Discriminant of a generic projection of a minimal normal surface singularity

Let (S,0) be a rational complex surface singularity with reduced fundamental cycle, also known as a minimal singularity. Using a fundamental result of M. Spivakovsky, we explain how to describe the equisingularity type of the discriminant curve for a generic projection of (S,0) onto $\text{(}\text{C}{}^2\text{,0)}$ from the resolution of (S,0). To cite this article: R. Bondil, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Efficient indirect electrochemical in-situ regeneration of nadh:electrochemically driven enzymatic reduction of pyruvate catalyzed by d-ldh

Using [Cp(Me)₅Rh(bipy)C1]C1 (1) as redox catalyst for the continous NADH regeneration it was possible to perform an electrochemically driven enzymatic reduction of pyruvate to D-lactate catalyzed by D-LDH at a rate of 5 turnovers per hour. This is by a factor of 20 faster than the best results obtained until now. Current yields of 50 to 70 % may be obtained.     

Small generators of number fields

If K is a number field of degree n over Q with discriminant D _K and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d ² such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real number field of prime degree n then one can find an integral generator α with . Received: 10 January 1997 / Revised version: 13 January 1998     

Strukturen und Molekül-Eigenschaften ladungsgestörter Moleküle. 52. Mitteilung. 2, 3-Diphenylchinoxalin-Radikalanionen in Lösung und im Kristall

Structures and Molecular Properties of Charge-Pertubed Molecules. 2, 3-Diphenylquinoxaline Radical Anions in Solution and in Crystals The Na⊕ and K⊕ radical-ion salts of 2, 3-diphenylquinoxaline seem to be (according to a structural database search) among the first ones of N-heterocyclic radical anions in crystals. The one-electron reduction in aprotic 1, 2-dimethoxyethan (DME) solution at metal mirrors and the crystallization under Ar have been preceded by cyclovoltammetric (CV) and ESR/ENDOR measurement. The first electron insertion at ?1.63 V proves to be reversible, whereas the irreversible second step, which is accompanied by an overcrossing of the CV line, can be rationalized by an ‘ECE-DISP’ mechanism via a dianion redox disproportionation. The ENDOR spectrum resolves four ¹H couplings and allows to simulate the ESR spectrum including the ¹⁴N hyperfine splittings. Both dark-blue single crystals of the radical ion salts $[2,3{\rm - diphenylquinoxaline}^{{.} \ominus} {\rm Met}^ \oplus ({\rm DME})]^.$ show unexpected similarities for Met⊕ = Na⊕, K⊕ despite the 36-pm difference in their ionic radii. The largest structural changes inflicted by the one-electron reduction of the N-heterocyclic molecule are observed in the vicinity of the N-centers bearing the highest effective nuclear charge. The DME-chelated metal cations coordinate at the N electron pairs and form Met⊕(DME)-bridged polymer chains of the radical anion, which are differently ondulated in the Na⊕ and K⊕ radical anion salts. The take-home lesson suggests that many more N-heterocyclic molecules might be analogously reduced under optimized conditions and isolated as single crystals.     

Colorful Friedel-Crafts chemistry of meso-tetraarylporphyrins. An unexpected route to porphyrinic spiro dimers

Under Friedel-Crafts conditions, meso-tetraarylporphyrins give porphyrin spiro dimers in good yield. This reaction involves acylation, acid-catalyzed cyclization, and dimerization. A stable dimer possessing three additional six-membered rings could be isolated and its structure determined. By modifying the substrate and reagents, intermediates could be isolated and characterized. The reactivity of the substrates, the side-reactions, and the concentration requirements to form the dimers, all explain why this reaction remained apparently unexplored in the widely used meso-tetraarylporphyrin series. [reaction: see text]     

Heptakis-6-(5-methylene-thioureido-5′-methyl-2,2′-bipyridyl)-β-cyclodextrin: synthesis and metal complexation study

A new heptapode heptakis-6-(5-methylene-thioureido-5′-methyl-2,2′-bipyridyl)-β-cyclodextrin was prepared and its complexation properties towards metal cations were investigated. Substituting the urea functions by the corresponding thioureas promoted the inversion of the metal coordination selectivity. Preliminary results showed the heptapode unable to complex lanthanides but authorise selective complexation of ‘soft’ and ‘borderline’ metal cations.     

Strukturen ladungsgestörter oder räumlich überfüllter Moleküle. 15. Tetracyanethen-Natrium-Dimethoxyethan

Structures of Charge-Perturbed or Sterically Overcrowded Molecules. 16. Tetracyanoethylene Sodium Dimethoxyethane The Single crystal structure of [(NC)₂C? C(CN)₂?·Na⊕(H₃CO? CH₂CH₂? OCH₃)]∞ reveals two formula units within the triclinic (P1 ) unit cell. The tetracyanoethylene radical anions are arranged along parallel double layers, which are shifted relative to each other, and in between which are interspersed the sodium counter cations and their dimethoxyethane ligands. The distances within the double layers amount to 300 pm and the ones between them to 385 pm. The six-fold coordinated Na⊕ centers are surrounded by four radical anions with contact distances Na…?N between 250 and 254 pm as well as by a twofold solvent ligand with Na…?O of 238 and 241 pm. Due to the electron transfer to the acceptor molecule, its (NC)₂C-halves twist by 8° and the bond lengths of the N?C? C subunits, bent by each 3°, are shortened up to 2 pm. The structural parameters are compared to those of the analogous potassium salt [TCNE^?K^⊕DME], of the dianion , of the sodium salts [(NC)₃C^?Na^⊕]∞ as well as [(NC)₂C? C(CHCH)₂? C(CN)₂^?Na^⊕]_∞ and, in addition, are discussed based on geometry-optimized MNDO calculations.