The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.

SYMMETRICAL ORTHOGONAL POLYNOMIALS AND THE ASSOCIATED ORTHOGONAL L-POLYNOMIALS

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx(2))(1 - x(2))(-1/2), k > 0.

Multivariate sobolev-type orthogonal polynomials

Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions. © 2011 Universidad de Jaén.

On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

Para-orthogonal polynomials from constant Verblunsky coefficients

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Loss of pace capture on the ablation line: a new marker for complete radiofrequency lesions to achieve pulmonary vein isolation

Catheter ablation procedures for atrial fibrillation (AF) often involve circumferential antral isolation of pulmonary veins (PV). Inability to reliably identify conduction gaps on the ablation line necessitates placing additional lesions within the intended lesion set.

Wild immunology: converging on the real world

Recently, the Centre for Immunity, Infection and Evolution sponsored a one-day symposium entitled "Wild Immunology." The CIIE is a new Wellcome Trust-funded initiative with the remit to connect evolutionary biology and ecology with research in immunology and infectious diseases in order to gain an interdisciplinary perspective on challenges to global health. The central question of the symposium was, "Why should we try to understand infection and immunity in wild systems?" Specifically, how does the immune response operate in the wild and how do multiple coinfections and commensalism affect immune responses and host health in these wild systems? The symposium brought together a broad program of speakers, ranging from laboratory immunologists to infectious disease ecologists, working on wild birds, unmanaged animals, wild and laboratory rodents, and on questions ranging from the dynamics of coinfection to how commensal bacteria affect the development of the immune system. The meeting on wild immunology, organized by Amy Pedersen, Simon Babayan, and Rick Maizels, was held at the University of Edinburgh on 30 June 2011.

Benefit of pulmonary vein isolation guided by loss of pace capture on the ablation line: results from a prospective 2-center randomized trial.

OBJECTIVES This study was conducted to determine if an additional procedural endpoint of unexcitability (UE) to pacing along the ablation line reduces recurrence of atrial fibrillation (AF) or atrial tachycardia (AT) after radiofrequency catheter ablation. BACKGROUND AF/AT recurrence is common after pulmonary vein isolation (PVI). METHODS We included 102 patients from 2 centers (age 63 ± 10 years; 33 women; left atrium 38 ± 7 mm; left ventricular ejection fraction 61 ± 6%) with symptomatic paroxysmal AF. A 3-dimensional mapping system and circumferential mapping catheter were used in all patients for PVI. In group 1 (n = 50), the procedural endpoint was bidirectional block across the ablation line. In group 2 (n = 52), additional UE to bipolar pacing at an output of 10 mA and 2-ms pulse width was required. The primary endpoint was freedom from any AF/AT (>30 s) after discontinuation of antiarrhythmic drugs. RESULTS Procedural endpoints were successfully achieved in all patients. Procedure duration was significantly longer in group 2 (185 ± 58 min vs. 139 ± 57 min; p < 0.001); however, fluoroscopy times were not different (23 ± 9 min vs. 23 ± 9 min; p = 0.49). After a follow-up of 12 months in all patients, 26 patients (52%) in group 1 versus 43 (82.7%) in group 2 were free from any AF/AT (p = 0.001) after a single procedure. No major complications occurred. CONCLUSIONS The use of pacing to ensure UE along the PVI line markedly improved near-term single-procedure success, compared with demonstration of bidirectional block alone. This additional endpoint significantly improved patient outcomes after PVI. (Unexcitability Along the Ablation as an Endpoint for Atrial Fibrillation Ablation; NCT01724437).

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Module optical analyzer: Identification of defects on the production line

The usefulness of the module optical analyzer when identifying module defects on production line is presented in this paper. Two different case studies performed with two different kind of CPV modules are presented to show the use of MOA both in IES-UPM and Daido Steel facilities.