We develop a theory of generalised solutions for elliptic boundary value problems subject to Robin boundary conditions on arbitrary domains, which resembles in many ways that of the Dirichlet problem. In particular, we establish Lp-Lq-estimates which turn out to be the best possible in that framework. We also discuss consequences to the spectrum of Robin boundary value problems. Finally, we app...

Suppose G is a semisimple Lie group with infinite center. As in the finite center case, the tempered spectrum of G consists of families of representations induced from cuspidal parabolic subgroups P = MAN. However, in the infinite center case, the representations of M to be induced are not discrete series, but are relative discrete series which occur in continuous families. In two previous pape...

The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic geometry. To do this, we use the parabolic partial differential equation for prescribing scalar curvature. In this equation the horizon geometry is contained within the freely specifiable part of the metric. This contrasts with the conformal method in which ...

The performance of a multidimensional finite-volume transport scheme is evaluated on the cubed-sphere geometry. Advection tests with prescribed winds are used to evaluate a variety of cubed-sphere projections and grid modifications including the gnomonic and conformal mappings, as well as two numerically generated grids by an elliptic solver and spring dynamics. We explore the impact of grid no...

Three alternatives for integrating a solar field with the bottoming cycle of a combined cycle plant are modeled: parabolic troughs with oil at intermediate and low cycle pressures and Fresnel linear collectors at low cycle pressure. It is assumed that the plant will always operate at nominal conditions, using post-combustion during the hours of no solar resource. A thermoeconomic study of the o...

We give a sufficient criterion on a highest weight module of a semisimple Lie algebra to admit a resolution in terms of sums of modules induced from a parabolic subalgebra. In particular, we show that all unitary highest weight modules admit such a resolution. As an application of our results we compute (minimal) resolutions and explicit formulas for the Hilbert series of the unitary highest we...

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical KazhdanLusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category O of the general linear supera...

We show existence and uniqueness results for nonlinear parabolic equations in noncylindrical domains with possible jumps in the time variable.

Parabolic triples of the form (E∗, θ, σ) are considered, where (E∗, θ) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and σ is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E∗, θ) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bu...