On the Ricci tensor in type II B string theory

Let $\nabla$ be a metric connection with totally skew-symmetric torsion \T on a Riemannian manifold. Given a spinor field $\Psi$ and a dilaton function $\Phi$, the basic equations in type II B string theory are \bdm \nabla \Psi = 0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi = b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations between the length ||\T||^2 of the torsion form, the scalar curvature of $\nabla$, the dilaton function $\Phi$ and the parameters $a,b,\mu$. The main results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the connection. In particular, if the supersymmetry $\Psi$ is non-trivial and if the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d \T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is divergence-free. We show that the latter condition is satisfied in many examples constructed out of special geometries. A special case is $a = b$. Then the divergence of the energy-momentum tensor vanishes if and only if one condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T = 0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq 0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2

Local twistors and the conformal field equations

This note establishes the connection between Friedrich's conformal field equations and the conformally invariant formalism of local twistors.Comment: LaTeX2e Minor corrections of misprints et

On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity

In Brodbeck et al 1999 it has been shown that the linearised time evolution equations of general relativity can be extended to a system whose solutions asymptotically approach solutions of the constraints. In this paper we extend the non-linear equations in similar ways and investigate the effect of various possibilities by numerical means. Although we were not able to make the constraint submanifold an attractor for all solutions of the extended system, we were able to significantly reduce the growth of the numerical violation of the constraints. Contrary to our expectations this improvement did not imply a numerical solution closer to the exact solution, and therefore did not improve the quality of the numerical solution.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.

Bifurcations and Complete Chaos for the Diamagnetic Kepler Problem

We describe the structure of bifurcations in the unbounded classical Diamagnetic Kepler problem. We conjecture that this system does not have any stable orbits and that the non-wandering set is described by a complete trinary symbolic dynamics for scaled energies larger then $\epsilon_c=0.328782\ldots$.Comment: 15 pages PostScript uuencoded with figure

On Killing vectors in initial value problems for asymptotically flat space-times

The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the asymptotic characteristic and in the hyperboloidal initial value problem (both of them are formulated on the conformally compactified space-time manifold)

State and local taxation

State and local taxation comprises those taxes that are collected at the sub-federal government levels in order to finance state and local public services, assigning discretion in the determination of rates and bases of these taxes to sub-federal governments. Consider a nation with different layers of government that are only serving administrative purposes. Each government level only distributes the public services to and collects the taxes from that nation’s citizens upon which they agreed at the national level. In such a country, no state or local taxation is necessary since the level of public goods and services is uniformly decided upon for the whole country. This leaves citizens in some local jurisdictions, which prefer more public services than the national average, as much dissatisfied as citizens in local jurisdictions, which prefer less. It is possible to provide public services, the benefits of which are geographically limited and which are not national in scope, at different levels in different sub-federal jurisdictions. Enabling citizens to consume publicly provided goods and services at different levels according to their preferences makes everyone better off without making someone worse off. In order to let people, who want to consume more, pay a higher tax price for those state and local services, taxes must be differentiated accordingly between states and local jurisdictions. In such a world with a differentiated supply of publicly provided goods, each individual can reside in a jurisdiction where a certain level of public services is provided to adequate tax prices. The art of state and local taxation is the assignment of different kinds of taxes to government levels such that an invisible hand properly guides a nation in an ideal world to an optimal multi-unit fiscal system. This is not necessarily the case in the real world and some answers exist why fiscal systems are not optimal.

General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1

Is the View from the Eurotower Purely European? - National Divergence and ECB Interest Rate Policy

The official view on ECB monetary policy claims that decisions are based on euro zone data and that diverging regional developments are disregarded. To test empirically whether regional developments have an impact on ECB decisions we develop a generalised monetary policy reaction function which allows for an influence of regional divergence. Reaction function estimations and a probit model of interest rate decisions for the first years of the euro area offer some first weak support for an impact of regional divergence. The results clarify that ignoring a potential national perspective may lead to biased estimates for the ECB reaction function.ECB, monetary policy, Taylor rule

Is the View from the Eurotower Purely European? National Divergence and ECB Interest Rate Policy

The official view on ECB monetary policy claims that monetary decisions are based solely on average data for the euro zone and that diverging regional developments are disregarded. However, experience from other two tier central banks and theoretical considerations suggest that this official view cannot be accepted without empirical testing. A generalised monetary policy reaction function is developed which allows for an influence of regional divergence. The empirical tests are based on reaction function estimations and a probit model of interest rate decisions for the first years of the euro area. The results offer some first weak support for an impact of regional divergence in ECB decision making. The results further clarify that ignoring a potential national perspective may lead to a serious bias in the estimation of ECB reaction functions. The paper concludes that the correct identification of a possible impact of regional divergence is important for the transparency issue. --ECB,monetary policy,Taylor rule

Directional States of Symmetric-Top Molecules Produced by Combined Static and Radiative Electric Fields

We show that combined electrostatic and radiative fields can greatly amplify the directional properties, such as axis orientation and alignment, of symmetric top molecules. In our computational study, we consider all four symmetry combinations of the prolate and oblate inertia and polarizability tensors, as well as the collinear and perpendicular (or tilted) geometries of the two fields. In, respectively, the collinear or perpendicular fields, the oblate or prolate polarizability interaction due to the radiative field forces the permanent dipole into alignment with the static field. Two mechanisms are found to be responsible for the amplification of the molecules' orientation, which ensues once the static field is turned on: (a) permanent-dipole coupling of the opposite-parity tunneling doublets created by the oblate polarizability interaction in collinear static and radiative fields; (b) hybridization of the opposite parity states via the polarizability interaction and their coupling by the permanent dipole interaction to the collinear or perpendicular static field. In perpendicular fields, the oblate polarizability interaction, along with the loss of cylindrical symmetry, is found to preclude the wrong-way orientation, causing all states to become high-field seeking with respect to the static field. The adiabatic labels of the states in the tilted fields depend on the adiabatic path taken through the parameter space comprised of the permanent and induced-dipole interaction parameters and the tilt angle between the two field vectors