Synthesis of 3-(2-Aryloxazolidin-3-yl)tropanes

We obtained 3-(2-aryloxazolidin-3-yl)tropanes by reaction of aromatic aldehydes with 3-[N-(2-hydroxyethyl)amino]tropane. We obtained 3-benzyloxazolidine-2-spiro-3'-(8'-carbethoxy)nortropane by reaction of benzylaminoethanol with 8-carbethoxynortropan-3-one.     

Acyclic and oriented chromatic numbers of graphs

The oriented chromatic number χ_o(G ^→) of an oriented graph G ^→ = (V, A) is the minimum number of vertices in an oriented graph H ^→ for which there exists a homomorphism of G ^→ to H ^→. The oriented chromatic number χ_o(G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the orientations of G. This paper discusses the relations between the oriented chromatic number and the acyclic chromatic number and some other parameters of a graph. We shall give a lower bound for χ_o(G) in terms of χ_a(G). An upper bound for χ_o(G) in terms of χ_a(G) was given by Raspaud and Sopena. We also give an upper bound for χ_o(G) in terms of the maximum degree of G. We shall show that this upper bound is not far from being optimal. © 1997 John Wiley & Sons, Inc.     

The Dimension of Interior Levels of the Boolean Lattice,II

Extending an old lemma by Dushnik, we establish the dimension d(3, k; n) of the containment order generated by the 3-element and k-element subsets of an n-element set for most k between and n.     

Photoinduced N-β-hydroxyalkylation of tropan derivatives

The photooxidation of tropan derivatives by ketones was studied; the targeting of the reaction to the N-CH₃ group with the formation of N-alkylation products and bis-tropan derivatives was demonstrated. The presence of two diastereomers in salts of N-alkyl derivatives of tropan was detected by PMR spectroscopy. An alternative method of synthesis of difficult-to-obtain amino alcohols was proposed.Scientific-Research Institute of Pharmacology, Russian Academy of Medical Sciences, Moscow 125315. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 179–183, February, 1995. Original article submitted September 5, 1994.     

Regio- and stereochemical features of the reactions of 1,2,5-trimethylpiperidin-4-one with chalcone

The reactions of N-substituted piperidin-4-ones with benzylideneacetophenone, resulting in the synthesis of a number of heterocyclic 1,5-dicarbonyl compounds, were studied. 1,2,5-Trimethylpiperidin-4-one enters into cascade-type chalcone addition accompanied by intramolecular aldol condensation giving rise to the 3-azabicyclo[3.3.1]nonane system. The conformations of the 1,5-dicarbonyl compounds and azabicyclononanes synthesized were determined; the regio- and stereochemical features of the reactions of 1,2,5-trimethylpiperidin-4-one with chalcone were studied.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2693–2697, December, 2004.     

Total colorings of planar graphs with large maximum degree

It is proved that a planar graph with maximum degree Δ ≥ 11 has total (vertex-edge) chromatic number $Delta; + 1. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 53–59, 1997