Related papers: Regularity vs. constructive complete (co)distribut…

For a formation $\mathfrak{F}$ of finite groups consider a graph whose vertices are elements of a finite group and two vertices are connected by an edge if and only if they generates non-$\mathfrak{F}$-group as elements of a group. A…

The concept of regularity in the meta-topological setting of projections in the double dual of a C*-algebra addresses the interrelations of a projection p with its closure, for instance in the form that such projections act identically, in…

Let $\varphi$ and $\psi$ be quadratic forms over a field $K$ of characteristic different from 2. In this paper, we give a criterion for isotropy of $\varphi$ over the function field of $\psi$ in terms of representations and we apply it to…

This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$…

In several different settings, one comes across situations in which the objects of study are locally consistent but globally inconsistent. Earlier work about probability distributions by Vorob'ev (1962) and about database relations by…

We extend McCarthy's stabilization construction to exact $\infty$-categories. This is achieved by constructing, for any functor from exact $\infty$-categories to a fixed stable $\infty$-category $\mathcal{A}$, a coherent chain complex in…

We show that the set of numbers that are $Q$-distribution normal but not simply $Q$-ratio normal has full Hausdorff dimension. It is further shown under some conditions that countable intersections of sets of this form still have full…

We discuss the existence of complete accumulation points of sequences in products of topological spaces. Then we collect and generalize many of the results proved in Parts I, II and IV. The present Part VI is complementary to Part V to the…

Motivated by a recently established result saying that within the class of bivariate Archimedean copulas standard pointwise convergence implies weak convergence of almost all conditional distributions this contribution studies the class…

We review some algebraic and combinatorial structures that underlie models in the KPZ universality class.Emphasis is placed on the Robinson-Schensted-Knuth correspondence and its geometric lifting due to A.N.Kirillov. We present how these…

In this talk, which popularizes some of our recent work, we provide novel insights into the bulk properties of light chiral quarks in a fixed Euclidean volume (e.g. lattice QCD). We show that the spontaneous breakdown of chiral symmetry…

A positive-definite integral quadratic form is called regular if it represents every positive integer which is locally represented. In this article, we classify all regular diagonal quadratic forms of rank greater than 3.

We prove that every finite distributive lattice $D$ can be represented as the congruence lattice of a rectangular lattice $K$ in which all congruences are principal. We verify this result in a stronger form as an extension theorem.

The main goal of this paper is to show that if a real valued function defined on a groupoid satisfies a certain Levi--Civita-type functional equation, then it also fulfills a Cauchy--Schwarz-type functional inequality. In particular, if the…

We present a series of recent results on the well-posedness of very singular parabolic stochastic partial differential equations. These equations are such that the question of what it even means to be a solution is highly non-trivial. This…

We show in this paper that representations of a finite product of categories satisfying certain combinatorial conditions have finite Castelnuovo-Mumford regularity if and only if they are presented in finite degrees, and hence the category…

We propose a regularization of the formal differential expression of order $m \geqslant 3$ $$ l(y) = i^my^{(m)}(t) + q(t)y(t), \,t \in (a, b), $$ applying quasi-derivatives. The distribution coefficient $q$ is supposed to have an…

We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence…

It has recently been demonstrated in quenched lattice simulations that the distribution of the low-lying eigenvalues of the QCD Dirac operator is universal and described by random-matrix theory. We present first evidence that this…

Let $K$ be a compact metric space and let $\varphi: K \to K$ be continuous. We study C*-algebra $\mathcal{MC}_\varphi$ generated by all multiplication operators by continuous functions on $K$ and a composition operator $C_\varphi$ induced…