A Dynamical System Associated with Newton's Method for Parametric Approximations of Convex Minimization Problems

We study the existence and asymptotic convergence when t→+∞ for the trajectories generated by where is a parametric family of convex functions which approximates a given convex function f we want to minimize, and ε(t) is a parametrization such that ε(t)→ 0 when t→+∞ . This method is obtained from the following variational characterization of Newton's method: where H is a real Hilbert space. We find conditions on the approximating family and the parametrization to ensure the norm convergence of the solution trajectories u(t) toward a particular minimizer of f . The asymptotic estimates obtained allow us to study the rate of convergence as well. The results are illustrated through some applications to barrier and penalty methods for linear programming, and to viscosity methods for an abstract noncoercive variational problem. Comparisons with the steepest descent method are also provided. Accepted 5 December 1996     

Primal and dual convergence of a proximal point exponential penalty method for linear programming

We consider the diagonal inexact proximal point iteration where f(x,r)=c ^T x+r∑exp[(A _i x-b _i )/r] is the exponential penalty approximation of the linear program min{c ^T x:Ax≤b}. We prove that under an appropriate choice of the sequences λ _k , ε _k and with some control on the residual ν ^k , for every r _k →0⁺ the sequence u ^k converges towards an optimal point u ^∞ of the linear program. We also study the convergence of the associated dual sequence μ _i ^k =exp[(A _i u ^k -b _i )/r _k ] towards a dual optimal solution. Received: May 2000 / Accepted: November 2001?Published online June 25, 2002     

Q-curvature flow on 4-manifolds

We formulate an appropriate gradient flow in order to study the evolution of the Q-curvature to a prescribed function on a 4-manifold. For a class of prescribed functions, we show convergence and describe the asymptotic behaviour at infinity.     

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials II

We present a definition of general Sobolev spaces with respect to arbitrary measures, Wh,p (Ω,μ) for 1 ≤p≤∞. In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cc∞ (R) is dense in thee spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.     

Comparison between a thin matrix decomposition method and the rigorous coupled wave theory applied to volume diffraction gratings

Diffraction gratings have been an interesting field during the last decades. A great deal of research has been done in order to understand how light propagates inside diffraction gratings. Since its formulation, the Rigorous Coupled Wave Theory (RCWT) has been applied to different periodic structures providing a basis to check the validity of approximate theories, such as Kogelnik's coupled wave theory or the coupled wave theory neglecting second derivatives. In this work we will compare the results of the diffraction efficiencies of the first and second orders at second on-Bragg replay angular condition, obtained by using an analytical formula provided by Alferness using an approximate thin-matrix decomposition method (TMDM) with the results obtained by using the RCWT. Good agreement between the results obtained using TMDM and the RCWT were found.     

Thermal conductivity of open‐cell polyolefin foams

The thermal conductivity and the cellular structure of novel open‐cell polyolefin foams produced by compression molding and based on blends of an ethylene‐vinyl acetate copolymer (EVA) and a low‐density polyethylene (LDPE) have been studied in the temperature range between 24 and 50 °C. The experimental results have shown that the cellular structure of the analyzed materials has interconnected cells because of the presence of large and small holes in the cell walls, this structure being clearly different to the typical structure of open‐cell polyurethane foams. It has been found that at low temperatures the materials have a slightly higher thermal conductivity than closed‐cell polyolefin foams of similar densities. The different mechanisms of heat flow, conduction, convection, and radiation have been analyzed by using experimental measurements and a theoretical model. It has been proved that, in spite of having an open‐cell structure, the convention mechanism is negligible, being the radiation mechanism the one which made different the conductivity of materials with varying cellular structures. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 212–221, 2008     

Orthopalladacycles derived from α-diphenylhydrazonoketene dithioacetals and their reactivity with terminal alkynes

In this paper, we present the synthesis and characterization of new orthopalladated complexes derived from α-diphenylhydrazonoketene dithioacetals. From their reaction with terminal alkynes, the intermediates of the expected C_sp-C_sp2coupling reaction were isolated in stable form and their structures were confirmed by X-ray diffraction studies.     

Effect of the Calcination Atmosphere on the Structural Properties of the Reduced Fe/SiO2 System

Iron supported systems are frequently used as catalysts in the Fischer–Tropsch synthesis being the Fe⁰ the active phase for the reaction. We have studied the influence of the calcination atmosphere (air or nitrogen) on the iron oxide reducibility and the metallic iron particle size obtained in Fe/SiO₂ system. We have impregnated a silicagel with Fe(NO₃)₃·9H₂O aqueous solution and the solid obtained was calcinated in air or N₂ stream. These precursors, with 5% (wt/wt) of Fe, were characterized by Mössbauer Spectroscopy at 298 and 15 K. Amorphous Fe₂O₃ species with 3 nm diameter in the former, and α-Fe₂O₃ crystals of 48 nm diameter were detected in the last one. Both precursors were reduced in H₂ stream. Two catalysts were obtained and characterized by Mössbauer spectroscopy in controlled atmosphere at 298 and 15 K, CO chemisorption and volumetric oxidation. α-Fe⁰, Fe₃O₄ and Fe²⁺ were identified in the catalyst calcined in air. Instead, only α-Fe⁰ was detected in the catalyst calcined in N₂. The iron metallic crystal sizes were estimated as ≈2 nm for the former and ≈29 nm for the last one. The different oxide crystal sizes, obtained from the diverse calcination atmospheres, have led to different structural properties of the reduced solids. It has been possible to reduce totally the existing iron in an Fe/SiO₂ system with iron loading lower than 10% (wt/wt).     

Heat flow for p-harmonic maps with small initial data

We study developing singularities for surfaces of rotation with free boundaries and evolving under volume-preserving mean curvature flow. We show that singularities form a finite, discrete set along the axis of rotation. We prove a monotonicity formula and conclude that type I singularities are asymtotically cylindrical.