We propose sharp results on the numerical approximation of low-regularity electromagnetic fields by edge finite elements. We consider general geometrical settings, including topologically non-trivial domains or domains with a nonconnected boundary. In the model, the electric permittivity and magnetic permeability are symmetric, tensor-valued, piecewise smooth coefficients. In all cases, the err...

We determine explicitly the formal moduli space of certain complete topological modules over a topologically finitely generated local k-algebra R, not necessarily commutative, where k is a field. The class of topological modules we consider include all those of finite rank over k and some of infinite rank as well, namely those with a Schauder basis in the sense of §1. This generalizes the resul...

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Despite the wide use of Caenorhabditis elegans as a model organism, the first virus naturally infecting this organism was not discovered until six years ago. The Orsay virus and its related nematode viruses have a positive-sense RNA genome, encoding three proteins: CP, RdRP, and a novel δ protein that shares no homology with any other proteins. δ can be expressed either as a free δ or a CP-δ fu...

We study δ-derivations – a construction simultaneously generalizing derivations and centroid. First, we compute δ-derivations of current Lie algebras and of modular Zassenhaus algebra. This enables us to provide examples of Lie algebras having 1 2 -derivations which are divisors of zero, thus answering negatively a question of Filippov. Second, we note that δ-derivations allow, in some circumst...

Zinc coating is formed by the heterogeneous assembly of the Γ, Γ1, δ, ζ and η phases whose mechanical properties greatly differ from each other. Thermal strains resulting from large differences between thermal expansion coefficients are partially relaxed by the formation of a crack network. In order to model this phenomenon, initial hardness, thermal expansion coefficient αi and toughness (KIC)...

We prove that every tower of normal filters of height δ (δ supercompact) is precipitous assuming that each normal filter in the tower is the club filter restricted to a stationary set. We give an example to show that this assumption is necessary. We also prove that every normal filter can be generically extended to a well-founded V -ultrafilter (assuming large cardinals). In this paper we inves...

We study the computational complexity of approximately counting the number of independent sets of a graph with maximum degree Δ. More generally, for an input graph G = (V,E) and an activity λ > 0, we are interested in the quantity ZG(λ) defined as the sum over independent sets I weighted as w(I) = λ|I|. In statistical physics, ZG(λ) is the partition function for the hard-core model, which is an...