Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and numerical experiments

This article is concerned with adaptive numerical frame methods for elliptic operator equations. We show how specific noncanonical frame expansions on domains can be constructed. Moreover, we study the approximation order of best n‐term frame approximation, which serves as the benchmark for the performance of adaptive schemes. We also discuss numerical experiments for second order elliptic boundary value problems in polygonal domains where the discretization is based on recent constructions of boundary adapted wavelet bases on the interval. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Global bifurcation of fixed points and the Poincaré translation operator on manifolds

Let M be a differentiable manifold and [0, )×MM be a C¹ map satisfying the condition (0, p)=p for all pM. Among other results, we prove that when the degree (also called Hopf index or Euler characteristic) of the tangent vector field wMTM, given by w(p)=(/)(0, p), is well defined and nonzero, then the set (of nontrivial pairs) admits a connected subset whose closure is not compact and meets the slice {0}×M of [0, )×M. This extends known results regarding the existence of harmonic solutions of periodic ordinary differential equations on manifolds.     

Simple eigenvalues for the Steklov problem in a domain with a small hole. A functional analytic approach

Let be a bounded open domain of . Let denote the outward unit normal of . We assume that the Steklov problem Δu = 0 in and on has a simple eigenvalue of . Then we consider an annular domain obtained by removing from a small‐cavity size of ε > 0, and we show that under proper assumptions there exists a real valued and real analytic function defined in an open neighborhood of (0,0) in and such that is a simple eigenvalue for the Steklov problem Δu = 0 in and on for all ε > 0 small enough, and such that . Here denotes the outward unit normal of , and δ_2,2 ≡ 1 and δ_2,n ≡ 0 if n ≥ 3. Then related statements have been proved for corresponding eigenfunctions. Copyright © 2013 John Wiley & Sons, Ltd.     

Can long-run dynamic optimal strategies outperform fixed-mix portfolios? Evidence from multiple data sets

Using five alternative data sets and a range of specifications concerning the underlying linear predictability models, we study whether long-run dynamic optimizing portfolio strategies may actually outperform simpler benchmarks in out-of-sample tests. The dynamic portfolio problems are solved using a combination of dynamic programming and Monte Carlo methods. The benchmarks are represented by two typical fixed mix strategies: the celebrated equally-weighted portfolio and a myopic, Markowitz-style strategy that fails to account for any predictability in asset returns. Within a framework in which the investor maximizes expected HARA (constant relative risk aversion) utility in a frictionless market, our key finding is that there are enormous difference in optimal long-horizon (in-sample) weights between the mean–variance benchmark and the optimal dynamic weights. In out-of-sample comparisons, there is however no clear-cut, systematic, evidence that long-horizon dynamic strategies outperform naively diversified portfolios.     

Analysis of the SG discretizatioin scheme on a multi-dimensional domain — application to impact ionization

An analysis is carried out of the multi-dimensional extension of the Scharfetter-Gummel method. It shown that, within the frame of the drift-diffusion model of semiconductor devices, the assumption of constant electric field and current densities over suitable subelements of the discretization grid preserves the necessary degrees of freedom of the problem and, at the same time, provides some information about the current-density field. These informations are exploited for treating a case in which the dependence of the model's coefficients on the current density is strong, namely, impact ionization.     

Adaptive frame methods for elliptic operator equations: the steepest descent approach

Massimo Fornasier^¶ Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università "La Sapienza" in Roma, Via Antonio Scarpa, 16/B, I-00161 Roma, Italy Rob Stevenson^|| Department of Mathematics, Utrecht University, PO Box 80.010, NL-3508 TA Utrecht, The Netherlands ^{This paper is concerned with the development of adaptive numericalmethods for elliptic operator equations. We are particularlyinterested in discretization schemes based on wavelet frames.We show that by using three basic subroutines an implementable,convergent scheme can be derived, which, moreover, has optimalcomputational complexity. The scheme is based on adaptive steepestdescent iterations. We illustrate our findings by numericalresults for the computation of solutions of the Poisson equationwith limited Sobolev smoothness on intervals in 1D and L-shapeddomains in 2D.}     

Strongly correlated superconductivity and pseudogap phase near a multiband Mott insulator

Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the dynamical mean field theory solution of a twofold-orbital degenerate Hubbard model with an inverted on-site Hund rule exchange, favoring local spin-singlet configurations. Close to the Mott insulator (which here is a local version of a valence bond insulator) a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of cuprates. The strongly correlated s-wave superconducting state has a larger Drude weight than the corresponding normal state. The role of the impurity Kondo problem is underscored.     

Consortium GARR and the European National Research and Education Networks Optical Infrastructure Developments

Abstract

GARR is engineering its next generation of the Italian Research and Education Network (GARR-X), which will exploit a countrywide optical infrastructure based on DWDM equipment and advanced multi-domain services. The trend is common in all National Research and Education Networks [1 TERENA NREN Compendium. http://www.terena.org/activities/compendium ISSN 1569-4496 [Google Scholar]] in Europe and worldwide. NRENs are relying more and more on direct use of optical equipment to fulfill the researchers' requirements. These hybrid networks are built to provide services on a multi-domain environment both at the circuit and at the IP layer for researchers in, for example, radio astronomy (eVLBI [2 European Very Long Baseline Interferometry http://www.evlbi.org [Google Scholar]]), GRID computing (EGEE [3 Enabling Grids for E-sciencE http://public.eu-egee.org [Google Scholar]], LHC [4 The Large Hadron Collider http://lhc.web.cern.ch/lhc [Google Scholar]]), high-performance computing (DEISA [5 The Distributed European Infrastructure for Supercomputing Applications http://www.deisa.org [Google Scholar]]). This article outlines the status and issues of ongoing research activities in GARR [6 http://www.garr.it/garr-b-home-engl.shtmlConsortium GARR, the Italian NREN [Google Scholar]] and NRENs to provide, manage, and evolve dedicated optical-based networks for providing multi-domain end-to-end services. The research is performed mainly in the framework of the European Commission co-funded project GÉANT2 [7 The pan-European R&E network http://www.geant2.net [Google Scholar]].