We present significantly improved estimates for the restricted isometry constants of partial random circulant matrices as they arise in the matrix formulation of subsampled convolution with a random pulse. We show that the required condition on the number m of rows in terms of the sparsity s and the vector length n is m & s log s log n.

A weak group element is introduced in a proper *-ring. Several equivalent conditions of elements are investigated. We prove that an pseudo core invertible if it both partial isometry and invertible. Reverse order law additive property the inverse presented. Finally, under certain assumption on a, a◯Wa∗=a∗a◯W presented by using normality part its group-EP decomposition.

Given a large sparse signal, great wishes are to reconstruct the signal precisely and accurately from lease number of measurements as possible as it could. Although this seems possible by theory, the difficulty is in built an algorithm to perform the accuracy and efficiency of reconstructing. This paper proposes a new proved method to reconstruct sparse signal depend on using new method called ...

We prove, in some cases terms of kippenhahn curve, that if 5-by-5 partial isometry whose numerical range is a circular disc then its center must be the origin. This gives affirmative answer to Conjecture 5.1. [H. l. Gau et al., Linear and Multilinear Algebra, 64 (1) 2016, 14–35.], for five-dimensional case.

We present an efficient computational framework for isometry-invariant comparison of smooth surfaces. We formulate the Gromov-Hausdorff distance as a multidimensional scaling (MDS)-like continuous optimization problem. In order to construct an efficient optimization scheme, we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances ...

Intrinsic shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency. While global isometric matching is well understood, only a few heuristic solutions are known for partial matching. Partial matching is particularly important for robustness to topological noise, which is a common prob...

The EPDiff equation for geodesic flow on the diffeomorphisms admits a remarkable ansatz for its singular solutions, called “diffeons.” Because this solution ansatz is a momentum map, the diffeons evolve according to canonical Hamiltonian equations. We examine diffeon solutions on Einstein spaces that are “mostly” symmetric, i.e., whose quotient by a subgroup of the isometry group is 1-dimension...

As the number of models in 3D databases grows, an efficient 3D models indexing mechanism and a similarity measure to ease model retrieval are necessary. In this paper, we present a query-by-model framework for NURBS based B-Rep models retrieval that combines partial symmetry of the object and the Fourier shape descriptor of canonical 2D projections of the 3D models. In fact, most objects are co...

Abstract We generalize to noncommutative cylinder the solution generation technique, originally suggested for gauge theories on noncommutative plane. For this purpose we construct partial isometry operators and complete set of orthogonal projectors in the algebra AC of the cylinder, and an isomorphism between the free module AC and its direct sum AC⊕FC with the Fock module on the cylinder. We c...