Related papers: Homogeneous distributions on finite dimensional ve…

The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into…

Let $V$ and $V'$ be vector spaces over division rings (possible infinite-dimensional) and let ${\mathcal P}(V)$ and ${\mathcal P}(V')$ be the associated projective spaces. We say that $f:{\mathcal P}(V)\to {\mathcal P}(V')$ is a PGL-{\it…

This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The…

A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.

We discuss, in a non-Archimedean setting, the distribution of the coefficients of $L$-polynomials of curves of genus $g$ over $\mathbb{F}_q$. Among other results, this allows us to prove that the $\mathbb{Q}$-vector space spanned by such…

We make a classification of codimension one degree 3 distributions on the projective three space, giving possible Chern classes of the tangent sheaf and describing de zero and one dimensional components of the singular scheme of the…

An inhomogeneous linear differential equation Ly=f over a global differential field can have a formal solution for each place without having a global solution. The vector space lgl(L) measures this phenomenon. This space is interpreted in…

Let $\Gamma$ be a finite group acting linearly on a vector space $V$. We compute the Lie algebra cohomology of the Lie algebra of $\Gamma$-invariant formal vector fields on $V$. We use this computation to define characteristic classes for…

26 different concrete representations of the space of vector valued distributions on a smooth manifold of dimension n are presented systematically, most of them new. In the particular case of representations as module homomorphisms acting…

In this paper we describe the geometry of distributions by their symmetries, and present a simplified proof of the Frobenius theorem and some related corollaries. Then, we study the geometry of solutions of $F-$Gordon equation; A PDE which…

In a metric $g.f.f$-manifold we study lightlike hypersurfaces $M$ tangent to the characteristic vector fields, and owing to the presence of the $f$-structure, we determine some decompositions of $TM$ and of a chosen screen distribution…

In this work, we mainly deal with a two-dimensional singular holomorphic distribution $\mathcal{D}$ defined on $M$, in the two situations $M=\mathbb{P}^n$ or $M=(\mathbb{C}^n,0)$, tangent to a one-dimensional foliation $\mathcal{G}$ on $M$,…

In this paper we investigate some methods on calculating the spaces of generalized semi-invariant distributions on p-adic spaces. Using homological methods, we give a criterion of automatic extension of (generalized) semi-invariant…

A vector space partition $\mathcal{P}$ in $\mathbb{F}_q^v$ is a set of subspaces such that every $1$-dimensional subspace of $\mathbb{F}_q^v$ is contained in exactly one element of $\mathcal{P}$. Replacing "every point" by "every…

In this note, we find a sharp bound for the minimal number (or in general, indexing set) of subspaces of a fixed (finite) codimension needed to cover any vector space V over any field. If V is a finite set, this is related to the problem of…

Let $F$ be a non-archimedean locally compact field of residue characteristic $p\neq2$, let $G=\mathrm{GL}_{n}(F)$ and let $H$ be an orthogonal subgroup of $G$. For $\pi$ a complex smooth supercuspidal representation of $G$, we give a full…

We present elements of a theory of translation-invariant integration on finite dimensional vector spaces and on GL_n over a valuation field with local field as residue field. We then discuss the case of an arbitrary algebraic group. This…

We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.

Let $\mathbb{F}$ be a non-archimedean local field of positive characteristic different from 2. We consider distributions on $\mathrm{GL}(n+1,\mathbb{F})$ which are invariant under the adjoint action of $\mathrm{GL}(n,\mathbb{F})$. We prove…

Let $\mathbb F$ be a finite field. Consider a direct sum $V$ of an infinite number of copies of $\mathbb F$, consider the dual space $V^\diamond$, i.~e., the direct product of an infinite number of copies of $\mathbb F$. Consider the direct…