In this paper we survey some of the relations between Plebański description of self-dual gravity through the heavenly equations and the physics (and mathematics) of N = 2 Strings. In particular we focus on the correspondence between the infinite hierarchy in the ground ring structure of BRST operators and its associated Boyer-Plebański construction of infinite conserved quantities in self-dual ...

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of Abstract Algebraic Logic. In [4], a Priestley-style duality is established between the category of positive modal alg...

The singular cochain complex of a topological space is a classical object. It is a Differential Graded algebra which has been studied intensively with a range of methods, not least within rational homotopy theory. More recently, the tools of Auslander-Reiten theory have also been applied to the singular cochain complex. One of the highlights is that by these methods, each Poincaré duality space...

Consider a ring K, a topological space X and a sheaf A on X of K[[~]]-algebras. Assuming A ~-adically complete and without ~torsion, we first show how to deduce a coherency theorem for complexes of A -modules from the corresponding property for complexes of A /~A -modules. We apply this result to prove that, under a natural properness condition, the convolution of two coherent kernels over defo...

Maximal monotone operators on a Banach space into its dual can be represented by convex functions bounded below by the duality product. It is natural to ask under which conditions a convex function represents a maximal monotone operator. A satisfactory answer, in the context of reflexive Banach spaces, has been obtained some years ago. Recently, a partial result on non-reflexive Banach spaces w...

During the last two decades, major developments in convex optimization were focusing on conic programming, primarily, on linear, conic quadratic and semidefinite optimization. Conic programming allows to reveal rich structure which usually is possessed by a convex program and to exploit this structure in order to process the program efficiently. In the paper, we overview the major components of...

Quantum toroidal algebras (or double affine quantum algebras) are defined from quantum affine Kac-Moody algebras by using the Drinfeld quantum affinization process. They are quantum groups analogs of elliptic Cherednik algebras (elliptic double affine Hecke algebras) to whom they are related via Schur-Weyl duality. In this review paper, we give a glimpse on some aspects of their very rich repre...

Four primal discontinuous Galerkin methods are applied to solve reactive transport problems, namely, Oden-Babuška-Baumann DG (OBB-DG), non-symmetric interior penalty Galerkin (NIPG), symmetric interior penalty Galerkin (SIPG), and incomplete interior penalty Galerkin (IIPG). A unified a posteriori residual-type error estimation is derived explicitly for these methods. From the computed solution...

* Correspondence: drizhar@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Full list of author information is available at the end of the article Abstract In this article, we are concerned with a nondifferentiable minimax fractional programming problem. We derive the sufficient condition for an optimal solution t...

We develop the theory of duality for projective varieties defined over fields of arbitrary characteristic. A central concept in this work is that of reflexivity and our main tool is the rank of certain local Hessians which provides a numerical criterion for reflexivity. Many of our results are necessary and sufficient conditions for reflexivity. We also analyze the reflexivity of a general hype...