Related papers: New Characterizations of Algebraic Regularity
New criterion of regularity for representation of canonical commutation relations algebra is given on the basis of concept of an analytical vector.
We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizations of this kind and yields a way to obtain more tilted…
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…
This paper is devoted to the comparison of the notions of regularity for algebraic connections and (holonomic) regularity for algebraic $\mathcal D$-modules.
We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.
We present a new, short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates, can…
We consider a nonlinear representation of a Lie algebra which is regular on an abelian ideal, we define a normal form which generalizes that defined in [D. Arnal, M. Ben Ammar, M. Selmi, {\rm Normalisation d'une repr\'esentation non…
In this paper we introduce a new property for normed algebras. This property which we call it stability, plays a key role in the studying of the theory of almost multiplier maps. In this note we study some of the basic properties of this…
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
Regularity theory for diffusive operators is among the finest treasures of the modern mathematical sciences. It appears in several different fields, such as, differential geometry, topology, numerical analysis, dynamical systems,…
We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…
We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
We obtain a new characterization for irrational numbers of constant type -- defined as irrationals with bounded partial quotients in their continued fraction expansion. The result is essential in the formulation of stability criteria for…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose an extension of the key concepts to arbitrary systems of…
We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.
A new understanding of the notion of regularizer is proposed. It is argued that this new notion is more realistic than the old one and better fits the practical computational needs. An example of the regularizer in the new sense is given. A…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
In this paper we consider quadratic stochastic operators designed on finite Abelian groups. It is proved that such operators have the property of regularity.
We develop a quantitative theory of stochastic homogenization in the more general framework of differential forms. Inspired by recent progress in the uniformly elliptic setting, the analysis relies on the study of certain subadditive…