Related papers: Coarse spaces using extended generalized eigenprob…
We construct finite-dimensional approximations of solution spaces of divergence form operators with $L^\infty$-coefficients. Our method does not rely on concepts of ergodicity or scale-separation, but on the property that the solution space…
Matlis proved a lot of homological properties of the fraction field of an integral domain. In this paper, we simplify and extend some of them from 1-dimensional (resp. rank one) cases to the higher dimensional (resp. finite rank) cases. For…
We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of $W_n$…
We introduce an abstract definition of a Hamming space that generalizes standard Hamming spaces $( \mathbb{Z}/ 2 \mathbb{Z})^n $. We classify countable locally standard Hamming spaces and show that each of them can be realized as the…
This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working…
In this paper we apply our results on the geometry of polygons in Cartan subspaces, symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the…
Restricted Heisenberg Lie superalgebras are studied over an algebraically closed field F of characteristic p > 2. We use the ordinary 1- and 2-cohomology spaces with trivial coefficients to compute the restricted 2-cohomology spaces. As an…
In this paper the structures of the generalised Euler-Lagrange equations and their associated conserved quantities are derived for one-dimensional Herglotz variational problems of order $n$. Their derivations use the framework of moving…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The use of the exotic cohomology of the symmetry algebras opens a way to formulate such…
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…
We consider an arbitrary selfadjoint operator on a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We prove a Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations, which improves a classical result by Crandall and Rabinowitz in the case where basic spaces are Hilbert spaces. Actually, our theorem does not need any…
The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to…
We construct complex root spaces remaining invariant under antilinear involutions related to all Coxeter groups. We provide two alternative constructions: One is based on deformations of factors of the Coxeter element and the other based on…
Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…
A new approach to the analytic theory of difference equations with rational and elliptic coefficients is proposed. It is based on the construction of canonical meromorphic solutions which are analytical along "thick paths". The concept of…
In this paper we give sharp extension results for convoluted solutions of abstract Cauchy problems in Banach spaces. The main technique is the use of algebraic structure (for usual convolution product $\ast$) of these solutions which are…