Synthesis of aggregation pheromone components of cerambycid species through α-hydroxylation of alkylketones

The synthesis of 3-hydroxy-2-hexanone and 2,3-hexanediol, two components of the aggregation pheromone of several cerambycid species, is disclosed in here. Starting from 2-hexanone, through an α-hydroxylation using (diacetoxyiodo)benzene, 3-hydroxy-2-hexanone is obtained in good yield. Further reduction of this compound, gives 2,3-hexanediol in excellent yield. A study of the α-hydroxylation reaction of several alkylketones using an hypervalent iodine reagent is also disclosed in here. The synthesis of optically active compounds (R)- and (S)-3-hydroxy-2-hexanone was achieved starting from 2-hexanone with nitrosobenzene and l- and d-proline respectively, in several reaction media.     

John’s Ellipsoid and the Integral Ratio of a Log-Concave Function

We extend the notion of John’s ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the log-concave function maximizing the integral ratio. A reverse functional affine isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality.     

Separation and kinetic analysis of the thermo-oxidative reactions of polyacrylonitrile upon heat treatment

A polyacrylonitrile (PAN) homopolymer and a copolymer with methyl acrylate were analyzed by differential scanning calorimetry (DSC) in order to establish a method for the kinetic analysis of the stabilization reaction steps during heat treatment. The application of a program rarely used for the study of the chemical transformation of PAN and its copolymers resulted in five separate steps, which can be assigned with large probability to various cyclization and oxidation reactions. A more exact identification of the reactions needs further measurements and considerations. Overlapping peaks appearing in the DSC traces were deconvoluted and then quantitatively analyzed to obtain kinetic parameters. The kinetics of the processes were described by the Kissinger model. The model could be fitted well to four of the five processes that may indicate that these belong to individual reactions of the first order. The parameters obtained agree well with the few values of similar investigations published in the literature up to now. The results have large practical relevance, since the kinetic parameters obtained can be used in the preparation of intermediates and for the optimization of the stabilization process.     

Zig-zagging in geometrical reasoning in technological collaborative environments: a Mathematical Working Space-framed study concerning cognition and affect

ZDM – Mathematics Education - This study highlights the importance of cognition-affect interaction pathways in the construction of mathematical knowledge. Scientific output demands further...