Finite reduction and Morse index estimates for mechanical systems

A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators. Moreover, the Hessian of the reduced function preserves all the relevant information of the original one, by Schur's complement, which spontaneously appears in this context. Finally, the results are straightforwardly extended to the case of a Dirichlet problem on a bounded domain.Comment: 13 pages; v2: minor changes, to appear in Nonlinear Differential Equations and Application

A weak KAM approach to the periodic stationary Hartree equation

AbstractWe present, through weak KAM theory, an investigation of the stationary Hartree equation in the periodic setting. More in details, we study the Mean Field asymptotics of quantum many body operators thanks to various integral identities providing the energy of the ground state and the minimum value of the Hartree functional. Finally, the ground state of the multiple-well case is studied in the semiclassical asymptotics thanks to the Agmon metric

Selective and highly efficient dye scavenging by a pH-responsive molecular hydrogelator

A structurally simple low molecular weight hydrogelator derived from isophthalic acid forms robust pH-responsive hydrogels capable of highly efficient and selective dye adsorption

On the nature of the stretched exponential photoluminescence decay for silicon nanocrystals

The influence of hydrogen rate on optical properties of silicon nanocrystals deposited by sputtering method was studied by means of time-resolved photoluminescence spectroscopy as well as transmission and reflection measurements. It was found that photoluminescence decay is strongly non-single exponential and can be described by the stretched exponential function. It was also shown that effective decay rate probability density function may be recovered by means of Stehfest algorithm. Moreover, it was proposed that the observed broadening of obtained decay rate distributions reflects the disorder in the samples

Shortening of the Short Refractory Periods in Short QT Syndrome.

BACKGROUND: Diagnosis of short QT syndrome (SQTS) remains difficult in case of borderline QT values as often found in normal populations. Whether some shortening of refractory periods (RP) may help in differentiating SQTS from normal subjects is unknown. METHODS AND RESULTS: Atrial and right ventricular RP at the apex and right ventricular outflow tract as determined during standard electrophysiological study were compared between 16 SQTS patients (QTc 324±24 ms) and 15 controls with similar clinical characteristics (QTc 417±32 ms). Atrial RP were significantly shorter in SQTS compared with controls at 600- and 500-ms basic cycle lengths. Baseline ventricular RP were significantly shorter in SQTS patients than in controls, both at the apex and right ventricular outflow tract and for any cycle length. Differences remained significant for RP of any subsequent extrastimulus at any cycle length and any pacing site. A cut-off value of baseline RP <200 ms at the right ventricular outflow tract either at 600- or 500-ms cycle length had a sensitivity of 86% and a specificity of 100% for the diagnosis of SQTS. CONCLUSIONS: Patients with SQTS have shorter ventricular RP than controls, both at baseline during various cycle lengths and after premature extrastimuli. A cut-off value of 200 ms at the right ventricular outflow tract during 600- and 500-ms basic cycle length may help in detecting true SQTS from normal subjects with borderline QT values