The first order absolute moment provides a ridge map similar to the one provided by the GoG (gradient of Gaussian) filter. However, unlike the GoG filter, the first order absolute moment provides ridges at both edges and lines and gives rise to local extrema of the ridges at line endings, corners and junctions. Furthermore, a class of filters is obtained by introducing three low-pass filters at...

Let G be a compact connected Lie group, and (M,ω) a Hamiltonian G-space with proper moment map μ. We give a surjectivity result which expresses the K-theory of the symplectic quotient M//G in terms of the equivariant K-theory of the original manifold M , under certain technical conditions on μ. This result is a natural K-theoretic analogue of the Kirwan surjectivity theorem in symplectic geomet...

Let R = F2m +uF2m + · · ·+u k F2m , where F2m is the finite field with 2 m elements, m is a positive integer, and u is an indeterminate with u = 0. In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined and a sufficient and necessary condition for the existence of dual-con...

Abstract We study a system of equations on compact complex manifold, that couples the scalar curvature Kähler metric with spectral function first-order deformation structure. The comes from an infinite-dimensional reduction, which is hyperkähler reduction for particular choice function. main tool studying flat connection space deformations structure, allows to obtain formal complexification mom...

We give a general procedure for the calculation of the intersection Poincaré polynomial of the symplectic quotient M/K, of a symplectic manifold M by a hamiltonian group action of a compact Lie group K. The procedure mirrors that used by Kirwan for the calculation of the intersection Poincaré polynomial of a geometric invariant theory quotient of a nonsingular complex projective variety. That i...

The convexity theorem of Atiyah and Guillemin-Sternberg says that any connected compact manifold with Hamiltonian torus action has a moment map whose image is the convex hull of the image of the fixed point set. Sjamaar-Lerman proved that the Marsden-Weinstein reduction of a connected Hamitonian G-manifold is a stratified symplectic space. Suppose 1 → A → G → T → 1 is an exact sequence of compa...

Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian S action. We prove that, as fundamental groups of topological spaces, π1(M) = π1(minimum) = π1(maximum) = π1(Mred), where Mred is the symplectic quotient at any value in the image of the moment map φ. Let (M,ω) be a connected, compact symplectic manifold equipped with a circle action. If the action is Hamiltonian,...

Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian SU(2) or SO(3) action. We prove that, as fundamental groups of topological spaces, π1(M) = π1(Mred), where Mred is the symplectic quotient at any value of the moment map φ.

We address the problem of computing the fundamental group of a symplectic S-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian S-action. Several examples are presented to illustrate our main results.

A generalized standard map is quantized as a model of quantum chaos. We show that, only in hyperbolic chaotic regime, second moment of quantum level velocity is ∼ 1/h̄ as predicted by the random matrix theory. As a semiclassical implication, all higher order classical time correlations are insignificant in this regime.