Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamic (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density $\Sigma_0\propto r^{-\alpha}$, a coplanar azimuthal magnetic field $B_0\propto r^{-\gamma}$, a consistent self-gravity and a power-law rotation curve $v_0\propto r^{-\beta}$ where $v_0$ is the linear azimuthal gas rotation speed. The barotropic equation of state $\Pi\propto\Sigma^{n}$ is adopted for both MHD background equilibrium and coplanar MHD perturbations where $\Pi$ is the vertically integrated pressure and $n$ is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among $\alpha$, $\beta$, $\gamma$ and $n$ such that only one parameter (e.g., $\beta$) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For nonaxisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e., fast and slow MHD density waves) can be derived once $\beta$ is specified. To complement the magnetized singular isothermal disc (MSID) analysis of Lou, we extend the analysis to a wider range of $-1/4<\beta<1/2$. As an example of illustration, we discuss specifically the $\beta=1/4$ case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.Comment: 25 page

Correlations among Multi-Wavelength Luminosities of Star-Forming Galaxies

It has been known for two decades that a tight correlation exists between far-infrared (FIR) and radio (1.4 and 4.8 GHz) global fluxes/luminosities from galaxies, which may be explained in terms of massive star formation activities in these galaxies. For this very reason, a correlation might also exist between X-ray and FIR/radio global luminosities of galaxies. We analyze data from {\it ROSAT} All-Sky Survey and {\it IRAS} to show that such correlation does indeed exist between FIR (42.5$-122.5\mu$m) and soft X-ray (0.1$-$2.4keV) luminosities in active star-forming galaxies (ASFGs).In order to establish a physical connection between the L_{\rmX}-L_{\rm FIR} correlation and global star formation rate (SFR) in galaxies, we empirically derive both $L_{\rm X}-L_{\rm B}$ and $L_{\rm FIR}-L_{\rm B}$ relations. Futhermore, we propose a relation between soft X-ray luminosity and SFR in star-forming galaxies. To further understand the $L_{\rm X}-L_{\rm FIR}$ relation, we construct an empirical model in which both FIR and X-ray emissions consist of two components with one being closely associated with star formation and the other not.Comment: 9 pages, 6 figures, accepted by MNRA

Stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs

We construct aligned and unaligned stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. In comparison with SID problems studied earlier, there exist three possible classes of stationary solutions allowed by more dynamic freedoms. Our exact global perturbation solutions and critical points are valuable for testing numerical magnetohydrodynamic codes. For galactic applications, our model analysis contains more realistic elements and offer useful insights for structures and dynamics of disc galaxies consisting of stars and magnetized gas.Comment: 25 pages, 31 figures, accepted by Monthly Notices of Royal Astronomical Society, style files include

Optimality Conditions for Semilinear Parabolic Equations with Controls in Leading Term

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.Comment: 22 apges, 1 figure

Heidegger’s 1924 Clearing of the Affects Using Aristotle’s Rhetoric, Book II

Heidegger famously said that the best treatment of the emotions in western history was Book 2 of Aristotle's RHETORIC. Heidegger then did an analysis of this material prior to the publication of Being and TIme (1927). This engages engages with Heidegger's treatment of Aristotle's treatment of the emotions in relation to Heidegger's design distinction of affectivity (Befindlichkeit), understanding, and discourse (Rede)

Corporate Influence in the Post-2015 Process

This working paper examines the role and influence of business actors in the process towards the Post-2015 agenda of the UN, with particular attention to the influence of large transnational corporations. The business sector certainly has an important role to play in the implementation process of the Post-2015 agenda, as sustainable development will require large-scale changes in business practices. Some pioneering companies are already on the path towards sustainable development solutions (for instance in the area of renewable energies). However, acknowledging corporations' role must not mean giving them undue influence on policymaking and ignoring their responsibility in creating and exacerbating many of the problems that the Post-2015 agenda is supposed to tackle.This working paper starts with a brief overview of the current process towards the Post-2015 agenda and assesses its political relevance. The second part maps out the key business players involved in various processes surrounding the post-2015 consultations. The third part of the paper analyzes the key messages and policy recommendations of business actors in the post-2015 process. The fourth part explores the problems, risks and side-effects of the corporate influence on the Post-2015 agenda. They relate, on the one hand, to the key messages, on the other hand to the promoted governance models. The final part draws some conclusions, provides policy recommendations for the UN, member states, civil society and academia, and highlights potential paths for future research and policy work