Related papers: Erratum to "Computation of maximal projection cons…
A general technique for proving the irrationality of the zeta constants $\zeta(s)$ for odd $s = 2n + 1 \geq 3$ from the known irrationality of the beta constants $L(2n+1)$ is developed in this note. The results on the irrationality of the…
We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.
In the paper, the problem of the existence of the maximum likelihood estimate and the REML estimate in the variance components model is considered. Errors in the proof of Theorem 3.1 in the article of Demidenko and Massam (Sankhy\=a 61,…
We discuss Birnbaum's result, its relevance to statistical reasoning, Mayo's objections and the result in [Electron. J. Statist. 7 (2013) 2645-2655] that the proof of this result doesn't establish what is commonly believed.…
We consider Brouwer's fixed point theorem and Sperner's lemma in one dimension. We present a proof of the Brouwer theorem using the Sperner lemma, and vice versa. However, we also show that they are not equivalent, because the Sperner lemma…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
The original paper, as published in Nuclear Physics B in 1988, had a few factor-of-two errors. Some people got confused by those errors. The purpose of these errata is to make things clear. The revised version of the complete article is…
The purpose of this note is to show that in a widely cited paper by Yakir [Ann. Statist. 25 (1997) 2117--2126, doi:10.1214/aos/1069362390], the proof that the so-called modified Shiryayev--Roberts procedure is exactly optimal is incorrect.…
In this corrigendum to arXiv:2305.02973, we justify that the motivation behind Conjecture 5.1 is based on a mistaken notion. Moreover, we prove a stronger theorem that disproves the conjecture, and obtain an optimal gradient vector field on…
In this work, a convergence lemma for function $f$ being finite compositions of analytic mappings and the maximum operator is proved. The lemma shows that the set of $\delta$-stationary points near an isolated local minimum point $x^*$ is…
The statement of item (ii) of Proposition 3.2 of the article referenced in the title is not correct. We provide a corrected version and show that, under the assumption that $\gcd(a_i, a_j, q-1)=1$ for any pair $i\neq j$ in $\{0, \cdots,…
We correct a mistake in the analytical expression for the energy density given in Phys. Rev. C76, 021902 (2007) [arXiv:0704.3625 [hep-ph]]. The expression should be multiplied by 16. One question then arises; how could it be possible to…
Menger conjectured that subsets of R with the Menger property must be ${\sigma}$-compact. While this is false when there is no restriction on the subsets of R, for projective subsets it is known to follow from the Axiom of Projective…
In this paper we present a new perspective on error analysis of Legendre approximations for differentiable functions. We start by introducing a sequence of Legendre-Gauss-Lobatto polynomials and prove their theoretical properties, such as…
We show, that the theoretical expression for the dispersion of collective excitations reported in [Phys. Rev. B {\bf 103}, 099901 (2021)], at variance with what was claimed in the paper, does not account for the energy fluctuations and does…
In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…
The purpose of this paper is to present an inexact version of the scaled gradient projection method on a convex set, which is inexact in two sense. First, an inexact projection on the feasible set is computed, allowing for an appropriate…
We verify a conjecture of Lutwak, Yang, Zhang about the equality case in the Orlicz-Petty projection inequality, and provide an essentially optimal stability version.
In this paper, we study optimal estimates and comparison of the coefficients in the Gegenbauer series expansion. We propose an alternative derivation of the contour integral representation of the Gegenbauer expansion coefficients which was…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…