Orbifolds, geometric structures and foliations. Applications to harmonic maps

In recent years a lot of attention has been paid to topological spaces which are a bit more general than smooth manifolds - orbifolds. Orbifolds are intuitively speaking manifolds with some singularities. The formal definition is also modelled on that of manifolds, an orbifold is a topological space which locally is homeomorphic to the orbit space of a finite group acting on $R^n$. Orbifolds were defined by Satake, as V-manifolds, then studied by W. Thurston, who introduced the term "orbifold". Due to their importance in physics, and in particular in the string theory, orbifolds have been drawing more and more attention. In this paper we propose to show that the classical theory of geometrical structures, easily translates itself to the context of orbifolds and is closely related to the theory of foliated geometrical structures, cf. \cite{Wo0}. Finally, we propose a foliated approach to the study of harmonic maps between Riemannian orbifolds based on our previous research into transversely harmonic maps

Transversely Hessian foliations and information geometry

A family of probability distributions parametrized by an open domain $\Lambda$ in $R^n$ defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix tensor is positive definite defining in this way a Riemannian metric on $\Lambda$. If we replace the "positive definite" assumption by the existence of a suitable torsion-free connection, a foliation with a transversely Hessian structure appears naturally. In the paper we develop the study of transversely Hessian foliations in view of applications in information geometry

ITC Injury Determination and the Abuse of Antidumping Law: Evidence from the United States Manufacturing Industries

International Relations/Trade,

The Impact of Market Rules and Market Structure on the Price Determination Process in the England and Wales Electricity Market

This paper argues that the market rules governing the operation of the England and Wales electricity market in combination with the structure of this market presents the two major generators National Power and PowerGen with opportunities to earn revenues substantially in excess of their costs of production for short periods of time. Generators competing to serve this market have two strategic weapons at their disposal: (1) the price bid for each generation set and (2) the capacity of each generation set made available to supply the market each half-hour period during the day. We argue that because of the rules governing the price determination process in this market, by the strategic use of capacity availability declarations, when conditions exogenous to the behavior of the two major generators favor it, these two generators are able to obtain prices for their output substantially in excess of their marginal costs of generation. The paper establishes these points in the following manner. First, we provide a description of the market structure and rules governing the operation of the England and Wales electricity market, emphasizing those aspects that are important to the success of the strategy we believe the two generators use to exercise market power. We then summarize the time series properties of the price of electricity emerging from this market structure and price-setting process. By analyzing four fiscal years of actual market prices, quantities and generator bids into the market, we provide various pieces of evidence in favor of the strategic use of the market rules by the two major participants. The paper closes with a discussion of the lessons that the England and Wales experience can provide for the design of competitive power markets in the US, particularly California, and other countries.

Measuring Industry Specific Protection: Antidumping in the United States

This paper provides estimates of the trade impacts of U.S. antidumping law and the determinants of suit filing activity from 1980-1985. We study three possible channels through which the threat or mere possibility of antidumping duties can restrict trade which we believe, when combined with the direct effects of duties, capture most of the trade effects of antidumping law. We refer to these three non- duty effects as the investigation effect, the suspension effect, and the withdrawal effect. Investigation effects occur when an antidumping investigation takes place; suspension effects occur under so-called 'suspension agreements'; and withdrawal effects occur after a petition is simply withdrawn without a final determination. We find substantial trade restrictions associated with the first two effects, but not with the third. Finally, we find evidence suggesting that some firms initiate antidumping procedures for the trade restricting investigation effects alone.

Pierrot's theorem for singular Riemanian foliations

Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves