Identified charged particle azimuthal anisotropy in PHENIX at RHIC

We present here v$_2$ of identified and inclusive charged particles measured in the PHENIX central arm detector ($|\eta| < 0.35$) with respect to the reaction plane defined at $|\eta| = 3 \sim 4$ in 200 GeV Au+Au collisions. We find that v$_2$ increases from central to mid-central collisions reaching a maximum at about 50% of the geometric cross section and then decreases again for more peripheral collisions. As a function of transverse momentum in minimum-bias collisions, the v$_2$ parameter increases linearly with p$_{\rm T}$ up to p$_{\rm T}$ $\simeq$ 2 GeV/c and then saturates for inclusive charged particles. The v$_2$ parameter of identified particles ($\pi^+$, $\pi^-$, $K^+$, $K^-$, $p$ and $\bar{p}$) follow a hydro-dynamic behavior up to 2 GeV/c in p$_{\rm T}$, where the lighter mass particles have larger v$_2$ at a given p$_{\rm T}$. However there is an indication that this trend is reversed at around p$_{\rm T}$ $\simeq$ 2 GeV/c, where $p$ and $\bar{p}$ have larger v$_2$ than $\pi$ and $K$.Comment: 4 pages, 4 figures. Talk presented at Quark Matter 2002, Nantes, France, July 18-24, 2002. To appear in the proceedings (Nucl. Phys. A

An Approach to Studying Quasiconformal Mappings on Generalized Grushin Planes

We demonstrate that the complex plane and a class of generalized Grushin planes $G_r$, where $r$ is a function satisfying specific requirements, are quasisymmetrically equivalent. Then using conjugation we are able to develop an analytic definition of quasisymmetry for homeomorphisms on $G_r$ spaces. In the last section we show our analytic definition of quasisymmetry is consistent with earlier notions of conformal mappings on the Grushin plane. This leads to several characterizations of conformal mappings on the generalized Grushin planes

Uniform Continuity and Br\'ezis-Lieb Type Splitting for Superposition Operators in Sobolev Space

Using concentration-compactness arguments we prove a variant of the Brezis-Lieb-Lemma under weaker assumptions on the nonlinearity than known before. An intermediate result on the uniform continuity of superposition operators in Sobolev space is of independent interest

(Fermionic)Mass Meets (Intrinsic)Curvature

Using the notion of vacuum pairs we show how the (square of the) mass matrix of the fermions can be considered geometrically as curvature. This curvature together with the curvature of space-time, defines the total curvature of the Clifford module bundle representing a ``free'' fermion within the geometrical setup of spontaneously broken Yang-Mills-Higgs gauge theories. The geometrical frame discussed here gives rise to a natural class of Lagrangian densities. It is shown that the geometry of the Clifford module bundle representing a free fermion is described by a canonical spectral invariant Lagrangian density.Comment: 14 page

External Price Benchmarking vs. Price Negotiation for Pharmaceuticals

External price benchmarking imposes a price cap for pharmaceuticals based on prices of identical products in other countries. Suppose that a regulatory agency can either directly negotiate drug prices with pharmaceutical manufacturers or implement a benchmarking regime based on foreign prices. Using a model where two countries differ only in their market size, we show that a country prefers benchmarking if its agency has considerably less bargaining power compared to the agency in the other country. Assuming that bargaining power is positively correlated to country size, we find that only small countries might have an incentive to engage in external price benchmarking. This incentive shrinks if population size grows.Pharmaceuticals; price negotiation; administered prices; external reference pricing

Litigation and Settlement under Court Error

Settlements are often considered to be welfare-enhancing because they save time and litigation costs. In the presence of court error, however, this conclusion may be wrong. Court decisions create positive externalities for future litigants which will not occur if a dispute is settled out of court. Focusing on private litigation, we examine the impact of court error on the deterrent effect of the strict liability rule. In an asymmetric information setup both, underdeterrence and overdeterrence are possible under court error. Moreover, court error increases the likelihood of out-of-court settlements which can offset the positive externality of litigation.litigation; settlement; asymmetric information; court error; strict liability rule

The generalized Lichnerowicz formula and analysis of Dirac operators

We study Dirac operators acting on sections of a Clifford module ${\cal E}$\ over a Riemannian manifold $M$. We prove the intrinsic decomposition formula for their square, which is the generalisation of the well-known formula due to Lichnerowicz [L]. This formula enables us to distinguish Dirac operators of simple type. For each Dirac operator of this natural class the local Atiyah-Singer index theorem holds. Furthermore, if $M$\ is compact and {{\petit \rm dim}\;M=2n\ge 4}, we derive an expression for the Wodzicki function $W_{\cal E}$, which is defined via the non-commutative residue on the space of all Dirac operators ${\cal D}({\cal E})$. We calculate this function for certain Dirac operators explicitly. From a physical point of view this provides a method to derive gravity, resp. combined gravity/Yang-Mills actions from the Dirac operators in question.Comment: 25 pages, plain te