The generation and classification of tile-k-transitive tilings of the Euclidean plane,the sphere and the hyperbolic plane

Algorithms based on the theory of Delaney-Dress symbols are discussed that can be used to recursively produce all possible equivariant types of tile-k-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane, for any (reasonable)k. A number of results can be obtained using computer implementations of the algorithms.     

Every triangle-free planar graph has a planar upward drawing

A planar ordered set has a triangle-free, planar covering graph; on the other hand, there are nonplanar ordered sets whose covering graphs are planar. We show thatevery triangle-free planar graph has a planar upward drawing. This planar upward drawing can be constructed in time, polynomial in the number of vertices.Our results shed light on the apparently difficult problem, of long-standing, whether there is aneffective planarity-testing procedure for an ordered set.Supported in part by the Alexander von Humboldt Stiftung.Supported in part by the Deutsche Forschungsgemeinschaft.     

Etude des conditions d'accès au triazino-1,2,4-[4,5-b] indazole

1,2,4-Triazino[4,5-b]indazol-1(2H)one and its derivatives were prepared by transposition of 3-[2-(-1,3,4-oxadiazolyl)]indazole or by ring closure of indazole ethoxymethylidenehydrazides. The synthesis of 1,2,3,4-tetrahydro-l,2,4-triazino[4,5-b]indazole-1,4-dione was achieved by cyclising the N-carbethoxyhydrazide of indazole-3-carboxylic acid and the synthesis of 1,2,4-triazino-[4,5-b]indazol-4(3H)one was made by cyclising the N-carbethoxy-hydrazone of indazole-3-carboxaldehyde. The Oxydation of 1,2,4-triazino[4,5-b]indazole-l(2H)thione gave 1,2,4-triazino-[4,5-b]indazoles. Nmr spectral data are reported.     

Studies on the preparation and exchange reactions of 5-deuterated uracils

The mechanism of base catalyzed proton exchange at the 5-position of uracil and its N-methylated derivatives has been studied. These reactions proceed by addition — elimination across the 5,6-double bond when the 1-nitrogen is substituted with a methyl group, or with anchimeric assistance of the N-1 anion if the 1-position is unsubstituted. The base catalyzed hydrolyses of 1,3-dimethyluracil and 3-methyluracil also appear to proceed through hydrated intermediates. A facile method for an acid catalyzed preparation of 5-deuterated uracils is described as well as a simple and accurate method for analysis of deuterium content.     

Mechanism of the aromatic hydroxylation of thiophene by acid-catalyzed peracid oxidation

The oxidation of thiophene (1) with peracids in a strongly acidic environment yielded thiophen-2-one (4) as the product of an apparent direct hydroxylation of the thiophene aromatic ring together with the anticipated thiophene-S-oxide dimers, 2a,b, as the main products. Formation of the latter dimers can be rationalized in a straightforward manner by initial oxidation at the sulfur atom of thiophene (1) to yield thiophene-S-oxide followed by subsequent dimerization in a Diels-Alder type reaction. Trapping experiments in the presence of a competing dienophile indicated that thiophen-2-one (4) did not originate from the monomeric thiophene-S-oxide but was the product of an independent reaction pathway. The extent of thiophen-2-one (4) formation correlated with the acidity of the reaction medium and was suppressed in the presence of water, the latter presumably acting as a competing base. As evidenced by the use of 2,5-dideuterated thiophene (1-D), its mechanism of formation involved a 1,2-hydride shift, a feature commonly described in the peracid-mediated epoxidation of aromatic hydrocarbons and indicative for the occurrence of cationic intermediates. In agreement with all these observations we propose a mechanism involving initial protonation of thiophene followed by nucleophilic attack of the peracid in position 2 of the thiophene ring. Intramolecular epoxidation may lead to the formation of thiophene 2,3-epoxide as a highly reactive intermediate that then undergoes heterolytic ring opening and a 1,2-hydride shift to yield thiophen-2-one (4) after a final, acid-catalyzed, isomerization of the double bond.     

Atomic beam scattering from single crystal surfaces

Application of atom-scattering to a variety of surface problems is expanding rapidly, owing in large part to the extreme surface- sensitivity of this probe. Helium is particularly useful because of its low mass and chemical inertness. Beams with velocity spreads of less than one percent and wavelength of the order of one Angstrom can be formed by nozzle expansion.

The scattered flux from a clean, well-ordered crystal surface contains elastic and inelastic, coherent and incoherent, components. The coherent elastic component (i.e., the specular and diffracted beams) contains information about the crystallographic structure of the outer- most atomic layer of the crystal and about the interaction potential between the crystal and the scattered particle. The latter manifests itself in the form of resonances between the incoming free-particle state, and the two-dimensional Bloch states bound in the potential well at the surface. Elastic scattering theory has reached the point where the resonance signatures in the various diffracted beams can be predicted accurately.

Crystallographic information resides in the diffracted beam intensities. Theoretical interpretation is less well advanced, though some progress has been made with “hard-wall” models. Experimental studies of reconstructed surfaces and chemisorbed overlayers appear very promising.

In inelastic scattering, energy resolution has been achieved by both time-of-flight and diffraction methods. High-resolution studies on alkali halide surfaces have led to experimental determination of Rayleighwave dispersion relations over the full Brillouin zone. Preliminary results have also been obtained on some metals.     

3H-Indol-3-ols by a novel ring contraction

Treatment of α-hydroxy-α-phenyl-o-toluidide with phosphorus tribromide afforded a series of 4H-3,1-benzoxazines. These last, when reacted with potassium amide in liquid ammonia, ring contracted to 2,3-disubstituted 3H-indol-3-ols. The scope of this rearrangement was examined. The indolols on treatment with hot base were found to rearrange to indoxyls. Several of these as well as their N-alkylation products are described.     

Mild cleavage of methoxymethyl (MOM) ethers with trimethylsilyl bromide

Trimethylsilyl bromide is an effective reagent for the deprotection of methoxymethyl ethers under mild conditions.     

Mass spectral study of ring E of taraxasterol and compounds with similar ring substitution

The origin of the [M–69]⁺ and [M–111]⁺ signals in the mass spectrum of taraxasterol was studied through the use of C(18), (19), (21), (22) and/or (30) deuteriated derivatives. The generality of these signals for ring systems with an exocyclic methylene group and a methyl moiety on an adjacent carbon was verified with 2-methylmethylenecyclohexane, 1-methyl-2-methylene-trans-decalin, 1,10-dimethyl-2-methylene-trans-decalin and some of their deuteriated derivatives. The most plausible mechanism for the formation of the [M–69]⁺ ion appears to involve cleavage of both bonds allylic to the exocyclic methylene group with a 1,3-hydrogen transfer from the adjacent ring. Genesis of the [M–111]⁺ ion is more complicated but a five-membered allylic ion generated from ring D is proposed.