X-Ray Crystallographic Structure of the Cyclic Di-amino Acid Peptide: <Emphasis Type="Italic">N,N</Emphasis>′-Diacetyl-cyclo(Gly-Gly)

Abstract  

The cyclic di-amino acid peptide N,N′-diacetyl-cyclo(Gly-Gly), C₈H₁₀N₂O₄, crystallizes in the triclinic space group P[`1] P\bar{1} with unit cell parameters a = 9.4855(4) ?, b = 10.0250(3) ?, c = 10.0763(4) ?, α = 73.682(2)°, β = 82.816(2)°, γ = 81.733(2)°, V = 906.40(6) ?<sup>3</sup>, Z = 4 (2 molecules, A and B, per asymmetric unit), D<sub>c</sub> = 1.452 g cm<sup>−3</sup> and linear absorption coefficient 0.118 mm<sup>−1</sup>. The crystal structure determination was carried out with MoKα X-ray data measured at 120(2) K. In the final refinement cycle the data/restraints/parameter ratios were 4124/0/258 and goodness-of-fit on F<sup>2</sup> = 1.0008. Final R indices for [I > 2σ(I)] were R<sub>1</sub> = 0.0501, wR<sub>2</sub> = 0.1007 and R indices (all data) R<sub>1</sub> = 0.0864, wR<sub>2</sub> = 0.11180. The largest electron density difference peak and hole were 0.241 and −0.232 e ?<sup>−3</sup>, respectively. The DKP rings in both molecules A and B have boat conformations with pseudo mm2 (C<sub>2v</sub>) symmetry if the N atoms and CH<sub>2</sub> groups are considered identical. In each case, the prow and stern of the boat are the α-carbons C(3) and C(6). The overall molecular symmetry of molecules A and B is approximately C<sub>2</sub> with the twofold symmetry axis of the DKP boat being maintained through the centre of the DKP ring. Details of the molecular geometry are compared with that of the parent compound cyclo(Gly-Gly) in which the DKP ring is planar with exact symmetry [`1] \bar{1} (C_i).     

Template-directed intramolecular C-glycosidation. cation-mediated synthesis of ketooxetanes from thioglycosides

Bicyclic ketooxetanes may be assembled using cation-mediated cyclisation reactions of thioglycosides possessing silyl enol ether-containing side-chains.     

On Two Squares of Opposition: the Leśniewski’s Style Formalization of Synthetic Propositions

In the paper we build up the ontology of Le?niewski’s type for formalizing synthetic propositions. We claim that for these propositions an unconventional square of opposition holds, where a, i are contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a, e (resp. i, o) are said to stand in the subalternation. Further, we construct a non-Archimedean extension of Boolean algebra and show that in this algebra just two squares of opposition are formalized: conventional and the square that we invented. As a result, we can claim that there are only two basic squares of opposition. All basic constructions of the paper (the new square of opposition, the formalization of synthetic propositions within ontology of Le?niewski’s type, the non-Archimedean explanation of square of opposition) are introduced for the first time.     

The Homogeneous Geometries of Real Hyperbolic Space

We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and Vanhecke, of the corresponding homogeneous tensors. We use our analysis to show that the moduli space of homogeneous structures on real hyperbolic space has two connected components.