On certain arithmetic functions involving the greatest common divisor

The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ²(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.     

On the quantification of OH*, CH*, and C2* chemiluminescence in flames

Absolute concentrations of all important chemiluminescent species, OH–A, CH–A, CH–B, and C₂-d have been measured for the first time in methane-oxygen flames at low pressure. The optical detection system for chemiluminescence measurements has been calibrated with Rayleigh and Raman scattering of a cw laser, with the latter approach yielding superior results. The measured ratio between the concentration of CH–B and CH–A suggests that the electronically excited CH* is formed close to thermal equilibrium. Introduction of different rate constants for reactions leading to CH–A and CH–B were not necessary to explain the experimental results. Results are compared with a recent numerical model. Deviations in profile shape and peak positions are relatively small for stoichiometric flames, but become more pronounced in richer mixtures. Larger discrepancies are observed for the absolute concentrations, depending on the chemiluminescent species and the stoichiometry. In an attempt to find an alternative method for the quantification of chemiluminescent species, MIR-CRDS has been performed around 3.9 μm. While H₂O and OH–X could be measured, the sensitivity was not high enough to detect the low sub-ppb concentration of OH–A—in part due to the limited reflectivity of mirrors in the MIR, in part due to a significant background of hot H₂O lines.     

A concise and stereoselective chemoenzymatic synthesis of Sitophilate,the male-produced aggregation pheromone of Sitophilus granarius (L.)

(2S,3R)-Sitophilate, the male-produced aggregation pheromone of the granary weevil Sitophilus granarius (L.) was prepared stereoselectively using a novel chemoenzymatic approach in 50% overall yield. The synthetic design was based on an enantioselective fungal reduction of ethyl 2-methyl-3-oxopentanoate with a strain of Aureobasidium pullulans (CCM H1), followed by a Mitsunobu inversion at C3. The last step in the synthetic sequence was a lipase-mediated transesterification using the commercially available Candida antarctica B lipase (CaL B, Novozym 435) using microwave irradiation under solvent-free conditions.     

Simple route to new oxadiazaboroles and oxadiazoles via amidoximes

Abstract

The novel push–pull alkene, the 2-(nitro-nitrosomethylene)-pyrrolidine with numerous aliphatic or aromatic amines as nucleophiles afforded amidoximes. Various substituted oxadiazaborole and oxadiazole derivatives were prepared starting from these amidoximes, widening the synthetic applicability of the push–pull alkenes. Acylation of the amidoximes was also examined. The mechanism of the amidoxime formation was investigated by computational methods.     

Efficient synthesis of branched poly(acrylic acid) derivatives via postpolymerization modification

The utility of pentafluorophenyl esters for the selective introduction of functional units and branch points in well-defined poly(acrylic acid) (PAA) derivatives is demonstrated using a combination of controlled radical polymerization and postpolymerization modification. Reversible addition-fragmentation chain transfer enables the synthesis of well-defined copolymers—poly(pentafluorophenyl acrylate-co-tert-butyl acrylate)—with the active ester repeat units serving as attachment points for reaction with primary amines, specifically tris(2-(t-butoxycarbonyl)ethyl)methyl amine (Behera's amine). Deprotection using trifluoroacetic acid removes both the backbone and side chain t-butyl esters to give a series of branched PAA derivatives containing novel tricarboxylic acid side chains that are well suited to complexation and multidentate interactions. Surprisingly, the active ester homopolymer is shown to have the highest reactivity with Behera's amine when compared to copolymers with lower incorporation of pentafluorophenyl esters, suggesting an intriguing interplay of neighboring group effects and steric interactions. The ability to tune the efficiency of postpolymerization modification gives a library of PAA derivatives.     

“Dial-In” Emission from a Unique Flexible Material with Polarization Tuneable Spectral Intensity

The development of organic photoluminescent materials, which show promising roles as catalysts, sensors, organic light-emitting diodes, logic gates, etc., is a major demand and challenge for the global scientific community. In this context, a photoclick polymerization method is adopted for the growth of a unique photoluminescent three-dimensional (3D) polymer film, E, as a model system that shows emission tunability over the range 350–650 nm against the excitation range 295–425 nm. The DFT analysis of energy calculations and π-stacking supports the spectroscopic observations for the material exhibiting a broad range of emission owing to newly formed chromophoric units within the film. Full polarization spectroscopic Mueller matrix studies were employed to extract and quantify the molecular orientational order of both the ground (excitation) and excited (emission) state anisotropies through a set of newly defined parameters, namely the fluorescence diattenuation and fluorescence polarizance. The information contained in the recorded fluorescence Mueller matrix of the organic polymer material provided a useful way to control the spectral intensity of emission by using pre- and post-selection of polarization states. The observation was based on the assumption that the longer lifetime of the excited dipolar orientation is attributed to the compactness of the film.