This paper analyzes the limits of applicability of the time domain surface impedance concept. Numerical results obtained by the boundary element formulation employing time domain surface impedance boundary conditions (SIBCs) of different orders of approximation are compared with experimental data and numerical results obtained using the finite element method. An analytical formula for evaluatio...

In this paper, we established a quantitative unique continuation results for a coupled heat equations, with the homogeneous Dirichlet boundary condition, on a bounded convex domain Ω of [Formula: see text] with smooth boundary ∂Ω. Our result shows that the value of the solutions can be determined uniquely by its value on an arbitrary open subset ω of Ω at any given positive time T.

The study of BTZ blackhole physics and the cosmological horizon of 3D de Sitter spaces are carried out in unified way using the connections to the Chern Simons theory on three manifolds with boundary. The relations to CFT on the boundary is exploited to construct exact partition functions and obtain logarithmic corrections to Bekenstein formula in the asymptotic regime. Comments are made on the...

In this work, an inverse problem for the time-independent vector transfer equation for polarized radiation in isotropic medium is examined. In the problem, it is required to find the attenuation factor from known solution of the equation at the medium boundary. A formula is derived that relates the Radon transform of the attenuation factor with the radiation-flux density at the boundary. The un...

Conditions for the gluing matrix defining consistent boundary conditions of twodimensional nonlinear σ–models are analyzed and reformulated. Transformation properties of the right–invariant fields under Poisson–Lie T–plurality are used to derive a formula for the transformation of the boundary conditions. Examples of transformation of D–branes in two and three dimensions are presented. We find ...

Let −∆ denote the Dirichlet Laplace operator on a bounded open set in Rd. We study the sum of the negative eigenvalues of the operator −h∆− 1 in the semiclassical limit h → 0+. We give a new proof that yields not only the first term of the asymptotic formula but also the second term involving the surface area of the boundary of the set. The proof is valid under weak smoothness assumptions on th...

Given a Borel function ψ defined on a bounded open set Ω with Lipschitz boundary and φ ∈ L1(∂Ω,Hn−1), we prove an explicit representation formula for the L lower semicontinuous envelope of Mumford-Shah type functionals with the obstacle constraint u ≥ ψ Hn−1 a.e. on Ω and the Dirichlet boundary condition u = φ on ∂Ω. Mathematics Subject Classification. 49J45, 74R10. Received December 12, 2006. ...

We analyse the general boundary conditions (branes) consistent with the Poisson-sigma model and study the structure of the phase space of the model defined on the strip with these boundary conditions. Finally, we discuss the perturbative quantization of the model on the disc with a PoissonDirac brane and relate it to Kontsevich’s formula for the deformation quantization of the Dirac bracket ind...

Abstract We study the form of the Turaev-Viro partition function Z(M) for different 3-manifolds with boundary. We show that for S2 boundaries Z(M) factorizes into a term which contains the boundary dependence and another which depends only on the topology of the underlying manifold. From this follows easily the formula for the connected sum of two manifolds Z(M#N ). For general Tg boundaries th...

We consider a viscous incompressible fluid flow governed by the Stokes system. We assume that a finite number of small inhomogeneities (particles) are immersed in the fluid. The reciprocity gap functional is introduced to describe the boundary data. An asymptotic formula for the reciprocity gap functional is derived. The obtained formulas can form the basis for very effective computational iden...