2,203 research outputs found
Axiomatic characterizations of the Walras correspondence for generalized economies
Equilibrium Theory;International Trade
Control of multiscale systems with constraints. 1. Basic principles of the concept of evolution of systems with varying constraints
Physical fundamentals of the self-organizing theory for the system with
varying constraints are considered. A variation principle, specifically the
principle of dynamic harmonization as a generalization of the Gauss-Hertz
principle for the systems with varying internal structure is formulated. In
compliance with this principle the system evolves through dynamics of the
processes leading to harmonization of the internal multiscale structure of the
system and its connections with external actions as a result of minimizing the
dynamic harmonization function. Main principles of the shell model of
self-organization under the action of the dominating entropic disturbance are
formulated.Comment: First par
Formulation, existence, and computation of boundedly rational dynamic user equilibrium with fixed or endogenous user tolerance
This paper analyzes dynamic user equilibrium (DUE) that incorporates the notion of boundedly rational (BR) user behavior in the selection of departure times and routes. Intrinsically, the boundedly rational dynamic user equilibrium (BR-DUE) model we present assumes that travelers do not always seek the least costly route-and-departure-time choice. Rather, their perception of travel cost is affected by an indifference band describing travelers’ tolerance of the difference between their experienced travel costs and the minimum travel cost. An extension of the BR-DUE problem is the so-called variable tolerance dynamic user equilibrium (VT-BR-DUE) wherein endogenously determined tolerances may depend not only on paths, but also on the established path departure rates. This paper presents a unified approach for modeling both BR-DUE and VT-BR-DUE, which makes significant contributions to the model formulation, analysis of existence, solution characterization, and numerical computation of such problems. The VT-BR-DUE problem, together with the BR-DUE problem as a special case, is formulated as a variational inequality. We provide a very general existence result for VT-BR-DUE and BR-DUE that relies on assumptions weaker than those required for normal DUE models. Moreover, a characterization of the solution set is provided based on rigorous topological analysis. Finally, three computational algorithms with convergence results are proposed based on the VI and DVI formulations. Numerical studies are conducted to assess the proposed algorithms in terms of solution quality, convergence, and computational efficiency
Mathematical general relativity: a sampler
We provide an introduction to selected recent advances in the mathematical
understanding of Einstein's theory of gravitation.Comment: Some updates. A shortened version, to appear in the Bulletin of the
AMS, is available online at
http://www.ams.org/journals/bull/0000-000-00/S0273-0979-2010-01304-
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