumptions, the strong convergence of the solutions and the characteristic functions of their coincidence sets is obtained in the passage of second order to first order problems. An application to a steady-state chemotaxis problem is given. The extension to the two obstacles problem of first order is also presented, having in view an application to a porous media model in presence of saturation arising in petroleum engineering.     

A monotone iterative scheme for a nonlinear second order equation based on a generalized anti–maximum principle

In this paper, a generalized anti–maximum principle for the second order differential operator with potentials is proved. As an application, we will give a monotone iterative scheme for periodic solutions of nonlinear second order equations. Such a scheme involves the L^p norms of the growth, 1 ≤ p ≤ ∞, while the usual one is just the case p = ∞.     

Chopped CW laser-induced optogalvanic effect in a neon hollow cathode discharge

A detailed model for the optogalvanic effect in a neon hollow cathode discharge irradiated by a chopped CW dye laser is presented. A rate equation formalism is used to calculate the evolution of the first and second electronic configuration populations coupled by the laser and of the electric charges number density. Processes as ambipolar-like electrons loss, electronic collisional coupling of level populations and electron emission by the cathode due to VUV radiation from the 1s ₂ resonant level are taken into account and further discussed.The transients and steady-state magnitude of the optogalvanic signal are calculated, compared with experimental data and related to population changes. We predict sign changes of the optogalvanic signal when the laser is tuned over transitions originating from the resonant level with respect to transitions involving the metastables states. The optogalvanic signal is shown to be basically determined by the laser-induced variations of the excited-state populations while changes in the electron temperature, due to laser energy transfer by collisions between electrons and excited atoms, play a negligible role.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

A nodal coupling of finite and boundary elements

This article presents and analyzes a simple method for the exterior Laplace equation through the coupling of finite and boundary element methods. The main novelty is the use of a smooth parametric artificial boundary where boundary elements fit without effort together with a straight approximate triangulation in the bounded area, with the coupling done only in nodes. A numerically integrated version of the algorithm is also analyzed. Finally, an isoparametric variant with higher order is proposed. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 555–570, 2003     

Orthogonal polynomials on the unit circle and their derivatives

We characterize the sequences of orthogonal polynomials on the unit circle whose derivatives are also orthogonal polynomials on the unit circle. Some relations for the sequences of derivatives of orthogonal polynomials are provided. Finally, we pose some problems about orthogonality-preserving maps and differential equations for orthogonal polynomials on the unit circle.     

Growth kinetics of iron boride layers: Dimensional analysis

Dimensional analysis is presented as a powerful tool in the study of the paste boriding process. In particular, a dimensional method is used to study the growth kinetics of the boride layers FeB and Fe₂B. Experiments were performed in AISI 1045 steel and AISI M2 steel, to test the suggested model. Samples of 1045 steel were prepared and treated using boron paste thickness of 3-5 mm, at temperatures of 1193, 1223 and 1273 K, with 2, 4 and 6 h of treatment time. The M2 specimens had boron paste thickness of 3 and 4 mm and temperatures of 1223, 1253 and 1273 K for 2 and 6 h. Results indicate that the growth of boron layers obeys power laws of the form y = αx^β, where α and β constants are a function of the material and the interface of interest. Validation of the model was carried out using experimental data with an average error percentage of 7.6% for Fe₂B in 1045 steel, 15.8% for FeB and 3.4% for Fe₂B in M2 steel.