In Mn(k), k an algebraically closed field, we call a matrix l-regular if each eigenspace is at most l-dimensional. We prove that the variety of commuting pairs in the centralizer of a 2-regular matrix is the direct product of various affine spaces and various determinantal varieties Zl,m obtained from matrices over truncated polynomial rings. We prove that these varieties Zl,m are irreducible, ...

We show that any regular Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra defined by a tolerance induced by an irredundant covering.

The concept of topological gyrogroups is a generalization group. In this work, ones prove that gyrogroup G metrizable iff has an {\omega}{\omega}-base and Frechet-Urysohn. Moreover, in gyrogroups, every (countably, sequentially) compact subset being strictly (strongly) Frechet-Urysohn having are all weakly three-space properties with H closed L-subgyrogroup

K: a global function field of characteristicp # 0 E a fixed algebraic closure of K 00: a distinguished place of K A: the ring of functions in K regular away from cx> F,: a finite field which is an A-algebra VI the A-characteristic of F, (this means that the prime ideal pt, of v is the kernel of the structure morphism A + F4) 4 : a Drinfeld A-module over F, of rank d 7~: The Frobenius endomorphi...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

We provide a new analysis framework for the adversarial multi-armed bandit problem. Using the notion of convex smoothing, we define a novel family of algorithms with minimax optimal regret guarantees. First, we show that regularization via the Tsallis entropy, which includes EXP3 as a special case, matches the O( √ NT ) minimax regret with a smaller constant factor. Second, we show that a wide ...