Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group

We present a characterization of the open unit ball in a separable infinite dimensional Hilbert space by the property of automorphism orbits among the domains that are not necessarily bounded. This generalizes the recent work of Kim and Krantz [6]. Key new features of this article include: a lower bound estimate of the Kobayashi metric and distance near a pluri-subharmonic peak boundary point of the domains in Banach spaces, an effective localization argument, and an improvement of weak-type convergence of sequences of biholomorphic mappings of domains in Banach spaces.     

Nevanlinna counting function and Carleson function of analytic maps

We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants.     

Slow-light spatial solitons

We numerically and experimentally report the observation of slow-light spatial solitons in a Kerr medium owing to light amplification by stimulated Raman scattering. This was achieved in a CS2 nonlinear planar waveguide that possesses both a strong self-focusing nonlinearity to generate the spatial Raman soliton and a Raman susceptibility sharp enough to induce the slow-light process simultaneously. We show that the Raman Stokes component is optically delayed by more than 120 ps for a 140 ps Raman pulse duration and only 3 cm of propagation length, while propagating as a spatial soliton beam.     

Optimization of wire connections design for power electronics

In automotive power electronics, low cost and reliability requirements both demand to optimize each part of the package in order to increase its life time during use. The wire bonding breakage accounts for one of the most common failures observed on power modules. In particular, the heel crack mechanism, mainly due to Joule self-heating, can occur in the module, leading to its death. Thus, the wire geometry design has to be set up to maximize its endurance. This paper presents an analytical method able to predict the optimal wire length regarding a wire displacement criterion. Finally, comparisons between experimental results and predictions of the analytical model are given.     

Cationic Phosphonolipids Containing Quaternary Phosphonium and Arsonium Groups for DNA Transfection with Good Efficiency and Low Cellular Toxicity**

Replacing the ammonium polar head in cationic lipids 1 (A=N) by a phosphonium or an arsonium group (A=P, As) improves their properties as synthetic vectors for DNA transfection. The increased volume of the cationic head is supposed to modify the interactions of the vector with the solvent and DNA.     

Enhancement of single-molecule fluorescence detection in subwavelength apertures

We report the experimental proof of molecular count rate enhancement (up to 6.5-fold) and lifetime reduction for single fluorescent molecules diffusing in subwavelength apertures milled in aluminum films. The observed enhancement dependence with the aperture diameter agrees qualitatively with numerical electromagnetic computations of the excitation power density into the aperture volume.     

Nonalgebraizable real analytic tubes in ℂ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We give necessary conditions for certain real analytic tube generic submanifolds in ⁿ to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in ⁿ. During the proof, we show that the local CR automorphism group of a minimal, finitely nondegenerate real algebraic generic submanifold is a real algebraic local Lie group. We may state one of the main results as follows. Let M be a real analytic hypersurface tube in ⁿ passing through the origin, having a defining equation of the form v= (y), where (z,w)=(x+iy,u+iv)^n–1×. Assume that M is Levi nondegenerate at the origin and that the real Lie algebra of local infinitesimal CR automorphisms of M is of minimal possible dimension n, i.e. generated by the real parts of the holomorphic vector fields _z1,...,_{z n–1},_w. Then M is locally algebraizable only if every second derivative ²_{yky l}; is an algebraic function of the collection of first derivatives _y1,,_ym.Mathematics Subject Classification (2000): 32V40, 32V25, 32H02, 32H40, 32V10     

Use of pruned computational neural networks for processing the response of oscillating chemical reactions with a view to analyzing nonlinear multicomponent mixtures

The suitability of pruned computational neural networks (CNNs) for resolving nonlinear multicomponent systems involving synergistic effects by use of oscillating chemical reaction-based methods implemented using the analyte pulse perturbation technique is demonstrated. The CNN input data used for this purpose are estimates provided by the Levenberg-Marquardt method in the form of a three-parameter Gaussian curve associated with the singular profile obtained when the oscillating system is perturbed by an analyte mixture. The performance of the proposed method was assessed by applying it to the resolution of mixtures of pyrogallol and gallic acid based on their perturbating effect on a classical oscillating chemical system, viz. the Belousov-Zhabotinskyi reaction. A straightforward network topology (3:3:2, with 18 connections after pruning) allowed the resolution of mixtures of the two analytes in concentration ratios from 1:7 to 6:2 with a standard error of prediction for the testing set of 4.01 and 8.98% for pyrogallol and gallic acid, respectively. The reduced dimensions of the selected CNN architecture allowed a mathematical transformation of the input vector into the output one that can be easily implemented via software. Finally, the suitability of response surface analysis as an alternative to CNNs was also tested. The results were poor (relative errors were high), which confirms that properly selected pruned CNNs are effective tools for solving the analytical problem addressed in this work.