Related papers: On Vojta's $1+\epsilon$ Conjecture

This erratum corrects the proof given in \cite{E1,E2} about the existence of $ 3D $ Skyrmions. This is done by changing the arguments of the proof while remaining in the same framework of concentration-compactness. Note however that the use…

The famous (3n + 1) or Collatz conjecture has admitted some progress over the last several decades towards the conclusion that the conjecture is true (i.e. that all Collatz sequences will eventually reach a value of one), but has stubbornly…

To appear in Encyclopedia of Mathematical Physics, published by Elsevier in early 2006. Comments/corrections welcome. The article surveys topological aspects in gauge theories.

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

Some remarks on the jump condition appearing in Theorems 1.1 and 1.2 in the article [1] and their implications are given.

Erratum to cond-mat 9309014

Typographical corrections to the original paper, intended for publication in Physical Review E.

This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…

The purpose of this erratum is to correct the proof of Theorem A.0.1 in the appendix to our article ``Hadamard spaces with isolated flats'' math.GR/0411232, which was jointly authored by Mohamad Hindawi, Hruska and Kleiner. In that…

We examine the prime gaps using a statistical approach. It is first shown that the Andrica's conjecture is true for half or more cases. Using the arguments of averages, it is further shown that Andrica's conjecture is true. We further…

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

We prove an improved form of an expectation of Polya and discuss several related questions

These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…

This erratum aims to correct 1) the wrong expressions, 2) some typographical errors, 3) some erroneous points made in discussion of the disparity of heat flux ratios between our full RPA model and the local conductivity model, and 4) the…

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

We give a short proof of Belaga's result on bounds to perigees of $(3x+d)$-cycles of a given oddlength. We also reformulate the Collatz cycle conjecture which is rather a algorithmic problem into a purely arithmetic problem.

We correct one erroneous statement made in our recent paper "Medial axis and singularities".

In this paper, we proved a special case of the DDVV Conjecture.

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 is an expository paper (in Spanish) describing the origin and history of the Hirsch Conjecture about the maximum diameter of graphs of polytopes, and the ideas that led to the counter-example to it recently announced by the author in…