Related papers: The continuity of Deligne's pairing

This note considers the notion of divergence-preserving branching bisimilarity. It briefly surveys results pertaining to the notion that have been obtained in the past one-and-a-half decade, discusses its role in the study of expressiveness…

We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.

We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreover, we present and discuss a quite recent multi-dimensional…

Given an infinite subset $\mathcal A \subseteq\mathbb N$, let $A$ denote its smallest $N$ elements. There is a rich and growing literature on the question of whether for typical $\alpha\in[0,1]$, the pair correlations of the set $\alpha A…

In this note, we provide a short proof of Feige's conjecture for identically distributed random variables.

In the paper a theorem of Piccard's type is proved and, consequently, the continuity of $\mathcal{D}$-measurable polynomial functions of $n$-th order as well as $\mathcal{D}$-measurable $n$-convex functions is shown. The paper refers to the…

Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential…

The aim of this note is to present some new results concerning "almost everywhere" well-posedness and stability of continuity equations with measure initial data. The proofs of all such results can be found in \cite{amfifrgi}, together with…

This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.

The separately continuity topology is considered and some its properties are investigated. With help of these properties a generalization of Sierpinski theorem on determination of real separately continuous function by its values on an…

We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincar\'e inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian…

In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…

In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…

We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…

In this paper we establish that the well-known Arithmetic System is consistent in the traditional sense. The proof is done within this Arithmetic System.

We extend Carleson's interpolation Theorem to sequences of matrices, by giving necessary and sufficient separation conditions for a sequence of matrices to be interpolating.

We show the semi-continuity property of minimal log discrepancies for varieties which have a crepant resolution in the category of Deligne-Mumford stacks. Using this property, we also prove the ideal-adic semi-continuity problem for toric…

A countable dense set of directions is sufficient for Steiner symmetrization, but the order of directions matters.

The Ramanujan conjecture for modular forms of holomorphic type was proved by Deligne almost half a century ago: the proof, based on his earlier proof of Weil's conjectures, was an achievement of algebraic geometry. We give here a short…

We consider combinatorial properties of the Mills' ratio, and explore the interplay between a continued fraction expansion for the Mills' ratio, the Laplace polynomials and a new family of combinatorial identities.