Wolff's Inequality for Radially Nonincreasing Kernels and Applications to Trace Inequalities

We extend Th. Wolff's inequality to a general class of radially decreasing convolution kernels. As an application we obtain characterizations of nonnegative Borel measures on R ⁿ such that the trace inequality holds for every f in L ^p (dx).     

Paths Clustering and an Existence Result for Stochastic Vortex Systems

We prove, via a pathwise analysis, an existence result for stochastic differential equations with singular coefficients that govern stochastic vortex systems. The techniques are self-contained and rely on careful estimates on the displacements of particles, obtained by recursively identifying “vortex clusters“ whose mutual interactions can be controlled. This provides a non trivial extension of techniques of Marchioro and Pulvirenti⁽⁷⁾ for deterministic motion of vortices. AMS subject classification: 60H10, 60K35, 76B47     

Methyl carbon chemical shifts of methylbenzoic acids and methylbenzoate anions

Methyl carbon chemical shifts have been assigned for methylbenzoic acids dissolved in CDCl₃, and for methylbenzoate anions obtained by dissolving these acids in aqueous NaOH solution. Chemical shifts have been interpreted by means of additive substituent parameters which reflect conformational features existing between adjacent substituents. Barriers to rotation of a methyl group adjacent to a carboxyl or carboxylate group have been estimated to differ by less than 2 kJ mol^?1 from the barrier of a methyl group in o-xylene.     

Extraction of monodisperse palladium nanoparticles from dendrimer templates

We describe a strategy for extracting nearly size-monodisperse, 1.7-nm-diameter Pd nanoparticles from within dendrimer hosts. The approach involves two steps. First, an aqueous solution of dendrimer-encapsulated Pd nanoparticles is prepared, followed by the addition of a toluene solution containing an n-alkanethiol. When the two-phase system is stirred, n-alkanethiols presumably self-assemble onto the surface of the Pd nanoparticles, extract them from the dendrimer, and transport them to toluene phase. UV-vis spectroscopy indicates that the Pd nanoparticles, in the form of monolayer-protected clusters, are transported into the toluene phase. FT-IR spectroscopy shows that the dendrimers remain in the aqueous phase. High-resolution transmission electron microscopy shows that the average size and size distribution of the particles do not change during the extraction process.     

Liquid chromatography/tandem mass spectrometry determination of (4S,2RS)-2,5,5-trimethylthiazolidine-4-carboxylic acid, a stable adduct formed between D-(-)-penicillamine and acetaldehyde (main biological metabolite of ethanol), in plasma, liver and brain rat tissues

Acetaldehyde, the main biological metabolite of ethanol, is nowadays considered to mediate some ethanol-induced effects. Previous studies on alcohol effect attenuation have shown that D-(-)-penicillamine (3-mercapto-D-valine), a thiol amino acid, acts as an effective agent for the inactivation of acetaldehyde. In the study reported here, laboratory rats were treated with ethanol and D-(-)-penicillamine at different doses looking for the interaction (in vivo) of D-(-)-penicillamine with metabolically formed acetaldehyde following a condensation reaction to form the stable adduct (4S,2RS)-2,5,5-trimethylthiazolidine-4-carboxylic acid (TMTCA). A novel and rapid procedure based on liquid chromatography coupled to tandem mass spectrometry (LC/MS/MS) was developed for quantification and reliable identification of TMTCA in different rat tissues, including plasma, liver and brain. Firstly, plasma was obtained from whole blood. Then, proteins were precipitated from plasma, brain and liver extracts with acetonitrile and the clarified extracts diluted 10-fold. A 20 microL aliquot of the final extracts was then analyzed using an Atlantis C18 5 microm, 100x2 mm column which was connected to the electrospray source of a LC/triple quadrupole mass spectrometer. The analyte was detected in positive ion mode acquiring four MS/MS transitions in selected reaction monitoring (SRM) mode.The method has been validated and it has proved to be fast, reliable and sensitive. The accuracy and precision were evaluated by means of recovery experiments from plasma, liver and brain samples fortified at two concentration levels obtaining satisfactory recoveries in all cases: 95 and 105% in plasma (at 10 and 100 ng/mL, respectively), 79 and 89% in brain (100 and 1000 ng/g), 85 and 99% in liver (100 and 1000 ng/g). Precision, expressed as repeatability, was in all tissues analyzed lower than 17% at the two concentrations tested. The estimated detection limits were 1 ng/mL in plasma, 4 ng/g in brain and 5 ng/g in liver. The limit of quantitation objective (the lowest concentration that was validated with acceptable results) was set up at 10 ng/mL for plasma and 100 ng/g for brain and liver tissue.The reliable identification of the analyte was ensured by the acquisition of four transitions and by their ion abundance ratio measurement. Due to its excellent selectivity and sensitivity, the method developed in this work provides an excellent tool for the specific determination of this cyclic amino acid in biological samples.     

Electron pairing and chemical bonds: pair localization in ELF domains from the analysis of domain averaged Fermi holes

This article reports the application of a recently proposed formalism of domain averaged Fermi holes to the problem of the localization of electron pairs in electron localization function (ELF) domains and its possible implications for the electron pair model of chemical bond. The main focus was on the systems, such as H2O or N2, in which the "unphysical" population of ELF domains makes the parallel between these domains and chemical bond questionable. On the basis of the results of the Fermi-hole analysis, we propose that the above problems could be due to the fact that in some cases the boundaries of the ELF domains need not be determined precisely enough.     

Norm Inequalities for Potential-Type Operators in Homogeneous Spaces

In this paper, we obtain a characterization of the positive Borel measures on a homogeneous space X, for which the trace inequality holds for any f ≥. Here I_Φ is a general potential type kernel, and 1 ≤ q < p < +∞. The characterization is given in terms of a generalized Wolff's potential.