Bayes estimation in linear models: A coordinate-free approach

The unified theory of Bayes estimation in linear models is presented, using a coordinate-free approach. The results are applied to the problem of linear and quadratic estimation in linear regression model.     

On the equations of the theory of shells of slowly varying curvatures

Zusammenfassung Es werden für die Schalen mit langsam veränderlichen Krümmungen die Gleichungen angegeben. Die Lösung wird in Form von zwei Gleichungen für die Spannungsfunktion und die Normalverschiebung erhalten.     

Micro- and ultramicrodetermination of the formyl and isonitrile groups in the presence of other acyl groups

Gravimetric and colorimetric micromethods for determination of formyl and isonitrile groups are reported. The gravimetric method is based on a quantitative cleavage of the formyl group and decomposition of formed formic acid to carbon monoxide by means of 60% sulfuric acid. Carbon monoxide is oxidized and the formed carbon dioxide is determined gravimetrically.The colorimetric ultramicromethod is based on the basic hydrolysis of the formyl group. After acidifying the hydrolysate, the quantitatively formed formic acid is distilled under special conditions. The acid is then reduced to formaldehyde. Its quantity is determined spectrophotometrically with chromotropic acid.     

Where does the planar-to-nonplanar turnover occur in small gold clusters?

Several levels of theory, including both Gaussian-based and plane wave density functional theory (DFT), second-order perturbation theory (MP2), and coupled cluster methods (CCSD(T)), are employed to study Au6 and Au8 clusters. All methods predict that the lowest energy isomer of Au6 is planar. For Au8, both DFT methods predict that the two lowest isomers are planar. In contrast, both MP2 and CCSD(T) predict the lowest Au8 isomers to be nonplanar.     

Mannich reactions of carbonyl compounds and enamines with benzotriazole as the NH component

Boron trifluoride catalyses reactions of 1-(hydroxymethyl)benzotriazole with ketones to give predominantly monosubstituted Mannich products. In unsymmetrical ketones, a methylene is slightly more reactive than a methyl group. For 1,3-diketones and diethyl malonate, substitution occurs on the central methylene group. β-Aminocrotononitrile and β-aminocrotonate undergo Mannich condensations with benzotri-azole and formaldehyde without any catalyst. Preliminary investigations of the reactivity of the Mannich bases thus obtained are reported.     

Radical-mediated silyl- and germyldesulfonylation of vinyl and (alpha-fluoro)vinyl sulfones: application of tris(trimethylsilyl)silanes and tris(trimethylsilyl)germanes in Pd-catalyzed couplings

[reaction: see text] Radical-mediated silyl- and germyldesulfonylations of various vinyl and (alpha-fluoro)vinyl sulfones with tris(trimethylsilyl)silane and germanium hydrides provide access to vinyl and (alpha-fluoro)vinyl silanes and germanes. Upon oxidative treatment with hydrogen peroxide in basic aqueous solution, the vinyl tris(trimethylsilyl)silanes and -germanes undergo Pd-catalyzed cross-couplings with aryl halides.     

Mechanism of action of aspartic proteinases: Application of transition-state analogue theory

Summary Applying the semiempirical MO methods AM1 and PM3 as well as the density functional theory to the model of the catalytic site composed of ca. 160–190 atoms, we have carried out studies aimed at the explanation of three aspects of the mechanism of action of aspartic proteinases: the site of dissociation within the catalytic diad COOH/COO^- (i) in the free enzyme and (ii) in the Michaelis complex, and (iii) the energy changes associated with the catalytic paths. We have found that the state of dissociation within the catalytic diad is ligand-sensitive. In the free enzyme and in the intermediate complexes, Asp³³ prefers to be dissociated with the outer oxygen of Asp²¹³ protonated, while in the Michaelis and product complexes the opposite holds true. This is in agreement with recent mechanistic hypotheses and with some experimental results by FTIR and NMR. The energy diagram for the catalysis indicates that electronic effects are responsible most of all for the relative reduction of energy of the intermediates and possibly transition states on the catalytic reaction path. The shape of the diagram qualitatively agrees with the transition-state analogue theory for the enzymatic reactions.     

Analytical application of triethylenetetraaminehexa- acetic acid: Part 2. Polarographic Investigation of the reactions of TTHA at the dropping mercury electrode

TTHA gives an anodic d.c. wave and s.w. peak corresponding to oxidation of mercury at the d.m.e. surface with formation of a Hg(II)—TTHA complex. Similar processes are known for other ligands, e.g. EDTA and DCTA, but the greater stability of the Hg(II)—TTHA complex gives a significant improvement in the shapes of the anodic wave and s.w. peak. An increase in pH shifts the E_{$\text{1}\text{2}$} and E_p values towards more negative values because the conditional stability constant of the Hg(II)—TTHA complex is increased. Although the half–wave potentials of the reduction wave of Hg(II)—TTHA and of the anodic wave of TTHA, are the same, other criteria for the reversibility of polarographic reactions suggest that the anodic TTHA process at the d.m.e. is not completely reversible. The temperature coefficient of the wave and s.w. peak as well as the dependence of the wave height on the square root of the mercury head prove that the process is diffusion–controlled. Supporting electrolytes are given for which the d.c. wave and the s.w. peak of TTHA are well-shaped, with linear dependence between the wave or peak height and the concentration of TTHA in the ranges 5 × 10^-5–5 × 10^-4 M (d.c.) and 1 0^-5–1 × 10^-4 M (s.w.).