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This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Converserly we show the…
Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…
We describe first-degree prime ideals of biquadratic extensions in terms of first-degree prime ideals of two underlying quadratic fields. The identification of the prime divisors is given by numerical conditions involving their ideal norms.…
We show how permutability of transforms of smooth surfaces with particular characteristics leads to discrete surfaces with discrete analogues of the same characteristics.
We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in…
We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations.
We prove that the foliated Euler caracteristic classifies amenable measured foliations up to those defined by ergodic actions of the euclidian plane.
A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear system is perturbed and a finite number of…
In the first part of this article, we study linear cones over totally ordered fields. We show that for each such cone there uniquely exists a universal vector space (called its spanned vector space) into which it embeds as a generating…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
This paper is devoted to the resolution of singularities of holomorphic vector fields and of one-dimensional holomorphic foliations in dimension 3 and it has two main objectives. First, from the general perspective of one-dimensional…
In this work, we study dominant rational maps preserving singular holomorphic codimension one foliations on projective manifolds and that exhibit non-trivial transverse dynamics.
Factorizations over cones and their duals play central roles for many areas of mathematics and computer science. One of the reasons behind this is the ability to find a representation for various objects using a well-structured family of…
The main aim of this paper is to investigate Darboux rectifying curves on a smooth surface immersed in the Euclidean space. First, we discuss the component of the position vector of a Darboux rectifying curve on a smooth immersed surface…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
This paper investigates atomic factorizations in the monoid $\mathcal I(R)$ of nonzero ideals of a multivariate polynomial ring $R$, under ideal multiplication. Building on recent advances in factorization theory for unit-cancellative…
In this paper we analyze the tangential symmetries of Darboux integrable decomposable exterior differential systems. The decomposable systems generalize the notion of a hyperbolic exterior differential system and include the classic notion…
We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal…
We study the family of depolarizations of a squarefree monomial ideal $I$, i.e. all monomial ideals whose polarization is $I$. We describe a method to find all depolarizations of $I$ and study some of the properties they share and some they…
The purpose of this article is to adapt the Frolicher-type inequality to the case of transversely holomorphic and transversely symplectic foliations. These inequalities can be used to e.g. determine whether a given foliation can be made…