相关论文: Recent results on $p$-ranks and Smith normal forms…

We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least $4$. For degrees $2$ and $3$ we improve the known bounds in general. The focus is on thin sets of type II, namely…

We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…

We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…

We construct normal forms for Levi degenerate hypersurfaces of finite type in $\mathbb C^2$. As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the…

The centrepiece of this paper is a normal form for primitive elements which facilitates the use of induction arguments to prove properties of primitive elements. The normal form arises from an elementary algorithm for constructing a…

We generalize results by Wakabayashi and Orevkov about rational cuspidal curves on the projective plane to that on $\mathbb{Q}$-homology projective planes. It turns out that the result is exactly the same as the projective plane case under…

We revisit finite racks and quandles using a perspective based on permutations which can aid in the understanding of the structure. As a consequence we recover old results and prove new ones. We also present and analyze several examples.

Some families of linear permutation polynomials of $\mathbb{F}_{q^{ms}}$ with coefficients in $\mathbb{F}_{q^{m}}$ are explicitly described (via conditions on their coefficients) as isomorphic images of classical subgroups of the general…

Some new infinite families of simple, indecomposable $m$-factorizations of the complete multigraph $\lambda K_v$ are presented. Most of the constructions come from finite geometries.

Affine structures on a Lie groupoid, including affine $k$-vector fields, $k$-forms and $(p,q)$-tensors are studied. We show that the space of affine structures is a 2-vector space over the space of multiplicative structures. Moreover, the…

In this article we study forbidden loci and typical ranks of forms with respect to the embeddings of $\mathbb P^1\times \mathbb P^1$ given by the line bundles $(2,2d)$. We introduce the Ranestad-Schreyer locus corresponding to supports of…

We present old and recent results on rank problems and linearizability of geodesic planar webs.

We consider a class of quasi-linear anisotropic elliptic equations, possibly degenerate or singular, which are of interest in several applications such as computer vision and continuum mechanics. We prove a Hopf Lemma as well as local and…

We show that if $\alpha$ is a positive $(2,2)$-form then so is $\alpha^2$. We also prove that this is no longer true for forms of higher degree.

We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or…

Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…

In this paper we give a thorough study of Lipschitz spaces. We obtain the following new results: (1) Sharp Jawerth-Franke-type embeddings between the Besov and Lipschitz spaces extending the classical results for Besov and Sobolev spaces;…

This paper proposes SAT-based techniques to calculate a specific normal form of a given finite mathematical structure (model). The normal form is obtained by permuting the domain elements so that the representation of the structure is…

We investigate the topological theory obtained by twisting the N=(2,2) supersymmetric nonlinear sigma model with target a bihermitian space with torsion. For the special case in which the two complex structures commute, we show that the…

The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.