On discontinuity and tail behaviours of the integrated density of states for nested pre-fractals

We consider a general finitely ramified fractal set called a nested fractal which is determined byN number of similitudes. Basic properties of the integrated density of statesN (x) for the discrete Laplacian on the associated nested prefractal are investigated. In particulard N is shown to be purely discontinuous ifM, whereM is the number of branches of the inverse of the rational function involved in the spectral decimation method due to Rammal-Toulouse. Sierpinski gaskets and the modified Koch curve are special examples.     

Pressure dependence of the optical-absorption edge of AlN and graphite-type BN

Effect of pressure on the band gaps on AlN and graphite-type BN (g-BN) has been studied up to 2.7 GPa at room temperature by measuring the optical-absorption edge of single crystals of each substance pressurized in a sapphire-anvil cell. The direct band gap of AlN shifted towards higher energy at a rate of 49±1 meV/GPa, whereas in g-BN the pressure dependence of the band gap was −36±1 meV/GPa. The results are compared with existing first-principles calculations.     

γ-linolenic acid production by microalgae

The production of γ-linolenic acid from algae in fresh and marine water was investigated. WhenSpirulina platensis was left in the dark condition, it contained about one and a half times γ-linolenic acid compared with conventionalSpirulina platensis. Marine microalga,Chlorella sp. NKG 042401 contained about 10% of γ-linolenic acid. The highest γ-linolenic acid content was obtained when this alga was cultured under the radiation of around 100 μEinstein/m²/s.     

Studies on hetero-cage compounds—VI : Transannular cyclizations in pentacyclo[6.2.1.0.2,70.4,1005,9]undecan-3,6-dione system

Several 4-oxa- and -aza-bird-cage compounds were prepared by transannular cyclizations of pentacyclo[6.2.1.0.^2,70.^4,100^5,9]undecan-3,6-dione (3). Diol derivatives of 3 cyclized to afford the corresponding 4-oxa-bird-cage derivatives such as 9, 16a and 16b. The corresponding 3-keto-6-ol derivatives (6, 10a and 10b) did not cyclize transannularly, while 3-imino-6-ol, 3-keto-6-amino, and 3- imino-6-amino type derivatives cyclized to afford 3-substituted 4-oxa- and -aza-bidr-cage compounds such as 12, 14 and 18. The transannular cyclization reactivity in the 3 system has been compared with that in the bicyclo[3.3.1]nona-3,7-dione system (1).     

A new electroreductive annellation useful in synthesis of alkaloids

Controlled potential reduction of immonium salts in the presence of bromo esters such as o-bromomethyl benzoates has afforded annellated products. The method is applicable to the synthesis of berbine alkaloids.     

Baryon duality solutions with the harmonic-oscillator spectrum and the amplitude signs in πN→πΔ

By constructing exact exchange-degenerate solutions of baryons with the harmonic-oscillator spectrum for a set of reactions MB→M′B′, MB → M′D′ and MD → M′D′, we investigate the duality constraints on the amplitude signs in MB → M′D′. It is shown that the amplitude signs determined by duality are consistent with those predicted by the extended version of SU(6)_W symmetry with the universal dominance of the ΔL_Z = 0 or ΔL_Z = ±1 amplitude in the mesonic transitions of the baryons.