Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian

We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem. We write an equivalent characterization as a thin obstacle problem. In this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

Mediterranean visceral leishmaniasis in immunocompetent children. Report of two cases relapsed after specific therapy

Visceral leishmaniasis (VL) is endemic in areas bordering the Mediterranean Sea (Spain, Italy, France, Greece, Morocco, Tunisia) where it is caused by Leishmania infantum and is transmitted by the bite of a hematophagous sandfly belonging to Phlebotomus spp.; the dog constitutes the main reservoir of infection. Two cases of VL in immunocompetent children are described. Both patients lived in endemic areas for leishmaniasis (Sicily) and at admission were febrile, pale and had splenomegaly. In both patients anti-leishmania antibodies were present and a definitive diagnosis was confirmed by demonstration of leishmania parasites by microscopy or polymerase chain reaction (PCR) in the bone marrow aspirates. The use of PCR performed on peripheral blood has been reported to be highly sensitive for the diagnosis and follow-up of children with VL. One patient was treated with N-dimethylglucamine, Glucantim, the other one with liposomal Amphotericin B (AmBisome). Both had symptomatic relapses 3 months later, and recovered following re-treatment with AmBisome administered intravenously at a dosage of 3 mg/Kg for ten consecutive days. The patients were monitored for one year after treatment was complete

Force traction microscopy: An inverse problem with pointwise observations

Force Traction Microscopy is an inversion method that allows to obtain the stress field applied by a living cell on the environment on the basis of a pointwise knowledge of the displacement produced by the cell itself. This classical biophysical problem, usually addressed in terms of Green functions, can be alternatively tackled using a variational framework and then a finite elements discretization. In such a case, a variation of the error functional under suitable regularization is operated in view of its minimization. This setting naturally suggests the introduction of a new equation, based on the adjoint operator of the elasticity problem. In this paper we illustrate the rigorous theory of the two-dimensional and three dimensional problem, involving in the former case a distributed control and in the latter case a surface control. The pointwise observations require to exploit the theory of elasticity extended to forcing terms that are Borel measure

Efficacy and safety of clarithromycin as treatment for Mediterranean spotted fever in children: a randomized controlled trial

Fifty-one children with Mediterranean spotted fever (MSF) were randomized to receive either clarithromycin, 15 mg/kg/day orally in 2 divided doses, or chloramphenicol, 50 mg/kg/day orally in 4 divided doses, for 7 days. Mean time to defervescence was 36.7 h in the clarithromycin group and 47.1 h in the chloramphenicol group (P=.047). Clarithromycin could be an acceptable therapeutic alternative to chloramphenicol and to tetracyclines for children aged <8 years with MS

A method for successful collection of multicores and gravity cores from Antarctic subglacial lakes

During the 2018–2019 Antarctic field season, the Subglacial Antarctic Lakes Scientific Access project team cleanly accessed Mercer Subglacial Lake, West Antarctica, to sample water and sediments beneath 1087 m of overlying ice. A multicorer was successful in sampling the sediment–water interface, with 4 deployments retrieving 10 cores between 0.3 and 0.4 m in length. Gravity coring was also successful, retrieving cores of 0.97 and 1.78 m in glacial diamict. However, sediment cores retrieved by the gravity cores were shorter than the core barrel penetration (as measured by mud streaks on the outside of the coring system), indicating that the system can likely be improved. This manuscript describes the design, implementation, successes, and lessons learned while coring sediments in a subglacial lake

Formulation and evaluation of carvedilol microcapsules using Eudragit NE30D and sodium alginate

Inclusion complexes of carvedilol(CR) with hydroxyl propyl beta-cyclodextrin (HPBCD) was prepared using co-grinding technique. Then, the inclusion complex was microencapsulated using combinations of Eudragit NE30D (EU) and sodium alginate (SA) utilizing orifice gelation technique. The formulations were analysed by using Scanning electron microscopy (SEM), Fourier Transform Infrared spectroscopy (FTIR), Differential scanning Calorimetry (DSC) and X-ray diffractometer (XRD) and also evaluated for particle size, encapsulation efficiency, production yield, swelling capacity, mucoadhesive properties, zeta potential and drug release. The microcapsules were smooth and showed no visible cracks and extended drug release of 55.2006% up to 12 hours in phosphate buffer of pH 6.8, showing particle size within the range of 264.5-358.5 µm, and encapsulation efficiency of 99.337±0.0100-66.2753±0.0014%.The in vitro release data of optimized batch of microcapsules were plotted in various kinetic equations to understand the mechanisms and kinetics of drug release, which followed first order kinetics, value of "n" is calculated to be 0.459 and drug release was diffusion controlled. The mice were fed with diet for inducing high blood pressure and the in vivo antihypertensive activity of formulations was carried out administering the optimized formulations and pure drug separately by oral feeding and measured by B.P Monwin IITC Life Science instrument and the results indicated that the bioavailability of carvedilol was increased both in vitro and in vivo with the mucoadhesive polymers showing primary role in retarding the drug release