Solutions of second-order and fourth-order ODEs on the half-line

We start by studying the existence of positive solutions for the differential equation u '' = a(x)u - g(u), with u ''(0) = u(+infinity) = 0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results concerning the existence of homoclinics for the autonomous case (where a is constant) are also true for the non-autonomous equation. This also motivates us to study the analogous fourth-order boundary value problem {u((4)) - cu '' + a(x)u = vertical bar u vertical bar(p-1)u u'(0) = u'''(0) = 0, u(+infinity) = u'(+infinity) = 0 for which we also find nontrivial (and, in some instances, positive) solutions.

On the real effects of financial pressure: Evidence from euro area firm-level employment during the recent financial crisis.

Using a large panel of unquoted euro-area firms over the period 2003-11, this paper examines the impact of financial pressure on firms’ employment. The analysis finds evidence that financial pressure negatively affects firms’ employment decisions. This effect is stronger during the 2007-2009 financial crisis, especially for firms in the periphery area compared to their counterparts in the core European economies. We also find that impact of financial pressure on employment is more potent for firms classified as financially constrained and operating in periphery economies during the financial crisis.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

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.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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).