An exact inversion formula from determining a planar fault from boundary measurements

Counting non planar diagrams: an exact formula

We present an explicit solution of a simply stated, yet unsolved, combinatorial problem, of interest both in quantum field theory (Feynman diagrams enumeration, beyond the planar approximation) and in statistical mechanics (high temperature loop expansion of some frustrated lattice spin model). PACS: 02.10.Eb, 02.10.Nj, 05.50.+q ∗e-mail: [email protected] The problem of counting the number of r...

An Improved Exact Inversion Formula for Cone Beam Vector Tomography

In this article we present an improved exact inversion formula for the 3D cone beam transform of vector fields. It is well known that only the solenoidal part of a vector field can be determined by the longitudinal ray transform of a vector field in cone beam geometry. The exact inversion formula, as it was developed in A. Katsevich and T. Schuster, An exact inversion formula for cone beam vect...

Determining Nonsmooth First Order Terms from Partial Boundary Measurements

We extend results of Dos Santos Ferreira-Kenig-SjöstrandUhlmann (arXiv:math.AP/0601466) to less smooth coefficients, and we show that measurements on part of the boundary for the magnetic Schrödinger operator determine uniquely the magnetic field related to a Hölder continuous potential. We give a similar result for determining a convection term. The proofs involve Carleman estimates, a smoothi...

The Planar Tree Lagrange Inversion Formula

Exact solution of the specific-heat-phonon spectrum inversion from the Mobius inverse formula

The application of the Mobius inversion formula to the specific-heat-phonon spectrum inversion problem (SPI) initially appeared promising [N.X. Chen, Phys. Rev. Lett. 64, 1193 (1990); J. Maddox, Nature (London) 344, 377 (1990)]. However, no one has previously been able to obtain the exact Debye spectrum with the correct cut-off factor and frequency dependence from the Mobius formula. The main d...