We give strengthened versions of the Herwig–Lascar and Hodkinson–Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous structures. For instance, we establish a coherent form of the extension property for partial automorphisms for certain Fräıssé classes. We deduce from these result...

‎In this paper‎, ‎first we develop the duality concept for $g$-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every $g$-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎$g$-frames and generalize some resu...

Let A be a fixed C*-algebra. In an arbitrary finitely generated projective A-module V ⊆ An, a spherical tight A-frame is a set of of k, k > n, elements f1, . . . , fk such that the associated matrix F = [f1, . . . , fk] up-to a constant multiple is a partial isometry of the Hilbert structure on the projective finitely generated A-module V . The space FA k,n of all such A-frames form a C*-algebr...

In this paper, we address the problem of detecting partial symmetries in 3D objects. In contrast to previous work, our algorithm is able to match deformed symmetric parts: We first develop an algorithm for the case of approximately isometric deformations, based on matching graphs of surface feature lines that are annotated with intrinsic geometric properties. The sensitivity to non-isometry is ...

We construct various isometry groups of Urysohn space (the unique complete separable metric space which is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.

We construct various isometry groups of Urysohn space (the unique complete separable metric space that is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.

Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with many important applications in machine learning and statistics. In this paper we propose a simple and fast algorithm SVP (Singular Value Projection) for rank minimization with affine constraints (ARMP) and show that SVP recovers the minimum rank solution for affine constraints that satisfy the restricted...

at each point z 2 H, making it a model of the hyperbolic plane. Consider the closed compact surface = H= . We aim to show that its isometry group is …nite, and furthermore that we can achieve a sharp upper bound directly proportional to the genus of the surface. Consider, by comparison, the isometries of R=Z, the Euclidean torus T . Any Euclidean translation of R descends to an isometry of T , ...