相关论文: Erratum : Existence of 3D Skyrmions. Complete vers…
Skyrmions are the magnetic defects in an ultrathin magnetic film, similar to the bubble domains in the thicker films. Even weak uniaxial anisotropy determines its radius unambiguously. We consider the dynamics of the skyrmion decay. We show…
This combines a reply to the Comment [hep-th/0203067 v1] by A. N. Vaidya and R. de L. Rodrigues with an erratum to our Letter [Phys. Rev. Lett. 87, 210405 (2001)]
We correct an error in our treatment of the tadpole contribution to the fluctuation determinant of the sphaleron, and also a minor mistake in a previous estimate. Thereby the overall agreement between the two existing exact computations and…
While large language models (LLMs) have shown remarkable capabilities to generate coherent text, they suffer from the issue of hallucinations -- factually inaccurate statements. Among numerous approaches to tackle hallucinations, especially…
We propose a modification of the Skyrme model that supports a self-dual sector possessing exact non-trivial finite energy solutions. The action of such a theory possesses the usual quadratic and quartic terms in field derivatives, but the…
We piece together ingredients, which are well known and documented in the literature, into a new proof of the existence of semistable 3-fold flips
The original version of this paper contains an error; when this is corrected the basic conclusion changes. A revised manuscript will be submitted shortly.
This paper unifies problems and results related to (embedding) universal and homomorphism universal structures. On the one side we give a new combinatorial proof of the existence of universal objects for homomorphism defined classes of…
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Edge-to-trail substitution…
A new mechanism is proposed to explain the appearance of the three known fermion generations in a natural way. The underlying idea is based on the discreteness of the spectrum of solutions of the gap equation appearing in models of…
By correcting an example by Polyanskii, we show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in $d$-dimensional Euclidean…
In this short commentary we provide our comment on the article "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$" and its subsequent Erratum that are recently published in Physical Review Letters. In that Letter, the…
This article contains a proof of the fact that, under certain mild technical conditions, the action of the automorphism group of a cyclic 3-manifold cover of the type SxR, where S is a compact surface, yields a compact quotient. This result…
We correct Definition 6.3, Proposition 6.7, and Section 7 in the published version of our paper.
A self-correcting quantum memory is a type of quantum error correcting code that can correct errors passively through cooling. A major open question in the field is whether self-correcting quantum memories can exist in 3D. In this work, we…
This is erratum of the paper [Phys. Rev. Lett. {\bf 84}, 4260 (2000)]
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
We discuss a classical mistake, made in earlier publications on the stick percolation problem in 3D, for generating the right isotropic configuration of sticks. We explain the observed systematic deviations from the excluded volume rule.…
This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety", and 2) the original (unchanged) version of the paper, published…
As indicated by the third author in [19], there is a gap in the previous version of this paper by the first two authors [5]. We provide in this version an argument to fix the aforementioned gap. The main proposition, whose proof uses…