On the particle paths and the stagnation points in small-amplitude deep-water waves

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with arXiv:1106.382

The "Hot Spots" Conjecture on the Vicsek Set

We prove the Hot Spot conjecture on the Vicsek set. Specifically, we show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set attains its maximum and minimum on the boundary.Comment: We made changes suggested by the anonymous referee and editors. The paper is accepted for publication in the Special Issue on Harmonic Analysis: Smooth and Non-Smooth, Demonstratio Mathematic

A para-differential renormalization technique for nonlinear dispersive equations

For \alpha \in (1,2) we prove that the initial-value problem \partial_t u+D^\alpha\partial_x u+\partial_x(u^2/2)=0 on \mathbb{R}_x\times\mathbb{R}_t; u(0)=\phi, is globally well-posed in the space of real-valued L^2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.Comment: 42 pages, no figure

On special quadratic birational transformations of a projective space into a hypersurface

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.Comment: Accepted for publication in Rendiconti del Circolo Matematico di Palerm

Environmental impact assessement related to metallurgical industry activities

In this work is presented the impact assess of metallurgical specific activities on the environment through global pollution index calculation. The pollution index value calculated for environmental components: air, water, soil, vegetation, noise, waste, population health status indicated an environment subject to human effect within acceptable limits

Metabolic alterations in experimental models of depression

Introduction: Major depressive disorder is one of the most prevalent psychiatric disorders and is associated with a severe impact on the personal functioning, thus with incurring significant direct and indirect costs. The presence of depression in patients with medical comorbidities increases the risks of myocardial infarction and decreases diabetes control, and adherence to treatment. The mechanism through which these effects are produced is still uncertain. Objectives of this study were to evaluate the metabolic alterations in female Wistar rats with induced depression, with and without administration of Agomelatine. The methods included two experiments. All data were analyzed by comparison with group I (control), and with each other. In the first experiment we induced depression by: exposure to chronic mild stress-group II; olfactory bulbectomy-group III; and exposure to chronic mild stress and hyperlipidic/ hyper caloric diet-group IV. The second experiment was similar with the first but the rats received Agomelatine (0.16mg/ animal): group V (depression induced through exposure to chronic mild stress), VI (depression induced through olfactory bulbectomy) and VII (depression induced through exposure to chronic mild stressing hyperlipidic/ hypercaloric diet). Weight, cholesterol, triglycerides and glycaemia were measured at day 0 and 28, and leptin value was measured at day 28. The results in the 1st experiment revealed significant differences (pconclusion, significant correlations were found between high level of triglycerides and depression induced by chronic stress and olfactory bulbectomy. Agomelatine groups had a lower increase of triglycerides levels

Theory for the phase behaviour of a colloidal fluid with competing interactions

We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances (the particles have a hard core). As well as exhibiting gas-liquid phase separation, this system also exhibits phase transitions from the uniform fluid phases to modulated inhomogeneous fluid phases. Starting from a microscopic density functional theory, we develop an order parameter theory for the phase transition in order to examine in detail the phase behaviour. The amplitude of the density modulations is the order parameter in our theory. The theory predicts that the phase transition from the uniform to the modulated fluid phase can be either first order or second order (continuous). The phase diagram exhibits two tricritical points, joined to one another by the line of second order transitions.Comment: 12 pages, 9 figures. Accepted for publication in J. Phys. Condens. Matte

Sensitive methods for estimating the anchoring strength of nematic liquid crystals on Langmuir-Blodgett monolayers of fatty acids

The anchoring of the nematic liquid crystal N-(p-methoxybenzylidene)-p-butylaniline (MBBA) on Langmuir-Blodgett monolayers of fatty acids (COOHC$_{n}$H$_{2n+1}$) was studied as a function of the length of the fatty acid alkyl chains, $n$ ($n = 15, 17, 19, 21$). The monolayers were deposited onto ITO-coated glass plates which were used to assemble sandwich cells of various thickness that were filled with MBBA in the nematic phase. The mechanism of relaxation from the flow-induced quasi-planar to the surface-induced homeotropic alignment was studied for the four decreases linearly with increasing the length of the alkyl chains $n$ which suggests that the Langmuir-Blodgett film plays a role in the phenomenon. This fact was confirmed by a sensitive estimation of the anchoring strength of MBBA on the fatty acid monolayers after anchoring breaking which takes place at the transition between two electric-field--induced turbulent states, denoted as DSM1 and DSM2. It was found that the threshold electric field for the anchoring breaking, which can be considered as a measure of the anchoring strength, also decreases linearly as $n$ increases. Both methods thus possess a high sensitivity in resolving small differences in anchoring strength. In cells coated with mixed Langmuir-Blodgett monolayers of two fatty acids ($n=15$ and $n=17$) a maximum of the relaxation speed was observed when the two acids were present in equal amount. This observation homeotropic cells by changing the ratio between the components of the surfactant film.Comment: LaTeX article, 20 pages, 15 figures, 17 EPS files. 1 figure added, references moved. Submitted to Phys. Rev.