Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains

We consider the problem in Ω_ε, u=0 on ∂Ω_ε, where Ω_ε:=ΩB(0,ε) and Ω is a bounded smooth domain in , which contains the origin and is symmetric with respect to the origin, N3 and ε is a positive parameter. As ε goes to zero, we construct sign changing solutions with multiple blow up at the origin.     

Counting Shi Regions with a Fixed Separating Wall

Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant regions which have the fixed hyperplane as a separating wall; that is, regions where the hyperplane supports a facet of the region and separates the region from the origin.     

A one-pot direct regioselective iodination of Fischer-Borsche product using periodic acid in PEG-400

A metal-free and greener approach for the one-pot direct iodination and dehydrogenation of dihydrobenzo[a]carbazoles has been developed using periodic acid in polyethylene glycol-400 (PEG-400) under mild condition. This method has been proven to be tolerate to a broad range of functional groups, with good to excellent yields include metal-free inexpensive catalyst, easy work-up, benign reaction condition and high regioselectivity. The solvent has been successfully recycled up to 5 times without any loss of activity in an aqueous medium.     

Mechanism and kinetics of thermal degradation of insulating materials developed from cellulose fiber and fire retardants

The mechanism and kinetics of thermal degradation of materials developed from cellulose fiber and synergetic fire retardant or expandable graphite have been investigated using thermogravimetric analysis. The model-free methods such as Kissinger–Akahira–Sunose (KAS), Friedman, and Flynn–Wall–Ozawa (FWO) were applied to measure apparent activation energy (E_α). The increased E_α indicated a greater thermal stability because of the formation of a thermally stable char, and the decreased E_α after the increasing region related to the catalytic reaction of the fire retardants, which revealed that the pyrolysis of fire retardant-containing cellulosic materials through more complex and multi-step kinetics. The Friedman method can be considered as the best method to evaluate the E_α of fire-retarded cellulose thermal insulation compared with the KAS and FWO methods. A master-plots method such as the Criado method was used to determine the possible degradation mechanisms. The degradation of cellulose thermal insulation without a fire retardant is governed by a D3 diffusion process when the conversion value is below 0.6, but the materials containing synergetic fire retardant and expandable graphite fire retardant may have a complicated reaction mechanism that fits several proposed theoretical models in different conversion ranges. Gases released during the thermal degradation were identified by pyrolysis–gas chromatography/mass spectrometry. Fire retardants could catalyze the dehydration of cellulosic thermal insulating materials at a lower temperature and facilitate the generation of furfural and levoglucosenone, thus promoting the formation of char. These results provide useful information to understand the pyrolysis and fire retardancy mechanism of fire-retarded cellulose thermal insulation.

     

Cell protection from Ca2+-overloading by bioactive molecules extracted from olive pomace

We are reporting in the present study that molecules extracted from olive pomace prevent cell death induced by Ca²⁺-overloading in different cell types. Exposure of cells to these molecules counteracts the Ca²⁺-induced cell damages by reducing the activation of the Ca²⁺-dependent protease calpain, acting possibly through the modification of the permeability to Ca²⁺ of the plasma membrane. The purification step by RP-HPLC suggests that effective compound(s), differing from the main biophenols known to be present in the olive pomace extract, could be responsible for this effect. Our observations suggest that bioactive molecules present in the olive pomace could be potential candidates for therapeutic applications in pathologies characterised by alterations of intracellular Ca²⁺ homeostasis.     

Interactions between oligopeptides and oxidised titanium surfaces detected by vibrational spectroscopy

Five alternating polar/hydrophobic oligopeptides derived from EAK 16 (AEAEAKAKAEAEAKAK) were examined in comparison with EAK 16 (peptide 1) both after solubilisation/lyophilisation and deposition on oxidised titanium surfaces. The peptides were synthesised for their possible use as biomimetic materials due to their self‐assembling properties and the presence, in one of them, of the arginine‐glycine‐aspartic (RGD) sequence, an active modulator of cell adhesion. Infrared (IR) and Raman spectroscopies were used to investigate the influence of the amino acid substitution on the self‐assembling properties of the peptides under both experimental conditions. In the lyophilised peptides, β‐sheet was the prevailing conformation (65–69%) as in EAK 16, irrespective of acid substitution (E→D, peptide 2), basic substitution (K→O, peptide 3), hydrophobic spacer substitution (A→Abu, peptide 4 and A→Y, peptide 5) and RGD insertion (peptide 6). After deposition on oxidised titanium, the main conformation remained β‐sheet. The side‐chain shortening of the acidic amino acid residue (peptide 2) or the insertion of a rigid and bulky residue such as Y (peptide 5) decreased the self‐assembling ability more than the side‐chain shortening of the basic amino acid residue (peptide 3) or the insertion of the RGD head (peptide 6). The interaction with the oxidised titanium surface was mainly due to carboxylate groups with a bidentate bridging coordination and C  O peptidic groups. Copyright © 2010 John Wiley & Sons, Ltd.     

Fluorescent Phthalocyanine-Encapsulated Bovine Serum Albumin Nanoparticles: Their Deployment as Therapeutic Agents in the NIR Region

In recent times, researchers have aimed for new strategies to combat cancer by the implementation of nanotechnologies in biomedical applications. This work focuses on developing protein-based nanoparticles loaded with a newly synthesized NIR emitting and absorbing phthalocyanine dye, with photodynamic and photothermal properties. More precisely, we synthesized highly reproducible bovine serum albumin-based nanoparticles (75% particle yield) through a two-step protocol and successfully encapsulated the NIR active photosensitizer agent, achieving a good loading efficiency of 91%. Making use of molecular docking simulations, we confirm that the NIR photosensitizer is well protected within the nanoparticles, docked in site I of the albumin molecule. Encouraging results were obtained for our nanoparticles towards biomedical use, thanks to their negatively charged surface (−13.6 ± 0.5 mV) and hydrodynamic diameter (25.06 ± 0.62 nm), favorable for benefitting from the enhanced permeability and retention effect; moreover, the MTT viability assay upholds the good biocompatibility of our NIR active nanoparticles. Finally, upon irradiation with an NIR 785 nm laser, the dual phototherapeutic effect of our NIR fluorescent nanoparticles was highlighted by their excellent light-to-heat conversion performance (photothermal conversion efficiency 20%) and good photothermal and size stability, supporting their further implementation as fluorescent therapeutic agents in biomedical applications.     

A Variational Approach to the Maximization of Preferences Without Numerical Representation

Journal of Optimization Theory and Applications - We introduce a variational approach to study a maximization problem of preferences that cannot be represented by a utility function. In such...