Acoustic transmission problems: Wavenumber-explicit bounds and resonance-free regions

We consider the Helmholtz transmission problem with one penetrable star-shaped Lipschitz obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds on the solution in terms of the data, with these bounds explicit in all parameters. In particular, the (weighted) [Formula: see text] norm of the solution is bounded by the [Formula: see text] norm of the source term, independently of the wavenumber. These bounds then imply the existence of a resonance-free strip beneath the real axis. The main novelty is that the only comparable results currently in the literature are for smooth, convex obstacles with strictly positive curvature, while here we assume only Lipschitz regularity and star-shapedness with respect to a point. Furthermore, our bounds are obtained using identities first introduced by Morawetz (essentially integration by parts), whereas the existing bounds use the much-more sophisticated technology of microlocal analysis and propagation of singularities. We also adapt existing results to show that if the assumption on the wavenumbers is lifted, then no bound with polynomial dependence on the wavenumber is possible.

Bounds on the solution of a Cauchy-type problem involving a weighted sequential fractional derivative

In this paper we establish some bounds for the solution of a Cauchytype problem for a class of fractional differential equations with a weighted sequential fractional derivative. The bounds are based on a Bihari-type inequality and a bound on the Gauss hypergeometric function.

RF Tomography in Free Space: Experimental Validation of the Forward Model and an Inversion Algorithm Based on the Algebraic Reconstruction Technique

Radio-frequency tomography was originally proposed to image underground cavities. Its flexible forward model can be used in free-space by choosing an appropriate dyadic Green's function and can be translated in the microwave domain. Experimental data are used to validate a novel inversion scheme, based on the algebraic reconstruction technique. The proposed method is improved by introducing physical bounds on the solution returned. As a result, the images of the dielectric permittivity profiles obtained are superior in quality to the ones obtained using classical regularization approaches such as the truncated singular value decomposition. The results from three experimental case studies are presented and discussed.

Coverage and Connectivity Improvement Algorithms for the Wireless Sensor Networks

In this paper we study the increase of coverage and connectivity in a sensor network with a view to improving coverage, while preserving the network’s coverage. We also examine the impact of on the related problem of coverage-boundary detection. We reduce both problems to the computation of Voronoi diagrams and intersectional point method prove and achieve lower bounds on the solution of these problems and present efficient distributed algorithms for computing and maintaining solutions in cases of sensor failures or insertion of new sensors. We prove the correctness and termination properties of our distributed algorithms, and analytically characterize the time complexity and the traffic generated by our algorithms. Our algorithms show that the increase coverage & Connectivity in wireless sensor density.