Frame expansions in separable Banach spaces

Banach frames are defined by straightforward generalization of (Hilbert space) frames. We characterize Banach frames (and Xd-frames) in separable Banach spaces, and relate them to series expansions in Banach spaces. In particular, our results show that we can not expect Banach frames to share all the nice properties of frames in Hilbert spaces.     

Bounded rational expectations and the stability of interest rate policy

The New Keynesian model has recently been subject to two serious criticisms: the model cannot produce plausible inflation and output dynamics following a monetary shock, and the stability of its dynamics suffers from indeterminacy. The procedures that have been proposed to eliminate these two shortcomings fall into two categories: the introduction of some sort of backward price indexation into the standard model and/or other forms of stickiness (like sticky information); and the adoption of some form of policy rule that completely offsets the effects of forward looking dynamics in the optimization process. In this paper we do not eradicate forward looking behavior from the dynamics of the New Keynesian model, neither do we impose some form of backward price indexation. We assume that private economic agents have forward looking behavior and that they do try to optimize with all available information; the only novelty is that they are allowed to make small mistakes near the rational expectations equilibrium, in a fully deterministic setup. These “near rational” or “bounded rational” expectations show that the dynamics of the model with active interest rate rules is much richer than the simple problem of local indeterminacy as is usually found in the literature.     

Book review

Ernest R. Alexander Published by Gordon and Breach Publishers, Amsterdam, Holland 1995. 355 pages. ISBN 2-88449-173-2     

Antibacterial and antifungal LDPE films for active packaging

Active antimicrobial packaging is a promising form of active packaging that can kill or inhibit microorganism growth in order to maintain product quality and safety. One of the most common approaches is based on the release of volatile antimicrobial agents from the packaging material such as essential oils. Due to their highly volatile nature, the challenge is to preserve the essential oils during the high‐temperature melt processing of the polymer, while maintaining high antimicrobial activity for a desired shelf life. This study suggests a new approach in order to achieve this goal. Antimicrobial active films are developed based on low‐density polyethylene (LDPE), organo‐modified montmorillonite clays (MMT) and carvacrol (used as an essential oil model). In order to minimize carvacrol loss throughout the polymer compounding, a pre‐compounding step is developed in which clay/carvacrol hybrids are produced. The hybrids exhibit a significant increase in the d‐spacing of clay and enhanced thermal stability. The resulting LDPE/(clay/carvacrol) films exhibit superior and prolonged antibacterial activity against Escherichia coli and Listeria innocua, while polymer compounded with pure carvacrol loses the antibacterial properties within days. The films also present an excellent antifungal activity against Alternaria alternata, used as a model plant pathogenic fungus. Furthermore, infrared spectroscopy analysis of the LDPE/(clay/carvacrol) system displayed significantly higher carvacrol content in the film as well as a slower out‐diffusion of the carvacrol molecules in comparison to LDPE/carvacrol films. Thus, these new films have a high potential for antimicrobial food packaging applications due to their long‐lasting and broad‐spectrum antimicrobial efficacy. Copyright © 2014 John Wiley & Sons, Ltd.     

Ultrasound‐assisted extraction method for the simultaneous determination of emerging contaminants in freshwater sediments

Sediments are the fate of several emerging organic contaminants, such as pharmaceuticals, personal care products and hormones, and therefore an important subject in environmental monitoring studies. In the present work, a simple and sensitive method was developed, validated and applied for the simultaneous extraction of atenolol, caffeine, carbamazepine, diclofenac, ibuprofen, naproxen, propranolol, triclosan, estrone, 17‐β‐estradiol and 17‐α‐ethinylestradiol using ultrasound‐assisted extraction from freshwater sediment samples followed by solid‐phase extraction clean‐up and liquid chromatography with tandem mass spectrometry detection. The solvent type and extraction pH were evaluated to obtain the highest recoveries of the compounds. The best method shows absolute recoveries between 54.0 and 94.4% at 50 ng/g concentration. The method exhibits good precision with relative standard deviation ranging from 1.0–16%. The detection and quantification limits ranged from 0.006–0.067 and 0.016–0.336 ng/g, respectively. The developed method was successfully applied to freshwater sediment samples collected from different sites in Jundiaí River basin of São Paulo State, Brazil. The compounds atenolol, caffeine, propranolol and triclosan were detected in all the sampling sites with concentrations of 13.8, 41.0, 28.5 and 176 ng/g, respectively.     

Synthesis of Heterocyclic Analogs of α‐aminoadipic Acid and its Esters Based on Imidazo[2,1‐b][1,3]Thiazole

A method for the preparation of heterocyclic analogs of α‐aminoadipic acid and its esters based on the imidazo[2,1‐b][1,3]thiazole ring system was developed. In this method, free‐radical bromination of ethyl 6‐methylimidazo[2,1‐b][1,3]thiazole‐5‐carboxylate with NBS afforded a versatile building block, ethyl 6‐bromomethylimidazo[2,1‐b][1,3]thiazole‐5‐carboxylate. Coupling of ethyl 6‐bromomethylimidazo[2,1‐b][1,3]thiazole‐5‐carboxylate with Schöllkopf's chiral auxiliary followed by acidic hydrolysis generated ethyl 6‐[(2S)‐2‐amino‐3‐methoxy‐3‐oxopropyl]imidazo[2,1‐b][1,3]thiazole‐5‐carboxylate. A similar procedure using diethyl (Boc‐amino)malonate yielded racemic 2‐amino‐3‐[(5‐ethoxycarbonyl)imidazo[2,1‐b][1,3]thiazol‐6‐yl]propanoic acid.     

On the generalized Bohnenblust–Hille inequality for real scalars

In this paper we obtain new lower and upper estimates for the sharp constants in the generalized Bohnenblust–Hille inequality introduced in Albuquerque et al. (J Funct Anal 266:3726–3740, 2014). We apply these results to find optimal constants in the generalized Bohnenblust–Hille inequality and also to recover the optimal constants of the mixed \(\left( \ell _{1},\ell _{2}\right) \)-Littlewood inequalities recently obtained in Pellegrino (J Number Theory 160:11–18, 2016) and Pellegrino and Teixeira (Commun Contemp Math, to appear).