This document presents two spectral methods for shape matching and recognition. Our first method computes the Laplace-Beltrami spectra on a domain to describe its shape. Since the spectrum is an isometry invariant and contains geometrical information, it is optimally suited for shape analysis and shape matching of geometric data. We have recently focused on global shape comparison with an appli...

A new linear system is constructed for Poincaré supergravities in two dimensions. In contrast to previous results, which were based on the conformal gauge, this linear system involves the topological world sheet degrees of freedom (the Beltrami and super-Beltrami differentials). The associated spectral parameter likewise depends on these and is itself subject to a pair of differential equations...

Abstract We review recent rigorous results on the phenomenon of vortex reconnection in classical and quantum fluids. In context Navier–Stokes equations $$\mathbb {T}^3$$ T 3 we show existence global smooth solutions that exhibit creation destructi...

The dynamics of low-energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation curved space-time. In Cartesian coordinates, a parametrization can be straightforwardly obtained, but resulting intricate for deformations. Two different strategies are introduced to simplify this problem: diagonal metric approximation and change variables isothermal...

We use Andreev-Thurston's theorem on the existence of circle packings to construct approximating solutions to the Beltrami equations on Riemann surfaces. The convergence of the approximating solutions on compact subsets will be shown. This gives a constructive proof of the existence theorem for Beltrami equations.

Recently, a symmetric differential operator (SDO) is attracted to studying in the field of mathematical analysis. A new formal SDO presented generalize some well known operators complex domain. According this formulation, we shall exam boundedness and compactness spaces, such as Hilbert space Sobolev space. For purpose, suggest norms solve fractional Beltrami equation open unit disk. This has a...

Symmetries play an important role in solving partial differential equations. In this paper, the determining equations for a class of nonlinear partial differential equations with arbitrary order are considered. It is shown that the determining equations for the nonclassical reduction can be obtained by requiring the compatibility between the original equation and the invariant surface condition...