Related papers: Erratum to "On Operations and Linear Extensions of…

In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then…

This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]

We introduce and study $\alpha$-embedded sets and apply them to generalize the Kuratowski Extension Theorem.

It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…

This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum describes: 1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak…

A way to add an extra dimension is briefly discussed.

We exhibit how the Rasiowa-Sikorski Lemma simplifies, in a sense, proofs of results that make use of the technique known as back-and-forth, often resulting in not very illustrative arguments. The first two sections seek to show one simple…

In the note an error in Low and Lapsley's article ("Optimization Flow Control, I: Basic Algorithm and Convergence", IEEE/ACM Transactions on Networking, 7(6), pp. 861-874, 1999) is pointed out. Because of this error the proof of the Theorem…

We study an alternative model of infinitary term rewriting. Instead of a metric on terms, a partial order on partial terms is employed to formalise convergence of reductions. We consider both a weak and a strong notion of convergence and…

This note provides a brief guide to the current state of the literature on Tarski's problems with emphasis on features that distinguish the approach based on combinatorial and algorithmic group theory from the topological approach to…

We show that the maximal linear extension theorem for well partial orders is equivalent over RCA_0 to ATR_0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR_0 over RCA_0.

The equations in cond-mat/0011020 and Phys. Rev, Lett. 86, 4652 (2001) are valid but a numerical estimate in the paper is incorrect.

We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…

An error is spotted in the statement of Theorem~1.3 of our published article titled "On oriented cliques with respect to push operation" (Discrete Applied Mathematics 2017). The theorem provided an exhaustive list of 16 minimal (up to…

Erratum to "From Uncertainty Principles to Wegner Estimates".

Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly…

This is an erratum to our previously published paper.

A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree…

The study of well quasi-orders, wqo, is a cornerstone of combinatorics and within wqo theory Kruskal's theorem plays a crucial role. Extending previous proof-theoretic results, we calculate the $\Pi^1_1$ ordinals of two different versions…

An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.