We present a space-time certified reduced basis method for Burgers’ equation over the spatial interval (0, 1) and the temporal interval (0, T ] parametrized with respect to the Peclet number. We first introduce a Petrov-Galerkin space-time finite element discretization, which enjoys a favorable inf-sup constant that decreases slowly with Peclet number and final time T . We then consider an hp i...

Proteins interact with other molecules, e.g. ligands or other proteins, in specific binding sites. Key factors for these interactions are the shape, size, and buriedness of the binding site, as well as its physicochemical composition. Since all these properties usually significantly vary among different proteins, up to now there is no standard definition what constitutes a binding site [1]. Thu...

for entire functions, the notions of their growth indicators such as ritt order are classical in complex analysis. but the concepts of relative ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. therefore the studies of the growths of entire functions in the light of thei...

The ring of quasisymmetric functions is free over the ring of symmetric functions. This result was previously proved by M. Hazewinkel combinatorially through constructing a polynomial basis for quasisymmetric functions. The recent work by A. Savage and O. Yacobi on representation theory provides a new proof to this result. In this paper, we proved that under certain conditions, the positive par...

Reliable a posteriori error estimates without generic constants can be obtained by a comparison of the finite element solution with a feasible function for the dual problem. A cheap computation of such functions via equilibration is well known for scalar equations of second order. We simplify and modify the equilibration such that it can be applied to the curl-curl equation and edge elements. T...

We study the explicit formula of Lusztig’s integral forms of the level one quantum affine algebra Uq(ŝl2) in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra of Z. Schur functions are realized as certain orthonormal basis vectors in the vertex representation associated to the standard Heisenberg algebra. In this picture the Littlewood-Ric...

Multivariate vertical Empirical Orthogonal Functions (EOF) are calculated for the entire Mediterranean Sea both from observations and model simulations, in order to find the optimal number of vertical modes to represent the upper thermocline vertical structure. For the first time, we show that the large-scale Mediterranean thermohaline vertical structure can be represented by a limited number o...

This article presents a new spatio-temporal method for M/EEG source reconstruction based on the assumption that only a small number of events, localized in space and/or time, are responsible for the measured signal. Each space-time event is represented using a basis function expansion which reflects the most relevant (or measurable) features of the signal. This model of neural activity leads na...

The paper deals with a non-conforming nite element method on a class of anisotropic meshes. The Crouzeix-Raviart element is used on triangles and tetrahedra. For rectangles and prismatic (pentahedral) elements a novel set of trial functions is proposed. Anisotropic local interpolation error estimates are derived for all these types of element and for functions from classical and weighted Sobole...