N=2 supersymmetric QCD and elliptic potentials

We investigate the relation between the four dimensional N=2 SU(2) super Yang-Mills theory with four fundamental flavors and the quantum mechanics model with Treibich-Verdier potential described by the Heun equation in the elliptic form. We study the precise correspondence of quantities in the gauge theory and the quantum mechanics model. An iterative method is used to obtain the asymptotic expansion of the spectrum for the Schr\"{o}dinger operator, we are able to fix the precise relation between the energy spectrum and the instanton partition function of the gauge theory. We also study asymptotic expansions for the spectrum which correspond to the strong coupling regions of the Seiberg-Witten theory.Comment: Latex, 29pp, published version, content restructured and simplifie

Rejoinder: Conditional Growth Charts

Rejoinder: Conditional Growth Charts [math.ST/0702634]Comment: Published at http://dx.doi.org/10.1214/009053606000000678 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dynamic Games with Almost Perfect Information

This paper aims to solve two fundamental problems on finite or infinite horizon dynamic games with perfect or almost perfect information. Under some mild conditions, we prove (1) the existence of subgame-perfect equilibria in general dynamic games with almost perfect information, and (2) the existence of pure-strategy subgame-perfect equilibria in perfect-information dynamic games with uncertainty. Our results go beyond previous works on continuous dynamic games in the sense that public randomization and the continuity requirement on the state variables are not needed. As an illustrative application, a dynamic stochastic oligopoly market with intertemporally dependent payoffs is considered