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

The Zero Number Diminishing Property under General Boundary Conditions

The so-called {\it zero number diminishing property} (or {\it zero number argument}) is a powerful tool in qualitative studies of one dimensional parabolic equations, which says that, under the zero- or non-zero-Dirichlet boundary conditions, the number of zeroes of the solution $u(x,t)$ of a linear equation is finite, non-increasing and strictly decreasing when there are multiple zeroes (cf. \cite{Ang}). In this paper we extend the result to the problems with more general boundary conditions: $u= 0$ sometime and $u\not= 0$ at other times on the domain boundaries. Such results can be applied in particular to parabolic equations with Robin and free boundary conditions.Comment: 7 page

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)

LRR Voices: Local 11 takes on L.A.

[Excerpt] [Maria Elena] Durazo became a leader of an increasingly vocal and militant opposition within the local. A challenge to the incumbent officers took shape. Durazo\u27s training and her close ties with Latino groups and the progressive elements in the Los Angeles labor movement made her a formidable candidate. Many of the activists who had energized the Farmworkers struggle of the previous decade came together again for her campaign. We had learned how to organize immigrant workers around issues of class and justice, says Durazo. We were doing that again