Related papers: Distributive decomposition of near-vector spaces

In a recent paper, Chernikov and Starchenko prove that graphs defined in distal theories have strong regularity properties, generalizing previous results about graphs defined by semi-algebraic relations. We give a shorter, purely…

This paper demonstrates that random, independently chosen equi-dimensional subspaces with a unitarily invariant distribution in a real Hilbert space provide nearly tight, nearly equiangular fusion frames. The angle between a pair of…

The division between two vectors belonging to the same vector space is obtained by elementary procedures of vector algebra and is defined by a matrix. This representation is obtained for two and three dimensional vector spaces. A new vector…

This paper makes a deep study of regular two-distance sets. A set of unit vectors $X$ in Euclidean space $\RR^n$ is said to be regular two-distance set if the inner product of any pair of its vectors is either $\alpha$ or $\beta$, and the…

Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…

The most fundamental notion for Hilbert space frames is the sequence of frame coefficients for a vector x in the space. Yet, we know little about the distribution of these coefficient sequences. In this paper, we make the first detailed…

The focus of this article is to define the descriptively approximations in proximal relator spaces. Afterwards, descriptive approximately algebraic structures such as groupoids, semigroups and groups in digital images endowed with…

Quasiminimal sets are sets for which a pertubation can decrease the area but only in a controlled manner. We prove that in dimensions $2$ and $3$, such sets separate a locally finite family of local John domains. Reciprocally, we show that…

Distributional semantics creates vector-space representations that capture many forms of semantic similarity, but their relation to semantic entailment has been less clear. We propose a vector-space model which provides a formal foundation…

We investigate regularizations of distributional sections of vector bundles by means of nets of smooth sections that preserve the main regularity properties of the original distributions (singular support, wavefront set, Sobolev…

We consider $\ell_p$-direct sums ($1\leq p<\infty$) and $c_0$-direct sums of countably many normed spaces and find the duals of these spaces. We characterize the support functionals of arbitrary elements in these spaces to characterize…

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields.…

We study ample stable vector bundles on minimal rational surfaces. We give a complete classification of those moduli spaces for which the general stable bundle is both ample and globally generated. We also prove that if $V$ is any stable…

We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.

In this work we classify the at-point regularities of set-valued mappings into two categories and then we analyze their relationship through several implications and examples. After this theoretical tour, we use the subregularity properties…

We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two…

We shall study special regularity properties of solutions to some nonlinear dispersive models. The goal is to show how regularity on the initial data is transferred to the solutions. This will depend on the spaces where regularity is…

Let A be a tame quasi-tilted algebra and d the dimension vector of an indecomposable A-module. In the paper we prove that each irreducible component of the variety of A-modules of dimension vector d is regular in codimension one.

We discuss regularity statements for equidistant decompositions of Riemannian manifolds and for the corresponding quotient spaces. We show that any stratum of the quotient space has curvature locally bounded from both sides.

We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…