Arithmetic toric varieties

We study toric varieties over a field k that split in a Galois extension using Galois cohomology with coefficients in the toric automorphism group. Part of this Galois cohomology fits into an exact sequence induced by the presentation of the class group of the toric variety. This perspective helps to compute the Galois cohomology, particularly for cyclic Galois groups. We use Galois cohomology to classify k‐forms of projective spaces when is cyclic, and we also study k‐forms of surfaces.     

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.     

Thermodynamics of a Peyrard–Bishop One-Dimensional Lattice with On-site “Hump” Potential

This paper presents a thermodynamic study of DNA through a Peyrard–Bishop one-dimensional lattice with an on-site “hump” potential. The transfer integral operator method was used to obtain the thermodynamic properties of the system and the solution of the Schrödinger-type equation that emerges from this formalism was determined by the variational method. With the parameters of the potential, commonly used in literature, the value obtained for the denaturation temperature was extremely high. This work suggests different parameters to describe the thermodynamics of DNA macromolecule.     

Pseudo-Newtonian potentials and the radiation emitted by a source swirling around a stellar object

We use pseudo-Newtonian potentials to compute the scalar radiation emitted by a source orbiting a stellar object. We compare the results obtained in this approach with the ones obtained via quantum field theory in Schwarzschild spacetime. We find that, up to the marginally stable circular orbit, the potential that better reproduces the Schwarzschild results is the Nowak–Wagoner one. For unstable circular orbits, none of the pseudo-Newtonian potentials considered in our analysis produces satisfactory results. We show that the Paczyński–Wiita potential, the most used in the literature to analyze accretion disks, generates the least satisfactory results for the scalar radiation emitted by the source in circular orbit around a Schwarzschild black hole.     

Augmentation of the Porcine Vocal Fold Using Autologous Composite Cervical Fascia and Fat Graft. Comparison Between the Transmuscular and Submuscular Approaches

Objectives

To assess the integration of an autologous composite fascia and fat graft implanted into the lamina propria of a porcine vocal fold using two different approaches.

Study Design

An experimental prospective study on the porcine larynx was conducted at a tertiary research institution.

Methods

An external cervical approach was used to expose the thyroid cartilage of 24 healthy minipigs under general anesthesia. The composite fascia/fat graft was implanted through two distinct approaches, transmuscular and submuscular. Animals were sacrificed at 7, 30, 90, and 180 days for macroscopic and histological study of the larynx. Graft integration and local inflammatory response were studied.

Results

The survival rate of the experimental model was 100% and all animals had local inflammatory response to the surgical procedure. Only 41.7% of the grafts placed inside the thyroarytenoid (TA) muscle fibers were identified postmortem, whereas 83.3% of the submuscular grafts remained intact.

Conclusions

Graft incorporation was better and there was less inflammation when the architecture of the TA muscle fibers was preserved. Graft extrusion was observed in the most of the cases where it was placed inside the muscle.     

Antinociceptive activity of discretamine isolated from Duguetia moricandiana

The phytochemical study of Duguetia moricandiana Mart. (Annonaceae) yielded the isolation of the alkaloid which was identified by spectral analysis as discretamine. The evaluation of antinociceptive activity carried out by the acetic acid-induced writhing, formalin and hot plate tests in mice, suggests a potent antinociceptive effect. Discretamine (5, 10 and 20?mg?kg?1, i.p.) significantly reduced the number of writhes similarly at all doses tested and the number of paw licks during the first phase of formalin test when compared to control. The effect of discretamine on hot plate response provides a confirmation of its central effect. These results indicate antinociceptive properties of this alkaloid.     

Antimicrobial activity of Piper gaudichaudianum Kuntze and its synergism with different antibiotics

One of the oldest forms of medical practice is the use of plants for the treatment and prevention of diseases that affect humans. We have studied the antimicrobial activity and synergism of Piper gaudichaudianum Kuntze with different antibiotics. The crude extract from the leaves of P. gaudichaudianum was submitted to chromatographic separation, resulting in five fractions. Fraction F3 contained a chromone (2,2-dimethyl-6-carboxycroman-4-one), and fraction F2 contained isomers that are prenylated derivatives of benzoic acid [4-hydroxy-(3',7'-dimethyl-1'-oxo-octa-E-2'-6'-dienyl)benzoic acid and 4-hydroxy-(3',7'-dimethyl-1'-oxo-octa-2'-Z-6'-dienyl) benzoic acid]. The chemical structures of both compounds were determined by analysis of 1H-NMR, 13C-NMR, COZY, DEPT, HMQC, and HMBC spectral data, and by comparison with data in the literature. The crude extract, fraction F2, and fraction F3 showed good activity against Staphylococcus aureus, Bacillus subtilis, and Candida tropicalis. The two benzoic acid derivatives only showed activity against S. aureus and B. subtilis. The bioauthographic analysis showed an inhibition zone only in fraction F2. Fractions F2 and F3 showed synergism in combination with ceftriaxone, tetracycline, and vancomycin. Morphological changes in form and structure were found by scanning electron microscopy in S. aureus treated with the combination of fraction F2 with vancomycin.     

Spectral bounds for the independence ratio and the chromatic number of an operator

We define the independence ratio and the chromatic number for bounded, self-adjoint operators on an L ²-space by extending the definitions for the adjacency matrix of finite graphs. In analogy to the Hoffman bounds for finite graphs, we give bounds for these parameters in terms of the numerical range of the operator. This provides a theoretical framework in which many packing and coloring problems for finite and infinite graphs can be conveniently studied with the help of harmonic analysis and convex optimization. The theory is applied to infinite geometric graphs on Euclidean space and on the unit sphere.     

The vanishing viscosity limit for some symmetric flows

The focus of this paper is on the analysis of the boundary layer and the associated vanishing viscosity limit for two classes of flows with symmetry, namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct explicit boundary layer correctors, which approximate the difference between the Navier–Stokes and the Euler solutions. Using properties of these correctors, we establish convergence of the Navier–Stokes solution to the Euler solution as viscosity vanishes with optimal rates of convergence. In addition, we investigate vorticity production on the boundary in the limit of vanishing viscosity. Our work significantly extends prior work in the literature.