Related papers: Correction to: Reductions to simple fusion systems
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
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…
This note fills a gap in the article with title above [1]. We provide the proof of Equation (82) of Lemma 5 in [1] and thereby complete its power counting analysis with a more precise next-to-leading-order estimate.
In this paper we present the formal, computer-supported verification of a functional implementation of Buchberger's critical-pair/completion algorithm for computing Gr\"obner bases in reduction rings. We describe how the algorithm can be…
Manfred Stelzer has pointed out that part of Corollary 4.5 of our paper "Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology" [Alg. Geo. Top. 8 (2008), 2109--2129] was not sufficiently proved,…
By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.
After the publication of [Compos. Math. 156 (2020), no. 4, 822-861], Andrew Putman pointed out a mistake in our paper and helped us fix it. In this note, we will explain what this mistake is and how to fix it.
We describe two distinct simple, short and self contained proofs of the composition lemma.
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).
It is well known that the strong subadditivity theorem is hold for classical system, but it is very difficult to prove that it is hold for quantum system. The first proof of this theorem is due to Lieb by using the Lieb's theorem. Here we…
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main Conjecture to an equality under some mild conditions. We do this by exploiting Wei Zhang's proof of the Kolyvagin conjecture. The main ingredient is an improvement of…
We extend the results of David Goldschmidt's thesis concerning fusion in finite groups to saturated fusion systems and to all primes.
We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.
Using Isabelle/HOL, we verify a union-find data structure with an explain operation due to Nieuwenhuis and Oliveras. We devise a simpler, more naive version of the explain operation whose soundness and completeness is easy to verify. Then,…
We prove a main gap theorem for e-saturated submodels of a homogeneous structure. We also study the number of e-saturated models, which are not elementarily embeddable to each other
Unfortunately, some proofs in the first version of this paper were incorrect. In this revised version, some minor gaps are fixed, one serious mistake found. The main theorem is now claimed only under a restrictive technical assumption. This…
We point out that a concise proof of Theorem 2 in the article, 'On a quadratic estimate of Shafer' by L. Zhu contains a small mistake. Correcting this mistake and giving alternative proofs of Theorem 2 is the main aim of this note.
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…