A note on the Manin-Mumford conjecture

In the article [PR1] {\it On Hrushovski's proof of the Manin-Mumford conjecture} (Proceedings of the ICM 2002), R. Pink and the author gave a short proof of the Manin-Mumford conjecture, which was inspired by an earlier model-theoretic proof by Hrushovski. The proof given in [PR1] uses a difficult unpublished ramification-theoretic result of Serre. It is the purpose of this note to show how the proof given in [PR1] can be modified so as to circumvent the reference to Serre's result. J. Oesterl\'e and R. Pink contributed several simplifications and shortcuts to this note.Comment: 11 page

Ising Dipoles on the Triangular Lattice

A cluster Monte Carlo method for systems of classical spins with purely dipolar couplings is presented. It is tested and applied for finite arrays of perpendicular Ising dipoles on the triangular lattice. This model is a modification with long-range interactions of the geometrically frustrated Ising antiferromagnet. From measurements of integrated autocorrelation times for energy, magnetization and staggered magnetizations, a high efficiency of the cluster Monte Carlo (MC) algorithm compared to a single-spin-flip algorithm is found. For the investigated model, a finite temperature transition is found which is characterized by a peak in the specific heat and in the staggered susceptibilities.Comment: 4 pages, 3 figures. Presented at the 8th Joint MMM-Intermag Conference, San Antonio 2001. To appear in J.Appl.Physic

\u27Dred Scott v. Sandford\u27 Analysis

The Scott v. Sandford decision will forever be known as a dark moment in America\u27s history. The Supreme Court chose to rule on a controversial issue, and they made the wrong decision. Scott v. Sandford is an example of what can happen when the Court chooses to side with personal opinion instead of what is right

Public Good Menus and Feature Complementarity

The distance metric on the location space for multidimensional public good varieties represents complementarity between the goods features. "Euclidean" feature complementarity has atypical strong properties that lead to a failure of intuition about the optimal-menu design problem. If the population is heterogeneous, increasing the distance between two varieties is welfare-improving in Euclidean space, but not generally. A basic optimal-direction principle always applies: "anticonvex" menu changes increase participation and surplus. A menu replacement is anticonvex if it moves the varieties apart in the common line space. The result extends to some impure public goods with break-even pricing and variety-specic costs. A sufficient condition for menus to be Pareto-optimal is that "personal price" (nominal price plus perceived distance from a variety) is linear in the norm that induces the distance metric.Public Good Menus; complementarity

Can Rivalry Increase Prices?

Spatially differentiated duopolists set higher-than-monopoly prices at some distances. This phenomenon is shown to occur in any finite- dimensional space for a class of reservation prices that covers concavity and convexity in perceived distance from a design. But an upper bound on the equilibrium duopoly price converges monotonically and quickly to the monopoly price in dimensionality. If consumers care about sufficiently many features of the product (a very small number of criteria is enough), monopoly nearly leads to an extreme price.price effect of competition, multidimensional product spaces, duopoly pricing, spatial competition

Physiological correlates of optimal performance Semiannual status report, 1 Dec. 1968 - 30 Apr. 1969

Physiological and psychological tests for determining optimum performanc

A microscopic approach to spin dynamics: about the meaning of spin relaxation times

We present an approach to spin dynamics by extending the optical Bloch equations for the driven two-level system to derive microscopic expressions for the transverse and longitudinal spin relaxation times. This is done for the 6-level system of electron and hole subband states in a semiconductor or a semiconductor quantum structure to account for the degrees-of-freedom of the carrier spin and the polarization of the exciting light and includes the scattering between carriers and lattice vibrations on a microscopic level. For the subsystem of the spin-split electron subbands we treat the electron-phonon interaction in second order and derive a set of equations of motion for the 2x2 spin-density matrix which describes the electron spin dynamics and contains microscopic expressions for the longitudinal (T_1) and the transverse (T_2) spin relaxation times. Their meaning will be discussed in relation to experimental investigations of these quantities.Comment: 9 pages, 3 figures, Replacement of cond-mat/0407358 due to substantial revisio