Local maximal function and weights in a general setting

For a proper open set $\Omega $ immersed in a metric space with the weak homogeneity property, and given a measure $\mu $ doubling on a certain family of balls lying “well inside” of $\Omega $ , we introduce a local maximal function and characterize the weights $w$ for which it is bounded on $L^p(\Omega ,w d\mu )$ when $1<p<\infty $ and of weak type $(1,1)$ . We generalize previous known results and we also present an application to interior Sobolev’s type estimates for appropriate solutions of the differential equation $\Delta ^m u=f$ , satisfied in an open proper subset $\Omega $ of $\mathbb R ^n$ . Here, the data $f$ belongs to some weighted $L^p$ space that could allow functions to increase polynomially when approaching the boundary of $\Omega $ .     

Stable solutions for optimal reinsurance problems involving risk measures

The optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advantages and shortcomings when compared with others.This paper deals with a discrete probability space and analyzes the stability of the optimal reinsurance with respect to the risk measure that the insurer uses. We will demonstrate that there is a “stable optimal retention” that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for many risk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop-loss contract, and it is easy to compute in practice. A fast linear time algorithm will be given and a numerical example presented.     

Hyperbranched polymers versus dendrimers containing a carbosilane framework and terminal ammonium groups as antimicrobial agents

A new family of amine- and ammonium-terminated hyperbranched polycarbosilanes (PCS) and dendrimers has been synthesized. The functionalization of a polycarbosilane matrix was carried out with peripheral allyl groups by two strategies in the case of PCS: 1) hydrosilylation of allyl amines with PCS containing terminal Si-H bonds, or 2) hydrosilylation of PCS-allyl with an aminosilane. Dendrimers with terminal amine groups were synthesized by hydrosilylation of allydimethylamine. Quaternized systems with MeI are soluble and stable in water or other protic solvent. The antibacterial properties of the ammonium-terminated hyperbranched polycarbosilanes and dendrimers have been evaluated showing that they act as potent biocides against Gram-positive and Gram-negative bacterial strains.     

Semicarbazones from N-hydroxyureas and amines: a novel entry in the reactivity of the acyl nitroso group

The condensation of carbamoyl nitroso compounds, obtained by oxidation of N-hydroxyureas, with amines unexpectedly afforded semicarbazones (aka carbamoyl hydrazones). Although the substitution of the nitrosyl moiety might compete to afford the corresponding urea, an excess of amine led to the semicarbazone as the major product, which is presumably formed via isomerization of an initially generated acyl azo compound.     

Derivatives of 10,16-dihydroxyhexadecanoic acid isolated from tomato (Solanum lycopersicum) as potential material for aliphatic polyesters

The main monomer of tomato cuticle, 10,16-dihydroxyhexadecanoic acid (or 10,16-dihydroxypalmitic acid; 10,16-DHPA), was isolated and used to efficiently synthesize two different monomers (16-hydroxy-10-oxo-hexadecanoic and 7-oxohexa-decanedioic acids) in addition to a dimer and linear and branched trimers. These compounds were fully characterized using NMR and MS techniques and could be used as starting materials for the synthesis of a wide range of chemicals and bio-polyesters, particularly the latter due to their physical properties, non-toxicity, and relative abundance among raw materials.     

Hydrogen rearrangement and ring cleavage reactions study of progesterone by triple quadrupole mass spectrometry and density functional theory

The fragmentation mechanisms of progesterone have been studied by triple quadrupole tandem mass spectrometry (MSMS) and density functional theory (DFT). Mechanisms leading to major product ions are proposed. The data suggest that progesterone fragments preferentially via hydrogen and other rearrangements lead to neutral losses. These fragmentations are quite complex and are preceded by σ-bond cleavages in most cases. Four major pathways for progesterone fragmentation are proposed involving: (1) cleavage of ring B at C9-C10, (2) cleavage of C6-C7 bond in ring B through m/z 191, (3) two types of cleavages of ring D, and (4) ketene elimination in ring A. Pathways (1)-(3) proceed via charge-remote fragmentations while pathway (4) proceeds via charge-site initiated mechanism. The geometry of product ions in these pathways were optimized using DFT at the B3LYP/6-311G(d,p) level of theory from which the free energies of the pathways were calculated. The effect that the choice of basis sets and density functionals has on the results was tested by performing additional calculations using B3LYP/6-31G(d) and B3PW91/6-311G(d,p).     

Vibrational spectra of bis(maltolato)oxovanadium(IV): a potent insulin mimetic agent

The FTIR and FT-Raman spectra of the oxovanadium(IV) complex of 3-hydroxy-2-methyl-4-pyrone (maltol) bis(maltolato)oxovanadium(IV) were recorded and briefly discussed by comparison with the spectra of uncoordinated maltol and with some related species.     

Experimental and theoretical study of N-hexylcytosine and N-hexylcytosinium nitrate: the crucial role of hydrophobic and anion–π interactions

We report the synthesis and X-ray characterization of N¹-hexylcytosine (1) and N¹-hexylcytosinium nitrate (2). N¹-hexylcytosine (1) does not follow the same behaviour previously described for N¹-hexylthymine and N¹-hexyluracil in the solid state. This different behavior has been analyzed by means of density functional theory (DFT) calculations including the latest available correction for dispersion (D3). In addition hydrophobic and anion–π noncovalent interactions play a key role in stabilizing the 3D architectures of the compounds, which have been energetically studied using theoretical calculations and compared with similar structures retrieved from the Cambridge Structural Database (CSD). The anion–π–anion binding mode observed for nitrate in compound 2 is also observed in several crystal structures involving cytosine ring coordinated to transition metals.     

Determination of chlorinated toluenes in soils using gas chromatography tandem mass spectrometry

A method for the analysis of chlorotoluenes (CTs) in soil has been developed based on ultrasonic assisted extraction with a low volume of organic solvent and determination by gas chromatography-tandem mass spectrometry (GC–MS/MS). A simultaneous clean-up on an alumina–anhydrous sodium sulphate mixture was carried out to remove soil interferences. However, an additional clean-up with graphitised carbon was needed for some very dirty samples. Several solvents were assayed and a mixture of ethyl acetate:hexane (80?:?20, v/v) was selected to carry out soil extractions. Recovery studies were performed at 0.2, 0.1, 0.05 and 0.02?ng?g^?1 fortification levels, and recoveries obtained for all the compounds and concentrations were higher than 81% with standard deviations fulfilling the requirements of the IUPAC. LODs from 0.7 to 5.2?ng?kg^?1 and LOQs from 2.2 to 17.5?ng?kg^?1 were achieved for the analysed compounds, being pentachlorotoluene the compound with the highest limits, followed by the monochlorinated toluenes. The proposed analytical method was applied to determine CT levels in agricultural and industrial soils. These compounds were found in all the industrial soils analysed and some CTs were present in agricultural soils at lower levels.     

Symmetric and asymmetric adsorption of pH-responsive gold nanoparticles onto microgel particles and dispersion characterisation

The interaction between carboxylic acid-stabilised gold nanoparticles (AuNP) and pH-responsive microgels is shown. The microgel particles are a copolymer of N-[3-(dimethylamino)propyl]methacrylamide (DMAPMA) and N-isopropylacrylamide (NIPAM). The microgel properties are presented by their hydrodynamic diameter and electrophoretic mobility in response to pH. These microgel particles are pH-responsive under neutral conditions decreasing in diameter beyond pH 7. The dispersion characteristics of AuNP adsorbed onto the microgel network are shown with respect to adsorbed amount and the pH-responsive properties of the AuNP. This data is presented between pH 3 and 6 where the microgel properties remain constant. Asymmetric adsorption of AuNP onto poly(DMAPMA-co-NIPAM) microgels is achieved by adsorption of nanoparticles, from the aqueous phase, onto microgel-stabilised oil-in-water emulsions. These asymmetrically modified microgels display very different dispersion behaviour, in response to pH, due to their dipolar nature.