Zero-Sum Stochastic Games with Partial Information and Average Payoff

We consider a discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we present a pair of optimal strategies for both the players.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

Novel 2,6-bis(4-methoxyphenyl)-1-methylpiperidin-4-one oxime esters: synthesis and a new insight into their antioxidant and antimicrobial potential

A simple and efficient protocol for the synthesis of novel 2,6-bis(4-methoxyphenyl)-1-methylpiperidin-4-one oxime esters 4(a-q) is described. Initially, p-anisaldehyde 1 was condensed (Mannich reaction) with acetone and ammonium acetate trihydrate afforded 2,6-bis(4-methoxyphenyl)piperidin-4-one 2. Then, methylation followed by oximation with hydroxylamine hydrochloride (NH(2)OHa (TM) HCl) furnished a key scaffold 4. Further, to explore the enhanced biological properties of the piperidin-4-one core i.e. the key scaffold 4 was conjugated with substituted benzoyl chlorides in the presence of anhydrous K2CO3 as base to obtain novel 2,6-bis(4-methoxyphenyl)-1-methylpiperidin-4-one oxime esters 4(a-q) in excellent yields. The newly synthesized compounds were characterized by elemental analysis, IR, H-1 NMR, C-13 NMR and mass spectroscopic techniques, and screened for their in vitro antioxidant and antimicrobial activities. Most of the compounds exerted positive efficacy towards the biological assays performed. Among the synthesized analogues, compounds 4l and 4m exhibited promising antioxidant activity and on the other hand compounds 4b and 4d manifested persuasive antibacterial activity, whereas compound 4b displayed stupendous antifungal activity against A. flavus strain.

Attraction, with boundaries

We study the basin of attraction of static extremal black holes, in the concrete setting of the STU model. By finding a connection to a decoupled Toda-like system and solving it exactly, we find a simple way to characterize the attraction basin via competing behaviors of certain parameters. The boundaries of attraction arise in the various limits where these parameters degenerate to zero. We find that these boundaries are generalizations of the recently introduced (extremal) subtracted geometry: the warp factors still exhibit asymptotic integer power law behaviors, but the powers can be different from one. As we cross over one of these boundaries ('generalized subttractors'), the solutions turn unstable and start blowing up at finite radius and lose their asymptotic region. Our results are fully analytic, but we also solve a simpler theory where the attraction basin is lower dimensional and easy to visualize, and present a simple picture that illustrates many of the basic ideas.

Three-Dimensional Study of Natural Convection in a Horizontal Channel With Discrete Heaters on One of Its Vertical Walls

Three-dimensional natural convection in a horizontal channel with an array of discrete flush-mounted heaters on one of its vertical walls is numerically studied. Effects of thermal conductivities of substrate and heaters and convection on outer sides of the channel walls on heat transfer are examined. The substrate affects heat transfer in a wider range of thermal conductivities than do the heaters. At lower heater thermal conductivities a higher heat portion is transferred by direct convection from the heaters to the adjacent coolant. However, higher substrate conductivity is associated with higher heat portion transferred through the substrate. The innermost heater column is found to become the hottest heater column due to the lower coolant accessibility. The heat transfer in the channel is strongly influenced by convection on the outer sides of the channel walls. Correlations are presented for dimensionless temperature maximum and average Nusselt number.

Supersolid in a one-dimensional model of hard-core bosons

We study a system of hard-core boson on a one-dimensional lattice with frustrated next-nearest-neighbor hopping and nearest-neighbor interaction. At half filling, for equal magnitude of nearest- and next-nearest-neighbor hopping, the ground state of this system exhibits a first-order phase transition from a bond-ordered solid to a charge-density-wave solid as a function of the nearest- neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a supersolid phase which has concurrent off-diagonal long-range order and density-wave order which is unusual in a system of hard-core bosons in one dimension. Using the finite-size density-matrix renormalization group method, we obtain the complete phase diagram for this model.