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...     

A rigid graph for every set

A graph G is called rigid if the identical mapping V(G)→V(G) is the only homomorphism G→G. In this note we give a simple construction of a rigid oriented graph on every set. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 108–110, 2002     

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.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

SPECTROSCOPIC STUDIES OF PURINES—I. FACTORS AFFECTING THE FIRST EXCITED LEVELS OF PURINE*

Abstract— Studies of purine absorption and emission in seven solvents differing greatly in dielectric constant and hydrogen bonding potential, reveal a variety of solvent effects. For example, the resolution of structure in the absorption spectrum, the position and/or intensity of the X₂ absorption band, the intensity of fluorescence, the magnitude of the long wave-lenth tail, and the position of the X₁ absorption band are differentially affected—in the order listed—by the solvents tested. Even though it is possible to correlate the extent of decrease in the n-π* tail with increasing solvent dielectric constant, probably alterations in all of these spectroscopic parameters depend most critically upon the ability of the various solvents to form hydrogen bonds with the hydrogen on N9 and/for with the non-bonding electrons on the purine nitrogens: it is tentatively concluded that the probability of hydrogen bonding is directly correlated with the electronegativity of the aza nitrogens (N7 > N3 > N1). In solvents like isopropanol not all of the non-bonding electrons must be solvated maximally in most purine molecules since there is appreciable fluorescence under conditions where a long wavelength tail is readily observed in the absorption spectrum (alternatively some noa-bonding electrons may not te relevant to fluorescence quenching.) Decreases in fluorescence yield are associated with red shifts in the fluorescence maximum, and in the solvents of highest polarity the fluorescence yield is again small indicating that glycerol and water can enhance radiationless tunneling—presumably by altering Franck-Condon configurations and/or improving electronic-vibrational coupling between solute and solvent. The quantum yield is uniform throughout the atsorption band for a given solvent, but studies in aqueous buffers varying from pH 1 to 11 show that the fluorescence yield is greater for charged than for neutral molecules. Further, the fluorescence excitation peak is red shifted in powders. Since phosphorescence is the predominant emission at 777deg;K and increases in fluorescence can be correlated with the presumed solvation of non-bonding electrons, the singlet excited state of lowest energy in ‘unperturbed’ purine must be n-π* in nature. The shape of the phosphorescence band and the decay lifetime of ? 1 sec at 77°K lead to the conclusion that the emitting triplet is a π-π* state. The eight vibrational structures in phosphorescence emission can be readily grouped into two progressions: there is an average separation of about 1300 cm^-1 between peaks within a given progression, and the two sets are mutually displaced by about 500 cm-^l. Individual vibrational peaks are favoured in different solvents and the whole band may be shifted up to 500 cm^-l. Even larger shifts are observed in charged purine molecules and in powders (up to 3000 cm^-l) and the presumed 0–0 band is not observed.