On the Hopf bifurcation in control systems with a bounded nonlinearity asymptotically homogeneous at infinity

The paper studies existence, uniqueness, and stability of large-amplitude periodic cycles arising in Hopf bifurcation at infinity of autonomous control systems with bounded nonlinear feedback. We consider systems with functional nonlinearities of Landesman-Lazer type and a class of systems with hysteresis nonlinearities. The method is based on the technique of parameter functionalization and methods of monotone concave and convex operators. (C) 2001 Academic Press.

Tide-induced water table fluctuations in coastal aquifers bounded by rhythmic shorelines

Previous studies on tidal water table dynamics in unconfined coastal aquifers have focused on the inland propagation of oceanic tides in the cross-shore direction based on the assumption of a straight coastline. Here, two-dimensional analytical solutions are derived to study the effects of rhythmic coastlines on tidal water table fluctuations. The computational results demonstrate that the alongshore variations of the coastline can affect the water table behavior significantly, especially in areas near the centers of the headland and embayment. With the coastline shape effects ignored, traditional analytical solutions may lead to large errors in predicting coastal water table fluctuations or in estimating the aquifer's properties based on these signals. The conditions under which the coastline shape needs to be considered are derived from the new analytical solution.

Existence of solutions for p(x)-Laplacian problems on a bounded domain

In this paper we study the following p(x)-Laplacian problem: -div(a(x)&VERBAR;&DEL; u&VERBAR;(p(x)-2)&DEL; u)+b(x)&VERBAR; u&VERBAR;(p(x)-2)u = f(x, u), x ε &UOmega;, u = 0, on &PARTIAL; &UOmega;, where 1< p(1) &LE; p(x) &LE; p(2) < n, &UOmega; &SUB; R-n is a bounded domain and applying the mountain pass theorem we obtain the existence of solutions in W-0(1,p(x)) for the p(x)-Laplacian problems in the superlinear and sublinear cases. © 2004 Elsevier Inc. All rights reserved.

Cost-benefit analyses for your group and yourself: The rationality of decision-making in conflict

Two studies in the context of English-French relations in Québec suggest that individuals who strongly identify with a group derive the individual-level costs and benefits that drive expectancy-value processes (rational decision-making) from group-level costs and benefits. In Study 1, high identifiers linked group- and individual-level outcomes of conflict choices whereas low identifiers did not. Group-level expectancy-value processes, in Study 2, mediated the relationship between social identity and perceptions that collective action benefits the individual actor and between social identity and intentions to act. These findings suggest the rational underpinnings of identity-driven political behavior, a relationship sometimes obscured in intergroup theory that focuses on cognitive processes of self-stereotyping. But the results also challenge the view that individuals' cost-benefit analyses are independent of identity processes. The findings suggest the importance of modeling the relationship of group and individual levels of expectancy-value processes as both hierarchical and contingent on social identity processes

Grumbling, voting, demonstrating, and rioting: ''Rationality'' and decision-making in intergroup conflict

An individual faced with intergroup conflict chooses A from a vast array of possible actions, ranging from grumbling among ingroup friends to voting and demonstrating to rioting and revolution. The present paper conceptualises these intergroup choices as rationally shaped by perceptions of the benefits and costs associated with the action (expectancy-value processes). However, in presenting a model of agentic normative influence, it is argued that in intergroup contexts group-level costs and benefits play a critical role in individuals' decision-making. In the context of English-French conflict in Quebec, in Canada, four studies provide evidence that group-level costs and benef influence individuals' decision-making in intergro conflict; that the individual level of analysis need mediate the group level of analysis; that group-level co and benefits mediate the relationship between soc identity and intentions to engage in collective action; a that perceptions of outgroup and ingroup norms for inte group behaviours are relatively invariant and predictal related to perceptions of the group- and individual-le, benefits and costs associated with individualistic vers collective actions. By modelling the relationship betwe group norms and group-level costs and benefits, soc psychologists may begin to address the processes th underlie identity-behaviour relationships in collecti action and intergroup conflict.

Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

Ockham's Razor: The Discovery of Neptune

The discovery of Neptune in September 1846 is a good example of scientific rationality but it has proven to be surprisingly difficult to explain how this is so from the perspective of Karl Popper, Thomas Kuhn and several other commentators who have been influenced by these thinkers. I try briefly to explain how to avoid these difficulties and understand the achievement of the astronomers who predicted the location of the new planet, Urbain J. J. Leverrier and John Couch Adams.