Weakly nonlocal irreversible thermodynamics

Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer‐Krumhansl, Ginzburg‐Landau and Cahn‐Hilliard type equations.     

Asymptotic behaviour of the least squares estimator of the mean of AR(1) models

The aim of the paper is to investigate the limit behaviour of the least squares estimator of the shift parameter of nearly unstable, nearly stable, and nearly explosive AR(1) models. Both zero start and stationary cases are treated. Connection with the maximum likelihood estimator of the shift parameter of continuous time AR(1) processes is also discussed.     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

Extrinsic Killing spinors

 Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of non-negative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a flat disc. Received: 2 February 2002; in final form: 1 August 2002 / Published online: 1 April 2003 Mathematics Subject Classification (1991): 53C27, 53C40, 53C80, 58G25 The authors would like to thank Lars Andersson for helpful discussions and for bringing to our knowledge the information regarding Remark 4. We are also grateful to the referee for pointing out that Corollary 5 and Corollary 6 are only valid when the boundary is at least 2-dimensional. Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Proper Efficiency in Vector Optimization on Real Linear Spaces

In this paper, we use an algebraic type of closure, which is called vector closure, and through it we introduce some adaptations to the proper efficiency in the sense of Hurwicz, Benson, and Borwein in real linear spaces without any particular topology. Scalarization, multiplier rules, and saddle-point theorems are obtained in order to characterize the proper efficiency in vector optimization with and without constraints. The usual convexlikeness concepts used in such theorems are weakened through the vector closure.     

Static and dynamic detection of axial surface defects on metallic wires by conical triple laser reflection

The quality of the surface of metallic wires is relevant for different applications. The reflection of a laser beam on the surface of a metallic cylindrical wire provides an efficient way to inspect the quality of its surface. Our interest is focused in the detection of axially oriented defects, which are the most relevant for the wire drawing process. We present a simple interference-geometrical model to describe the light pattern reflected from a wire with defects. This model adequately accounts for the observed results from an industrial prototype developed for the purpose. It incorporates three-laser beams incident on the wire at equidistant locations in its perimeter, which produce three reflection cones with a CCD. This configuration permits to explore the whole perimeter of the wire. Several results are presented, both in static operation and in production line, in agreement with qualitative and quantitative predictions.