A short proof for a generalization of Vizing's theorem

For a simple graph of maximum degree Δ, it is always possible to color the edges with Δ + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Δ colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these results to multigraphs. Instead of considering several color interchanges along alternating chains (Vizing, Gupta), using counting arguments (Ehrenfeucht, Faber, Kierstead), or improving nonvalid colorings with Fournier's Lemma, the method of proof consists of using one single easy transformation, called “sequential recoloring”, to augment a partial k-coloring of the edges.     

Event-by-event net charge fluctuations

We present analyses of event-by-event dynamical net charge fluctuations measured in 130 and 200 GeV Au+Au collisions with the STAR detector. The dynamical net charge fluctuations are evaluated using the ν _+-,dyn observable. Dynamical fluctuations measured in Au+Au collisions at 130 and 200 GeV are finite, and exceed charge conservation limits. They deviate from a perfect 1/N scaling and provide an indication that the collision dynamics varies with collision centrality.     

Large families of mutually embeddable vertex‐transitive graphs

For each infinite cardinal κ, we give examples of 2^κ many non‐isomorphic vertex‐transitive graphs of order κ that are pairwise isomorphic to induced subgraphs of each other. We consider examples of graphs with these properties that are also universal, in the sense that they embed all graphs with smaller orders as induced subgraphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 99–106, 2003     

Intensités des transitions optiques de [PtCl4]2−

The oscillator strengths of the “d-d” transitions of the ion [PtCl₄]^2? were calculated. The method, based on the evaluation of the MO of the distorted ion, gives results in good accordance with the experimental data. The transition to ¹ B _1g (a _1g →b _1g ^* ), as a consequence of the participation of the orbital 6s, mixed with \(5d_{z^2 } \) in \(a_{1_g } ,a_{1_g } \) is characterized by a very low intensity in the case of thex,y polarization.     

Differentiation of isomeric 5- and 7-oxo derivatives of tetrahydrothiazolo[3,2-a]pyrimidine by electron impact mass spectrometry

The electron impact mass spectra of two series of 5-oxo-tetrahydro-5H-thiazolo [3,2-a]pyrimidine-6-ethylcarboxylates and 7-oxo-tetrahydro-7H-thiazolo [3,2-a]pyrimidine-6-ethylcarboxylates were measured and fragmentation patterns examined. Structures were assigned from analysis of oxo molecular ion fragmentations. Compounds of the 5-oxo series gave an [M – CO₂C₂H₅]⁺ fragmentation whereas compounds of the 7-oxo series gave three characteristic cleavages. This decomposition was confirmed for one pair of isomers by high-resolution mass spectrometry and unimolecular mass-analysed ion kinetic energy spectrometry. Electron impact mass spectrometry is a convenient method for assigning structures of 5- and 7-oxo regioisomers of tetrahydrothiazolo[3,2-a]pyrimidine-6-carboxylates.     

PHOTOREACTIVATING ENZYME FROM NEUROSPORA CRASSA*

Abstract— Extracts of Neurospora crassa contain photoreactivating enzyme by the criteria of ability to split thymine-containing dimers and to increase the transforming ability of u.v.-irradiated Hemophilus influenzae DNA. The latter activity is heat-labile and is destroyed by trypsin. The action spectrum of such in vitro photoreactivation is a simple one (with a single maximum at 405 nm in the range 313 to 436 nm), differing from the more complicated in vitro spectra for yeast and Escherichia coli. However, the in vitro Neurospora spectrum coincides closely with the in vivo spectrum for this organism, suggesting that there is little or no “indirect” photoreactivation in Neurospora. It is concluded that the Neurospora photoreactivating enzyme is probably of a different type than those of yeast and Escherichia coli.     

A rapid access to chiral alkylidene cyclopentenone prostaglandins involving ring-closing metathesis reaction

A synthesis of the alkylidene cyclopentenone prostaglandin TEI 9826 has been realized. The synthesis involved the preparation of the chiral 1,5-diene 8 using a stereoselective Claisen rearrangement from the allylic alcohol 6 giving the ester 7 after vinylation. Then a key RCM reaction allowed the preparation of the cyclopentenol 9 which, after oxidation, gave the cyclopentenone 10, precursor of the prostaglandin.     

CHEMILUMINESCENCE AND ENERGY TRANSFER FROM SINGLET OXYGEN PAIRS

Abstract— Chemiluminescence and photochemiluminescence of systems generating excited (singlet) molecular oxygen has been studied at low temperature in fluid media. A possible interpretation is proposed: that dimers of singlet oxygen are directly or indirectly responsible for the observed emission, the species [¹δg +¹σg⁺] predominating. Energy transfer to a fluorescent molecule is possible only when conditions of spectral overlap, required for transfer by inductive resonance, are fulfilled. Evidence is also presented for the formation of a transient complex between oxygen and a sensitiser or acceptor molecule [S…O₂], which is the precursor of singlet oxygen in these systems. However, other possible mechanisms cannot be excluded.     

Etudes stéréochimiques XIV. Adduits de Diels-Alder en série résiniques; action des peracides et ouvertures acido-catalysées d'époxydes

Studies in Stereochemistry XIV. Diels-Alder adducts in the resin series; action of peracids and acid-catalysed ring opening of epoxides The synthesis of Diels-Alder compounds of type 2 with a 17-nor-13(14)-atisène skeleton is described (cf. Schemes 1–3). Depending on the nature and configuration of substituents R¹ and R² on the carbon atoms 15 and 16, an epoxide ( 24–33 ) or a ketone ( 35–38 ) or a mixture of epoxide, ketone and lactone is obtained by the action of p-nitroperbenzoic acid on the double bond of these adducts (cf. Scheme 4). A simplified reaction scheme is suggested to explain the formation of the various products. In an acid-catalysed reaction, the epoxides isomerize mainly into ketones. Nevertherless, in some cases, dienes (e.g. 52 ) or hydroxy-γ-lactones of (13R*, 14S*)-configuration (e.g. 50 ) resulting from the opening of the epoxide ring with retention of configuration were obtained.