Critical Gevrey index for hypoellipticity of parabolic operators and Newton polygones

Summary In this paper we give geometrical expressions of the (non) hypoellipticity in Gevrey spaces of parabolic operators via Newton polygones. We also determine the critical Gevrey class for which the hypoellipticity holds.Partially supported by GNAFA, CNR, Italy.Partially supported by JSPS, Japan and a grant MM-410/94 with MES, Bulgaria.Partially supported by Chuo University special research fund.     

Additive action of two or more solutes on lipid membranes

A wide variety of biological processes, pharmaceutical applications, and technical procedures is based on the combined action of two or more soluble compounds to perturb, permeabilize, or lyse biological membranes. Here we present a general model describing the additive action of solutes on the properties of membranes or micelles. The onset and completion of membrane solubilization induced by two surfactants (lauryl maltoside, with nonyl maltoside, octyl glucoside, or CHAPS, respectively) are very well described by our model on the basis of their individual partition coefficients, cmc's, and critical mole ratios R e sat and R e sol as detected by isothermal titration calorimetry. This suggests that the thermodynamic phase transition is governed by a single parameter (e.g., spontaneous curvature) in spite of the complexity of structural changes. Such surfactant mixtures show unique features such as nonlinear solubilization boundaries and concentration-dependent effective partition coefficients. Other phenomena such as membrane leakage are predicted to obey additive action if the solutes act via the same mechanism (e.g., toroidal pore formation) but deviate from the model in the case of independent, synergistic, or antagonistic action.     

Antibacterial effect of silver nanoparticles deposited on corona‐treated polyester and polyamide fabrics

The possibility of using a corona treatment (electrical discharge at atmospheric pressure) for fiber surface activation, which can facilitate the loading of silver nanoparticles (NPs) from colloids onto the polyester (PES) and polyamide (PA) fabrics and thus improve their antibacterial properties, was studied. Bactericidal efficiency and its laundering durability on silver‐loaded fabrics for Gram‐positive bacterium Staphylococcus aureus and Gram‐negative bacterium Escherichia coli were evaluated. The fiber morphology after corona treatment and subsequent loading of silver NPs was followed by SEM. Corona‐treated fabrics loaded with silver NPs exhibited better antibacterial properties in comparison with untreated fabrics. In order to obtain acceptable laundering durability, it is necessary to use highly concentrated silver colloids. Copyright © 2008 John Wiley & Sons, Ltd.     

Design of branched and chiral solvatochromic probes: toward quantifying polarity gradients in dendritic macromolecules

[reaction: see text] A pair of chiral, branched monomer building blocks, consisting of a solvatochromic probe and a spectroscopically inactive volume dummy, has been developed. The probe can selectively be excited, and its fluorescence characteristics provide information about local polarity. Incorporation of these monomers into high-generation polyester dendrimers should enable a detailed investigation of the polarity/density profile in dendritic architectures and ultimately allow for the realization of energy gradients from one chromophore building block only.     

<Emphasis Type="Italic">SU</Emphasis>(3)-Instantons and <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>,<Emphasis Type="Italic">Spin</Emphasis>(7)-Heterotic String Solitons

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. A formula for the Riemannian scalar curvature is obtained. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimension 6. Non-conformally flat non-compact solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 7 and 8. A Riemannian metric with holonomy contained in G₂ arises from our considerations and Hitchin’s flow equations, which seems to be new. Compact examples of SU(3),G₂ and Spin(7) instanton satisfying the anomaly cancellation conditions are presented.     

Gaussian interval quadrature formula

Summary. We prove the existence of a Gaussian quadrature formula for Tchebycheff systems, based on integrals over non-overlapping subintervals of arbitrary fixed lengths and the uniqueness of this formula in the case the subintervals have equal lengths. Received July 6, 1999 / Published online August 24, 2000     

Recent trends in image evaluation of HPTLC chromatograms

Abstract

In the current article, an overview of recent applications and opportunities of image evaluation of high-performance thin-layer chromatograms (HPTLC) in food analysis and natural product research is presented. The article shortly covers the aspects of specialized software packages for image analysis, image post-correction, signal acquisition, and preprocessing. Contemporary aspects of image-based HPTLC fingerprinting, quantification of target compounds, and advanced chemometric modeling were reviewed. Special attention was dedicated to freely available software packages. Advantages and disadvantages of each one were discussed in terms of abilities to obtain chromatographic profiles and perform crucial steps in signal manipulation, such as background subtraction, denoising, and background detrending. The most frequently applied techniques for signal manipulation have been discussed and recommendation provided. In that sense, the article aims to provide a valuable guideline for readers dealing with the application of HPTLC image analysis in food and natural products research, especially in connection with the most frequently used chemometric techniques, in domains of pattern recognition, classification, and regression.     

Sharp Riesz-Fejér Inequality for Harmonic Hardy Spaces

Potential Analysis - We prove sharp version of Riesz-Fejér inequality for functions in harmonic Hardy space $h^{p}(\mathbb {D})$ on the unit disk $\mathbb {D}$ , for p &gt;?1, thus...