Related papers: Classe d'equivalence Formelle D'un D-Module D'Airy

We consider a suitable extension of the complex Airy operator, $-d^2/dx^2 + ix$, on the real line with a transmission boundary condition at the origin. We provide a rigorous definition of this operator and study its spectral properties. In…

We calculate the rational cohomology of the classifying space of the diffeomorphism group of the manifolds $U_{g,1}^n:= \#^g(S^n \times S^{n+1})\setminus \mathrm{int}{D^{2n+1}}$, for large $g$ and $n$, up to approximately degree $n$. The…

We give a deterministic algorithm that, given a composite number $N$ and a target order $D \ge N^{1/6}$, runs in time $D^{1/2+o(1)}$ and finds either an element $a \in \mathbb{Z}_N^*$ of multiplicative order at least $D$, or a nontrivial…

The distributions of the $k$-th largest level at the soft edge scaling limit of Gaussian ensembles are some of the most important distributions in random matrix theory, and their numerical evaluation is a subject of great practical…

An explicit construction of all the homogeneous holomorphic Hermitian vector bundles over the unit disc $\mathbb D$ is given. It is shown that every such vector bundle is a direct sum of irreducible ones. Among these irreducible homogeneous…

The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…

The first part of these notes is devoted to an introduction to algebraic $D$-modules. Several basic notions are introduced. In the second part, $D$-modules with group action are treated. Several important examples in this situation are…

Form factors in the sinh-Gordon model are studied semiclassically for small values of the parameter $b\sim\hbar^{1/2}$ in the background of a radial classical solution, which describes a heavy exponential operator placed at the origin. For…

It is useful to have canonical forms of boundary conditions in the study of the eigenvalues of boundary value problems and associated numerical applications. In [J. Appl. Anal. Comput., 2024, 14(4), {1854--1868}], a canonical form is given…

If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominatorsof very high degree. When the base field is $\mathbb C$, we give a completely explicit…

We introduce notions of ${\mathcal O}$-operators of the Loday algebras including the dendriform algebras and quadri-algebras as a natural generalization of Rota-Baxter operators. The invertible $\mathcal O$-operators give a sufficient and…

Given a planar algebra we show the equivalence of the notions of a module over this algebra (in the operadic sense), and module over a universal annular algebra. We classify such modules, with invariant inner products, in the generic region…

In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…

The number $\nu_{n,d}(k)$ of linearly independed homogeneous invariants of degree $k$ for the $n$-ary form of degree $d$ is calculated.

We compute the Form Factors of the relevant scaling operators in a class of integrable models without internal symmetries by exploiting their cluster properties. Their identification is established by computing the corresponding anomalous…

Factorization is the central ingredient in any theoretical prediction for collider experiments. We introduce a factorization formalism that can be applied to any desired observable, like event shapes or jet observables, for any number of…

We study direct product representations of algebras in varieties. We collect several conditions expressing that these representations are "definable" in a first-order-logic sense, among them the concept of Definable Factor Congruences…

We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful…

We aim to generalize Lurie-Pridham's famous $\infty$-correspondence between formal moduli problems and differential graded Lie algebras to the context where some cohomological conditions are imposed. Specifically, a natural equivalence…

Let $D:\Omega\xrightarrow{}\Omega$ be a differential operator defined in the exterior algebra $\Omega$ of differential forms over the polynomial ring $S$ in $n$ variables. In this work we give conditions for deforming the module structure…