Proximal methods in reflexive Banach spaces without monotonicity

We introduce the concept of hypomonotone point-to-set operators in Banach spaces, with respect to a regularizing function. This notion coincides with the one given by Rockafellar and Wets in Hilbertian spaces, when the regularizing function is the square of the norm. We study the associated proximal mapping, which leads to a hybrid proximal-extragradient and proximal-projection methods for nonmonotone operators in reflexive Banach spaces. These methods allow for inexact solution of the proximal subproblems with relative error criteria. We then consider the notion of local hypomonotonicity and propose localized versions of the algorithms, which are locally convergent.     

Direct determination of molybdenum in mineral waters by atomic absorption spectrometry with electrothermal atomization

A new method for the direct determination of molybdenum by ETA-AAS in mineral waters without prior separation or concentration is proposed. With careful control of the graphite furnace conditions selective volatilization of the salt matrix is successfully attained. The possible spectroscopic interference due to common metals as well as the reproducibility, precision and repeatability of the method has been studied and the molybdenum content of 21 mineral waters measured.     

Bulk derivatization and cation exchange restricted access media-based trap-and-elute liquid chromatography–mass spectrometry method for determination of trace estrogens in serum

Estrone (E1), estradiols (α/β-E2), and estriol (E3) are four major metabolically active estrogens exerting strong biological activities at very low circulating concentrations. This paper reports a sensitive and efficient method with automated, on-line clean-up and detection to determine trace estrogens in a small volume of serum samples using liquid chromatography–electrospray ionization–tandem mass spectrometry directly, without off-line liquid–liquid or solid-phase extraction pretreatments. Serum aliquots (charcoal stripped fetal bovine serum, 100 μL) were spiked with four estrogen standards and their corresponding isotope-labeled internal standards, then bulk derivatized with 2-fluoro-1-methyl-pyridium p-toluenesulfonate (2-FMP) to establish the calibration curves and perform method validation. Calibration was established in the concentration ranges of 5–1000 pg mL⁻¹, and demonstrated good linearity of R² from 0.9944 to 0.9997 for the four derivatized estrogens. The lower detection limits obtained were 3–7 pg mL⁻¹. Good accuracy and precision in the range of 86–112% and 2.3–11.9%, respectively, were observed for the quality control (QC) samples at low, medium, and high concentration levels. The stability tests showed that the derivatized serum samples were stable 8 h after derivatization at room temperature and at least to 48 h if stored at −20 °C. The method was applied to measure trace estrogens in real human and bovine serum samples, and three of four estrogen compounds studied were observed and quantified.     

Regiospecific synthesis of quercetin O-β-d-glucosylated and O-β-d-glucuronidated isomers

Quercetin, the polyphenolic compound, which has the highest daily intake, is well known for its protective effects against aging diseases and has received a lot of attention for this reason. Both quercetin 3-O-β-d-glucuronide and quercetin 3′-O-β-d-glucuronide are human metabolites, which, together with their regioisomers, are required for biological as well as physical chemistry studies. We present here a novel synthetic route based on the sequential and selective protections of the hydroxyl functions of quercetin allowing selective glycosylation, followed by TEMPO-mediated oxidation to the glucuronide. This methodology enabled us to synthesize the five O-β-d-glucosides and four O-β-d-glucuronides of quercetin, including the major human metabolite, quercetin 3-O-β-d-glucuronide.     

Electrical conductivity relaxation in PVOH+LiH2PO4+Al2O3 polymer composites

Low-frequency conductivity measurements have been performed in solid polymer electrolyte composites based on the anhydrous PVOH–LiH₂PO₄–Al₂O₃ system. A typical power law dependency in the real part of the conductivity, at higher frequencies, of the form ω ⁿ is observed, with an exponent n that depends on the alumina content and nearly independent of temperature. An analysis of the frequency dependence of the electrical susceptibility is conducted to obtain relaxation functions of the form exp[?(t/τ) ^β ], with an exponent β?≈?n???1. Correlation times, τ, and parameters characterizing the electrical relaxation in time and frequency domains are compared to show the equivalence of these representations. The anhydrous dc conductivity of the electrolytes increases with increasing lithium salt content, becoming of the order of 10^?5 S/cm for a salt molar fraction of x?=?0.14. This conductivity value increased by about one order of magnitude by addition of nanoporous particles of Al₂O₃. The temperature dependence of the samples conductivity was well described by the Vogel–Tammann–Fulcher’s equation indicating the effect of the polymer chains flexibility on ion migration. Although all membranes exhibited a “universal dynamic response” associated to the random hopping of the mobile carriers, variations in the measured relaxation parameters with alumina content indicate an increase of ionic correlations when adding the nonporous particles to the polyelectrolyte.     

Determination of strain and stress distribution on shearwalls by using the speckle photography technique

Speckle photography (SP) is a powerful tool that is adequate to determine small displacements in micrometer range. This information shows other characteristics of structure deformation under loads and can be determined as stress and strain distribution. In this paper we present the results of the application of the SP technique used to study the behaviour of discontinuities in a shearwall model. These structural elements are very important to the stability of buildings. The displacement whole field around the discontinuities and loading points was determined using the pointwise method. This allows us to determine stress distribution at the point of interest by means of the suitable equations. We also present the stress distribution obtained through the finite element method in order to compare the results obtained by means of these two techniques. Good correspondence was found between the displacements determined by both techniques (r=0.982) and also between the stress values we obtained.     

Transience and recurrence of quantum Markov semigroups

 This article introduces a concept of transience and recurrence for a Quantum Markov Semigroup and explores its main properties via the associated potential. We show that an irreducible semigroup is either recurrent or transient and characterize transient semigroups by means of the existence of non trivial superharmonic operators. Received: 27 January 2003 / Revised version: 19 February 2003 / Published online: 12 May 2003 This research has been partially supported by the ``Cátedra Presidencial en Análisis Cualitativo de Sistemas Dinámicos Cuánticos', DIPUC, FONDECYT project 1030552, MIUR program ``Probabilità Quantistica e Applicazioni', 2003-2004 and MECESUP PUC 0103. Mathematics Subject Classification (2000): 60J45, 81S25, 60J99, 37A50, 47A40 Key words or phrases: Quantum Markov semigroups – Potential theory – Markov processes     

Combinatorial Space from Loop Quantum Gravity

The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills fields (with or without fermions) coupled to gravity. It is argued that the operators induced by classical diffeomorphism invariant or covariant functions are respectively invariant or covariant under a suitable completion of the diffeomorphism group. The canonical quantization in terms of loop variables described here, yields a representation of the algebra of observables in a separable Hilbert space. Furthermore, the resulting quantum theory is equivalent to a model for diffeomorphism invariant gauge theories which replaces space with a manifestly combinatorial object.