We consider limiting Carleman weights for Dirac operators and prove corresponding Carleman estimates. In particular, we show that harmonic functions can be considered as limiting Carleman weights for Dirac operators. As an application we consider the inverse problem of recovering a Lipschitz continuous magnetic field and electric potential from boundary measurements for the Pauli Dirac operator.

The electronic bandstructure of Au$_2$Pb has a Dirac cone which gaps when undergoing structural transition into low temperature superconducting phase. This suggests that the phase ($T_c=1.1$ K) might hold topological properties at surface. Here we make Scanning Tunneling Microscopy experiments on surface Au$_2$Pb. We measure gap and find sizeable density states Fermi level. discuss possible ori...

2 Poisson geometry and some generalizations 3 2.1 Poisson manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Dirac structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Twisted structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Symplectic leaves and local structure of Poisson manifolds ...

The angular momentum of the physical electron, modelled as a Dirac fermion coupled to the electromagnetic field, is found to be /2, the same as that of a bare Dirac fermion and independent of the size of the electric charge. The coupled Maxwell-Dirac equations

This article is one of squeal papers. For this decade, I have been studying the Dirac operator on a submanifold as a restriction of the Dirac operator in E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a conformal surface case and complet...

This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in n-dimensional euclidean space E n to a surface or a space curve as physical models. These Dirac operators are identified with operators of the Frenet-Serret relation for a space curve case and of the generalized Weierstrass relation for a con...

The determination of the optimal distribution of the catalytic activity profile, whichmaximizes the catalytic effectiveness, in created unsteady state conditions, is analyzed andtreated numerically for the case of a simple reaction. It was proven that the modulation, of thetemperature and the reactant concentration of the external bulk fluid, leads to a considerableincrease of the catalytic eff...

Given a distribution ρ on persistence diagrams and observations X1, ...Xn iid ∼ ρ we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X1, ...Xn. If the underlying measure ρ is a combination of Dirac masses ρ = 1 m ∑m i=1 δZi then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fréchet mean computed by the alg...

Progress in Probability 49(2001), 241-256. The quasigeostrophic model describes large scale and relatively slow fluid motion in geophysical flows. We investigate the quasigeostrophic model under random forcing and random boundary conditions. We first transform the model into a partial differential equation with random coefficients. Then we show that, under suitable conditions on the random forc...

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topological non-trivial configurations (instantons). Due to the explicit infrared regularization there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the i...