Halogen-Mikrobestimmung in organischen Substanzen mit Hilfe von Filterbechern

Zusammenfassung Es wird ein Verfahren beschrieben, diePreglschen Asbestfilterröhrchen für die Halogenbestimmung durch Jenaer Filterbecher nachEmich undSchwarz-Bergkampf zu ersetzen. Dadurch werden einige Fehlerquellen vermieden und überdies die Dauer der Bestimmung abgekürzt.

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Summary A new method for the determination of halogen in micro-elementar-analysis is described.Pregl's asbestos-filled filter-tubes are substituted by Jena micro filter-beakers followingEmich andSchwarz-Bergkampf. Thus, several sources of error are avoided and the determination is shortened.

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Résumé Le tube-filtre a l'amiante suivantPregl pour la filtration des résidus halogeniques est remplacé par le micro bécher-filtre selonEmich etSchwarz-Bergkampf. Ainsi on évite quelques sources d'erreurs et de plus on raccourcit la durée de la détermination.

     

On the structure of clique‐free graphs

Using a clever inductive counting argument Erd?s, Kleitman and Rothschild showed in 1976 that almost all triangle‐free graphs are bipartite, i.e., that the cardinality of the two graph classes is asymptotically equal. In this paper we investigate the structure of the “few” triangle‐free graphs which are not bipartite. As it turns out, with high probability, these graphs are bipartite up to a few vertices. More precisely, almost all of them can be made bipartite by removing just one vertex. Almost all others can be made bipartite by removing two vertices, and then three vertices and so on. We also show that similar results hold if we replace “triangle‐free” by K_??+1‐free and “bipartite” by ??‐partite. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19, 37–53, 2001     

One-dimensional quantum chaos: Explicitly solvable cases

We present quantum graphs with remarkably regular spectral characteristics. We call them regular quantum graphs. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansions for each individual energy level.     

Relation between habit and structure of liquid single crystals of blue phases (Reply to the preceding Comment by P. Pieranski and P. E. Cladis)

Abstract

In the preceding Comment [1] Pieranski and Cladis assert that the blue phase space groups derived in our Invited Article [2] are not consistent with the growth forms observed for our BP single crystals (cf. table 3 of [2]). We wish to reply as follows.     

Synthesis, purification, and characterization of phosphine oxides and their hydrogen peroxide adducts

Reactions of the tertiary phosphines R(3)P (R = Me, Bu, Oct, Cy, Ph) with 35% aqueous H(2)O(2) gives the corresponding oxides as the H(2)O(2) adducts R(3)P=O·(H(2)O(2))(x) (x = 0.5-1.0). Air oxidation leads to a mixture of products due to the insertion of oxygen into one or more P-C bonds. (31)P NMR spectroscopy in solution and in the solid state, as well as IR spectroscopy reveal distinct features of the phosphine oxides as compared to their H(2)O(2) adducts. The single crystal X-ray analyses of Bu(3)P=O and [Cy(3)P=O·(H(2)O(2))](2) show a P=O stacking motif for the phosphine oxide and a cyclic structure, in which the six oxygen atoms exhibit a chair conformation for the dimeric H(2)O(2) adduct. Different methods for the decomposition of the bound H(2)O(2) and the removal of the ensuing strongly adsorbed H(2)O are evaluated. Treating R(3)P=O·(H(2)O(2))(x) with molecular sieves destroys the bound H(2)O(2) safely under mild conditions (room temperature, toluene) within one hour and quantitatively removes the adsorbed H(2)O from the hygroscopic phosphine oxides within four hours. At 60 °C the entire decomposition/drying process is complete within one hour.     

Synthesis of trifluoromethyl-substituted cyclopropanes via sequential Kharasch-dehalogenation reactions

A two-step process for the synthesis of trifluoromethyl-substituted cyclopropanes is described. Halothane, an anesthetic agent, is added to olefins in a ruthenium-catalyzed Kharasch reaction. The resulting 1,3-dihalides are converted into cyclopropanes by dehalogenation with magnesium. This procedure represents an alternative to metal-catalyzed cyclopropanations involving trifluoromethyl diazomethane.     

Random I-colorable graphs

In this article we investigate properties of the class of all l-colorable graphs on n vertices, where l = l(n) may depend on n. Let G^l_n denote a uniformly chosen element of this class, i.e., a random l-colorable graph. For a random graph G^l_n we study in particular the property of being uniquely l-colorable. We show that not only does there exist a threshold function l = l(n) for this property, but this threshold corresponds to the chromatic number of a random graph. We also prove similar results for the class of all l-colorable graphs on n vertices with m = m(n) edges.