In the context of D-dimensional Euclidean gravity, we define the natural generalisation to D-dimensions of the self-dual Yang-Mills equations, as duality conditions on the curvature 2-form of a Rie-mannian manifold. Solutions to these self-duality equations are provided by manifolds of SU (2), SU (3), G 2 and Spin(7) holonomy. The equations in eight dimensions are a master set for those in lowe...

We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two dual sets of generalized reflection equations with associated consistent fusion procedures. Products of their respective solutions yield commuting quantum traces.

We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neug...

We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two dual sets of generalized reflection equations with associated consistent fusion procedures. Products of their respective solutions yield commuting quantum traces.

Two technical solutions using single or dual shot offer different advantages and disadvantages for dual eceived 1 March 2009 ccepted 23 March 2009

In our note we discuss some strongly elliptic modifications of the total variation inpainting model formulated in the space BV(Ω) and investigate the corresponding dual variational problems. Remarkable features are the uniqueness of the dual solution and the uniqueness of the absolutely continuous part ∇ a u of the gradient of BV-solutions u on the whole domain. Additionally, any BV-minimizer u...

`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method h...

We propose type IIA supergravity solutions dual to the 1/2 BPS vacua of the BMN matrix model. These dual solutions are analyzed using the Polchinski-Strassler method and have brane configurations of concentric shells of D2 branes (or NS5 branes) with various radii and D0 charge. These branes can be viewed as polarized from N D0 branes by a transverse R-R magnetic 6-form flux and an NS-NS 3-form...

We construct the non-relativistic counterparts of some well-known supergravity solutions dual to relevant and marginal deformations of N = 4 super Yang-Mills. The main tool we use is the null Melvin twist and we apply it to the N = 1 and N = 2∗ Pilch-Warner RG flow solutions as well as the Lunin-Maldacena solution dual to β-deformations of N = 4 super Yang-Mills. We also obtain a family of supe...