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The remap phase in arbitrary Lagrangian-Eulerian (ALE) hydrodynamics involves the transfer of field quantities defined on a post-Lagrangian mesh to some new mesh, usually generated by a mesh optimization algorithm. This problem is often posed in terms of transporting (or advecting) some state variable from the old mesh to the new mesh over a fictitious time interval. It is imperative that this remap process be monotonic, that is, not generate any new extrema in the field variables. It is well known that the only linear methods that are guaranteed to be monotonic for such problems are first-order accurate; however, much work has been performed in developing non-linear methods, which blend both high and low (first) order solutions to achieve monotonicity and preserve high-order accuracy when the field is sufficiently smooth. In this paper, we present a set of methods for enforcing monotonicity targeting high-order discontinuous Galerkin methods for advection equations in the context of high-order curvilinear ALE hydrodynamics. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. [ABSTRACT FROM AUTHOR]

This paper continues the project of constructing the character formulae for the positive energy unitary irreducible representations of the N-extended D = 4 conformal superalgebras su(2, 2/N). In the first paper we gave the bare characters which represent the defining odd entries of the characters. Now we give the full explicit character formulae for N = 1 and for several important examples for N = 2 and N = 4. [ABSTRACT FROM AUTHOR]

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras su( n, n). Our choice of these algebras is motivated by the fact that for n = 2 this is the conformal algebra of 4-dimensional Minkowski space-time. Furthermore for general n these algebras belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of n-dimensional Minkowski space-time. We give the main multiplets of indecomposable elementary representations for n = 2, 3, 4, including the necessary data for all relevant invariant differential operators. [ABSTRACT FROM AUTHOR]

The exotic bialgebras that arise from a 9 × 9 unitary braid matrix are constructed. The dual bialgebra of one of these exotic bialgebras is presented. [ABSTRACT FROM AUTHOR]

The singular vectors in Verma modules over the Schrödinger algebra ŝ( n) in ( n + 1)-dimensional space-time are found for the case of general representations. Using the singular vectors, hierarchies of equations invariant under Schrödinger algebras are constructed. [ABSTRACT FROM AUTHOR]

The solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves are given. [ABSTRACT FROM AUTHOR]

We give the classification of the positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n, R).© 2005 Pleiades Publishing, Inc. [ABSTRACT FROM AUTHOR]

We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the study of quantum linear conformal (Weyl) gravity by writing the corresponding q-deformed equations. [ABSTRACT FROM AUTHOR]

We give explicit expressions for the singular vectors of U(A) in terms of the Poincaré–Birkhoff–Witt (PBW) basis. We relate these expressions with those in terms of the simple root vectors. [ABSTRACT FROM AUTHOR]

The structure of the groups SL(4,R) and GL(4,R) and their universal cover- ing groups SL(4,R) and GL(4,R), respectively, and Lie algebras sl(4,R) and gl(4,R), respectively, are studied. The parabolic subgroups and subalgebras are identified and the cuspidal parabolic subgroups singled out. The Iwasawa and Bruhat decompositions are given explicitly. All elementary representations (ER) of SL(4,R) are explicitly given in two equivalent realizations. Using the preceding detailed structural analysis the SL(4,R) constructions are used for the explicit realization of all ER of SL(4,R), GL(4,R), and GL(4,R). The results shall be applied (among other things) elsewhere for the construction of all irreducible representations of the above groups. [ABSTRACT FROM AUTHOR]

The structure of the group SU(2, 2) and of its Lie algebra is studied in detail. The results will be applied in subsequent parts devoted to the explicit construction of elementary representations of SU(2, 2) induced from different parabolic subgroups and of the intertwining operators between these representations. A summary of some results of Parts II and III is given. [ABSTRACT FROM AUTHOR]