We establish versions of Szegő’s distance formula and Widom’s theorem on invertibility (a family of) Toeplitz operators in a class finite codimension subalgebras uniform algebras, obtained by imposing number linear constraints. Each such algebra is naturally represented reproducing kernel Hilbert spaces, which play central role the proofs.

The paper presents a modification of the Frechet distance for nonisomorphic trees. While classical between trees is undefined, new measure called similarity tree to reference given that defined wider class A polynomial-time algorithm determine whether one tree’s another less than number.

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied fo...

We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of locus tensors expressed as uMPS, their defining equations and identifiability. By an interplay theorems algebra, quantum physics we answer several questions conjectures posed by Critch, Morton Hackbusch.

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

A basic problem in classifying, or searching for similar objects in, a large set of geometric objects is computing similarity between two objects. This has led to extensive work on computing geometric similarity between two objects. This talk discusses some old and some new geometric-similarity algorithms, with an emphasis on transportation distance (also called earth mover’s distance) and Frec...

Until recently it was impractical to use general purpose computer algebra systems to investigate Chevalley groups except for those of small rank over small fields. But computer algebra systems (such as Magma (Bosma et al. 1997) and GAP (Schönert et al. 1994)) now have the power to deal with some aspects of all finite groups of Lie type. A natural way to represent these groups is via matrices ov...