Almost maximal spaces

A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents.     

Synthesis and biological evaluation of 6-oxa-nor-tropane glycomimetics as glycosidase inhibitors

The preparation of polyhydroxylated 6-oxa-nor-tropane glycomimetics structurally related to the glycosidase inhibitor family of the calystegines is reported. The synthetic strategy involves the furanose→piperidine rearrangement of 5-deoxy-5-ureido-l-idose precursors, followed by intramolecular glycosylation involving the primary hydroxyl group. Inversion of the configuration at C-3 in the resulting 6-oxa-(+)-calystegine B₂ analogue allows accessing the elusive 3-epi-6-oxa-(+)-calystegine B₂ skeleton. Acid-catalyzed opening of the nor-tropane bicycle was observed, however, which could be avoided by careful neutralization of the reaction mixture. The inhibition results suggest that (+)-calystegine B₂ derivatives and the corresponding C-3 epimers can be seen as glucomimetics and galactomimetics, respectively, pointing to a 1-azasugar mode of action for this family of alkaloids.     

Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type

We consider a hyperbolic-parabolic singular perturbation problem for a quasilinear equation of Kirchhoff type, and obtain parameter-dependent time decay estimates of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation. For this purpose we show time decay estimates for hyperbolic-parabolic singular perturbation problem for linear equations with a time-dependent coefficient.     

A fiberwise analogue of the Borsuk-Ulam theorem for sphere bundles over a 2-cell complex II

We describe a finite complex B as I-trivial if there does not exist a Z₂-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP² is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0.     

2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Comparative kinetics of phospholipase A2 action on liposomes and monolayers of phosphatidylcholine spread at the air-water interface

A detailed kinetic model describing the surface transformation of spread liposomes along with their enzymatic hydrolysis was developed. The model was applied to the hydrolysis of the long-chain phosphatidylcholine generating reaction products which remain at the interface and to medium-chain substrates from which the products desorb rapidly into the bulk phase. The overall kinetic constants of the hydrolysis in liposomal systems were compared with those obtained with monolayers under barostatic conditions. The values of the interfacial Michaelis-Menten constant were estimated.     

Recent studies on phosphorus-bridging carbonyl derivatives: organophosphorus analogs of aldehydes and ketones

Reactions of disodium tetracarbonylferrate, Na₂Fe(CO)₄, with sterically hindered dialkylaminodichlorophosphines, R₂NPCl₂ (R₂N=diisopropylamino, dicyclohexylamino, and 2,2, 6, 6-tetramethylpiperidino) in diethyl ether lead to the air-stable phosphorus-bridging carbonyl derivatives (R₂NP)₂COFe₂(CO)₆ as the major products. The phosphorus-bridging carbonyl group in (i-Pr₂NP)₂COFe₂(CO)₆ has been found to undergo the following types of reactions: 1)Reduction, 2)Acylation, 3)Extrusion of the carbonyl group. The mechanisms of the reactions have been considered.This work was presented at the Workshop «The Modern Problems of Heteroorganic Chemistry» held on the ship «Nikolai Bauman» during the period May 8–13, 1993.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1858–1867, November, 1993.     

Synthesis of benzofurans via Pd-catalyzed oxidative cyclization of 2-allylphenols

Substituted 2-methylbenzofurans were obtained from 2-allylphenols via Pd²⁺-catalyzed oxidative cyclization using Cu(OAc)₂–LiCl as a reoxidant and wet DMF as a solvent.