Uniform persistence for population interaction models with time delay

In this paper uniform persistence is establised for kolmogorov type Prey‐Predator and competion models with per capitals ent growth rates that are dependent on time‐lagged population densities.     

Single‐pulse pulsed laser polymerization–electron paramagnetic resonance investigations into the termination kinetics of n‐butyl acrylate macromonomers

The termination of model mid‐chain radicals (MCRs), which mimic radicals that occur in acrylate polymerization over a broad range of reaction conditions, has been studied by single‐pulse pulsed laser polymerization (SP‐PLP) in conjunction with electron paramagnetic resonance spectroscopy. The model radicals were generated by initiator‐fragment addition to acrylic macromonomers that were preformed prior to the kinetic experiments, thus enabling separation of termination from the propagation reaction, for these model radicals propagate sparingly, if at all, on the timescale of SP‐PLP experiments. Termination rate coefficients of the MCRs were determined in the temperature range of 0–60°C in acetonitrile and butyl propionate solution as well as in bulk macromonomer over the range of 0–100 °C. Termination rate coefficients slightly below those of the corresponding secondary radicals were deduced, demonstrating the relatively high termination activity of this species, even when undergoing MCR–MCR termination. For chain length of 10, a reduction by a factor of 6 is observed. Unusually high activation energies were found for the termination rate coefficient in these systems, with 35 kJ mol^?1 being determined for bulk macromonomer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Small embeddings for partial 5‐cycle systems

It has been conjectured that any partial 5‐cycle system of order u can be embedded in a 5‐cycle system of order v whenever v ≥ 3 u/ 2+1 and v ≡ 1 , 5 (mod 10) . The smallest known embeddings for any partial 5‐cycle system of order u is 10 u +5 . In this paper we significantly improve this result by proving that for any partial 5‐cycle system of order u ≥ 255 , there exists a 5‐cycle system of order at most (9 u +146) / 4 into which the partial 5‐cycle system of order u can be embedded. © 2011 Wiley Periodicals, Inc. J Combin Designs     

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.