From biased coin to any discrete distribution

Periodica Mathematica Hungarica - In this note we construct an algorithm generating any discrete distribution with an arbitrary coin (and, as a result, with arbitrary initial distribution). The...     

From Y- to Siamese-twin shaped glycolipids

Summary A set of Y-shaped and Siamese-twin shaped carbohydrate based glycolipids was investigated using polarising microscopy. The structure was changed from the normal type (1 head, two chains) to complex inverted structures (2 heads outside 1 to 3 chains in the middle part). The carbohydrate headgroup was changed from mono- to disaccharide; also the alkyl chain length was varied systematically. The compounds displayed different thermotropic mesophases (Smectic A phases, columnar phases and cubic phases) depending on the type of carbohydrate headgroup and the alkyl chain length.     

The 2:1 cocrystal of benzamide and penta­fluoro­benzoic acid

The crystal structure of the title compound, benzamide–2,3,4,5,6‐penta­fluoro­benzoic acid (2/1), 2C₇H₇NO·C₇HF₅O₂, consists of centrosymmetric hexa­meric supermolecules composed of four amide and two carboxylic acid mol­ecules connected via O—H⋯O and N—H⋯O hydrogen bonds. No phen­yl–perfluoro­phenyl π–π stacking inter­actions are observed in this cocrystal.     

A Comparison of the Experimental and ab Initio Values of theO NMR Chemical Shifts in the Carbonyl Group

New experimental and theoretical results are presented for the NMR shielding of oxygen in the carbonyl group. The experimental values clearly demonstrate that the solvent effects are very significant. The new results for the chemical shifts are in better agreement than the previous literature data with the corresponding ab initio values calculated for isolated molecules.     

Davidson-type corrections for quasidegenerate states

Two new extensions of Davidson-type size-consistency collections to the case of quasidegenerate states are presented and applied to a simple model system in which the degree of quasidegeneracy can be continuously varied. The eight-electron model studied is a minimum basis set model involving eight hydrogen atoms in various spatial arrangements. The results are compared with the full CI energies as well as with those obtained with the CI-D, MRCI-D, coupled-pair, and linear coupled-pair methods. Two extensions of the Davidson correction recently devised by Paldus are also employed. The results indicate that all the Davidson-type corrections yield reliable correlation energies in the case of strong quasidegeneracies.     

Accuracy of first-order wavefunctions for ten-electron atomic systems

It is demonstrated that for Ne-like systems, the zeroth-plus-first-order wavefunctions, obtained within Rayleigh—Schrödinger perturbation theory based on H₀ = H_HF, are of the same accuracy as variational wavefunctions obtained in CI calculations using very extensive sets of singly and doubly excited configurations. Variational correlation energies for Na⁺, Mg²⁺ and Ar⁸⁺ are reported for the first time.     

Equation de Karplus et l'Hybridation du Carbone. Correlation de la Constante de Couplage Vicinale 3J(Hi,Hj) et la Somme de Constantes de Couplages 1J(C,H)

The vicinal coupling constant ¹H? ¹H exhibits a marked hybridization dependence. The coupling constants ¹³C? ¹H could be used to correlate the Karplus type equation for calculation of ³J(Hi, Hj). The correction term to this equation is proposed.     

Ultra-thin Ag layers on low-index faces of Cu and Ni

The atomic structure and mechanism of growth, thermal desorption and dissolution of ultra-thin silver layers deposited in ultra-high vacuum on low-index faces of copper and nickel crystals were investigated with the use of AES, LEED, directional Auger (DAES) and elastic (DEPES) electron spectroscopies, and isothermal desorption. On (111) and (001) faces of copper and nickel the growth of (111) oriented silver islands was observed with epitaxial relations different for particular faces, while for (011) faces a parallel epitaxy occured for the first silver layer. Different mechanisms of growth (Frank — van der Merwe, Stranski — Krastanov, and duolayer) were found for particular substrates using the analysis of Auger peak kinetics basea on comparison of the substrate Auger peak height at the beginning of adsorption and at the first and second breaks of its kinetics. Annealing of the deposited layers leads to dissolution of silver in the copper substrate and to its evaporation from the nickel substrate. Binding energy of silver atoms in the first and second layers of silver on the (001) nickel face was determined using isothermal desorption kinetics.