We prove wavenumber-explicit bounds on the Dirichlet-to-Neumann map for the Helmholtz equation in the exterior of a bounded obstacle when one of the following three conditions holds: (i) the exterior of the obstacle is smooth and nontrapping, (ii) the obstacle is a nontrapping polygon, (iii) the obstacle is star-shaped and Lipschitz. We prove bounds on the Neumann-to-Dirichlet map when one of c...

We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism ...

Within front-form dynamics and in the Breit frame where initial and final three-momenta of the system are directed along the z axis, Poincaré covariance constrains the current operator only through kinematical rotations around the z axis. Therefore, in this frame the current can be taken in the one-body form. Applications to deep inelastic structure functions in an exactly solvable model and to...

The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré group.

In spite of its almost photographic realism, the Arnolfi ni Portrait by naturalistic painter Jan van Eyck exhibits faulty linear perspective. This paper describes the creation of a three-dimensional virtual reconstruction of the painting’s interior scene using commercial modelling and image processing software. The result presented here is a rendering of the reconstructed scene closely resembli...

Ω |∇u| dx )1/p holds for 1 ≤ p < n whenever u is smooth, uΩ = |Ω|−1 ∫ Ω u dx, and Ω ⊂ R is bounded and satisfies the cone condition. By the density of smooth functions, (1.1) then holds for all functions in the Sobolev space W (Ω) consisting of all functions in L(Ω) whose distributional gradients belong to L(Ω). For 1 < p < n, inequality (1.1) was proved by Sobolev [S1], [S2], and, for p = 1, t...

A novel approach for pitch mark determination based on dynamical systems theory is presented. Pitch marks are used for speech analysis and modification, such as jitter measurement or time scale modification. The algorithm works in a pseudo-state space and calculates the Poincaré section at a chosen point in the state space. Pitch marks are then found at the crossing of the trajectories with the...