On Asymptotic Symmetries of 3d Extended Supergravities

We study asymptotic symmetry algebras for classes of three dimensional supergravities with and without cosmological constant. In the first part we generalise some of the non-Dirichlet boundary conditions of $AdS_3$ gravity to extended supergravity theories, and compute their asymptotic symmetries. In particular, we show that the boundary conditions proposed to holographically describe the chiral induced gravity and Liouville gravity do admit extension to the supergravity contexts with appropriate superalgebras as their asymptotic symmetry algebras. In the second part we consider generalisation of the 3d $BMS$ computation to extended supergravities without cosmological constant, and show that their asymptotic symmetry algebras provide examples of nonlinear extended superalgebras containing the $BMS_3$ algebra

Holographic chiral induced W-gravities

We study boundary conditions for 3-dimensional higher spin gravity that admit asymptotic symmetry algebras expected of 2-dimensional induced higher spin theories in the light cone gauge. For the higher spin theory based on sl(3, R) plus sl(3,R) algebra, our boundary conditions give rise to one copy of classical W3 and a copy of sl(3,R) or su(1,2) Kac-Moody symmetry algebra. We propose that the higher spin theories with these boundary conditions describe appropriate chiral induced W-gravity theories on the boundary. We also consider boundary conditions of spin-3 higher spin gravity that admit u(1) plus u(1) current algebra.Comment: 19 page

An sl(2, R) current algebra from AdS_3 gravity

We provide a set of chiral boundary conditions for three-dimensional gravity that allow for asymptotic symmetries identical to those of two-dimensional induced gravity in light-cone gauge considered by Polyakov. These are the most general boundary conditions consistent with the boundary terms introduced by Compere, Song and Strominger recently. We show that the asymptotic symmetry algebra of our boundary conditions is an sl(2,R) current algebra with level given by c/6. The fully non-linear solution in Fefferman--Graham coordinates is also provided along with its charges.Comment: 8 page

Physiological, Biochemical and Biotechnological Studies on some selected Algae

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Some results on the choice of run order for experimental designs with correlated errors : a thesis presented in partial fulfilment of the requirements for the degree of M.Sc. in Statistics at Massey University

This thesis examines the efficiency of some commonly used experimental designs in situations where the assumption of independent errors is violated. In particular this research mainly involves finding efficient run orders for various models of two level factorial experiments, three level factorial experiments and response surface designs when errors are assumed to follow either first order moving average model or first order autoregressive model. In this thesis, attention is given to systematic methods of allocating treatments based on various algorithms which provide more efficient designs and lead to good estimates of the parameters

Modelling of acoustic transmission through perforated layer

The paper deals with modeling the acoustic transmission through a perforated interface plane separating two halfspaces occupied by the acoustic medium. We considered the two-scale homogenization limit of the standard acoustic problem imposed in the layer with the perforated periodic structure embedded inside. The homogenized transmission conditions govern the interface discontinuity of the acoustic pressure associated with the two halfspaces and the magnitude of the fictitious transversal acoustic velocity. By numerical examples we illustrate this novel approach of modeling the acoustic impedance of perforated interfaces

Modeling flows in periodically heterogeneous porous media with deformation-dependent permeability

The paper proposes a non-linear model of the Biot continuum. The nonlienarity is introduced in terms of the material coefficients which are expressed as linear functions of the macroscopic response. These functions are obtained by the sensitivity analysis of the homogenized coefficients computed for a given geometry of the porous structure which transforms due to the local deformation. Linear kinematics is assumed, however, the approach can be extended to large deforming porous materials