We classify the tube domains in C 4 with affinely homogeneous base whose boundary contains a non-degenerate affinely homogeneous hypersurface. It follows that these domains are holo-morphically homogeneous and amongst them there are four new examples of unbounded homogeneous domains (that do not have bounded realisations). These domains lie to either side of a pair of Levi-indefinite hypersurfa...

We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.

We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.

Definition 1. Let f and g be functions in ω. We say that f is dominated by g iff there is some natural number n such that f ≤n g, i.e. (∀i ≥ n)(f(i) ≤ g(i)). Then <∗= ∪ ≤n is called the bounding relation on ω. If F is a family of functions in ω we say that F is dominated by the function g, and denote it by F <∗ g iff (∀f ∈ F)(f <∗ g). We say that F is unbounded (also not dominated) iff there is...

This work establishes an exponential stability result for a porous-elastic system, where the dissipation mechanisms act on porous and elastic equations. Our completes some of results in literature unbounded domains.

This article concerns the asymptotic behavior of solutions to the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. First we introduce a continuous cocycle for the equations and then prove the existence and uniqueness of tempered random attractors. We also characterize the structures of the random attractors by comp...

We study the numerical solution of scalar time-harmonic wave equations on unbounded domains which can be split into a bounded interior domain primary interest and an exterior with separab...

In this work, we analyse the Galerkin Infinite Element method for option pricing. The Infinite Element method is a very simple and efficient modification of the more common Finite Element method. It keeps the best features of Finite Elements, i.e. bandedness, easiness of programming, accuracy, and it is particularly useful when solving problems in unbounded domains. Three main aspects are consi...

AhtractThis paper discusses the rationale for employing alternative basis functions to the ubiquitous Gaussian in Radial Basis Function networks. In particular we concentrate upon employing unbounded basis functions (though the network as a whole remains bounded), and non positive definite basis functions. The use of unbounded and nonpositive basis functions, though counterintuitive in applicat...