A hierarchy of coupled maps

A large number of logistic maps are coupled together as a mathematical metaphor for complex natural systems with hierarchical organization. The elementary maps are first collected into globally coupled lattices. These lattices are then coupled together in a hierarchical way to form a system with many degrees of freedom. We summarize the behavior of the individual blocks, and then explore the dynamics of the hierarchy. We offer some ideas that guide our understanding of this type of system. (c) 2002 American Institute of Physics.     

Towards the nonstick egg: designing fluorous proteins

Anyone who has made scrambled eggs will have had cause to praise the properties of Teflon. Teflon's highly chemically inert and nonstick nature derives from the perfluorinated polymer polytetrafluoroethylene. Perfluorocarbons have unique and valuable physical properties not found in nature. By incorporating fluorine into proteins, it might be possible to produce biological molecules with novel and useful properties.     

Diastereofacial selectivity in some 4‐substituted (X) 2‐adamantyl derivatives: electronic versus steric effects

π‐Facial selectivity data for the reduction and methylation of some 4^ax‐substituted (X) 2‐adamantanones ( 3 , Y = O) as well as the nucleophilic trapping of secondary and tertiary 4^ax‐substituted (X)‐2‐adamantyl cations ( 4 ; R = H and CH₃, respectively) and the 4‐methylene‐2‐adamantyl radical ( 8 ) are presented. The pronounced anti‐face selectivities observed for ( 3 , Y = O and 4 , R = CH₃) emphasize the importance of the steric factor as expected for systems with a strong steric bias. However, the dominant syn‐face capture of 4 (R = H) was completely unexpected and highlights a subtle interplay between steric and electronic effects. Finally, the very high anti‐face stereoselectivity for the trapping of ( 8 ) with the trimethylstannyl anion (Me₃Sn^?) is rationalized in terms of an electrostatic effect overwhelming the steric factor. Copyright © 2007 John Wiley & Sons, Ltd.     

Rates and mechanisms of the intermolecular cation-exchange reactions of sodium tetraphenylboron with sodium–nitrobenzene and with sodium–p-nitrobenzonitrile

The rates of the exchange of sodium ions between sodium tetraphenylborate and sodium–nitrobenzene or sodium–p-nitrobenzonitrile were measured from analysis of the line broadening effect on the ESR spectra off the paramagnetic ion pairs. The rate is significantly lower for the substituted nitro compound, and it is suggested that this reflects a difference in mechanism for the two systems.     

Taxol® (Paclitaxel)

Taxol® (paclitaxel) has been hailed by many as the most promising new cancer treatment in two decades. The FDA requires that paclitaxel intended for human consumption be obtained only from the bark ofTaxus brevifolia, the Pacific yew. As this may become increasingly uneconomical, new strategies must be explored to ensure the continued availability of taxol and related molecules. This article examines the planning that must be engaged in and the contingencies that must be prepared for in this changing arena.     

Gel permeation chromatographic studies of the degradation of polyethylene with fuming nitric acid. I. Single crystals

This paper describes the application of gel permeation chromatography to the morphology of polymer single crystals. Various types of single crystals of polyethylene were etched with fuming nitric acid, and the molecular weight distributions of the degraded fragments determined. The crystal preparations studied were monolayer crystals grown from xylene solution at 85°C and multilayer crystals grown at 84°C and 70°C. In all cases peaks in the molecular weight distribution were observed corresponding to single and double transverses of the molecular chains through the lamellae. By using the chromatograph calibration described in a previous paper, the position of these peaks were compared and correlated with previous estimates of lamellar thickness from low-angle x-ray measurements. The relative positions of the peaks provide information regarding the nature of the fold surface. The results are found to be consistent with a model in which the majority of the molecules are tightly folded.     

Partitions and sums of integers with repetition

A partition of N is called “admissible” provided some cell has arbitrarily long arithmetic progressions of even integers in a fixed increment. The principal result is that the statement “Whenever {A_i}_{i < r} is an admissible partition of N, there are some i < r and some sequence 〈x_n〉_{n < ω} of distinct members of N such that x_n + x_m?A_i whenever {m, n} ? ω″ is true when r = 2 and false when r ? 3.