New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1

Deflation based nonlinear canonical correlation analysis

This paper introduces two new techniques for determining nonlinear canonical correlation coefficients between two variable sets. A genetic strategy is incorporated to determine these coefficients. Compared to existing methods for nonlinear canonical correlation analysis (NLCCA), the benefits here are that the nonlinear mapping requires fewer parameters to be determined, consequently a more parsimonious NLCCA model can be established which is therefore simpler to interpret. A further contribution of the paper is the investigation of a variety of nonlinear deflation procedures for determining the subsequent nonlinear canonical coefficients. The benefits of the new approaches presented are demonstrated by application to an example from the literature and to recorded data from an industrial melter process. These studies show the advantages of the new NLCCA techniques presented and suggest that a nonlinear deflation procedure should be considered. (c) 2006 Elsevier B.V. All rights reserved.

Polarization and Angular Correlation Studies of X-Rays Emitted in Relativistic Ion-Atom Collisions

Particle and photon polarization phenomena occurring in collisions of relativistic ions with matter have recently attracted particular interest. Investiga- tions of the emitted characteristic x-ray and radiative electron capture radiation has been found to be a versatile tool for probing our present understanding of the dynamics of particles in extreme electromagnetic ¯elds. Owing to the progress in x-ray detector technology, in addition, accurate measurements of the linear po- larization for hard x-ray photons as well as the determination of the polarization plane became possible. This new diagnostic tool enables one today to derive in- formation about the polarization of the ion beams from the photon polarization features of the radiative electron capture process.

Development of a QSPR correlation for the parachor of 1,3-dialkyl imidazolium based ionic liquids

Ionic liquids have received significant interest from both academia and industry for a wide range of applications which often requires knowledge of their thermophysical properties. Quantitative structure-property relationship correlations and group contribution methods for thermophysical properties of ionic liquids are a basic necessity for the development of computer aided molecular design approaches for these liquids and subsequently offer the potential for designing an ionic liquid having a desirable set of thermophysical properties. However, the limited availability of experimental thermophysical data and their quality have prevented the development of such tools. Based on previously reported experimental surface tension data, a correlation of the parachors with the molar volume of the ionic liquids has been developed. The predicted parachor values have been shown to be in good agreement with the experimental data. A maximum deviation of