In this paper we present and compare a support for setting up and execution of multiscale applications in two types of infrastructures: local HPC cluster and Amazon AWS cloud solutions. We focus on applications based on the MUS-CLE framework where distributed single scale modules running concurrently form one multiscale application. We also integrate presented solution with the GridSpace virtual laboratory that enables users to develop and execute virtual experiments on the underlying computational and storage resources through its website based interface. Finally, we present a design of a user friendly visual tool supporting application distribution.
This paper deals with the so-called Radon inversion problem formulated in the following way: Given a $$p>0$$ p > 0 and a strictly positive function H continuous on the unit circle $${\partial {\mathbb {D}}}$$ ∂ D , find a function f holomorphic in the unit disc $${\mathbb {D}}$$ D such that $$\int _0^1|f(zt)|^pdt=H(z)$$ ∫ 0 1 | f ( z t ) | p d t = H ( z ) for $$z \in {\partial {\mathbb {D}}}$$ z ∈ ∂ D . We prove solvability of the problem under consideration. For $$p=2$$ p = 2 , a technical improvement of the main result related to convergence and divergence of certain series of Taylor coefficients is obtained.
In this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with $${\mathcal {C}}^2$$ C 2 boundary. We show that given $$p>0$$ p > 0 and a strictly positive, continuous function $$\Phi $$ Φ on $$\partial \Omega $$ ∂ Ω , by use of homogeneous polynomials it is possible to construct a holomorphic function $$f \in {\mathcal {O}}(\Omega )$$ f ∈ O ( Ω ) such that $$\displaystyle \smallint _0^1 |f(zt)|^pdt = \Phi (z)$$ ∫ 0 1 | f ( z t ) | p d t = Φ ( z ) for all $$z \in \partial \Omega $$ z ∈ ∂ Ω . In our approach we make use of so-called lacunary K-summing polynomials (see definition below) that allow us to construct solutions with in some sense extremal properties.
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