Related papers: Recent progress on Favard length estimates for pla…
We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums…
This survey is devoted to necessary and suffcient conditions for a rational number to be representable by a Cantor series. Necessary and suffcient conditions are formulated for the case of an arbitrary sequence $(q_k)$.
We show that for a large class of planar $1$-dimensional random fractals $S$, the Favard length $\operatorname{Fav}(S(r))$ of the neighborhood $S(r)$ is comparable to $\log^{-1}(1/r)$, matching a universal lower bound; up to now, this was…
Cantor sets in \(\mathbb{R}\) are common examples of sets for which Hausdorff measures can be positive and finite. However, there exist Cantor sets for which no Hausdorff measure is supported and finite. The purpose of this paper is to try…
This paper examines the possibilities of extending Cantor's two arguments on the uncountable nature of the set of real numbers to one of its proper denumerable subsets: the set of rational numbers. The paper proves that, unless certain…
In this paper we investigate the recent advances by Zhang, Maynard and Pintz towards Polignac's conjecture and give some new results concerning the relationship between Polignac numbers and arithmetic progressions.
Recent progress in Lattice QCD is highlighted. After a brief introduction to the methodology of lattice computations the presentation focuses on three main topics: Hadron Spectroscopy, Hadron Structure and Lattice Flavor Physics. In each…
This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.
We show the middle Nth cantor set contains arithmetic progressions of length at least proportional to N/log_2(N).
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.
This article summarizes several analyses I discussed at Moriond and I attempt to maintain my speaking voice throughout. I extract several broad themes in the recent development of QCD,and emphasize how the latest results on jet physics…
In view of recent developments of the study of reproducing kernel Hilbert spaces, in particular with the context the Hardy spaces on tubes, aspects of rational approximation for functions of finite energy in several complex and several real…
We give a heuristic for the number of reduced rationals on Cantor's middle thirds set, with a fixed bound on the denominator. We also describe extensive numerical computations supporting this heuristic.
It is possible to numerically solve QCD in the planar limit using standard numerical techniques on existing computer clusters. The basic ideas behind the computational strategy an recent numerical results in the fermionic sector of large N…
The connection between continued fractions and orthogonality which is familiar for $J$-fractions and $T$-fractions is extended to what we call $R$-fractions of type I and II. These continued fractions are associated with recurrence…
In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand's Theorem, and quantify the…
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
In this paper, we consider the positional numeration system, called the Cantor real expansion, on the unit interval $[\gamma, \gamma+1]$, where $\gamma \in \mathbb{R}$, with respect to an alternate base (i.e., a base which is a purely…
Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We show that under suitable thickness assumptions on the sets…