相关论文: On certain families of Drinfeld quasi-modular form…
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions,…
We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the…
In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator $A$ and a cocoercive operator $B$. We study the asymptotic behaviour of the trajectories generated by a second…
The initial value problem is considered for a higher order nonlinear Schr\"odinger equation with quadratic nonlinearity. Results on existence and uniqueness of weak solutions are obtained. In the case of an effective at infinity additional…
The goal of this paper is twofold. First, we write down the semi-infinite Pl\"ucker relations, describing the Drinfeld-Pl\"ucker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous…
Let R be a Cohen-Macaulay ring and M a maximal Cohen-Macaulay R-module. Inspired by recent striking work by Iyama, Burban-Iyama-Keller-Reiten and Van den Bergh we study the question of when the endomorphism ring of M has finite global…
The maximum principle forms an important qualitative property of second order elliptic equations, therefore its discrete analogues, the so-called discrete maximum principles (DMPs) have drawn much attention. In this paper DMPs are…
We have discussed the problem of finding the condition on coefficients of $f''+A(z)f'+B(z)f=0, \quad B(z)(\not \equiv 0)$ so that all non-trivial solutions are of infinite order. The hyper-order of these non-trivial solutions of infinite…
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…
This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain…
Two results on the completeness of maximal solutions to first and second order ordinary differential equations (or inclusions) over complete Riemannian manifolds, with possibly time-dependent metrics, are obtained. Applications to…
We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to second-order interpolation inequalities with weights.
Quasimodules for vertex algebras are generalizations of modules for vertex algebras. These new objects arise from a generalization of locality for fields. Quasimodules tie together module theory and twisted module theory, and both twisted…
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…
We study properties of recently introduced Wieferich primes for Drinfeld modules, as their relation with Fermat equations and finitess or non-finiteness of their number. We also introduce Mersenne numbers for Drinfeld modules, and study the…
In this survey we review different instances in which the Drinfeld double of a finite group and its representations play a role, touching upon some of Tom Koornwinder's research interests: harmonic analysis, Lie algebras, quantum groups,…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
The construction and classification of super-modular categories is an ongoing project, of interest in algebra, topology and physics. In a recent paper, Cho, Kim, Seo and You produced two mysterious families of super-modular data, with no…
The present article aims to provide a brief account of the theories of Drinfeld modules and Anderson's $t$-modules and $t$-motives. As such the article is not meant to be comprehensive, but we have endeavored to summarize aspects of the…
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…