Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.

Interactions of an anionic surfactant with poly(oxyalkylene) copolymers in aqueous solution

The interactions of sodium dodecyl sulfate (SDS) with poly(ethylene oxide)/poly(alkylene oxide) (E/A) block copolymers are explored in this study: With respect to the specific compositional characteristics of the copolymer, introduction of SDS can induce fundamentally different effects to the self-assembly behavior of E/A copolymer solutions. In the case of the E18B10-SDS system (E = poly(ethylene oxide) and B = poly(butylene oxide)) development of large surfactant-polymer aggregates was observed. In the case of B20E610-SDS, B12E227B12-SDS, E40B10E40-SDS, E19P43E19-SDS (P = poly(propylene oxide)), the formation of smaller particles compared to pure polymeric micelles points to micellar suppression induced by the ionic surfactant. This effect can be ascribed to a physical binding between the hydrophobic block of unassociated macromolecules and the non-polar tail of the surfactant. Analysis of critical micelle concentrations (cmc*) of polymer-surfactant aqueous solutions within the framework of regular solution theory for binary surfactants revealed negative deviations from ideal behavior for E40B10E40-SDS and E19P43E19-SDS, but positive deviations for E18B10-SDS. Ultrasonic studies performed for the E19P43E19-SDS system enabled the identification of three distinct regions, corresponding to three main steps of the complexation; SDS absorption to the hydrophobic backbone of polymer, development of polymer-surfactant complexes and gradual breakdown of the mixed aggregates. (C) 2008 Elsevier Inc. All rights reserved.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Stabilizing swarm intelligence search via positive feedback resource allocation

A novel Swarm Intelligence method for best-fit search, Stochastic Diffusion Search, is presented capable of rapid location of the optimal solution in the search space. Population based search mechanisms employed by Swarm Intelligence methods can suffer lack of convergence resulting in ill defined stopping criteria and loss of the best solution. Conversely, as a result of its resource allocation mechanism, the solutions SDS discovers enjoy excellent stability.

Overseas trained teachers: part of a problem or part of a solution?

Overseas trained teachers (OTTs) have grown in numbers during the past decade, particularly in London and the South East of England. In this recruitment explosion many OTTs have experienced difficulties. In professional literature as well as press coverage OTTs often become part of a deficit discourse. A small-scale pilot investigation of OTT experience has begun to suggest why OTTs have been successful as well as the principal challenges they have faced. An important factor in their success was felt to be the quality of support in school from others on the staff. Major challenges included the complexity of the primary curriculum. The argument that globalisation leads to brain-drain may be exaggerated. Suggestions for further research are made, which might indicate the positive benefits OTTs can bring to a school.