Let V (t) = etGb , t ≥ 0, be the semigroup generated by Maxwell’s equations in an exterior domain Ω ⊂ R3 with dissipative boundary condition Etan − γ(x)(ν ∧ Btan) = 0, γ(x) > 0, ∀x ∈ Γ = ∂Ω. We study the case when Ω = {x ∈ R3 : |x| > 1} and γ 6= 1 is a constant. We establish a Weyl formula for the counting function of the negative real eigenvalues of Gb.

In this paper we consider the inverse problem of identifying a linear inclusion inside an elastic body from exterior boundary measurements. Based on the asymptotic formula by Beretta and Francini (2006 SIAM J. Math. Anal. 38 1249–61), we design an effective reconstruction algorithm to find the endpoints and the thickness of a linear inclusion. Numerical experiments show that the algorithm is ef...

In this paper we are interested in the Quartapelle–Napolitano approach to calculation of forces in viscous incompressible flows in exterior domains. We study the possibility of deriving a simpler formulation of this approach which might lead to a more convenient expression for the hydrodynamic force, but conclude that such a simplification is, within the family of approaches considered, impossi...

A non-commutative version of the Bernštĕın-GelfandGelfand (BGG) correspondence is set up, and a sample application is given to periodic injective resolutions. 0. Introduction The Bernštĕın-Gelfand-Gelfand correspondence is surprising. It gives an equivalence of categories gr(E) ≃ D(coh P). This was proved in [4, thm. 2] and as always, to explain such a formula requires lots of words. On the lef...

Let V be a multiplication operator, whose negative part, V-(V-< 0) obeys-A + (1 + c)V->-c for some c, c > 0. Let W = Vx where x is the characteristic function of the exterior of a ball. Our main result asserts that the scattering for-A + V is complete if and only if that for-A + W is complete. Our technical estimates exploit Wiener integrals and the Feynman-Kac formula. We also make an applicat...

Let Ω ⊆ Rn be a compact convex set and x be a point in the exterior of Ω. The aperture angle of x relative to Ω is defined as the maximal angle of the smallest closed convex cone that contains Ω − x. This note provides an explicit formula, based on eigenvalues of symmetric matrices, for the aperture angle of a point relative to an ellipsoid.

Abstract. We extend our earlier work in [TZ1], where an analytic approach to the GuilleminSternberg conjecture [GS] was developed, to cases where the Spin-complex under consideration is allowed to be further twisted by certain exterior power bundles of the cotangent bundle. The main result is a weighted quantization formula in the presence of commuting Hamiltonian actions. The corresponding Mor...

We argue that the statistical entropy relevant for the thermal interactions of a black hole with its surroundings is (the logarithm of) the number of quantum microstates of the hole which are distinguishable from the hole's exterior, and which correspond to a given hole's macroscopic conguration. We compute this number explicitly from rst principles, for a Schwarzschild black hole, using nonper...

where V is the number of vertices, E is the number of edges, and F is the number of faces in the given graph, including the exterior face. This formula corresponds to the special case g = 0 (simple connectedness) of the more general Poincaré formula for genus g surfaces, in which χ ≡ χ(g) = 2− 2g. In this note we derive several analytical relations, similar to Euler’s formula, which hold for so...

We define the Dirichlet to Neumann operator on exterior differential forms for a compact Riemannian manifold with boundary and prove that the real additive cohomology structure of the manifold is determined by the DN operator. In particular, an explicit formula is obtained which expresses Betti numbers of the manifold through the DN operator. We express also the Hilbert transform through the DN...