A non-autonomous scalar one-dimensional dissipative parabolic problem: The description of the dynamics

The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem $u_t= u_{xx} + \lambda u - \beta(t)u^3$ when the parameter $\lambda > 0$ varies. Also, we answer a question proposed in [11], concerning the complete description of the structure of the pullback attractor of the problem when $1<\lambda <4$ and, more generally, for $\lambda \neq N^2$, $2 \leq N \in \mathbb{N}$. We construct global bounded solutions , "non-autonomous equilibria", connections between the trivial solution these "non-autonomous equilibria" and characterize the $\alpha$-limit and $\omega$-limit set of global bounded solutions. As a consequence, we show that the global attractor of the associated skew-product flow has a gradient structure. The structure of the related pullback an uniform attractors are derived from that.Comment: 32 pages, 04 figure

Maximally Localized States in Quantum Mechanics with a Modified Commutation Relation to All Orders

We construct the states of maximal localization taking into account a modification of the commutation relation between position and momentum operators to all orders of the minimum length parameter. To first order, the algebra we use reproduces the one proposed by Kempft, Mangano and Mann. It is emphasized that a minimal length acts as a natural regulator for the theory, thus eliminating the otherwise ever appearing infinities. So, we use our results to calculate the first correction to the Casimir Effect due to the minimal length. We also discuss some of the physical consequences of the existence of a minimal length, culminating in a proposal to reformulate the very concept of "position measurement"

Lower semicontinuity of attractors for non-autonomous dynamical systems

This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic solutions, generalizing previous results valid only for gradient-like systems in which the hyperbolic solutions are equilibria. The tools employed are a study of the continuity of the local unstable manifolds of the hyperbolic solutions and results on the continuity of the exponential dichotomy of the linearization around each of these solutions

Nonlinear dynamical analysis for globally modified incompressible non-Newtonian fluids

We present the global modification of the Ladyzhenskaya equations, for incompressible non-Newtonian fluids. This modification is through a cut-off function that multiplies the convective term of the equation and an additional artificial smoothing dissipation term as part of the viscous term of the equation. The goal of this work is the comparative analysis between the modified system and the non-modified system. Therefore, we show the existence and regularity of weak solutions, the existence of global attractors, the estimation of the fractal dimension of the global attractors, and finally, the relationship of the autonomous dynamics between the modified system and the non-modified system

Mini-Project of Ethanol Production from Waste as a Teaching Methodology

The development of sustainable alternative fuel, energy and chemical products is happening all over the world. Some of the main reasons for this increase are the increasing demand for fuel and energy due to population growth and economic development; climate change and the need for decreasing greenhouse gas (GHG) emissions; enhancement of waste recovery efforts to redirect waste away from landfills and decrease the reliance on primary raw materials. Thus, it is important to make students aware of these aspects and explore the development of alternative fuels, while giving them the tools to be creative and autonomous. The aim of this paper is to show how the implementation of a mini-project can improve not only students’ knowledge about the production of a biofuel from waste, but also their development of the theoretical and basic skills needed to carry out the mini-project. This paper presents in addition to the methodology used, some results to the implementation of the mini project, specifically the students’ points of view.info:eu-repo/semantics/publishedVersio

A taxonomic revision of the Neotropical termite genera Labiotermes Holmgren and Paracornitermes Emerson (Isoptera: Termitidae: Nasutitermitinae)

The taxonomy of the South American termite genus Labiotermes Holmgren (sensu novo) is revised,including identification keys to soldiers and workers, and distribution maps for all 10 species.Paracornitermes Emerson is treated as a new synonym of Labiotermes. Two new species aredescribed: L. guasu, from the Amazon rain forest and L. oreadicus, from the Cerrado of centralBrazil. Paracornitermes caapora Bandeira & Cancello and P. hirsutus Araujo are placed under thesynonymy of L. orthocephalus. The imagos of L. emersoni and L. orthocephalus are described forthe first time. The workers of all species are described and illustrated, including the enteric valve armature and the mixed segment. The soldiers of the species previously included inParacornitermes are redescribed.Fil: Constantino, Reginaldo. Universidade de Brasília; BrasilFil: Acioli, Agmo N. S.. PPG Entomologia; BrasilFil: Smith, Karen. Universidade de Brasília; BrasilFil: Cuezzo, Adriana Carolina. Fundación Miguel Lillo. Dirección de Zoología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán; ArgentinaFil: Carvalho, Sergio H. C. Universidade de Brasília; BrasilFil: Vasconcellos, Alexandre. Universidade Federal do Rio Grande do Norte; Brasi

Vancomycin-Loaded, Nanohydroxyapatite-Based Scaffold for Osteomyelitis Treatment: In Vivo Rabbit Toxicological Tests and In Vivo Efficacy Tests in a Sheep Model

The treatment for osteomyelitis consists of surgical debridement, filling of the dead space, soft tissue coverage, and intravenous administration of antimicrobial (AM) agents for long periods. Biomaterials for local delivery of AM agents, while providing controllable antibiotic release rates and simultaneously acting as a bone scaffold, may be a valuable alternative; thus, avoiding systemic AM side effects. V-HEPHAPC is a heparinized nanohydroxyapatite (nHA)/collagen biocomposite loaded with vancomycin that has been previously studied and tested in vitro. It enables a vancomycin-releasing profile with an intense initial burst, followed by a sustained release with concentrations above the Minimum Inhibitory Concentration (MIC) for MRSA. In vitro results have also shown that cellular viability is not compromised, suggesting that V-HEPHAPC granules may be a promising alternative device for the treatment of osteomyelitis. In the present study, V-HEPHAPC (HEPHAPC with vancomycin) granules were used as a vancomycin carrier to treat MRSA osteomyelitis. First, in vivo Good Laboratory Practice (GLP) toxicological tests were performed in a rabbit model, assuring that HEPHAPC and V-HEPHAPC have no relevant side effects. Second, V-HEPHAPC proved to be an efficient drug carrier and bone substitute to control MRSA infection and simultaneously reconstruct the bone cavity in a sheep model.This work was financed by FEDER-Fundo Europeu de Desenvolvimento Regional funds through the COMPETE 2020-Operacional Programme for Competitiveness and Internationalisation (POCI), Portugal 2020; by Portuguese funds through FCT/MCTES in the framework of the project institute for Research and Innovation in Health Sciences (POCI-01-0145-FEDER-007274); by the Project Biotherapies (NORTE-01-0145-FEDER-000012); and by the project HEPHAPC Program RESOLVE, Norte 2020 (NORTE-01-0246-FEDER-000018). The authors would also like to acknowledge the technical support for histology and histochemical studies of Rui Fernandes and Rossana Correia and all the staff from HEMS/i3S, as well as the support of all the staff and students at the Hospital Veterinario-Universidade de Evora