Discrete structures equivalent to nonlinear Dirichlet and wave equations

The Amann–Conley–Zehnder (ACZ) reduction is a global Lyapunov–Schmidt reduction for PDEs based on spectral decomposition. ACZ has been applied in conjunction to diverse topological methods, to derive existence and multiplicity results for Hamiltonian systems, for elliptic boundary value problems, and for nonlinear wave equations. Recently, the ACZ reduction has been translated numerically for semilinear Dirichlet problems and for modeling molecular dynamics, showing competitive performances with standard techniques. In this paper, we apply ACZ to a class of nonlinear wave equations in , attaining to the definition of a finite lattice of harmonic oscillators weakly nonlinearly coupled exactly equivalent to the continuum model. This result can be thought as a thermodynamic limit arrested at a small but finite scale without residuals. Reduced dimensional models reveal the macroscopic scaled features of the continuum, which could be interpreted as collective variables.      

Determination of Commercial Animal and Vegetable Milks’ Lipid Profile and Its Correlation with Cell Viability and Antioxidant Activity on Human Intestinal Caco-2 Cells

Lipids from milk are important nutritional components, although their health effects, especially for animal milks, are still questioned. Four types of commercial milks, two semi-skimmed animal milks (bovine and goat) and two vegetable ones (soy and rice), along with their total and free lipid fractions recovered by sequential centrifugation or by ethyl acetate extraction, respectively, have been analyzed. A higher antioxidant ability, reported as Trolox equivalent antioxidant capacity, was found for all raw milks compared to that of rice. This trend was confirmed, except for soy milk, as ROS reduction in Caco-2 cells. The free lipid fraction was shown to have the highest antioxidant potential in both chemical and biological tests. Moreover, goat and soy raw milks positively regulated Caco-2 cell viability after an inflammatory stimulus. This effect was lost when their total lipid fraction was tested. Finally, only the free lipid fraction from rice milk preserved the Caco-2 viability after LPS stimulation. Our data demonstrated that the lipid profile of each milk, characterized by GC-MS analysis, could contribute to dictate its biological effects, and, although additional in vitro and in vivo studies are needed, they could support the literature re-evaluating the health effects of animal-based versus plant-based milks in the intestinal cellular model.     

Principle of Symmetric Bracket Invariance as the Origin of First and Second Quantization

The principle of invariance of the c-number symmetric bracket is used to derive both the quantum operator commutator relation and the time-dependent Schrödinger equation. A c-number dynamical equation is found, which leads to the second quantized field theory of bosons and fermions.     

Safety controls and applications to the Dubins’ car

In this paper we consider systems with cooperative controls. Such a model turns out to be efficient in those cases where one has to deal with different goals, as optimality and safety issues, at the same time. On the other hand, the drawback of this approach is the presence of discontinuities of the various controls. To deal with this problem, we give a general strategy, which is based on the concept of Krasowskii solution to discontinuous ODEs. Such a strategy is then applied to the safety driving of the Dubins car.     

Properties of two interlinked chi(2) interactions in noncollinear phase matching

We present a compact experimental realization of the interaction among five field modes in a chi(2) nonlinear crystal. The classical evolution of the fields can be analytically described assuming that two of the fields play the role of nondepleted pumps. If one of the fields has a nonzero input amplitude, then the other two fields at the output are holographic replicas of the input signal.     

Iridoids from seeds of Gentiana lutea

In the seeds of Gentiana lutea L. there were also detected, in addition to the known sweroside and getiopicroside, loganic acid 3 and trifloroside 4 that is present as main glycosidic component. The structures of 3 and 4 were established by spectroscopic studies.     

Determination of inorganic and organic anionic arsenic species in water by ion chromatography coupled to hydride generation-inductively coupled plasma atomic emission spectrometry

The development of an analytical methodology for the specific determination of arsenite, arsenate and the organic species monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA), is described. The method is based on an ion chromatographic separation, coupled on-line to post-column generation of the gaseous hydrides by reaction with sodium tetrahydroborate in acidic medium. Detection and measurement were performed by inductively coupled plasma spectrometry operated in the atomic emission mode. Arsenic emission was monitored at 193.7 nm. Different types and sizes of anion-exchange columns, silica and polymeric, were tested using EDTA as eluent. Composition, acidity and flow-rate of the mobile phase were optimized in order to obtain the required resolution. Complete elution and resolution of the four species was achieved in about 6 min. Linear calibration curves were obtained in the 0.05-2 microg ml(-1) range for As(III), As(V) and MMA, and between 0.1 and 2.0 microg ml(-1) for DMA. The absolute limits of detection for 200-microl sample injections were in the ng range, with DMA the compound measured with less sensitivity. Results of the analyses of natural samples, such as river and ground waters spiked with the studied species, suggested that analyte recoveries might be dependent on the sample composition.     

Ultra‐high performance separation of basic compounds on reversed‐phase columns packed with fully/superficially porous silica and hybrid particles by using ultraviolet transparent hydrophobic cationic additives

The use of the tetrabutylammonium additive was investigated in the ultra‐high performance reversed‐phase liquid chromatographic elution of basic molecules of pharmaceutical interest. When added to the mobile phase at low pH, the hydrophobic tetrabutylammonium cation interacts with the octadecyl chains and with the residual silanols, thus imparting a positive charge to the stationary phase, modulating retention and improving peak shape of protonated basic solutes. Two sources of additive were tested: a mixture of tetrabutylammonium hydroxide/trifluoroacetic acid and tetrabutylammonium hydrogen sulfate. Retention and peak shape of 11 basic pharmaceutical compounds were evaluated on commercially available ultra‐fast columns packed with octadecyl stationary phases (Ascentis Express C18 2.0 µm, Acquity BEH C18 1.7 µm, Titan C18 1.9 µm). All columns benefit from the use of additive, especially tetrabutylammonium hydrogen sulfate, providing very symmetric peaks with reasonable retention times. Focusing on the probe compounds amitriptyline and sertraline, efficiency and asymmetry values were investigated at increasing retention factor. The trend is very different to that obtained in reversed‐phase conditions and the effect lies in the complex molecular interaction mechanisms based on hydrophobic and ion exchange interactions as well as electrostatic repulsion.