Crystal structure of 2-cyano-2-[3-cyano-4-diethyl-amino-1H-quinolylidene-2]-N,N-diethylacetamide,C21H25N5O

Crystals of the title compound, C₂₁H₂₅N₅O, are monoclinic: space groupP2₁/c,a = 12·680,b = 11·844,c = 13·550 Å, = 104·13 °,Z = 4. The structure was determined with CuK diffractometer data by direct methods and was refined by full-matrix least-squares methods toR = 0·076 for 2340 observed reflexions. All non-methyl hydrogen atom positions were determined. The hydrogen atom which is bonded to the ring nitrogen atom forms an intramolecular hydrogen bond with the carbonyl oxygen atom. Neither the six-membered homocyclic ring nor the six-membered heterocyclic ring is exactly planar. The molecular geometry and the detailed bond distances suggest that electron delocalization into the side chains is stabilized by the intramolecular hydrogen bond. This molecular structure determination has aided in the formulation of a reaction path for the 21 addition of cyano ynamine to phenylisocyanate.We thank Dr. M. E. Kuehne for suggesting the problem and for crystals, the National Research Council of Canada for financial support, and the University of British Columbia Computing Centre for assistance.     

Crystal structure of 2-N,N-diethylamino-1-carbomethoxy-2a,8a-dihydro-2a-methoxycyclobuta [b]naphthalene-3,8-dione,C19H21NO5

Crystals of the title compound, C₁₉H₂₁NO₅, are monoclinic, space groupP2₁/c,a = 7·706,b = 14·470,c = 16·836 Å, = 106·45°,Z = 4. The structure was determined with CuK diffractometer data by symbolic addition procedures and Fourier syntheses, and was refined by full-matrix least-squares methods toR = 0·079 for 2192 observed reflexions. All non-methyl hydrogen atom positions were determined. The non-aromatic six-membered ring has aboat conformation. The four-membered ring, which iscis-fused to the six-membered ring, is slightly folded, and the planar amino and carboxyl groups lie almost in the four-membered ring plane. This geometry, and the detailed bond distances suggest electron delocalization, which may make the compound a useful intermediate in the synthesis of a stable cyclobutadiene system.We thank Dr M. E. Kuehne for suggesting the problem and for crystals, the National Research Council of Canada for financial support, and the University of British Columbia Computing Centre for assistance.     

Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.     

Threshold tolerance graphs

In this paper, we introduce a class of graphs that generalize threshold graphs by introducing threshold tolerances. Several characterizations of these graphs are presented, one of which leads to a polynomial-time recognition algorithm. It is also shown that the complements of these graphs contain interval graphs and threshold graphs, and are contained in the subclass of chordal graphs called strongly chordal graphs, and in the class of interval tolerance graphs.