The asymptotic enumeration of rooted convex polyhedra

An asymptotic formula is obtained for the number of rooted c-nets with m vertices and n edges as m, n → ∞ with $\text{1}\text{2}\text{+ ε <}\text{n}\text{m}\text{< 2 ? ε}$ for some ε > 0.     

Additionsverbindungen zwischen Antimon(III)-Halogeniden und 1,4-Dithiacycloheptan

Addition Compounds between Antimony(III)-Halides and 1,4-Dithiacycloheptane SbCl₃, SbBr₃, and SbI₃ do form the addition compounds SbCl₃ · 1,4-Dithiacycloheptane, SbBr₃ · 1,4-Dithiaheptane and 2 SbI₃ · 1,4-Dithiacycloheptane from benzene solutions. The new compounds are only stable in the solid form. FIR spectra of the SbCl₃ and SbBr₃ complexes are recorded as well as the X-ray structure of the SbCl₃ compound.     

The Photorearrangements of a Naphthobarrelene-like System. Dependence on excited-state spin multiplicity and electronic configuration,and evidence for biradical intermediates. Preliminary communication

8-Benzoyl-9-deuterio-naphtho [de-2.3.4]bicyclo [3.2.2]nona-2,6,8-triene ( 1 ) rearranged quantitatively in a photochemical di-π-methane-type process to 2-, 6-, and 9-deuteriated 1-benzoyl-naphtho [de-2.3.4]tricyclo [4.3.0.0^2,9]nona-2, 6-diene ( 8a–c ). The phenylhydroxymethyl analogue 2 underwent a similar regioselective rearrangement to 9a–c . The rearrangement 1 → 8a–c is proposed to proceed along three reaction paths evolving from two primary photochemical processes of naphthylvinyl and vinyl-vinyl bonding ( 1 → 3 + 6 ). Evidence for a competition between several paths and involvement of biradical intermediates derives from changes in the isotopomeric composition with temperature, and from laser flash detection (λ_exc 353 nm) of a transient. The dependence of the quantum yield for product formation from 1 on excitation wavelength and sensitizer triplet energy leads to the conclusion that reaction to the primary biradicals occurs directly from the S₁ (n, π*) and T₂ (n, π* ) states, and that reaction from T₁ (π, π*) and from S₂ (π, π*) proceed either directly or via T₂.