This paper studies a prototype of inverse obstacle scattering problems whose governing equation is the Helmholtz equation in two dimensions. An explicit method to extract information about the location and shape of unknown obstacles from the far field operator with a fixed wave number is given. The method is based on: an explicit construction of a modification of Mittag-Leffler’s function via t...

2 Although multiple pulse and multi-dimensional NMR techniques permit generation of off-diagonal density matrix elements and observation of complex coherence transfer processes, eventually the density operator returns to an equilibrium state in which all coherences (off-diagonal elements of the density operator) have decayed to zero and the populations of the energy levels of the system (diagon...

We propose Steklov geometry processing, an extrinsic approach to spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace–Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, while many previous extrinsic methods lack theoretical justi cation. Instead, we propose a systematic approach by considering the Steklov eigenva...

We compute the microscopic spectrum of the QCD Dirac operator in the presence of dynamical fermions in the framework of random-matrix theory for the chiral Gaussian unitary ensemble. We obtain results for the microscopic spectral correlators, the microscopic spectral density, and the distribution of the smallest eigenvalue for an arbitrary number of flavors, arbitrary quark masses, and arbitrar...