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In this note, we introduce a multi-parameter quantized enveloping algebra U q,Q (g) associated with an arbitrary symmetrizable Kac-Moody Lie algebra g. Here Q = (q ij ) denotes a square matrix of degree rank g whose entries are parameters satisfying q ii = 1, q ii q ji = 1. If we put all q ij equal to 1, a quotient of U q,Q (g) turns out to be the Drinfeld-Jimbo quantized enveloping algebra U q (g) [1,2]. Recently, Takeuchi [6] introduced two-parameter quantized enveloping algebras U α,s and U’ α,β associated with g[(n) and 𝔰[(n), respectively. The Hopf algebra U’ α,s can be obtained as a special case of U q,Q (𝔰[(n)) by setting \(q = \sqrt {a\beta } ,{q_{ii + 1}} = \sqrt {\alpha {\beta ^{ - 1}}} ,{q_{ij}} = 1for\left| {j - i} \right| > 1\).

The effect of the molecular orientation on the molecular electronic structure is studied on the Cu-phthalocyanine∕graphite system via film thickness dependences of metastable-atom electron spectra and ultraviolet photoelectron spectra. We observed a decrease in the vacuum-level position and a corresponding band-bending-like shift in the highest occupied state only for thick films where the molecular tilt angle increases gradually with the film thickness. These shifts are explained by electric dipoles produced in the film by a gradient of the intermolecular electronic interaction along the surface normal due to the continuous increase in the molecular tilt angle. The result indicates that the change in the molecular orientation is an important origin of the band-bending-like shift in the molecular electronic states even if the molecule has no permanent electric dipole.

In this paper, we construct an explicit basis of the quantized universal enveloping algebra Uq(slN + 1(C)). Let A = (%-)i

In this paper, we classify the irreducible projective modules, or, equivalently (see, e.g., [6]), the irreducible principal indecomposable modules, of a non-semisimple Hecke algebra H( W, [*), {E @, of a finite Coxeter group W. Let ( W, 3) be a finite Coxeter system [2], and t an indeterminate, q = t*. We denote by H( W, q) the generic Hecke-Iwaho~ algebra [9,2, lo]. This means that H( W, q) is the C(t)-algebra with the basis (T(w)/ WE W> and the multiplication defined by

Photolysis of 1, 2, 3, 4-tetrahydro-6, 7, 4', 5'-tetramethoxyisoquinoline-1-spiro-2'-indan-1'-one (II) gave 5, 6-dihydro-2, 3, 10, 11-tetramethoxyberbinium salt (IV) which was further converted into 2, 3, 10, 11-tetramethoxyberbine (VI) by treatment with sodium borohydride. In the same reaction sequence, 1, 2, 3, 4-tetrahydro-6, 7, 5', 6'-tetramethoxyisoquinoline-1-spiro-2'-indan-1'-one (IX) was transformed into xylopinine (VII)

Soit #7B-G une algebre Lie semi simple complexe et soit Uq#7B-G l'algebre de Hopf associee avec un parametre complexe non nul q. On donne une base lineaire explicite de Uq#7B-G quand #7B-G=sl N+1 (C)

Low-energy-electron transmission (LEET) spectra were measured for graphite using electron energies below 30 eV. The observed LEET spectra have broadened square-wave-like features, and comparison with the conduction-band density of states above the vacuum level measured by ultraviolet photoemission and inverse photoemission spectroscopies indicated that the conduction-band density of states was not observed in the LEET spectra except band gaps. It is concluded that band gaps are more strongly reflected in LEET spectra than other features in the density-of-states. It is expected that electron-interference effects along the surface normal dominate LEET features, even for a very thick sample, where the energy dependence of electron-transmission probability through a one-dimensional periodic potential along the surface normal does not reflect the variation of the density of states (except band gaps).

Rhoeadine (I) and alpinigenine (III) have been synthesised by a route involving the skeletal rearrangement of 1,2,3,4-tetrahydro-2-methyl-4′,5′,6,7-bismethylenedioxyisoquinoline-1-spiro-2′-indan-1′-ol (VII) into 5,6,7,7a-tetrahydro-2,3:10,11-bismethylenedioxy-7-methylbenz[d]indeno[1,2-b]azepine (VIII) by treatment with methanesulphonyl chloride and triethylamine. Oxidation of the indenoazepine (VIII) with osmium tetroxide gave 5,6,7,7a,12,12a-hexahydro-2,3:10,11-bismethylenedioxy-7-methylbenz[d]indeno[1,2-b]azepine-12,12a-diol (X), which was converted into (±)-rhoeagenine diol (XII) by treatment with sodium periodate followed by sodium borohydride. From 1,2,3,4-tetrahydro-2-methyl-4′,5′,6,7-tetramethoxy-1-spiro-2′-indan-1′-ol (XVII), (±)-alpinigenine diol (XXI) was synthesised. Oxidation of the diol (XXI) with manganese dioxide furnished (±)-alpinigenine (III).

Rhoeadine, an alkaloid from a variety of species of the genus Papaver, Papaveraceae, has been synthesised.