相关论文: Invariant ideals of local analytic and formal vect…

It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to…

Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$ the module of $\mathcal{A}$--derivations. First, we give a dynamical interpretation of $\mathcal{D}(\mathcal{A})$ as the set of polynomial vector fields which…

In this thesis we are interested in describing some homological invariants of certain classes of monomial ideals. We will pay attention to the squarefree and non-squarefree lexsegment ideals.

If for a vector space V of dimension g over a characteristic zero field we denote by $\wedge^iV$ its alternating powers, and by $V^\vee$ its linear dual, then there are natural Poincar\'e isomorphisms: $\wedge^i V^\vee \cong \wedge^{g-i}…

We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.

We consider analytic maps and vector fields defined in $\mathbb{R}^2 \times \mathbb{T}^d$, having a $d$-dimensional invariant torus $\mathcal{T}$. The map (resp. vector field) restricted to $\mathcal{T}$ defines a rotation of frequency…

An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. This paper develops a novel structure theory for primary ideals in…

Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$ the module of $\mathcal{A}$-derivations view as the set of polynomial vector fields which possess $\mathcal{A}$ as an invariant set. We first characterize…

We derive several tools for classifying tensor ideals in monoidal categories. We use these results to classify tensor ideals in Deligne's universal categories RepO, RepGL and RepP. These results are then used to obtain new insight into the…

We review a recent generalization of Normal Form Theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference with the standard case relies on the non…

We introduce a notion of quasi-lisse vertex algebras, which generalizes admissible affine vertex algebras. We show that the normalized character of an ordinary module over a quasi-lisse vertex operator algebra has a modular invariance…

An analytic classification of generic anti-polynomial vector fields $\dot z = \overline{P(z)}$ is given in term of a topological and an analytic invariants. The number of generic strata in the parameter space is counted for each degree of…

In this paper we obtain some statements concerning ideals of polynomials and apply these results in a number of different situations. Among other results, we present new characterizations of $\mathcal{L}_{\infty}$-spaces, Coincidence…

In this paper we provide a unifying approach to the study of Banach ideals of linear and multilinear operators defined, or characterized, by the transformation of vector-valued sequences. We investigate and apply the linear and multilinear…

Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

The representations of dimension vector $\alpha$ of the quiver Q can be parametrised by a vector space $R(Q,\alpha)$ on which an algebraic group $\Gl(\alpha)$ acts so that the set of orbits is bijective with the set of isomorphism classes…

This paper has two parts. We first survey recent efforts on the Bloom conjecture which still remains open in the case of complex dimension at least 4. Bloom's conjecture concerns the equivalence of three regular types. There is a more…

We determine the set of catenary degrees, the set of distances, and the unions of sets of lengths of the monoid of nonzero ideals and of the monoid of invertible ideals of orders in quadratic number fields.

Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…