Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid

Assessment of oil contamination in the bay of Porto Grande (Cape Verde) using the mullet Chelon bispinosus

Polycyclic aromatic hydrocarbons (PAHs) are a group of persistent organic pollutants, some of which are mutagenic and carcinogenic so PAH concentrations in fish used for human consumption are crucial to assess impact to human health. Total PAH concentrations in muscle and liver of mullets Chelon bispinosus from the Bay of Porto Grande (Cape Verde) (four sites in the bay and a control) ranged from 112.7 to 779.5 and 291.5 to 7548.7 ng/g d. w., respectively. Two and three ring PAHs were the most frequent (72.8 to 90.8% in the muscle and 75.9 to 98.3% in the liver), but levels of carcinogenic PAHs (mainly Dibenzo (a,h) antracene) in certain sites (CN and PG) are of concern. Results reflect a chronic PAH pollution in the bay and sources are a mixture of anthropogenic (petrogenic and pyrolytic) and natural sources, making their identification extremely complex. Although, BaP levels were below the threshold established by Cape Verde and the European Union, BaPEs levels in muscle ranged from 0.28 to 3.66 ng/g w. w. and BAPEs and TPAHs exposure for the average adult was 0.02 to 0.26 and 1.6 to 11.2 μg/day, respectively. Further knowledge of PAH concentrations in other species are necessary for a proper environmental risk assessment policy.Key words: Bay of Porto Grande, Cape Verde, Chelon bispinosus, mullets, PAHs, BaPEs, daily intake

Improved production of lutein and β-carotene by thermal and light intensity upshifts in the marine microalga Tetraselmis sp. CTP4

The industrial microalga Tetraselmis sp. CTP4 is a promising candidate for aquaculture feed, novel food, cosmeceutical and nutraceutical due to its balanced biochemical profile. To further upgrade its biomass value, carotenogenesis was investigated by testing four environmental factors, namely temperature, light intensity, salinity and nutrient availability over different growth stages. The most important factor for carotenoid induction in this species is a sufficient supply of nitrates leading to an exponential growth of the cells. Furthermore, high temperatures of over 30 degrees C compared to lower temperatures (10 and 20 degrees C) induced the accumulation of carotenoids in this species. Remarkably, the two different branches of carotenoid synthesis were regulated depending on different light intensities. Contents of beta-carotene were 3-fold higher under low light intensities (33 mu mol m(-2) s(-1)) while lutein contents increased 1.5-fold under higher light intensities (170 and 280 mu mol m(-2) s(-1)). Nevertheless, highest contents of carotenoids (8.48 +/- 0.47 mg g(-1) DW) were found upon a thermal upshift from 20 degrees C to 35 degrees C after only two days at a light intensity of 170 mu mol m(-2) s(-1). Under these conditions, high contents of both lutein and beta-carotene were reached accounting for 3.17 +/- 0.18 and 3.21 +/- 0.18 mg g(-1) DW, respectively. This study indicates that Tetraselmis sp. CTP4 could be a sustainable source of lutein and beta-carotene at locations where a robust, euryhaline, thermotolerant microalgal strain is required.Funding Agency Portuguese Foundation for Science and Technology UID/Multi/04326/2019 SFRH/BD/115325/2016 SFRH/BD/140143/2018 SFRH/BD/105541/2014 0055 ALGARED+ 05 INTERREG V-A -Espana Portugal project national Portuguese funding PPBI-POCI-01-0145-FEDER-22122 Nord Universityinfo:eu-repo/semantics/publishedVersio

A Giant Hand Lipoma As a Rare Cause of Secondary Carpal Tunnel Syndrome - a Case Report

Introduction: Lipomas are a rare cause of compressive neuropathy and they lead to atypical clinical presentation that can mimic carpal tunnel syndrome. Case presentation: The authors describe a rare presentation of a carpal tunnel syndrome recurrence after a hand giant lipoma, presenting with rapidly compression neuropathy of the median nerve, 6 months after de primary surgery. Discussion: Lipomas are common benign soft tumours. Their occurrence in the hand remains rare and they rarely cause secondary entrapment neuropathies. Carpal tunnel syndrome is mostly idiopathic and bilateral. Local factors should be suspected when these neuropathies present with atypical symptomatology or even when they recur after primary conventional surgical release. Investigation should consider images studies as this correct preoperative assessment leads to successful diagnosis and treatment.info:eu-repo/semantics/publishedVersio

Thermodynamic formalism for contracting Lorenz flows

We study the expansion properties of the contracting Lorenz flow introduced by Rovella via thermodynamic formalism. Specifically, we prove the existence of an equilibrium state for the natural potential $\hat\phi_t(x,y, z):=-t\log J_{(x, y, z)}^{cu}$ for the contracting Lorenz flow and for $t$ in an interval containing $[0,1]$. We also analyse the Lyapunov spectrum of the flow in terms of the pressure

Delocalization of slowly damped eigenmodes on Anosov manifolds

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a "strip" of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.Comment: 28 pages; compared with version 1, minor modifications, add two reference

Anterior Slope Correction-Flexion Osteotomy in Traumatic Genu Recurvatum

A decreased posterior tibial slope has been associated with an increased risk of posterior cruciate ligament failure, anterior knee pain, and premature knee osteoarthritis. Trauma is a common cause of osseous genu recurvatum. Surgical management is recommended to correct the tibial slope and prevent knee pain and osteoarthritis progression. This article discusses our preferred treatment using a proximal tibial opening-wedge osteotomy for surgical management of genu recurvatum secondary to significant anterior tibial slope.info:eu-repo/semantics/publishedVersio

Entropy of semiclassical measures for nonpositively curved surfaces

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2