Related papers: Rejoinder on "Conjectures on exact solution of thr…
We show that the key formula in the works [Ding, Zhu, and Berakdar, Phys. Rev. B {\bf 79}, 045405 (2009); {\bf 84}, 115433 (2011); Ding, Zhu, Zhang, and Berakdar, Phys. Rev. B {\bf 82}, 155143 (2010)] is invalid in the extended graphene…
The claim in \cite{Al-Badawi:2025ipr} that *"the errors in the foundational components (3) and (5) of Ref. [1] invalidate all subsequent analyses, numerical results, and physical interpretations that depend on them"* is **entirely…
This note is a corrigendum to the previous version arXiv:0711.2735v3 published in J. Lie Theory. As it has been recently pointed out to me by Alexander Premet, Remark 3 of arXiv:0711.2735v3 is incorrect. We verify in this note thanks to…
We reply to the comment by Ying Zhang and S. Das Sarma on our PRL 94, 226405 (2005).
The article provides a counterexample to a conjecture by Blocki-Zwonek.
This is a response to the article arXiv:1212.3130v1 by Xu-Jia Wang, where he attempted to address a mathematical question we raised. We point out that, and explain why, the article is far from answering our objections. Moreover, we have…
This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.
John Morgan and G,Tian pointed out a mistake in the concluding argument for our paper entitled "$C_1$ in [2] is zero", which was recently published in arXiv:1512.02098. We hereby acknowledge this mistake and correct the computation, leading…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
A constructive and straightforward proof of the existence of the Zeeman topology is provided, contradicting a fallacious claim contained in the paper "Does Zeeman's Fine Topology Exist?" available at arXiv:1003.3703v1.
In this note we correct a paper by D. Kang ("On the Mazur-Ulam theorem in non-Archimedean fuzzy anti-2-normed spaces", Filomat, 2017). The research in that paper applies to what the author calls strictly convex spaces. Nevertheless, we…
We prove that the Arithmetic Fundamental Lemma conjecture of Wei Zhang is equivalent to a similar conjecture, but for Lie algebras, in the case of non-degenerate intersection. We use this result to give a simplified proof of the AFL for…
In a recent paper, Wang. et al. (2009) claim that Tsallis' nonadditivity of q-nonextensive statistical mechanics (Gell-Mann and Tsallis 2004, Tsallis 2009) is mathematically inconsistent and hence one should carefully review Tsallis' ideas…
The above comment [E. I. Lashin, D. Dou, arXiv:1606.04738] claims that the paper "Quantum Raychaudhuri Equation" by S. Das, Phys. Rev. D89 (2014) 084068 [arXiv:1404.3093] has "problematic points" with regards to its derivation and…
This is the reply to the comment arXiv:0801.4620 by Vidal, Dusuel, and Schmidt.
Kashuba and Mathieu proposed a conjecture on vanishing of some components of the homology of certain Lie algebras, implying a description of the $GL_d$-module structure of the free $d$-generated Jordan algebra. Their conjecture relies on a…
It is shown that the recent Comment [cond-mat/0306019] by Y. Yu on the above article is not substantiated.
Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough,…
Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler…
We disprove a conjecture of Kuznetsov--Shinder, which posits that $D$-equivalent simply connected varieties are $L$-equivalent, by constructing a counterexample using moduli spaces of sheaves on K3 surfaces.