We deal with the problem of determining an inclusion within an electrical conductor from electrical boundary measurements. Under mild a priori assumptions we establish an optimal stability estimate.

We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫ BR |∇v|dx + Per({v > 0}), 1 < p < ∞, over the set {v ∈ H 0 (BR)| v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.

We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially determines that of the boundary. When the hypersurface defines a hyperplane arrangement, the cohomology of the boundary is completely determined by the combina...

We prove existence results for travelling waves in discrete, damped, dc-driven sine-Gordon equations with periodic boundary conditions.

This paper investigates how social images and image change detection techniques can be applied to identify the damages caused by natural disasters for disaster assessment. We propose a framework that takes advantages of near duplicate image detection and robust boundary matching for the change detection in disasters. First we perform the near duplicate detection by local interest point-based ma...

Over twenty years ago, Marc Kac posed what is arguably one of the simplest inverse problems in pure mathematics: "Can one hear the shape of a drum?" [19]. Mathematically, the question is formulated as follows. Let /2 be a simply connected, plane domain (the drumhead) bounded by a smooth curve 7, and consider the wave equation on /2 with Dirichlet boundary condition on 7 (the drumhead is clamped...

in this study, calcareous nannofossils at the boundary between tirgan and sarcheshmeh formations at taherabad and mozduran sections have been studied. these sections are located in the eastern kopet-dagh basin. 22 nannoplankton species of 14 genera in taherabad section and 20 species of 14 genera in mozduran section were identified. according to the first occurrence of index species and fossil ...