Polymeric bidimensional self-assembling of [Hg(RC6H4NNNC6H4R)2Py] (R = m-acetyl) through metal-η,η-arene π-interactions and non classical C-H?O bonding: Synthesis and X-ray characterization of a bis diaryl symmetric-substituted triazenide complex of Hg(II)

Deprotonated 1,3-bis(3-acetylphenyl)triazene reacts with Hg(CH₃COO)₂ and pyridine to give light-yellow crystals of {[Hg^II(RC₆H₄NNNC₆H₄R)₂Py]}_n (R = acetyl). The tectons [Hg^II(RC₆H₄NNNC₆H₄R)₂Py] [R = CH₃C(O)] are linked to pairs as centrosymmetric dimers through reciprocal metal-η²-arene π-interactions. The dimeric units are operated by a screw axis 2₁ parallel to the crystallographic direction [0 1 0], also through a reflection-translation plane parallel to the c-axis, resulting a supramolecular bidimensional (2D) assembling of the dimeric tectons through non classical C-H?(O)CCH₃ bonding.     

Preparation and Characterization of Niobium Oxide Coated Cellulose Fiber

The Nb₂O₅/cellulose composite was prepared by reacting α-cellulose with NbCl_5-n(OC₂H₅)_n, in nonaqueous solvent, under nitrogen atmosphere and submitting the obtained material to hydrolysis. An increase in the crystallinity degree is observed in the composite material because the precursor reagent reacts with the amorphous phase of the cellulose fibers. Loadings between 4.5 and 16.0% of the oxide were achieved and in every case the oxide particles uniformly cover the fiber surface. Lewis and Brønsted acid sites were determined by using pyridine as the basic molecular probe.     

Applications of stratifying systems to the finitistic dimension

Given an Ext-injective stratifying system of Λ-modules satisfying that the projective dimension of Y is finite, we prove that the finitistic dimension of the algebra Λ is equal to the finitistic dimension of the category . Moreover, using the theory of stratifying systems we obtain bounds for the finitistic dimension of Λ. In particular, we get the optimal bound 2n-2 for the finitistic dimension of a standardly stratified algebra with n simples.     

Analysis of signal fluctuations of Cortical Spreading Depression: Preliminary findings

In this work, we apply Detrended Fluctuation Analysis (DFA) to study the dynamics of electrical cortical activity in rats during the phenomenon of Cortical Spreading Depression (CSD), as well as the periods before and after this phenomenon. The characteristic of CSD is reduced electrical activity that occurs and spreads in the cerebral cortex after the application of electrical, chemical or mechanical stimulus. Our results show that the electrocorticogram signal shows long range temporal correlations and scaling behavior, except during the pre-CSD burst phase (significant increase of amplitude provoked by stimulus).     

Parametric inference for discrete observations of diffusion processes with mixed effects

Stochastic differential equations with mixed effects provide means to model intra-individual and inter-individual variability in repeated experiments leading to longitudinal data. We consider N i.i.d. stochastic processes defined by a stochastic differential equation with linear mixed effects which are discretely observed. We study a parametric framework with distributions leading to explicit approximate likelihood functions and investigate the asymptotic behavior of estimators under the asymptotic framework : the number N of individuals (trajectories) and the number n of observations per individual tend to infinity within a fixed time interval. The estimation method is assessed on simulated data for various models.     

Soliton solutions for quasilinear Schrödinger equations with critical growth

In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9].     

Mathematical Analysis and Numerical Simulation of a Nonlinear Thermoelastic System

Abstract

In this paper, we give a theoretical and numerical analysis of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to linear mixed boundary conditions. We establish the existence, uniqueness, and a uniform decay rate for global solutions to this nonlinear non-local thermoelastic coupled system with linear boundary conditions. Furthermore, we introduced a numerical method based on finite element discretization in a spatial variable and finite difference scheme in time which results in a nonlinear system to be solved by Newton’s method. Numerical experiments for one-dimensional and two-dimensional cases are presented in order to estimate the rate of convergence of the numerical solution that confirm our analysis and show the efficiency of the method.