Related papers: New Characterizations of Algebraic Regularity

We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…

We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.

This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford regularity. We describe several techniques to establish the Koszulness of algebras. We discuss variants of the Koszul property such as strongly Koszul, absolutely…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

A previously introduced scheme for describing integrable deformations of of algebraic curves is completed. Lenard relations are used to characterize and classify these deformations in terms of hydrodynamic type systems. A general solution…

We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.

We introduce a notion of an algebra of generalized pseudo-differential operators and prove that a spectral triple is regular if and only if it admits an algebra of generalized pseudo-differential operators. We also provide a self-contained…

We investigate the properties of arithmetic differentiation, an attempt to adapt the notion of differentiation to the integers by preserving the Leibniz rule, (ab)' = a'b + ab'. This has proved to be a very rich topic with many different…

Let B be a ring and $A=B[X,Y]/(aX^2+bXY+cY^2-1)$ where $a,b,c\in B$. We study the smoothness of A over B, and the regularity of B when B is a ring of algebraic integers.

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…

We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the…

Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…

In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian.

This paper contains an algebraic constructive and self-contained account of the invariance rule of the digital root under division for an arbitrary natural basis representation. Both the cases of repeating and non-repeating fractionals are…

This survey paper is a structured concise summary of four of our recent papers on the stochastic regularity of diffusions that are associated to regular strongly local (but not necessarily symmetric) Dirichlet forms. Here by stochastic…

We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…