On Hopf's Lemma and the Strong Maximum Principle

In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle.Comment: 27 pages,4 figure

Global attractors for nonlinear viscoelastic equations with memory

We study the asymptotic properties of the semigroup S(t) arising from a nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain written in the past history framework of Dafermos. We establish the existence of the global attractor of optimal regularity for S(t) for a wide class of nonlinearities as well as within the most general condition on the memory kernel

On second order necessary conditions in infinite dimensional optimal control with state constraints

This paper is devoted to second order necessary optimality conditions for control problems in infinite dimensions. The main novelty of our work is the presence of pure state constraints together with end point constraints, quite useful in the applications. Second order analysis for control problems involving PDEs has been extensively discussed in the literature. The most usual approach to derive necessary optimality conditions is to rewrite the control problem as an abstract mathematical programming one. Our approach is different, we avoid the reformulation of the optimal control problem and use instead second order variational analysis. The necessary optimality conditions are in the form of a maximum principle and a second order variational inequality. They are first obtained in the form of nonintersection of convex sets. A suitable separation theorem allows to deduce their dual characterization

Pediatric glaucoma: current perspectives

Giorgio Marchini, Marco Toscani, Francesca Chemello Eye Clinic, Department of Neurological and Movement Sciences, University of Verona, Verona, Italy Abstract: "Childhood glaucoma" is a heterogeneous group of severe pediatric conditions often associated with significant visual loss and characterized by elevated intraocular pressure (IOP) and optic-disk cupping. Successful IOP control is crucial but challenging and most often achieved surgically, with medical therapy playing a supportive role. There are many classifications of childhood glaucoma, but they can simply be divided into primary, in which a developmental abnormality of the anterior chamber angle only exists, and secondary, in which aqueous outflow is reduced due to independent mechanisms that secondarily impair the function of the filtration angle. The worldwide prevalence of childhood blindness ranges from 0.03% in high-income countries to 0.12% in undeveloped countries. The majority of cases do not have an identified genetic mutation and, where the mutation is known, the genes often account for only a small proportion of cases. Several pathogenetic mechanisms are known to contribute to the development of childhood glaucoma. Whatever the cause, it results in a reduced aqueous outflow at the level of the trabecular meshwork. Age of onset and magnitude of the elevated IOP largely determine the clinical manifestation the high variability of clinical manifestations. Glaucoma from any cause in a neonate and infant is characterized by the classic triad of epiphora, photophobia, and blepharospasm, and could be associated with eye enlargement (buphthalmos) and Haab striae. The eye examination, usually performed under general anesthesia, includes: tonometry, anterior-segment examination, gonioscopy, corneal diameter and axial length measurement, dilated fundoscopy with optic-nerve-head evaluation. Medical therapy, considering the high frequency of side effects, is generally used as temporizing IOP-lowering treatment before surgery or as adjuvant treatment postoperatively in case of partially successful procedures for refractory glaucomas. Surgery is the nodal point of the management of refractory childhood glaucoma, so it is crucial to opt for a forward-looking strategy to reach the target IOP and minimize the visual loss. Keywords: childhood glaucoma, congenital glaucoma, glaucoma surgical therapy, childhood visual los

Ectopic mineralization in heart valves: New insights from in vivo and in vitro procalcific models and promising perspectives on noncalcifiable bioengineered valves

Ectopic calcification of native and bioprosthetic heart valves represents a major public health problem causing severe morbidity and mortality worldwide. Valve procalcific degeneration is known to be caused mainly by calcium salt precipitation onto membranes of suffering non-scavenged cells and dead-cellderived products acting as major hydroxyapatite nucleators. Although etiopathogenesis of calcification in native valves is still far from being exhaustively elucidated, it is well known that bioprosthesis mineralization may be primed by glutaraldehyde-mediated toxicity for xenografts, cryopreservation-related damage for allografts and graft immune rejection for both. Instead, mechanical valves, which are free from calcification, are extremely thrombogenic, requiring chronic anticoagulation therapies for transplanted patients. Since surgical substitution of failed valves is still the leading therapeutic option, progressive improvements in tissue engineering techniques are crucial to attain readily available valve implants with good biocompatibility, proper functionality and long-term durability in order to meet the considerable clinical demand for valve substitutes. Bioengineered valves obtained from acellular non-valvular scaffolds or decellularized native valves are proving to be a compelling alternative to mechanical and bioprosthetic valve implants, as they appear to permit repopulation by the host\u2019s own cells with associated tissue remodelling, growth and repair, besides showing less propensity to calcification and adequate hemodynamic performances. In this review, insights into valve calcification onset as revealed by in vivo and in vitro procalcific models are updated as well as advances in the field of valve bioengineering

Biochar impact on the estimation of the colorimetric-based enzymatic assays of soil

This study was carried out in order to assess the influence of biochar applications on the estimation of colorimetric-based enzymatic assays and to verify the effectiveness of the most common methods. Since most methods used to determine enzymatic activities in the soil are based on colorimetry, biochar may absorb substrates and/ or coloured products thereby distorting the analytical result. Biochar was added to two soils, with different textures and cation exchangeable capacities, at a rate of 2% (w/w), and seven enzyme activities were determined following standard methods. The biochar amendment lowered the spectrophotometer reading of the activity of FDAase and dehydrogenase in the sandy soil. In the three enzymatic activities based on p-nitrophenol production (β-glucosidase, phosphatase and arylsulphatase), the addition of biochar did not change the enzyme assays. The biochar led to an overestimation in terms of the protease and urease activities in the sandy soil. In the clay loamy soil, biochar did not change the response of any of the enzyme activities tested. A biochar dose of up to 2% only guarantees the effectiveness of the most common spectrophotometric methods for not excessively sandy soils

Análisis y ejecución de estrategias en la industria de sensores mediante la simulación CAPSIM

Documento en el que se muestra el trabajo realizado en la dirección de una empresa de la industria de sensores dentro del simulador de negocios Capsim. Se presenta un análisis de la industria de los sensores, se describe la empresa en la que se trabajó, las estrategias de negocio y el proceso de su implementación, así como los resultados finales