Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

Can increasing the viscosity of formulations be used to reduce the human skin penetration of the sunscreen oxybenzone?

The effect of adding thickening agents on the penetration of a sunscreen benzophenone-3 through epidermal and a high-density polyethylene membrane was studied using both very thick (infinite dose) and thin tin use) applications. Contradictory results were obtained. Thickening agents retard skin penetration, in a manner consistent with a diffusional resistance in the formulation, when applied as an infinite dose. In contrast, when applied as in thin (in use) doses, thickening agents promote penetration, most likely through greater stratum corneum diffusivity arising from an enhanced hydration by the thicker formulations. The two key implications from this work are (i) a recognition of the danger in the potential extrapolation of infinite dosing to in use situations, and (ii) to recognize that thicker formulations may sometimes enhance the penetration of other topical agents when applied in use.

Conversion of glucosamine to galactosamine and allosamine derivatives: Control of inversions of stereochemistry at C-3 and C-4

The reactions of sodium benzoate with a series of trimesylates derived from glucosamine have been examined in an attempt to gain facile access to galactosamine analogues. Trimesylate 17, in which the amino group was protected as a phthalimide, underwent double displacement at positions 4 and 6 to give the dibenzoate 18 with the desired galactosamine configuration. In contrast, trimesylates 21 and 27, in which the amino groups were protected as acetamides, unexpectedly underwent double displacement at positions 3 and 6, giving products 22 and 28, respectively, with allosamine configurations.

A novel method for solid-phase synthesis of oligosaccharides using the N-1-(4,4-dimethyl-2,6-dioxocyclohexylidene)ethyl (Dde) linker

The application of the N-1-(4,4-dimethyl-2,6-dioxocyclohexylidene)ethyl (Dde) linker for the solid-phase synthesis of oligosaccharides is described. The oligosaccharide products can be cleaved from the resin by hydrazine, ammonia or primary amines, but the linker is stable under the conditions of oligosaccharide synthesis. The first sugar can be attached to the resin linker via a vinylogous amide bond, or by ether linkage using a p-aminobenzyl alcohol converter. (C) 2001 Elsevier Science Ltd. All rights reserved.