Pointwise gradient estimates in exterior domains

We consider a class of elliptic operators with unbounded coefficients in a smooth exterior domain Ω and we prove that the Cauchy-Neumann problem associated with admits, for any bounded and continuous initial datum, a unique bounded classical solution. We also provide pointwise gradient estimates for such a solution. Received: 5 July 2005; Revised: 20 December 2005     

Homogenization of two-phase metrics and applications

We consider two-phase metrics of the form ϕ(x, ξ) ≔ , where α,β are fixed positive constants and B _α, B _β are disjoint Borel sets whose union is ℝ^N, and prove that they are dense in the class of symmetric Finsler metrics ϕ satisfying

Artificial sieves for quasimassless particles

Brownian motion on a symmetric vibrated periodic substrate is shown to be extremely sensitive to the particle mass even in the regime of large damping. This phenomenon is the most apparent for high vibration frequencies, a condition of technological interest, which is investigated here both analytically and numerically. When plotted versus the damping constant, both the particle mobility and the diffusion coefficient develop sharp (correlated) peaks, thus suggesting efficient schemes for separating submicron particles according to their mass or geometry.     

Cardiac resynchronization therapy and phase resetting of the sinoatrial node: a conjecture

Congestive heart failure is a severe chronic disease often associated with disorders that alter the mechanisms of excitation-contraction coupling that may result in an asynchronous left ventricular motion which may further impair the ability of the failing heart to eject blood. In recent years a therapeutic approach to resynchronize the ventricles (cardiac resynchronization therapy, CRT) has been performed through the use of a pacemaker device able to provide atrial-based biventricular stimulation. Atrial lead senses the spontaneous occurrence of cells depolarization and sends the information to the generator which, in turn, after a settled delay [atrioventricular (AV) delay], sends electrical impulses to both ventricles to stimulate their synchronous contraction. Recent studies performed on heart rate behavior of chronically implanted patients at different epochs after implantation have shown that CRT can lead to sustained overall improvement of heart function with a reduction in morbidity and mortality. At this moment, however, there are no studies about CRT effects on spontaneous heart activity of chronically implanted patients. We performed an experimental study in which the electrocardiographic signal of five subjects under chronic CRT was recorded during the activity of the pacemaker programmed at different AV delays and under spontaneous cardiac activity after pacemaker deactivation. The different behavior of heart rate variability during pacemaker activity and after pacemaker deactivation suggested the hypothesis of a phase resetting mechanism induced by the pacemaker stimulus on the sinoatrial (SA) node, a phenomenon already known in literature for aggregate of cardiac cells, but still unexplored in vivo. The constraints imposed by the nature of our study (in vivo tests) made it impossible to plan an experiment to prove our hypothesis directly. We therefore considered the best attainable result would be to prove the accordance of our data to the conjecture through the use of models and physical considerations. We first used the data of literature on far-field effects of cardiac defibrillators to prove that the pacemaker impulses delivered to the two ventricles were able to induce modifications in membrane voltage at the level of the SA node. To simulate a phase resetting mechanism of the SA node, we used a Van der Pol modified model to allow the possibility of changing the refractory period and the firing frequency of the cells separately. With appropriate parameters of the model we reproduced phase response curves that can account for our experimental data. Furthermore, the simulated curves closely resemble the functional form proposed in literature for perturbed aggregate of cardiac cells. Despite the small sample of subjects investigated and the limited number of ECG recordings at different AV delays, we think we have proved the plausibility of the proposed conjecture.     

Liquid crystals carrying stereodefined vicinal difluoro- and trifluoro- alkyl motifs

The synthesis of the stereospecifically fluorinated difluoro- and trifluoro- rac-3 and rac-4 is described where the fluorine atoms are positioned adjacent/vicinal to each other and the physical characteristics of these candidate liquid crystals including negative dielectric anisotropy are measured and rationalised.     

Investigation of the amino acids glycine, proline, and methionine by photoemission spectroscopy

The valence and core level photoelectron spectra of glycine, proline, and methionine in the gas phase have been investigated by VUV and soft X-ray radiation. The outer valence band photoemission spectra are similar to previously reported He I spectra, although relative peak intensities are different due to the different photon energy. We extended the spectral range to include the inner valence region. The carbon, nitrogen, and oxygen 1s as well as the sulfur 2p core level spectra of these amino acids have been measured and the states identified. Valence band spectra of proline have been recorded as a function of temperature, and they provide information about the relative populations of the lowest energy conformers.     

New Insight into the Chemical Composition,Antimicrobial and Synergistic Effects of the Moroccan Endemic Thymus atlanticus (Ball) Roussine Essential Oil in Combination with Conventional Antibiotics

This study reported the volatile profile, the antimicrobial activity and the synergistic potential of essential oil (EO) from the Moroccan endemic Thymus atlanticus (Ball) Roussine, in combination with the antibiotics ciprofloxacin and fluconazole for the first time, to the best of our knowledge. The EO chemical composition was determined by gas chromatography coupled to mass spectrometry (GC-MS) analysis and the antimicrobial activity assessed by the disc diffusion method against three Gram positive (Bacillus subtilis, Micrococcus luteus, Staphylococcus aureus) and three Gram-negative bacteria (Pseudomonas aeruginosa, Escherichia coli and one clinical isolate, Klebsiella pneumonia). The antifungal activity was evaluated in four pathogenic yeasts (Candida albicans, C. glabrata, C. krusei and C. parapsilosis). The minimum inhibition concentration (MIC) and the synergistic effect with ciprofloxacin and fluconazole were determined by the two-fold dilution technique and checkerboard test, respectively. Twenty-one constituents were identified by GC-MS in the EO, including carvacrol (21.62%) and borneol (21.13%) as the major components. The EO exhibited a significant antimicrobial activity with inhibition zones ranging from 0.7 mm to 22 mm for P. aeruginosa and B. subtilis, respectively, and MIC values varying from 0.56 mg/mL to 4.47 mg/mL. The fractional inhibitory concentration index (FICI) values ranged from 0.25 to 0.50 for bacteria and from 0.25 to 0.28 for yeasts. The maximum synergistic effect was observed for K. pneumonia with a 256-fold gain of antibiotic MIC. Our results have suggested that EO from T. atlanticus may be used alone or in association with antibiotics as a new potential alternative to prevent and control the emergence of resistant microbial strains both in the medical field and in the food industry.     

A discrete approach for a generalized Beck’s column in parametric resonance

A Galerkin projection based on non-standard bases is conceived to derive an equivalent discrete model of a continuous system under non-conservative forces. The problem of deriving a discrete model capable of describing critical and post-critical scenarios for non-selfadjoint systems is discussed and an heuristic rule for a proper choice of trial functions is given. The procedure is utilized to analyze the effect of non-conservative autonomous and non-autonomous (pulsating) forces acting on a linearly damped Beck’s column involving geometrical nonlinearities. The linear and nonlinear behaviours arising from the analysis of the proposed discrete model are in good agreement with those observed through the unavoidably more involved direct continuous approach. Critical scenarios for the autonomous and non-autonomous cases are investigated and the multiple scales method is applied in order to obtain the bifurcation equations in the neighborhood of a Hopf bifurcation point in primary parametric resonance. A comparison between critical and post-critical continuous and discrete model is performed adopting two control parameters, namely the amplitudes of the static and dynamic components of the forces, playing the role of detuning and bifurcation parameters, respectively.     

PEEK–WC-Based Mixed Matrix Membranes Containing Polyimine Cages for Gas Separation

Membrane-based processes are taking a more and more prominent position in the search for sustainable and energy-efficient gas separation applications. It is known that the separation performance of pure polymers may significantly be improved by the dispersion of suitable filler materials in the polymer matrix, to produce so-called mixed matrix membranes. In the present work, four different organic cages were dispersed in the poly(ether ether ketone) with cardo group, PEEK-WC. The m-xylyl imine and furanyl imine-based fillers yielded mechanically robust and selective films after silicone coating. Instead, poor dispersion of p-xylyl imine and diphenyl imine cages did not allow the formation of selective films. The H₂, He, O₂, N₂, CH₄, and CO₂ pure gas permeability of the neat polymer and the MMMs were measured, and the effect of filler was compared with the maximum limits expected for infinitely permeable and impermeable fillers, according to the Maxwell model. Time lag measurements allowed the calculation of the diffusion coefficient and demonstrated that 20 wt % of furanyl imine cage strongly increased the diffusion coefficient of the bulkier gases and decreased the diffusion selectivity, whereas the m-xylyl imine cage slightly increased the diffusion coefficient and improved the size-selectivity. The performance and properties of the membranes were discussed in relation to their composition and morphology.     

Hydroxyl and acid number prediction in polyester resins by near infrared spectroscopy and artificial neural networks

Back-propagation artificial neural networks (BP-ANN) are applied for modeling hydroxyl number and acid value of a set of 62 samples of polyester resins from their near infrared (NIR) spectra. The results are compared to the classical calibration approaches, i.e. principal component regression (PCR) and partial least squares (PLS). The set of available samples is split into: (i) a training set, for models calculation; (ii) a test set, for setting the correct number of latent variables in PCR and PLS and for selecting the end point of the training phase of BP-ANN; (iii) a “production set” of samples, which are predicted to evaluate the models predictive ability. This approach guarantees that the predictive ability of the models is evaluated by genuine predictions. BP-ANN resulted always better than the classical PCR and PLS, from the point of view of the predictive ability. The study of the breakdown number of experiments to include in the training set showed instead that this factor does influence PCR and PLS at a lesser degree than what happens for BP-ANN. The latter approach requires a larger number of experiments for obtaining good results. The choice of optimal training sets is efficiently performed by Kohonen self-organizing maps (SOMs). It can be concluded that FT-NIR spectroscopy and BP-ANN models can be properly employed for monitoring the polyesterification of dicarboxylic acids with diols by predicting the acid and hydroxyl numbers directly along the process line.