On the development of the Papaloizou-Pringle instability of the black hole-torus systems and quasi-periodic oscillations

We present the numerical study of dynamical instability of a pressure-supported relativistic torus, rotating around the black hole with a constant specific angular momentum on a fixed space-time background, in case of perturbation by a matter coming from the outer boundary. Two dimensional hydrodynamical equations are solved at equatorial plane using the HRSCS to study the effect of perturbation on the stable systems. We have found that the perturbed torus creates an instability which causes the gas falling into the black hole in a certain dynamical time. All the models indicate an oscillating torus with certain frequency around their instant equilibrium. The dynamic of the accreted torus varies with the size of initial stable torus, black hole spin and other variables, such as Mach number, sound speed, cusp location of the torus, etc. The mass accretion rate is slightly proportional to the torus-to-hole mass ratio in the black hole-torus system, but it strongly depends on the cusp location of the torus. The cusp located in the equipotential surfaces of the effective potential moves outwards into the torus. The dynamical change of the torus increases the mass accretion rate and triggers the Papaloizou-Pringle instability. It is also observed that the growth of the $m=1$ mode of the Papaloizou-Pringle instability occurs for a wide range of fluid and hydrodynamical parameters and a black hole spin. We have also computed the QPOs from the oscillating relativistic torus.Comment: 14 Pages, 14 Figures, High resolution version of Figs.1 and 7 can be found in the original manuscript. Substantial revision has been made. The title, abstract and whole text are revise

Influence of osmotic and metal stresses on nitrogenase activity of cyanobacteria ýsolated from paddy fields

Samples were collected from paddy fields in Corum-Turk.ye. Nitrogen-free BG-11 medium was used for isolation of nitrogen fixing cyanobacteria. Acetylene reduction technique was used to determine the effects of different chemical agents on the nitrogenase activities of the cyanobacteria, which were identified at the genus level. Nostoc showed the highest nitrogenase activity (0.09 ethylene ƒÊl/mg.h) at 50 mM salt concentration. At 60 mM sucrose concentration, Nostoc showed the highest nitrogenase activity (0.08 ethylene ƒÊl/mg.h). The highest tolerances for the metals were present in Anabaena (0.006 ethylene ƒÊl/mg.h) for iron (20 ppm), Nodularia 0.1 ethylene ƒÊl/mg.h (for manganese 20 ppm) and Nostoc 0.96 ethylene ƒÊl/mg.h (for zinc 5 ppm)

Optimal Investment Under Transaction Costs: A Threshold Rebalanced Portfolio Approach

We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the market levies proportional transaction costs in buying and selling stocks. We achieve this using "threshold rebalanced portfolios", where trading occurs only if the portfolio breaches certain thresholds. Under the assumption that the relative price sequences have log-normal distribution from the Black-Scholes model, we evaluate the expected wealth under proportional transaction costs and find the threshold rebalanced portfolio that achieves the maximal expected cumulative wealth over any investment period. Our derivations can be readily extended to markets having more than two stocks, where these extensions are pointed out in the paper. As predicted from our derivations, we significantly improve the achieved wealth over portfolio selection algorithms from the literature on historical data sets.Comment: Submitted to IEEE Transactions on Signal Processin