Surface photochemistry: The photo-chlorination of aromatic hydrocarbons with ferric chloride on alumina

Irradiation of a number of aromatic hydrocarbons adsorbed on alumina in the presence of ferric chloride leads to monochlorination.     

Carbon-13 NMR studies of the biologically active nor-diterpenoid dilactones from Podocarpus plants

Carbon-13 NMR signals of the biologically active norditerpenoid dilactones from Podocarpus plants were fully assigned by using selective ¹H decoupling, coupling constants (²J_CH), spin-lattice relaxation times (T₁) and correlation of the spectra of more than thirty dilactone congeners. The spectra of five nagilactones, B, C, D, E and F, which constitute representative members of three major structural types of the dilactones: (A) 8:14, 9:11-dienolide (α-pyrone) type, (B) 7α:8α-epoxy-9:11-enolide type, and (C) 7:8,9:11-dienolide type, were extensively analysed. Some characteristic steric interactions for the substituents on the ring system can be demonstrated from the spectral properties.     

Zeta functions of<Emphasis Type="Italic">q</Emphasis>-perfect numbers

We introduce a notion ofq-analogue of the perfect numbers. We also define a new zeta function which we call a zeta function ofq-perfect numbers. In this paper, the properties of theq-perfect numbers and the zeta functions are studied. Especially, we determine theq-perfect numbers whenq is a root of unity.     

Radical deoxygenation of hydroxyl groups via phosphites

A highly efficient, two-step sequence method for the deoxygenation of hydroxyl groups has been developed. The method involves the preparation of the 2-(2-iodophenyl)ethyl methyl phosphite derivative of an alcohol using methyl dichlorophosphite and 2-(2-iodophenyl)ethanol. Treatment of the phosphite intermediate with (n-Bu)3SnH/AIBN in refluxing benzene cleanly produces the deoxygenation product of the original alcohol.     

On a p-Local Geometry Associated with a Complex of Non-Trivial p-Subgroups

Let D be a complex of non-trivial p-subgroups of a finite groupG, closed under G-conjugation. In this paper, a p-local geometry^p(G; D) is introduced for G associated with the complex D. Thehomotopy equivalence between ^p(G; D) and D is also studied.2000 Mathematics Subject Classification 20E15, 51E24.     

Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Luminescent Polymer Consisting of 9,12‐Linked o‐Carborane

The synthesis of novel luminescent polymer containing p‐phenylene‐ethynylene and 9,12‐linked o‐carborane units alternately in the main chain is reported. The obtained polymer exhibits intense blue photoluminescence, providing the first insights into the optical properties of a 9,12‐disubstituted o‐carborane dye.  π‐Conjugated substituent at 9 and/or 12‐positions in o‐carborane is electrically independent, and both the HOMO and the LUMO levels slightly increase, whereas LUMO of the π‐conjugated substituent at 1 and/or 2‐positions in o‐carborane decrease.  Thus, it is deduced that polymers consisting of the 9,12‐linked o‐carborane unit are able to be applied as light‐emitting materials.