Related papers: Correction to: Reductions to simple fusion systems

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.

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…

Since no fusion theory neither rule fully satisfy all needed applications, the author proposes a Unification of Fusion Theories and a combination of fusion rules in solving problems/applications. For each particular application, one selects…

The main purpose of the following article is to give a proof of Y. Kawamata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an $\displaystyle L^{2\over…

The purpose of the paper is to rectify a series of errors occurred in [2], [17], [20] for a particular situation. To get a fruitful solution and to overcome the issue, we introduce a new form of set sharing namely restricted set sharing,…

Some mistaken reasonings at the end of the paper omitted.

Remarks on the Obstructedness of Cones Over Curves of Low Genus. Reason for replacement: proof of the main lemma was significantly improved.

Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We show how to make O(a) corrections in the bare parameters of 3-D lattice SU(2) times U(1) Higgs theory which remove O(a) errors in the match between the infrared behavior and the infrared behavior of the continuum theory. The corrections…

In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.

We give an alternate proof of the main theorem of Kawamata's paper: Pluricanonical systems on minimal algebraic varieties. Our proof also works for varieties in class $\mathcal C$. We note that our proof is completely different from…

In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…

This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…

Corrections are brought to an article of Friesen on continued fractions of a given period.

In the erratum we correct a mistake (due to a wrong choice of basic polynomial invariants over Z[1/2]) in the original paper (v1). Using the correct basic polynomial invariants we improve our results and bounds on the annihilator. We also…

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

In this paper, we present a constructive proof of Herschfeld's Convergence Theorem. Our formulation differs from Herschfeld's in a few ways: We consider radicals that nest transfinitely many times, as these are essential to the proof;…

In this article we prove that for any saturated fusion system, that the (unique) smallest weakly normal subsystem of it on a given strongly closed subgroup is actually normal. This has a variety of corollaries, such as the statement that…