Related papers: Comment to "Almost disjoint sets, the dense set pr…
This paper is devoted to present two counterexamples to the theorem from \cite{MK} Maria R., Katherine T. M., Bernardo S. M., Extremal graphs with bounded vertex bipartiteness number, Linear Algebra Appl. 493 (2016) 28-36. Moreover, the…
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…
By a re-examination of MacMahon's original proof of his celebrated theorem on the distribution of the major indices over permutations, we give a reformulation of his argument in terms of the structure of labeled partitions. In this…
In this article, we discuss the notion of partition of elements in an arbitrary Coxeter system $(W,S)$: a partition of an element $w$ is a subset $\mathcal P\subseteq W$ such that the left inversion set of $w$ is the disjoint union of the…
We present new, simple proofs for the enumeration of five of the ten symmetry classes of plane partitions contained in a given box. Four of them are derived from a simple determinant evaluation, using combinatorial arguments. The previous…
We present a variety of refined conditions for $\sigma$ algebras $\mathcal{A}$ (on a set $X$), $\mathcal{F}, \mathcal{G}$ (on a set $U$) such that the distributivity equation…
There are some inaccuracies and errors in my article "Dual and almost-dual homogeneous spaces". Here I will describe in detail how to correct incorrect statements from this article and which statements there will have to be reformulated in…
This paper is a corrigendum to the article 'Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic Shifts; and Finitely Defined Shifts'. In this article we correct Lemma 5.3. Therefore, we follow correcting…
This survey is a slightly extended version of the lecture given by the author at the \emph{VI International Course of Mathematical Analysis in Andaluc\'\i a} (CIDAMA), in September 2014. Most results are contained (in a slightly less…
We study the set of almost quantum correlations and their refinements in the simplest tripartite Bell scenario where each party is allowed to perform two dichotomic measurements. In contrast to its bipartite counterpart, we find that there…
I comment on Zaccone, Phys. Rev. Lett. {\bf 128}, 028002 (2022) highlighting a flaw in the derivation that led to a spurious divergent factor. This renders the derivation of the random close packing density invalid.
Asaf Karagila pointed out that Remark 3.4 [1], directly contradicts Theorem 3.3 (c) [2] which was incorrectly stated. This note contains a proof of this remark. [1] Miller, Arnold W.; A Dedekind Finite Borel Set, Arch. Math. Logic 50…
Recent results on second order quantum corrections to semileptonic decays of b quarks and positronium spectroscopy are reviewed. Similarities between calculations in these seemingly different problems are demonstrated. Technical aspects of…
In this note we study a quantitative version of Bernstein's approximation problem when the polynomials are dense in weighted spaces on the real line completing a result of S.~N.~Mergelyan (1960). We estimate in the logarithmic scale the…
This is a commentary on Teichm{\"u}ller's paper Ein Verschiebungssatz der quasikonformen Abbildung (A displacement theorem of quasiconformal mapping), published in 1944. We explain in detail how Teichm{\"u}ller solves the problem of finding…
We give a sketch for an alternative proof of a recent result by J. Tseng.
We correct an error in the second part of Theorem 3 of our original paper (arXiv:1512.07161).
Motivated by Gentzen disjunction elimination rule in his Natural Deduction calculus and reading inequalities with meet in a natural way, we conceive a notion of distributivity for join-semilattices. We prove that it is equivalent to a…