Every real Banach space can be renormed to satisfy the denseness of numerical radius attaining operators

First we show that every real Banach space satisfying a certain property, calledβ (used by Lindenstrauss and Partington) verifies the denseness of the numerical radius attaining operators. Using this result and a renorming theorem by Partington we conclude that every Banach space is isomorphic to a new one satisfying the denseness of the numerical radius attaining operators.     

There is no bilinear Bishop-Phelps theorem

We answer a question posed by R. Aron, C. Finet and E. Werner, on the bilinear version of the Bishop-Phelps theorem, by exhibiting an example of a Banach spaceX such that the set of norm-attaining bilinear forms onX×X is not dense in the space of all continuous bilinear forms. Research partially supported by D.G.I.C.Y.T., project no. PB93-1142.     

The HLD–NAC equation of state for microemulsions formulated with nonionic alcohol ethoxylate and alkylphenol ethoxylate surfactants

The net–average curvature (NAC) model (Langmuir, 19, 186, 2003) is a simple, yet powerful, equation of state to fit and predict the phase behavior of microemulsions (μEs) formulated with ionic surfactants. However, its use for nonionic surfactants systems has not been evaluated until now. The objective of this work is to use the NAC equation of state to model the phase behavior of μEs formulated with pure alcohol ethoxylate (CiEj) and commercial nonylphenol ethoxylate (NPEj) surfactants with a range of alkanes (Cn). The NAC model requires three basic parameters: the characteristic curvature of the nonionic surfactant (Ccn), the characteristic length (ξ), and the scaling length parameter (L). The first part of this contribution presents a brief review of the NAC model and other thermodynamic models of μEs. Later, five example applications of the NAC model are presented and discussed: (I) fit/prediction of phase inversion temperature (PIT) values, (II) prediction of phase transition temperatures and characteristic lengths, (III) fit/prediction of interfacial tensions, (IV) prediction of “fish” phase diagrams, and (V) prediction of the composition of bicontinuous systems. The NAC model was able to fit the phase behavior observed in all the experimental scenarios, and predict within 30% the value of phase volumes and transition temperatures for CiEj systems. The largest deviations can be attributed to a poor estimation of ξ obtained through empirical correlations. It was also noted that for commercial NPEj surfactants, the NAC model can also fit and predict the phase behavior of these systems, only that more complex empirical correlations are needed for ξ and Ccn due to the partition of different surfactant n-mers into the excess oil and aqueous phases. In all cases, a good agreement was found when the length parameter (L) was estimated as 1.4 times the extended length of the surfactant tail.     

Diastereoisomeric forms of 11‐ethyl‐6,11‐dihydro‐5H‐dibenzo[b,e]azepine‐6‐carboxamide: syntheses and the molecular and supramolecular structure of the minor form (6RS,11RS)‐11‐ethyl‐6,11‐dihydro‐5H‐dibenzo[b,e]azepine‐6‐carboxamide

Compounds containing the tricyclic dibenzo[b,e]azepine system have potential activity in the treatment of a number of diseases. Continuing with our studies on the synthesis of new small and potentially bioactive molecules, a synthetic route, involving acid‐catalysed intramolecular Friedel–Crafts cyclization, to the readily separable diastereoisomers of 11‐ethyl‐6,11‐dihydro‐5H‐dibenzo[b,e]azepine‐6‐carboxamide, a potentially useful precursor in the synthesis of analogues of some anti‐allergenic, antidepressant and antihistaminic drugs currently in use, has been developed starting from 2‐allylphenylamine and methyl 2‐bromo‐2‐phenylacetate and proceeding via racemic methyl 2‐[(2‐allylphenyl)amino]‐2‐phenylacetate (A) and racemic 2‐[(2‐allylphenyl)amino]‐2‐phenylacetamide (B), to give the two diastereoisomers (I) and (II), C₁₇H₁₈N₂O. Isomers (I) and (II), and their precursors (A) and (B), have all been fully characterized spectroscopically. Structure analysis of the minor isomer (I) shows that it has the (6RS,11RS) configuration, and that the azepine ring adopts a conformation intermediate between the boat and twist‐boat forms, with the carboxamide and ethyl substituents both occupying quasi‐equatorial sites. The molecules of (I) are linked by a combination of N—H…O, N—H…π(arene) and C—H…π(arene) hydrogen bonds to form complex sheets. Comparisons are made with the structures of some related compounds.     

Pharmacokinetic study of puerarin in rat serum by liquid chromatography tandem mass spectrometry

A highly sensitive and specific atmospheric pressure chemical ionization liquid chromatography-tandem mass spectrometry method was developed for serum pharmacokinetic studies of puerarin in rats. Chromatography was carried out on a reversed-phase Phenomenex Synergi 4 microm Fusion-RP80 column (150 x 2.0 mm i.d.) using a mobile phase consisting of acetonitrile-water (10:90, v/v) in 10 mm NH(4)OAc with a flow rate of 0.2 mL/min. Puerarin was analyzed in the multiple reaction monitoring mode with a precursor/product ion transition of m/z 415/267. The method was demonstrated to be specific and sensitive, and a linear response was observed over a range of 2-5000 ng/mL in rat serum. The validated method was successfully applied to the characterization of the pharmacokinetics of puerarin in rat serum after oral administration to spontaneously hypertensive rats. The blood concentration-time profile of puerarin showed a rapid initial increase, reaching a maximum and then declining within 1 h. Puerarin could not be detected after 24 h. The main pharmacokinetic parameters for puerarin after oral administration were as follows: C(max) (3.54 +/- 2.03 mg/L), T(max) (0.68 +/- 0.37 h), AUC(0-t) (7.29 +/- 3.79 mg h/L), AUC(0-infinity) (9.17 +/- 4.87 mg h/L), T(1/2) (1.7 +/- 0.6 h), CL/F (7.24 +/- 4.27 L/h/kg) and V/F (17.88 +/- 13.55 L/h/kg).     

An immunochemical strategy based on peptidoglycan synthetic peptide epitopes to diagnose Staphylococcus aureus infections

The characteristic pentaglycyl cross-bridge of the Staphylococcus aureus peptidoglycan (PG) cell wall component is an attractive epitope to raise specific antibodies against this microorganism. Based on this approach, we report here for the first time a competitive ELISA able to detect S. aureus down to 10⁴ CFU mL⁻¹, without pre-enrichment on cell culture. The antibodies were raised against peptide-protein bioconjugates prepared by covalently coupling peptide haptens (PSau6 and PSau8) designed and synthesized taking into consideration the complex tridimensional structure in the PG polymer. Deglycosylation of the PG under acidic conditions has found to increase assay detectability. Assay performance has been evaluated in clinical samples such as bronchoalveolar lavage (BAL) and bronchoalveolar endotracheal aspirates (BAS) showing promising results for further implementation of this immunoassay as a daily routine diagnostic tool. Cross-reactivity studies have demonstrated that the immunoassay is specific for S. aureus.     

Imaging of a mixture of hyperpolarized 3He and 129Xe

With the use of hyperpolarized gases, a great number of experiments have been carried out in order to improve the diagnostics of the lung, both from a structural and a functional point of view. 3He is best suited for structural studies, whereas 129Xe gives more detailed information about the functionality of the lung because it enters the bloodstream. In this work, we propose the use of a gas mixture to perform consecutive analysis of lung structure and functionality upon the delivery of a single bolus of gas. We show images of a helium-xenon gas mixture in the presence of a small amount of liquid toluene in order to demonstrate how both nuclei can be detected independently, extracting the spectroscopic information provided by the 129Xe spectra and obtaining an image with high sensitivity for 3He. A second experiment performed on a dissected mouse lung was used to demonstrate how the mixture of gases can enhance sensitivity in the larger airways of the lung.     

Weakly open sets in the unit ball of the projective tensor product of Banach spaces

A Banach space is said to have the diameter two property if every non-empty relatively weakly open subset of its unit ball has diameter two. We prove that the projective tensor product of two Banach spaces whose centralizer is infinite-dimensional has the diameter two property. The same statement also holds for if the centralizer of X is infinite-dimensional and the unit sphere of Y^? contains an element of numerical index one. We provide examples of classical Banach spaces satisfying the assumptions of the results. If K is any infinite compact Hausdorff topological space, then has the diameter two property for any nonzero Banach space Y. We also provide a result on the diameter two property for the injective tensor product.     

The hydrophobicity of silicone-based oils and surfactants and their use in reactive microemulsions

In this work, for the first time, the Hydrophilic-Lipophilic Difference (HLD) framework for microemulsion formulation has been applied to silicone oils and silicone alkyl polyether surfactants. Based on the HLD equations and recently introduced mixing rules, we have quantified the hydrophobicity of the oils according to the equivalent alkane carbon number (EACN). We have found that, in a reference system containing sodium dihexyl sulfosuccinate (SDHS) as the surfactant, 0.65 centistoke (cSt) and 3.0 cSt silicone oils behave like n-dodecane and n-pentadecane, respectively. Silicone alkyl polyether surfactants were found to have characteristic curvatures ranging 3.4-18.9, exceeding that of most non-ionic surfactants. The introduction of methacrylic acid (MAA) and hydroxyethyl methacrylate (HEMA) to the aqueous phase caused a significant negative shift in HLD, indicative of an aqueous phase that is less hydrophilic than pure water. The more hydrophobic surfactants (largest positive curvatures) were used in order to compensate for this effect. These findings have led to the formulation of bicontinuous microemulsions (μEs) containing silicone oil, silicone alkyl polyether and reactive monomers in aqueous solution. Ternary phase diagrams of these systems revealed the potential for silicone-containing polymer composites with bicontinuous morphologies. These findings have also helped to explain the phase behavior of formulations previously reported in literature, and could help in providing a systematic, consistent approach to future silicone oil based microemulsion formulation.