On the Lagrangian formulation of a Lane-Emden-type equation and double reduction

We classify all Noether point symmetries of the Lane-Emden-type equation x y ″ + n y ′ + x^νf (y) = 0 with respect to the standard Lagrangian L = 1/2 xⁿy ′² – x^{n +ν –1} ∫ f (y)dy for various functions f (y). We then obtain first integrals of the various cases which admit Noether point symmetries and obtain reduction to quadratures for these cases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

7‐Phenyl‐1‐oxa‐4‐thiaspiro[4.5]decan‐7‐ol stereoisomers

The stereoisomers of 7‐phenyl‐1‐oxa‐4‐thia­spiro­[4.5]­decan‐7‐ol, C₁₄H₁₈O₂S, have the same stereochemistry at the C atom bearing an OH group, i.e. axial OH and equatorial phenyl groups. However, the acetal S and O atoms are axial and equatorial, respectively, in one isomer and reversed in the second. Furthermore, the crystals of one isomer are composed of hydrogen‐bonded mol­ecules involving the hydroxyl H atom and the O atom of the five‐membered heterocyclic ring, with an O?O distance of 2.962 (3) Å, forming a polymeric chain along the b axis. The asymmetric unit of the other isomer is composed of two mol­ecules, wherein hydroxyl H atoms and the O atoms of the five‐membered heterocyclic rings display intramolecular O—H?O hydrogen bonds with O?O separations of 2.820 (2) and 2.834 (2) Å.     

Identifiability of kinetic models of isotope transient tracing in fixed bed plug flow reactors

A novel method is presented to address the identifiability of a class of kinetic models of monoatomic isotope transient tracing in plug flow reactors. It is shown that the identifiability of these models can be addressed solely from a knowledge of the rate functions. Dedicated to Professor Pál Tétényi on the occasion of his 70th birthday     

On the reaction of 1-oxa-4-thiaspiro[4.5]decan-7-one with PhLi. A reinvestigation

Two diastereomeric alcohols are formed from the reaction of 1-oxa-4-thiaspiro[4.5]decan-7-one with PhLi as against the single diastereomer reported earlier. The diastereoselectivity achieved from PhMgBr is significantly higher than with PhLi. The use of Et(2)O/hexane = 2:1 as the solvent for the reaction with PhMgBr offered the highest (14:1) diastereocontrol.     

Synthesis, characterization, and reactivity of new copper(II) complexes of 2-methylthio-N-(2-pyridylmethyl)acetamide

Copper(II) complexes were prepared with the new N(2)S(thioether) ligand 2-methylthio-N-(2-pyridylmethyl)acetamide (2-HL(N2S)). [Cu(2-L(N2S))Cl(MeOH)], which formed in the presence of excess triethylamine, is a distorted square pyramidal complex containing the ligand with the amide nitrogen deprotonated. The structurally analogous complex, [Cu(2-HL(N2S))Cl(2)], which formed in the absence of triethylamine, contains 2-HL(N2S) in the tautomeric imidic acid form. Neutral copper(II) N(2)S(thioether)S(thiolate) species were generated by addition of alkyl or aromatic thiolates to [Cu(2-L(N2S))Cl(MeOH)] and an unusual decomposition pathway was discovered.     

Electrochemical evidence for the existence of three stable oxidation states for heterocycles of the type X?C6H4?CN2E2 (E = S,Se). X-ray crystal structure of the dimer with X = Cl,E = S

The preparation and isolation in the solid state of five aryl 1,2,3,5-dithia- and diselenadiazolyls is reported. The structure of the dimer of 4-Cl? C₆H₄? CN₂S₂ in the solid state was obtained: monoclinic, C2/c with Z = 8, a = 20.982(10), b = 10.058(3), c = 15.867(6) Å, β = 93.34(4)°, R = 0.066, R_w = 0.053 for 1 099 data. Cyclic voltammetry shows reversible oxidation to a 6π cation for all 10 compounds in both CH₂Cl₂ and CH₃CN; reversible reduction to an 8π anion is observed in CH₂Cl₂ for all except X = CF₃, E = S. The reductions are only quasi-reversible in CH₃CN for E = Se. The oxidation process is independent of chalcogen type; the reduction process is found to be about 0.2 V more negative for E = S vs E = Se.