An averaging method applied to a duffing equation

We approximate a Duffing equation by an averaged system. We solve the system explicitely and draw bifurcation diagrams in dependence of the forcing term. We discuss the goodness of the averaging method, relative to the behavior of the solutions in dependence of involved parameters, by comparing with results obtained in [6,10] for the original Duffing equation.     

Uniform resolvent convergence for strip with fast oscillating boundary

In a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small. On the oscillating boundary we impose Dirichlet, Neumann or Robin boundary condition. In all cases we describe the homogenized operator, establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. These results are obtained as the order of the amplitude of the oscillations is less, equal or greater than that of the period. It is shown that under the homogenization the type of the boundary condition can change.     

A Characterization of Nilpotent Injectors in Finite Groups

In this article a class of subgroups of a finite group G, called Q-injectors, is introduced. If G is soluble, the Q-injectors are precisely the injectors of the Fitting sets. A characterization of nilpotent Q-injectors is given as well as a sufficient condition for the solubility of a finite group G, in terms of Q-injectors, which generalizes a well known result.     

Improved extraction of vegetable oils under high-intensity ultrasound and/or microwaves

Ultrasound-assisted extraction (UAE) and microwave-assisted extraction (MAE) techniques have been employed as complementary techniques to extract oils from vegetable sources, viz, soybean germ and a cultivated marine microalga rich in docosahexaenoic acid (DHA). Ultrasound (US) devices developed by ourselves, working at several frequencies (19, 25, 40 and 300 kHz), were used for US-based protocols, while a multimode microwave (MW) oven (operating with both open and closed vessels) was used for MAE. Combined treatments were also studied, such as simultaneous double sonication (at 19 and 25 kHz) and simultaneous US/MW irradiation, achieved by inserting a non-metallic horn in a MW oven. Extraction times and yields were compared with those resulting from conventional procedures. With soybean germ the best yield was obtained with a ‘cavitating tube’ prototype (19 kHz, 80 W), featuring a thin titanium cylinder instead of a conventional horn. Double sonication, carried out by inserting an immersion horn (25 kHz) in the same tube, improved the yield only slightly but halved the extraction time. Almost comparable yields were achieved by closed-vessel MAE and simultaneous US/MW irradiation. Compared with conventional methods, extraction times were reduced by up to 10-fold and yields increased by 50–500%. In the case of marine microalgae, UAE worked best, as the disruption by US of the tough algal cell wall considerably improved the extraction yield from 4.8% in soxhlet to 25.9%. Our results indicate that US and MW, either alone or combined, can greatly improve the extraction of bioactive substances, achieving higher efficiency and shorter reaction times at low or moderate costs, with minimal added toxicity.     

Screening of fluoroquinolones in environmental waters using disk-based solid-phase extraction combined to microplate fluorimetric determination and LC-MS/MS

Fluoroquinolones are in the order of the day concerning environmental contamination through anthropogenic activities, resulting in increased risk for antibiotic resistance dissemination. In this context, accessible, low-cost analytical methods are required for implementation of comprehensive surveillance and screening schemes. In this work, we propose a down-scaled disk-based solid-phase extraction system from which the eluate can be first screened by miniaturized fluorimetric reading, followed by individual determination of target fluoroquinolones (ciprofloxacin, norfloxacin, and enrofloxacin) by liquid chromatography combined to tandem mass spectrometry. The fluorimetric measurement is based on the intrinsic fluorescence of fluoroquinolones. Disk-based retention was performed after sample acidification (pH 4.0) by mixed-mode cation exchange using polystyrene divinylbenzene sulphonated sorbent. Sample loading was precisely controlled in a dedicated flow system operating at 4.0 mL min^?1. Different eluent compositions were tested, with elution performed by 1.00 mL of methanol-ammonium hydroxide (98:2, v/v), with subsequent reading of eluate in both detectors. Quantification was attained for 2–25 µg L^?1 range, with LOD values at 1 µg L^?1. The proposed approach was successfully applied to estuarine waters from the Douro River, with comparable results to a conventional SPE-LC-MS/MS procedure.     

Unprecedented Diastereoselective Arylogous Michael Addition of Unactivated Phthalides

The first highly enantioselective arylogous Michael reaction (AMR) of 3-unsubstituted phthalides has been described. This phase-transfer methodology, which uses catalytic amounts of KOH/18-crown-6 catalyst in mesitylene in the presence of N,O-bis(trimethylsilyl)acetamide (BSA), gives access to a broad range of 3-monosubstituted phthalides with high levels of syn diastereoselectivity and good yields, starting from 3-unsubstituted derivatives and diverse α,β-unsaturated carbonyl compounds. The reaction also applies to unactivated 3-alkyl phthalides to afford 3,3-dialkyl derivatives. A plausible mechanism has been suggested. DFT analysis of possible transition states gives a rationale of the high syn diastereoselectivity observed and its correlation with the solvent's dielectric constant.     

Role of the solvent on the stability of cycloserine under ESI‐MS conditions

The effects of methanol (M) and acetonitrile (A) on the stability of cycloserine (1) have been studied. InfraRed Multiphoton PhotoDissociation (IRMPD) spectroscopy of the ionic species from electrospray ionization tandem mass spectrometry (ESI‐MS) of 1/M and 1/A solutions points to extensive dimerization of 1 to cis‐3,6‐bis(aminooxymethyl)‐2,5‐piperidinedione (2), while the same process is not observed in the ESI‐MS of 1/M solutions. 1D and 2D nuclear magnetic resonance experiments confirmed these findings by showing that partial dimerization of 1 actually takes place at room temperature in acetonitrile even before ESI‐MS analysis. Comparison of nuclear magnetic resonance and IRMPD spectroscopic data from the same 1/A solution suggests that dimerization of cycloserine is enhanced in the ESI source. Copyright © 2014 John Wiley & Sons, Ltd.     

Lactoferrin and Its Derived Peptides: An Alternative for Combating Virulence Mechanisms Developed by Pathogens

Due to the emergence of multidrug-resistant pathogens, it is necessary to develop options to fight infections caused by these agents. Lactoferrin (Lf) is a cationic nonheme multifunctional glycoprotein of the innate immune system of mammals that provides numerous benefits. Lf is bacteriostatic and/or bactericidal, can stimulate cell proliferation and differentiation, facilitate iron absorption, improve neural development and cognition, promote bone growth, prevent cancer and exert anti-inflammatory and immunoregulatory effects. Lactoferrin is present in colostrum and milk and is also produced by the secondary granules of polymorphonuclear leukocytes, which store this glycoprotein and release it at sites of infection. Lf is also present in many fluids and exocrine secretions, on the surfaces of the digestive, respiratory and reproductive systems that are commonly exposed to pathogens. Apo-Lf (an iron-free molecule) can be microbiostatic due to its ability to capture ferric iron, blocking the availability of host iron to pathogens. However, apo-Lf is mostly microbicidal via its interaction with the microbial surface, causing membrane damage and altering its permeability function. Lf can inhibit viral entry by binding to cell receptors or viral particles. Lf is also able to counter different important mechanisms evolved by microbial pathogens to infect and invade the host, such as adherence, colonization, invasion, production of biofilms and production of virulence factors such as proteases and toxins. Lf can also cause mitochondrial and caspase-dependent regulated cell death and apoptosis-like in pathogenic yeasts. All of these mechanisms are important targets for treatment with Lf. Holo-Lf (the iron-saturated molecule) can contain up to two ferric ions and can also be microbicidal against some pathogens. On the other hand, lactoferricins (Lfcins) are peptides derived from the N-terminus of Lf that are produced by proteolysis with pepsin under acidic conditions, and they cause similar effects on pathogens to those caused by the parental Lf. Synthetic analog peptides comprising the N-terminus Lf region similarly exhibit potent antimicrobial properties. Importantly, there are no reported pathogens that are resistant to Lf and Lfcins; in addition, Lf and Lfcins have shown a synergistic effect with antimicrobial and antiviral drugs. Due to the Lf properties being microbiostatic, microbicidal, anti-inflammatory and an immune modulator, it represents an excellent natural alternative either alone or as adjuvant in the combat to antibiotic multidrug-resistant bacteria and other pathogens. This review aimed to evaluate the data that appeared in the literature about the effects of Lf and its derived peptides on pathogenic bacteria, protozoa, fungi and viruses and how Lf and Lfcins inhibit the mechanisms developed by these pathogens to cause disease.