79,548 research outputs found

### Trace functions as Laplace transforms

We study trace functions on the form t\to\tr f(A+tB) where $f$ is a
real function defined on the positive half-line, and $A$ and $B$ are
matrices such that $A$ is positive definite and $B$ is positive
semi-definite. If $f$ is non-negative and operator monotone decreasing, then
such a trace function can be written as the Laplace transform of a positive
measure. The question is related to the Bessis-Moussa-Villani conjecture.
Key words: Trace functions, BMV-conjecture.Comment: Minor change of style, update of referenc

### Cluster temperatures and non-extensive thermo-statistics

We propose a novel component to the understanding of the temperature
structure of galaxy clusters which does not rely on any heating or cooling
mechanism. The new ingredient is the use of non-extensive thermo-statistics
which is based on the natural generalization of entropy for systems with
long-range interactions. Such interactions include gravity and attraction or
repulsion due to charges. We explain that there is growing theoretical
indications for the need of this generalization for large cosmological
structures. The observed pseudo temperature is generally different from the
true thermodynamic temperature, and we clarify the connection between the two.
We explain that this distinction is most important in the central part of the
cluster where the density profile is most shallow. We show that the observed
pseudo temperature may differ up to a factor 2/5 from the true thermodynamic
temperature, either larger or smaller. In general the M-T and L-T relations
will be affected, and the central DM slope derived through hydrostatic
equilibrium may be either more shallow or steeper. We show how the true
temperature can be extracted correctly either from the spectrum or from the
shape of the Doppler broadening of spectral lines.Comment: 11 pages, 1 figur

### 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

### New developments in fruit and vegetables consumption in the period 1999-2004 in Denmark - A quantile regression approach

The development in the consumption of fruit and vegetables in the period 1999-2004 in Denmark was investigated using quantile regression and two previously overlooked problems were identified. First, the change in the ten percent quantile samples decreased. This could have been caused by changes in the distribution of covariates. Therefore, the counterfactual decomposition of Machado and Mata (2005) was used and the methodology established that the change was not caused by alterations in the distribution of covariates but by changes in the coefficients and therefore a change in behaviour. The reason for this development is probably due to low income groups becoming relatively more income constrained since the gap to the high income group have grown considerably at the lower end of the distribution. The second problem was that the education inducing gap became larger in 2004 indicating that uneducated people have not responded as well to the health related information flow. These results suggest that information campaigns have not been as successful as previously thought; more importantly the results indicate that information campaigns alone will do a poor job in solving the identified problems. Other instruments targeting uneducated and low income groups more directly are needed. Instruments which make fruit and vegetables relatively cheaper would undoubtedly have an effect on low income groups and send a strong signal to the uneducated population.Quantile regression, Counterfactual decomposition, Expenditure distribution, Food Consumption/Nutrition/Food Safety,

### Forecasting the consumption effect of taxing foods containing saturated fat

The purpose of the current paper is to explain how one can forecast the effect of an elected tax on saturated fat on the demand for butter. The tax is to take affect from the first of January 2010 in Denmark. The tax is supposed to affect the consumption of saturated fat and especially high consuming households are of interest. Quantile regression is thus better suited than mean regression. Interest centre on at risk groups with larger consumption, but we are also interested in a simple measure that measure the total effect of the tax change, i.e. the unconditional quantile. The former can easily be obtained from the quantile regression while it is proposed to use simulations in the latter case. In mean regression a close form formula for calculating the unconditional mean from the conditional mean exist; unfortunately this is not the case for quantile regression. Hence, simulations are needed. The principle in the proposed method is the same as the methodology used in a recent published paper for comparing labour income distributions. A refinement of this methodology is suggested.Quantile Regression, Simulation, Healthy Diet, Public Policy., Agricultural and Food Policy,

### The behaviour of shape and velocity anisotropy in dark matter haloes

Dark matter haloes from cosmological N-body simulations typically have
triaxial shapes and anisotropic velocity distributions. Recently it has been
shown that the velocity anisotropy, beta, of cosmological haloes and major
merger remnants depends on direction in such a way that beta is largest along
the major axis and smallest along the minor axis. In this work we use a wide
range of non-cosmological N-body simulations to examine halo shapes and
direction-dependence of velocity anisotropy profiles. For each of our simulated
haloes we define 48 cones pointing in different directions, and from the
particles inside each cone we compute velocity anisotropy profiles. We find
that elongated haloes can have very distinct velocity anisotropies. We group
the behaviour of haloes into three different categories, that range from
spherically symmetric profiles to a much more complex behaviour, where
significant differences are found for beta along the major and minor axes. We
encourage future studies of velocity anisotropies in haloes from cosmological
simulations to calculate beta-profiles in cones, since it reveals information,
which is hidden from a spherically averaged profile. Finally, we show that
spherically averaged profiles often obey a linear relation between beta and the
logarithmic density slope in the inner parts of haloes, but this relation is
not necessarily obeyed, when properties are calculated in cones.Comment: 23 pages, 14 figures. Accepted for publication in JCA

### Observational constraints on the inflaton potential combined with flow-equations in inflaton space

Direct observations provide constraints on the first two derivatives of the
inflaton potential in slow roll models. We discuss how present day
observations, combined with the flow equations in slow roll parameter space,
provide a non-trivial constraint on the third derivative of the inflaton
potential. We find a lower bound on the third derivative of the inflaton
potential V'''/V > -0.2. We also show that unless the third derivative of the
inflaton potential is unreasonably large, then one predicts the tensor to
scalar ratio, r, to be bounded from below r > 3 * 10^{-6}.Comment: 4 pages, 2 figures. Important sign mistake corrected. Conclusions,
abstract and discussion change

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