Asymptotics of Spectral Clusters for a Perturbation of the Hydrogen Atom

We consider perturbations of the Schrödinger operator of the hydrogen atom, of size $O(\hbar^{1+\delta})We consider perturbations of the Schr?dinger operator of the hydrogen atom, of size with . We show that, if is restricted to take values along a certain sequence converging to zero, the multiple eigenvalue −1/2 of the unperturbed Hamiltonian breaks into a cluster of eigenvalues disjoint from the rest of the spectrum. Then we obtain a Szeg? limit theorem for the spectral shifts in this cluster, as . Specifically, we prove: The weak limit of the normalized spectral measure of the spectral shifts is the push-forward of Liouville measure of the unperturbed energy surface H = −1/2 by the averaged symbol of the perturbation. A. Uribe supported in part by NSF grant DMS-0401064. C. Villegas-Blas supported in part by PAPIIT-UNAM IN106106-2.     

Acid–base interactions between formamide and tetrahydrofuran molecules: Raman investigation of speciation in a binary system of biological interest

Raman spectra of formamide (FA) and tetrahydrofuran (THF) mixtures at different compositions were obtained. The appearance of new bands at 897 and 1612 cm⁻¹, whose intensities show large dependence on the FA concentration, are assigned to an FA–THF adduct. This assignment is supported by the Lewis acid–base theory, where the two H‐bond donor sites of FA and the strong donor character of THF became the environment propitious for the donor‐acceptor reaction. Quantitative measurements performed in the band envelope at ∼915 cm⁻¹ allowed to determine the stoichiometry of the Lewis acid–base adduct. The experimental evidence of the 2:1 FA–THF adduct is presented for the first time using Raman spectroscopy and our results show an excellent agreement with similar systems. The present work also shows hydrogen interactions which can be involved in systems containing peptide groups and constituents of nucleic acids. Copyright © 2008 John Wiley & Sons, Ltd.     

Phase transitions in geometrothermodynamics

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic metrics for the equilibrium manifold whose curvature becomes singular at those points where phase transitions of first and second order occur. We conclude that the thermodynamic curvature of the equilibrium manifold, as defined in geometrothermodynamics, can be used as a measure of thermodynamic interaction in diverse systems with two and three thermodynamic degrees of freedom.     

How environment affects drug activity: Localization,compartmentalization and reactions of a vanadium insulin-enhancing compound,dipicolinatooxovanadium(V)

The chemical and biological properties of a simple and traditional V(5+) coordination complex, dipicolinatooxovanadium(V) (abbreviated [VO₂dipic]^?), are described in order to present a hypothesis for a novel mode of action wherein a hydrophobic membrane environment plays a key role. Specifically, we propose that the compartmentalization and both chemical and biological transformations of vanadium-complexes direct whether beneficial or toxic effects will be observed with this class of compounds. This concept is based on the formation of high levels of uncontrollable reactive oxygen species (ROS) from one-electron reactions or alternative events possibly initiated by a two-electron reaction which may be directly or indirectly beneficial by reducing the high levels of ROS. The properties of dipicolinatooxovanadium(V) compounds in aqueous solution (D.C. Crans, et al., Inorg. Chem. 39 (2000) 4409–4416) are very different from those in organic solvents (S.K. Hanson, et al., J. Am. Chem. Soc. 131 (2009) 428–429) and these differences may be key for their mode of action. Since other vanadium complexes are known to hydrolyze upon administration, the low stability of the aqueous complex requires entrapment in hydrophobic environments for such a complex to exist sufficiently long to have an effect. The suggestion that the environment changes the reactivity of the compounds is consistent with the very different modes of action by which one complex act. In short, a novel hypothesis is presented for a mode of action of vanadium compounds based on differences in properties resulting from environmental conditions. These considerations are supported by recent evidence supporting a role for membranes and signal transduction events (D.A. Roess, et al. Chem. Biodivers. 5 (2008) 1558–1570) of the insulin-enhancing properties of these compounds.     

Ellipticity criteria for ballistic behavior of random walks in random environment

We introduce ellipticity criteria for random walks in i.i.d. random environments under which we can extend the ballisticity conditions of Sznitman and the polynomial effective criteria of Berger, Drewitz and Ramírez originally defined for uniformly elliptic random walks. We prove under them the equivalence of Sznitman’s \((T')\) condition with the polynomial effective criterion \((P)_M\) , for \(M\) large enough. We furthermore give ellipticity criteria under which a random walk satisfying the polynomial effective criterion, is ballistic, satisfies the annealed central limit theorem or the quenched central limit theorem.     

Lipschitz factorization through subsets of Hilbert space

The Euclidean distortion of a metric space, a measure of how well the metric space can be embedded into a Hilbert space, is currently an active interdisciplinary research topic. We study the corresponding notion for mappings instead of spaces, which is that of Lipschitz factorization through subsets of Hilbert space. The main theorems are two characterizations of when a mapping admits such a factorization, both of them inspired by results dealing with linear factorizations through Hilbert space. The first is a nonlinear version of a classical theorem of Kwapień in terms of “dominated” sequences of vectors, whereas the second is a duality result by means of a tensor-product approach.     

A Novel Application of Sodium Borohydride for the Regiospecific and Stereoselective Reduction of Conjugated Alkadiynes

Alkynes, when carrying an α-sulfonyl group, are shown to be stereoselectively reduced to z-alkenes using sodium borohydride under mildly basic conditions.     

Simultaneous determination of diclofenac and its common counter‐ions in less than 1 minute using capillary electrophoresis with contactless conductivity detection

This paper presents a method for fast and simultaneous determination of diclofenac (DCF) and its common counter‐ions (potassium, sodium, and diethylammonium) using CE with capacitively coupled contactless conductivity detection (CE‐C⁴D). On the basis of a single electropherogram (about 50 s), the proposed method allows the determination of the stoichiometry, absolute quantification and evaluation of the degradation degree of the active pharmaceutical ingredient (DCF). A linear working range from 100 to 500 μmol/L was obtained for all analytes in an equimolar TRIS/TAPS (10 mmol/L) solution as the background electrolyte as well as adequate LOD (7, 6, 7, and 10 μmol/L for K⁺, Na⁺, diethylammonium, and DCF, respectively). The proposed method was applied to the analysis of pharmaceutical formulations (tablets and spray form) with similar results to those achieved by HPLC (DCF) or flame photometry (K and Na) at a 95% confidence level.