Let G be a real form of a complex reductive group. Suppose that we are given involutions σ and θ of G. Let H = G denote the fixed group of σ and let K = G denote the fixed group of θ. We are interested in calculating the double coset space H\G/K. We use moment map and invariant theoretic techniques to calculate the double cosets, especially the ones that are closed. One salient point of our res...

Let G be a real form of a complex reductive group. Suppose that we are given involutions σ and θ of G. Let H = G denote the fixed group of σ and let K = G denote the fixed group of θ. We are interested in calculating the double coset space H\G/K. We use moment map and invariant theoretic techniques to calculate the double cosets, especially the ones that are closed. One salient point of our res...

The first absolute central moment is a statistical filter which measures the variability of the gray levels of the image with respect to the local mean. The analysis of the responses of the central and absolute central moments at noiseless isolated step discontinuities shows how the first absolute central moment can be usefully used to enhance these discontinuities. Moreover, experimental resul...

We generalize the concept of global moment maps to local moment maps whose different branches are labelled by the elements of the fundamental group of the underlying symplectic manifold. These branches can be smoothly glued together by employing fundamental-group-valued C̆ech cocycles on the phase space. In the course of this work we prove a couple of theorems on the liftability of group actions...

In this paper, we propose a novel idea for improvement performances of the leader M-BCJR algorithm functioning in low complexity. The basic idea consists to localize error instant possibility, and then increase the complexity around this moment. We also propose an easy and important idea for early localisation of erroneous moments. We call this new algorithm Z-MAP. The simulations show that the...

We use a version of localization in equivariant cohomology for the norm-square of the moment map, described by Paradan, to give several weighted decompositions for simple polytopes. As an application, we study Euler-Maclaurin formulas.

This paper presents a data-driven model reduction by moment-matching approach to construct control-oriented models for point absorber device. The methodology chosen and developed generates which are input-to-state linear, with any nonlinear behaviour confined the output map. Such map is result of approximation procedure, where so-called moment system estimated via least-squares procedure. resul...

Suppose given an holomorphic and Hamiltonian action of a compact torus $T$ on polarized Hodge manifold $M$. Assume that the lifts to quantizing line bundle, so there is induced unitary representation associated Hardy space. If in addition moment map nowhere zero, for each weight $\boldsymbol{\nu}$ $\boldsymbol{\nu}$-th isotypical component space polarization finite-dimensional. Assuming transve...

The paradigmatic result in symplectic toric geometry is the paper of Delzant that classifies compact connected symplectic manifolds with effective completely integrable torus actions, the so called (compact) symplectic toric manifolds. The moment map induces an embedding of the quotient of the manifold by the torus action into the dual of the Lie algebra of the torus; its image is a simple unim...

This paper surveys the role of moment maps in Kähler geometry. The first section discusses Ricci form as a map and then moves on to interpretations Kähler–Einstein condition scalar curvature (Quillen–Fujiki–Donaldson). second examines ramifications these results for various Teichmüller spaces their Weil–Petersson symplectic forms explains how arise naturally from construction quotients. third i...