相关论文: A relative Yoneda Lemma (manuscript)
We construct maximal $\Lambda(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.
For every finitely generated free group we construct an explicit left order extending the lexicographic order on the free monoid generated by the positive letters. The order is defined by a left, free action on the orbit of 0 of a free…
We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander--Reiten theory. More precisely, for each Nakayama algebra $A$ and each positive integer $d$, we construct a finite dimensional…
We propose a fairly simple and natural extension of Stollmann's lemma to correlated random variables. This extension allows (just as the original Stollmann's lemma does) to obtain Wegner-type estimates even in some problems of spectral…
We prove a variation of Gronwall's lemma.
In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.
We develop a theory of categories which are simultaneously (1) indexed over a base category S with finite products, and (2) enriched over an S-indexed monoidal category V. This includes classical enriched categories, indexed and fibered…
For a given length and a given degree and an arbitrary partition of the positive integers, there always is a cell containing a polynomial progression of that length and that degree; moreover, the coefficients of the generating polynomial…
We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational…
We construct manifold structures on various sets of solutions of the general relativistic initial data sets.
We introduce a new method of constructing complete sequences of key polynomials for simple extensions of tame fields. In our approach the key polynomials are taken to be the minimal polynomials over the base field of suitably constructed…
In the first part of the paper, some extensions of the classical Dynkin-Specht-Wever lemma are developed. In the second part, we extend Burgunder's splitting construction, and relate back to the Kashiwara-Vergne problem.
Let $\Gamma = \Lambda[M]$ be the one-point extension of an algebra $\Lambda$ by a $\Lambda$-module $M$. We establish a method to lift projectively Wakamatsu tilting (PWT) modules from $\mathrm{mod}\,\Lambda$ to $\mathrm{mod}\,\Gamma$ by…
(i) We provide a short and simple proof of the first selection lemma. (ii) We also prove a selection lemma of a new type in $\Re^d$. For example, when $d=2$ assuming $n$ is large enough we prove that for any set $P$ of $n$ points in general…
We extend Hadamard's Lemma to the setting of a separable Hilbert space.
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
We give an extension of the Fekete's Subadditive Lemma for a set of submultiplicative functionals on countable product of compact spaces. Our method can be considered as an unfolding of the ideas [1]Theorem 3.1 and our main result is an…
Previous work has demonstrated that efficient algorithms exist for computing Kan extensions and that some Kan extensions have interesting similarities to various machine learning algorithms. This paper closes the gap by proving that all…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…
Let $K\to L$ be an algebraic field extension and $\nu$ a valuation of $K$. The purpose of this paper is to describe the totality of extensions $\left\{\nu'\right\}$ of $\nu$ to $L$ using a refined version of MacLane's key polynomials. In…