Bestimmung von iridiumspuren mit thiodibenzoylmethan mittels substöchiometrischer isotopenverdünnungs-analyse: Determination of traces of iridium with thiodibenzoylmethane by substoichiometric isotope dilution analysis

Determination of traces of iridium with thiodibenzoylmethane by substoichiometric isotope dilution analysisIridium(III or IV) reacts with thiodibenzoylmethane on heating at pH 6 to form a 1:3 complex, which can be concentrated by extraction into chloroform. Based on this reaction, a reproducible, selective determination of iridium is achieved by means of substoichiometric isotope dilution analysis, based on ¹⁹²Ir. The linear range is 1–11 nmol of iridium.     

Diffraction dissociation of nuclei in 450 GeV/c proton-nucleus collisions

Diffractive dissociation of nuclei (Be, Al, W) in collisions with 450 GeV/c protons,pApX, has been measured with the HELIOS spectrometer at the CERN Super Proton synchrotron. The dependence of the single-diffraction cross-section on the nuclear massA can be parametrized as _SD mb×A ^0.35±0.02, showing the peripheral nature of the process. The differential cross-section d_SD=(3.8±0.3)mb ×A ^0.35±0.02, is exponential with the slope parameter, increasing from 6.2±0.4 (GeV/c)^–2 for beryllium to 7.9±0.5 (GeV/c)^–2 for tungsten. The slope parameter also increases with increasing massM _X of the diffractively produced state. The rapidity, multiplicity, and transverse-momentum distributions of the particles of the diffractively produced stateX show a longitudinal phase-space population and are remarkably insensitive to the nuclear mass. This, together with theA ^1/3 dependence of _SD, suggests that the dominant process of nuclear diffractive excitation is the dissociation of single nucleons.Deceased     

Ketalizations of aryl ω-(2-imidazolyl)alkyl ketones by glycerol and 3-mercapto-1,2-propanediol. synthesis and characterization of cis- and trans-{2-aryl-2-[ω-(2-imidazolyl)alkyl](1,3-dioxolan-4-yl and 1,3-oxathiolan-5-yl)}methanols

Aryl 2-[(2-imidazolyl)ethyl or 3-(2-imidazolyl)propyl]ketones were ketalized by glycerol or 3-mercapto-1,2-propanediol in boiling benzene in the presence of 4-toluenesulfonic acid to provide the title compounds. The aryl substituents are 4-chloro-, 4-bromo-, 4-fluoro-, or 2,4-dichlorophenyl. While aryl (2-imidazolyl)methyl ketones condensed with glycerol to form cis- and trans-{2-aryl-2-[(2-imidazolyl)methyl]-4-(hydroxymethyl)}-1,3-dioxolanes, related condensations with 3-mercapto-1,2-propanediol, under similar, or even more stringent reaction conditions, produced no 1,3-oxathiolane analogs, with the starting ketones being recovered. Separation and structure determination of these racemic cis and trans isomeric products are described. The structure of these stereoisomers was established by means of ¹H and ¹³C nmr correlation and nOe experiments. Selective methylation of the N-unsubstituted 2-imidazolyl alcohols with one equivalent sodium hydride and methyl iodide provided the corresponding N-methyl alcohols in excellent yields. With excess benzoyl chloride, N-unsubstituted 2-imidazolyl alcohols were initially converted to O, N-dibenzoates from which the N-benzoyl group was easily cleaved by ammonium hydroxide in ethanol to provide benzoate esters.     

Purification and characterization of a laccase from the white-rot fungus Trametes multicolor

The wood-degrading fungus Trametes multicolor secretes several laccase isoforms when grown on a simple medium containing copper in the millimolar range for stimulating laccase synthesis. The main isoenzyme laccase II was purified to apparent homogeneity from the culture supernatant by using anion-exchange chromatography and gel filtration. Laccase II is a monomeric glycoprotein with a molecular mass of 63 kDa as determined by sodium dodecylsulfate polyacrylamide gel electrophoresis, contains 18% glycosylation, and has a pI of 3.0. It oxidizes a variety of phenolic substrates as well as ferrocyanide and iodide. The pH optimum depends on the substrate employed and shows a bell-shaped pH activity profile with an optimum of 4.0 to 5.0 for the phenolic substrates, while the nonphenolic substrates ferrocyanide and 2,2′-azino-bis(3-ethylbenzthiazoline-6-sulfonate) show a monotonic pH profile with a rate decreasing with increasing pH.     

Synthesis of 1-[3-methyl-2(3H)-benzazolon-5- or 6-yl]-4-{4-[cis-2-(2,4-dichlorophenyl)-2-(1H-imidazol-1-yl-methyl)-1,3-dioxolan-4-yl]methyleneoxyphenyl}piperazines

Reactions of 3-methyl-6-[4-(4-hydroxyphenyl)-1-piperazinyl]-2(3H)-benzoxazolone, 3-methyl-6-[4-(4-hydroxy-phenyl)-1-piperazinyl]-2(3H)-benzothiazolone and 1,3-dimethyl-5-[4-(4-hydroxyphenyl)-1-piperazinyl]-2(3H)-benzimidazolone with cis-{[2-(2,4-dichlorophenyl) -2-(1H-imidazol-1-ylmethyl)]-1,3-dioxolan-4-yl}methyl meth-anesulfonate in the presence of sodium hydride furnish the title compounds.     

Deterministic version of Wigner's semicircle law for the distribution of matrix eigenvalues

It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let A_n=(a_ij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ⁽ⁿ⁾}_1?k?n its eigenvalues, and {u_k⁽ⁿ⁾}_1?k?n the corresponding (orthonormalized column) eigenvectors. Let $\text{v}{}^1{}_{\mathrm{n}}\text{=(a}{}_{\mathrm{n1}}\text{,a}{}_{\mathrm{n2}}\text{,?,a}{}_{\mathrm{n,n?1}}\text{)}$, put

$\text{X}{}_{\mathrm{n}}\text{(t)=[n(n-1)]}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}\text{∑}\text{k=1}\text{[(n-1)t]}\text{|v}{}_{\mathrm{n}}{}^1\text{u}{}_{\mathrm{f}}{}^{\mathrm{(n-1)}}\text{|}{}^2\text{,}\text{0?t?1}$

(bookeeping function for the length of the projections of the new row v¹_n of A_n onto the eigenvectors of the preceding matrix A_n?1), and let finally

$\text{F}{}_{\mathrm{n}}\text{(x)=n}{}^{-1}\text{(}\text{number of}\text{λ}{}_{\mathrm{k}}{}^{\mathrm{(n)}}\text{?x}\text{n}\text{,1?k?n)}$

(empirical distribution function of the eigenvalues of $\text{A}{}_{\mathrm{n}}\text{n}$. Suppose (i) $\text{lim}{}_{\mathrm{n}}\text{a}{}_{\mathrm{nn}}\text{n}\text{=0}$, (ii) lim_nX_n(t)=Ct(0<C<∞,0?t?1). Then

$\text{F}{}_{\mathrm{n}}\text{?W(·,C)}\text{(n→∞)}$

,where W is absolutely continuous with (semicircle) density

$\text{w(x,C)=}\text{(2Cπ)}{}^{-1}\text{(4C-x}{}^2{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{for}\text{|x|?2}\text{C}\text{0}\text{for}\text{|x|?2}\text{C}$

     

Stochastic Control for Bayesian Neural Network Training

In this paper, we propose to leverage the Bayesian uncertainty information encoded in parameter distributions to inform the learning procedure for Bayesian models. We derive a first principle stochastic differential equation for the training dynamics of the mean and uncertainty parameter in the variational distributions. On the basis of the derived Bayesian stochastic differential equation, we apply the methodology of stochastic optimal control on the variational parameters to obtain individually controlled learning rates. We show that the resulting optimizer, StochControlSGD, is significantly more robust to large learning rates and can adaptively and individually control the learning rates of the variational parameters. The evolution of the control suggests separate and distinct dynamical behaviours in the training regimes for the mean and uncertainty parameters in Bayesian neural networks.