Free group functors

We construct group functors whose Lie algebras are free.     

The polyhedral product functor: A method of decomposition for moment-angle complexes, arrangements and related spaces

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. The geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of Goresky-MacPherson concerning complements of certain subspace arrangements, as well as Davis-Januszkiewicz and Buchstaber-Panov concerning moment-angle complexes. Since the stable decompositions here are geometric, they provide corresponding homological decompositions for generalized moment-angle complexes for any homology theory.     

Aqueous Cobalt(II) ion as a Nitrogen-14 Chemical Shift Reagent and Its Application to the Determination of Betaine,Glycerophosphorylcholine and Ammonium Ion

Aqueous cobalt(II) ion is shown to be an effective chemical shift reagent for nitrogen-14 nuclear magnetic resonance spectroscopy. Addition of an 8 fold excess of cobalt (II) ion to a mixture of betaine, glycerophosphorylcholine and ammonium ion results in baseline resolution of the three components. The chemical shift of each component is a function of cobalt concentration up to a molar ratio of about 4:1 after which, the shifts     

Physical Image vs. Structure Relation. Part 3 [1]. Basic Properties and Protonation Mechanism of Some Tetraaza Macrocyclic Ligands

The protonation constants, log K, for 1,4,7,11-tetraazacyclotetradecane (isocyclam, 2), 1-(2-aminoethyl)-1,4,8,11-tetraazacyclotetradecane (scorpiand, 3), 5,12-dimethyl-1,4,8,11-tetraazacyclotetradecane (Me₂cyclam, 4) and 5,5,7,12,14,14-hexamethyl-1,4,8,11- tetraazacyclotetradecane (Me₆cyclam, 5) were determined pH-metrically. Attempts of correlation of the calculated enthalpy of protonation in the gas phase (AM1 method) with experimental values of the protonation constants for ligands 1, 2, 4–7 were done 1,4,8,11-tetraazacyclotetradecane, cyclam, 1; 1,4,7,10-tetraazacyclotetradecane, cyclen, 6; 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane, (N-Me)₄cyclam, 7. Extensive NMR pH-titrations, i.e., determination of pH vs. chemical shifts (¹H and/or ¹³C) plots, (_X = f(pH), allowed to suggest the most likely protonation schemes of all nitrogen atoms in the cyclic polyamines 1–3. The possibility of the formation-breaking of the intramolecular hydrogen bonds, as well as the change of conformation of these polybasic macrocycles during protonation-deprotonation steps, has been considered on the basis of the supplementary theoretical calculations (MMX/STO-3G study).     

On affine images of regular pentagons and pentagrams

In this paper we explore pentagons that are affine images of the regular pentagon and the regular pentagram. We obtain their characterizations in terms of two mild forms of regularity that deal with the notions of medians for a pentagon and the natural requirement that they are concurrent. Using these characterizations we show that there are various values involving the number 5 (thus related to the golden section) for which a careful selection of division points on appropriate segments determined by any pentagon will result in a pentagon that is the affine image of either a regular pentagon or a regular pentagram.