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.     

Synthesis and Crystal Structure of Peptide‐2,2′‐Biphenyl Hybrids

1,1′‐Biphenyl derivatives with amino acid/peptide substitution at C(2) and C(2′) (‘peptide‐biphenyl hybrids', 6 – 8 ) have been prepared by direct N‐acylation of amino acid/peptide derivatives with 1,1′‐biphenyl‐2,2′‐dicarbonyl dichloride ( 5 ). Both conformers, which arise from the rotation around the aryl aryl bond, have been detected by ¹H‐NMR spectroscopy. Single atropisomers of each 6 ((R)‐configuration at the stereogenic axis) and 7 ((S)‐configuration at the stereogenic axis) have been obtained in quantitative yield by slow evaporation of methanolic solutions. The procedures are dynamic atropselective resolutions (asymmetric transformations of the second kind). The crystal structures of the peptide‐biphenyl hybrids 6 and 7 show highly ordered molecular and supramolecular structures with extensive intramolecular and intermolecular H‐bonding.     

First‐ and second‐ sphere coordination of the uranyl ion by bis­[2‐(2‐hydroxy­phenoxy)­ethoxy]­ethane

Uranyl nitrate hexahydrate reacts with bis­[2‐(2‐hydroxy­phenoxy)­ethoxy]­ethane (C₁₈H₂₂O₆), denoted LH₂ hereafter, in the presence of triethylamine to give ­triethylammonium aqua[2,2′‐(3,6‐dioxaoctane‐1,8‐diyldioxy)diphenolato‐κ²O,O′](nitrato‐κ²O,O′)dioxouranium(VI), (Et₃NH)[UO₂(H₂O)L(NO₃)], which possesses a symmetry plane. The uranyl ion is coordinated to the two phenoxide O atoms, a nitrate ion and a water mol­ecule (first sphere); the water mol­ecule is itself held in the crown ether chain by hydrogen‐bonding interactions, thus ensuring second‐sphere coordination by the ligand L.     

The structural development of linear canonical transforms

Physics of Atomic Nuclei - We consider that the simultaneous development of the theory of linear canonical integral transforms among two quite distinct scientific communities, provides an...     

Synthesis and potent cytotoxic activity of 8- and 9-anilinophenanthridine-7,10-diones

A series of 8-anilino and 9-anilinophenanthridine-7,10-diones was prepared and screened against various cancer cell lines to measure anti-proliferative activity. The compounds tested display potent cytotoxic activity in the micromolar and sub-micromolar range. These compounds are promising new leads for developing anticancer compounds.     

A simplified Quick, Easy, Cheap, Effective, Rugged and Safe approach for the determination of trihalomethanes and benzene, toluene, ethylbenzene and xylenes in soil matrices by fast gas chromatography with mass spectrometry detection

A method based on simplified QuEChERS (Quick, Easy, Cheap, Effective, Rugged and Safe) extraction followed by large-injection volume-fast gas chromatography and mass spectrometry detection has been developed for the determination of trihalomethanes (chloroform, bromodichloromethane, dibromochloromethane and bromoform) and BTEX (benzene, toluene, ethylbenzene and xylenes) in soil samples.The simplified version of QuEChERS used meets the requirements of the “green chemistry” and provides reliable results with high sample throughput, low solvent consumption, little labour and the use of materials commonly employed in laboratories. The GC device used is equipped with a programmable temperature vaporizer (PTV), with a liner packed with Tenax-TA^®. Using the solvent-vent mode, the PTV allows the injection of large volumes of sample, affording an improvement in the sensitivity of the method. The chromatographic conditions used here allowed the separation of the compounds in less than 5.50 min. Good linearity was obtained for all the target compounds, with highly satisfactory repeatability and reproducibility values. The limits of detection were in the 0.2 to 15 μg kg⁻¹ range. The method was validated by the analysis of two certified reference materials.