Porto Oscillation Code (POSC)

The Porto Oscillation Code (POSC) has been developed in 1995 and improved over the years, with the main goal of calculating linear adiabatic oscillations for models of solar-type stars. It has also been used to estimate the frequencies and eigenfunctions of stars from the pre-main sequence up to the sub-giant phase, having a mass between 0.8 and 4 solar masses. The code solves the linearised perturbation equations of adiabatic pulsations for an equilibrium model using a second order numerical integration method. The possibility of using Richardson extrapolation is implemented. Several options for the surface boundary condition can be used. In this work we briefly review the key ingredients of the calculations, namely the equations, the numerical scheme and the output.Comment: Accepted for publication in Astrophysics and Space Science

Representation of Nelson Algebras by Rough Sets Determined by Quasiorders

In this paper, we show that every quasiorder $R$ induces a Nelson algebra $\mathbb{RS}$ such that the underlying rough set lattice $RS$ is algebraic. We note that $\mathbb{RS}$ is a three-valued {\L}ukasiewicz algebra if and only if $R$ is an equivalence. Our main result says that if $\mathbb{A}$ is a Nelson algebra defined on an algebraic lattice, then there exists a set $U$ and a quasiorder $R$ on $U$ such that $\mathbb{A} \cong \mathbb{RS}$.Comment: 16 page

Consumption Externalities, Production Externalities and Efficient Capital Accumulation under Time Non-separable Preferences

We examine the effects of both consumption and production externalities on capital accumulation and economic performance under time non-separable preferences and a non-scale production technology. We show that a consumption externality in isolation has long-run distortionary effects if and only if labour is supplied elastically. With fixed labour supply, it has only transitional distortionary effects, though it may generate long-run distortions through its interaction with the production externality. Production externalities always generate long-run distortions, irrespective of labour supply. The optimal taxation to correct for the distortions is characterized. Further quantitative insights are obtained by supplementing the theoretical analysis with numerical simulations based on the calibration of a plausible macroeconomic growth model.Time non-separable preferences; consumption and production externalities; capital accumulation; optimal tax policy

Negative modes and the thermodynamics of Reissner-Nordstr\"om black holes

We analyse the problem of negative modes of the Euclidean section of the Reissner-Nordstr\"om black hole in four dimensions. We find analytically that a negative mode disappears when the specific heat at constant charge becomes positive. The sector of perturbations analysed here is included in the canonical partition function of the magnetically charged black hole. The result obeys the usual rule that the partition function is only well-defined when there is local thermodynamical equilibrium. We point out the difficulty in quantising Einstein-Maxwell theory, where the so-called conformal factor problem is considerably more intricate. Our method, inspired by hep-th/0608001, allows us to decouple the divergent gauge volume and treat the metric perturbations sector in a gauge-invariant way.Comment: 24 pages, 1 figure; v2 minor changes to fit published versio