This paper addresses the issue of 3D mesh indexation by using shape descriptors (SDs) under constraints of geometric and topological invariance. A new shape descriptor, the Canonical 3D Hough Transform Descriptor (C3DHTD) is here proposed. Intrinsically topologically stable, the C3DHTD is not invariant to geometric transformations. Nevertheless, we show mathematically how the C3DHTD can be opti...

A quadratic polynomial differential system can be identified with a single point of R12 through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of R12 having an integrable saddle. We show that there are only 47 topologically different phase portraits in the Poincaré disc associated to this family of quadratic systems up to a r...

We study edge states of noncentrosymmetric superconductors where spin-singlet d-wave pairing mixes with spin-triplet p (or f)-wave one by spin-orbit coupling. For d(xy)-wave pairing, the obtained Andreev bound state has an anomalous dispersion as compared to conventional helical edge modes. A unique topologically protected time-reversal invariant Majorana bound state appears at the edge. The ch...

A pseudoclassical model for P ,T -invariant system of topologically massive U(1) gauge fields is proposed. The model demonstrates a nontrivial relationship between continuous and discrete symmetries and reveals a phenomenon of “classical quantization”. It allows one to identify SU(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. We show this P ,T ...