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.     

Analyse theoretique des lois cinetiques couramment utilisees en thermoanalyse pour l'etude des reactions solid-gaz. III. proposition d'une nouvelle methode d'approche en regime dynamique

Résumé Dans la première partie de ce travail, les auteurs mettent en évidence que la vitesse d'une réaction en régime non isotherme dépend d'un facteur supplémentaire: le régime de montée en température. Cette assertion est basée sur le fait que le taux de réactionx est une fonction de trois variables: températureT, tempst, et vitesse de chauffeT, variable qui n'avait pas été prise en considération jusqu'ici par les autres auteurs travaillant sur ce problème.Puis, se basant sur les deux hypothèses suivantes: a) l'équation de vitesse en régime isotherme est la forme limite de l'équation de vitesse en régime dynamique, b) la variation de température en régime dynamique affecte la fréquence d'apparition des germes de la nouvelle phase, une formulation théorique des loisg(x) est proposée pour le régime non-isotherme. Cette formulation est explicitée en fonction de l'écart, à une température donnée, entre les valeurs de Lnk _i (isotherme) et Lnk _d (dynamique) dans le diagramme Lnk = f(1/T).L'étude, par thermogravimétrie, de la décomposition du gypse, du sulfate de calcium semihydraté, et de l'oxalate de calcium monohydraté, réalisée en montée linéaire de température, permet de vérifier expérimentalement la formulation théorique proposée.Pour obtenir une bonne interprétation cinétique d'une réaction chimique en régime dynamique, la vitesse de chauffe ne doit pas excéder 20°/heure.

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In the first part of this paper, the authors point out that the rate of reaction with non-isothermal kinetics depends on a supplementary factor: the heating rate. This assertion is based on the fact that the degreex of reaction is a function of three variables:T (temperature),t (time) andT (heating rate); this was not taken into account by other authors concerned with the subject.Then from the two following hypotheses: a) the rate equation for isothermal conditions is the limit form of the rate equation for non-isothermal conditions, b) the temperature change under dynamic conditions affects the frequency of nucleus formation of the new phase, a theoretical formulation of non-isothermalg(x) laws is proposed. This formulation involves the value of the difference, at constant temperature, between Ink _i (isothermal) and In k_d (dynamic) in the Ink=f(1/T) diagram.The thermogravimetric study of the dehydration of gypsum, of calcium sulfate hemihydrate, and of calcium oxalate monohydrate, under non-isothermal conditions, allows experimental verification of the theoretical formulation proposed.For a good kinetic approach of a chemical reaction under dynamic conditions, the heating rate must not exceed 20°/hour.

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Zusammenfassung Im ersten Teil dieser Arbeit wird von den Autoren bewiesen, daß die Geschwindigkeit einer Reaktion unter nicht-isothermen Bedingungen von einem zusätzlichen Faktor, den Bedingungen des Temperaturenstiegs, abhängt. Diese Behauptung beruht auf der Tatsache, daß der Reaktionsverlauf eine Funktion dreier Variablen ist: der TemperaturT, der Zeitt und der AufheizungsgeschwindigkeitT, wobei letztere Variable bisher von den auf diesem Gebiet arbeitenden Autoren außer Acht gelassen worden ist.Nachfolgend wird an Hand der zwei Voraussetzungen, daß a) die Geschwindigkeitsgleichung unter isothermen Bedingungen die Grenzform der Geschwindigkeitsgleichung unter dynamischen Bedingungen ist und b) die Temperaturänderung unter dynamischen Bedingungen sich auf die Erscheinungsfrequenz der Keime der neuen Phase auswirkt, eine theoretische Formulierung der Gesetzeg(x) für nicht-isotherme Bedingungen vorgeschlagen. Diese Formulierung wird als Funktion der Abweichung ausgedrückt, welche bei einer gegebenen Temperatur zwischen den Werten von Lnk _i (isotherm) und Lnk _d (dynamisch) im Diagramm Lnk=f(1/T) besteht.Die bei linearem Temperaturanstieg thermogravimetrisch durchgeführte Untersuchung der Zersetzung von Gips, von Calciumsulfat Semihydrat und von Calciumoxalat Monohydrat ermöglicht die vorgeschlagene theoretische Formulierung experimentell zu bestätigen.Um unter dynamischen Bedingungen eine gute kinetische Interpretation einer chemischen Reaktion zu erhalten, darf die Aufheizungsgeschwindigkeit den Wert von 20° pro Stunde nicht überschreiten.

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, : . , : (),t () ' ( ), , . : ) ) t(x) . Lnk _j () Lnk _d ( ) Lnk=f(1/T) . , , . , 20° .