1-Meixner Random Vectors

Journal of Theoretical Probability - A definition of d-dimensional n-Meixner random vectors is given first. This definition involves the commutators of their semi-quantum operators. After that we...     

Rough solutions of the Einstein vacuum equationsSolutions peu régulières des équations d'Einstein dans le vide

We announce a new result, contained in [10–12], concerning rough solutions to Einstein vacuum equations expressed relative to wave coordinates. Our methods blend paradifferential techniques with a geometric approach to Strichartz type inequlities, which takes advantage of the specific structure of the Einstein equations. This results in a gain of half a derivative relative to the classical result of [3] and [5]. To cite this article: S. Klainerman, I. Rodnianski, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 125–130     

A Galois Connection

The connection presented in this paper mirror-links two metamathematical structures, the finitary closure operators, and the compact consistency properties, in such a way that a specification of one structure induces a provably equivalent specification of the other. Mathematics Subject Classification (2000): Primary 06A15, Secondary 28E10 03B22     

Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments

We consider a modulated process S which, conditional on a background process X, has independent increments. Assuming that S drifts to −∞ and that its increments (jumps) are heavy-tailed (in a sense made precise in the paper), we exhibit natural conditions under which the asymptotics of the tail distribution of the overall maximum of S can be computed. We present results in discrete and in continuous time. In particular, in the absence of modulation, the process S in continuous time reduces to a Lévy process with heavy-tailed Lévy measure. A central point of the paper is that we make full use of the so-called “principle of a single big jump” in order to obtain both upper and lower bounds. Thus, the proofs are entirely probabilistic. The paper is motivated by queueing and Lévy stochastic networks.     

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

Chlorokomplexe von Cu2+ und Ni2+ in Dimethylformamid

Zusammenfassung Durch spektrophotometrische Messungen in Dimethylformamid (DMF) werden die Koordinationsformen [CuCl]⁺ und [CuCl₃]^– sowie [NiCl]⁺, [NiCl₃]^– und [NiCl₄]^2– nachgewiesen. Bei Nickel(II)-chlorid und Kupfer(II)-chlorid wird Autokomplexbildung diskutiert. Die Solvate [Cu(DMF)₄] (ClO₄)₂ und [Ni(DMF)₆] (ClO₄)₂ werden isoliert.Im Zuge der Untersuchungen über Chlorokomplexe von Ionen der Übergangsmetalle^{1, 2} in nichtwäßrigen Lösungsmitteln wurden die Spektren der Lösungen von Kupfer(II)- und Nikkel(II)-perchlorat inDMF in Gegenwart verschiedener Mengen Tetraäthylammoniumchlorid aufgenommen.Mit 5 Abbildungen     

Size exclusion chromatographic characterization of sodium hyaluronate fractions prepared by high energetic sonication

Summary A high molecular weight sodium hyaluronate isolated from rooster combs was degraded by ultrasonication. High-performance size exclusion chromatography allowed rapid and accurate determination of molecular weight parameters (M_z, M_w, M_n) and distributions. The time dependence of hyaluronan ultrasonication to the molecular characteristics of the polymer was investigated. A non-random nature of the degradation process was demonstrated and the reciprocal M_n value was found to be linearly proportional to the time of ultrasonication.     

Structural and mechanistic look at the orthoplatination of aryl oximes by dichlorobis(sulfoxide or sulfide)platinum(II) complexes

Structural and mechanistic aspects of orthoplatination of acetophenone and benzaldehyde oximes by the platinum(II) sulfoxide and sulfide complexes [PtCl(2)L(2)] (2, L = SOMe(2) (a), rac-SOMePh (b), R-SOMe(C(6)H(4)Me-4) (c), and SMe(2) (d)) to afford the corresponding platinacycles cis-(C,S)-[Pt(II)(C(6)H(3)-2-CR'=NOH-5-R)Cl(L)] (3, R, R' = H, Me) have been investigated. The reaction of acetophenone oxime with sulfoxide complex 2a in methanol solvent occurs noticeably faster than with sulfide complex 2d due to the fact that the sulfoxide is a much better platinum(II) leaving ligand than the sulfide. Evidence is presented that the orthoplatination is a multistep process. The formation of unreactive dichlorobis(N-oxime)platinum(II) cations accounts for the rate retardation by excess acetophenone oxime and suggests the importance of pseudocoordinatively unsaturated species for the C-H bond activation by Pt(II). A comparative X-ray structural study of dimethyl sulfoxide platinacycle 3b (R = R' = Me) and its sulfide analogue 3e (R = H, R' = Me), as well as of SOMePh complex 3c (R = H, R' = Me), indicated that they are structurally similar and a sulfur ligand is coordinated in the cis position with respect to the sigma-bound phenyl carbon. The differences concern the Pt-S bond distance, which is notably longer in the sulfide complex 3e (2.2677(11) A) as compared to that in sulfoxide complexes 3b (2.201(2)-2.215(2) A) and 3c (2.2196(12) A). Whereas the metal plane is practically a plane of symmetry in 3b due to the H-bonding between the sulfoxide oxygen and the proton at carbon ortho to the Pt-C bond, an S-bonded methyl of SOMePh and SMe(2) is basically in the platinum(II) plane in complexes 3c and 3e, respectively. There are intra- and intermolecular hydrogen bond networks in complex 3b. An interesting structural feature of complex 3c is that the two independent molecules in the asymmetric unit of the crystal reveal an extremely short Pt-Pt contact of 3.337 A.     

Kontinuierliche Messung von 14C-markierten Aminos?uregemischen mit Hilfe eines Scintillatorschlauches nach der Trennung an Ionenaustauschers?ulen

Zusammenfassung Es wird eine Methode beschrieben, die es gestattet, während einer automatischen Aminosäuretrennung an Ionenaustauschersäulen die Radioaktivität der einzelnen ¹⁴C-markierten Aminosäuren zu messen. Die aufgetrennten Fraktionen werden unmittelbar am Säulenausgang durch eine Meßanordnung geschickt, bestehend aus einem Scintillatorschlauch, der sich zwischen zwei in Koinzidenz geschalteten Photomultipliern befindet. Anschließend wird mit Ninhydrin angefärbt. Die Nachweisgrenze beträgt 2 · 10^–3 C. Die Methode ist einfach zu handhaben, die Meßgeräte, einschließlich der Meßzelle, sind im Handel erhältlich.

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Summary A method is described for the continuous measurement of ¹⁴C-labelled amino-acids during automatic separation by ion-exchanger columns. Immediately after emerging from the column the single fractions are passed through a measuring device consisting of a plastic scintillator between two photomultipliers in a coincidence circuit. Subsequently the eluate is reacted with ninhydrin. The limit of detection is 2 · 10^–3 C. The procedure is simple and the measuring device is commercially available.

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Die Untersuchungen wurden durch den Minister für Atomkernenergie gefördert. Hierfür danken wir auch an dieser Stelle verbindlich.

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Am Ausbau der Methode waren zeitweilig die Herren Dr. Ing. W. Heptner und Dr. Ing. S. Vierkötter beteiligt.