相关论文: Corrigendum: 'On bounds for the effective differen…

We fix a gap in the proof of a result in our earlier paper arXiv:1908.09548

Understanding bounds for the effective differential Nullstellensatz is a central problem in differential algebraic geometry. Recently, several bounds have been obtained using Dicksonian and antichains sequences (with a given growth rate).…

There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.

We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings. More precisely, we compute an explicit function of geometric quantities associated to a system of difference equations (and these…

We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed by A. Seidenberg but no complete solution was…

A gap in the proof of Theorem 3.5 in the paper ``A new iteration process for approximation of common fixed points for finite families of total asymtotically nonexpansive mappings". Int. J. Math. Math. Sci. vol. 2009,…

Some of my previous publications were incomplete in the sense that non trivial zeros belonging to a particular type of fundamental domain have been inadvertently ignored. Due to this fact, I was brought to believe that computations done by…

We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…

We show new upper and lower bounds for the effective differential Nullstellensatz for differential fields of characteristic zero with several commuting derivations. Seidenberg was the first to address this problem in 1956, without giving a…

In this short note, it is shown that there is a gap in the proof of Theorem 11 in the paper of Meyer and Neutsch (J. of Algebra, 1993). We prove, nevertheless, that the statement of the theorem is true and fix the proof by using a certain…

In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.

This paper is devoted to present new error bounds of regularized gap functions for polynomial variational inequalities with exponents explicitly determined by the dimension of the underlying space and the number/degree of the involved…

We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275-1308.]

We prove a generalized Faulhaber inequality to bound the sums of the $j$-th powers of the first $n$ (possibly shifted) natural numbers. With the help of this inequality we are able to improve the known bounds for bracketing numbers of…

In this paper, first by employing inequalities derived from the Opial inequality due to David Boyd with best constant, we will establish new unconditional lower bounds for the gaps between the zeros of the Riemann zeta function. Second, on…

The aim of this short note is to clarify some of the claims made in the comparison made in [S. Lloyd, On the uncomputability of the spectral gap, arXiv:1602.05924] between our recent result [T.S. Cubitt, D. Perez-Garcia, M.M. Wolf,…

This paper is a corrigendum to the article 'On the ideal theorem for number fields`. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.

The inequality of Clauser and Horne [ Phys. Rev. D 10, 526 (1974)], intended to overcome the limited scope of other inequalities to deterministic theories, is shown to have a resticted validity even in case of perfect detectors and perfect…

Since its original formulation, Jensen's inequality has played a fundamental role across mathematics, statistics, and machine learning, with its probabilistic version highlighting the nonnegativity of the so-called Jensen's gap, i.e., the…

In a recent mathematical approach, Netzel (2018) proposes a method for determining the statistical error of spectral line equivalent widths. Using various approximations, he derives a determination equation that differs significantly from…