On the possibility of a warped disc origin of the inclined stellar discs at the Galactic Centre

(Abridged) The Galactic Center (GC) hosts a population of young stars some of which seem to form mutually inclined discs of clockwise and counter clockwise rotating stars. We present a warped disc origin scenario for these stars assuming that an initially flat accretion disc becomes warped due to the Pringle instability, or due to Bardeen-Petterson effect, before it fragments to stars. We show that this is plausible if the star formation efficiency $\epsilon_{SF} \lesssim 1$, and the viscosity parameter $\alpha \sim 0.1$. After fragmentation, we model the disc as a collection of concentric, circular, mutually tilted rings, and construct warped disc models for mass ratios and other parameters relevant to the GC environment, but also for more massive discs. We take into account the disc's self-gravity and the torques exerted by a surrounding star cluster. We show that a self-gravitating low-mass disc ($M_d / M_{bh} \sim 0.001$) precesses in integrity in the life-time of the stars, but precesses freely when the torques from a non-spherical cluster are included. An intermediate-mass disc ($M_d / M_{bh} \sim 0.01$) breaks into pieces which precess independently in the self-gravity-only case, and become disrupted in the presence of the star cluster torques. For a high-mass disc ($M_d / M_{bh} \sim 0.1$) the evolution is dominated by self-gravity and the disc is broken but not dissolved. The time-scale after which the disc breaks scales almost linearly with ($M_d / M_{bh}$) for self-gravitating models. Typical values are longer than the age of the stars for a low mass disc, and are in the range $\sim 8 \times 10^4-10^5$ yr for high and intermediate-mass discs respectively. None of these models explain the rotation properties of the two GC discs, but a comparison of them with the clockwise disc shows that the lowest mass model in a spherical star cluster matches the data best.Comment: 16 pages, 19 figures, abstract abridged to meet arXiv requirements. Accepted for publication in MNRA

Capacity Regions and Sum-Rate Capacities of Vector Gaussian Interference Channels

The capacity regions of vector, or multiple-input multiple-output, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sum-rate capacities are established for Z interference, noisy interference, and mixed (aligned weak/intermediate and aligned strong) interference. These results generalize known results for scalar Gaussian interference channels.Comment: 33 pages, 1 figure, submitted to IEEE trans. on Information theor

Does oil price uncertainty affect energy use?

Theory predicts that the presence of fixed costs affects the relationship between energy use and energy price changes, as the firm's output and investment decisions respond differently to energy price increases and decreases. The asymmetry in response to energy price changes is exacerbated by uncertainty with respect to future energy prices, but to date the empirical literature does not explicitly take uncertainty into account. The contribution of this paper is twofold. First, we develop a new measure of energy price uncertainty. Second, we apply the measure to explain energy use in 8 OECD countries between 1978 and 1996, trying to identify whether indeed energy price uncertainty effects the asymmetry resulting from changes in energy use.

THE FINANCIAL POSITION OF SOUTH AFRICAN AGRICULTURE

The agricultural sector in South Africa is subjected to major changes due to a simultaneous influence of external and internal forces after the political changes in South Africa and its opening to the rest of the world. The external forces are mostly linked to increasing globalisation including a changing internal trade regime. Internal forces have to do with the liberalisation of agriculture and for example the changing role of government with respect to the provision of financial services. This paper indicates the effect of these influences on the financial position of the farming sector and provides a point of departure for the monitoring of future trends. It further indicates the strategies followed by farmers to counter the negative trends experienced. It is a component of a much broader study on the agricultural finance situation in South Africa.Agricultural Finance,