Related papers: Counterexamples to the pseudo-Riemannian Lichnerow…
The main goal in this paper is to point out that quantity $||\nabla R||^2(p)$ on a harmonic space can not be determined by the spectra of local geodesic spheres or balls, therefore the main results of [AM-S] (quoted in the title) are wrong.…
We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.
This paper has been withdrawn by the author due to an error in the proof of Theorem 2.
We show that the claims expressed in the Comment arXiv:0810.3244v1 by R.S. Decca et al against our paper, D.A.R. Dalvit and S.K. Lamoreaux, Phys. Rev. Lett. {\bf 101}, 163203 (2008), are wrong and manifestly inconsistent with basic…
Let $G$ be a complex reductive algebraic group. In arxiv:2108.03453 Ivan Losev, Lucas mason-Brown and the third-named author suggested a symplectic duality between nilpotent Slodowy slices in $\mathfrak{g}^\vee$ and affinizations of certain…
The purpose of this note is to show by constructing counterexamples that two conjectures of M\'{o}ri and Sz\'{e}kely for the Borel-Cantelli lemma are false.
The purpose of this note is to provide a detailed proof of Nazarov's inequality stated in Lemma A.1 in Chernozhukov, Chetverikov, and Kato (2017, Annals of Probability).
This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576
We describe an error in the proof of a key proposition, which was necessary for the proof of the main result. Alternate proofs of the main result are given by Ozsvath-Stipsicz-Szabo and Dai-Hom-Stoffregen-Truong.
We make plausible the existence of counterexamples to the Riemann hypothesis located in the neighbourhood of unusually large peaks of $\vert \zeta \vert$. The main ingredient in our argument is an identity which links the zeros of a…
It is shown that the title Comment by W. Szczepanik, M. Dulak, and T. A. Wesolowski [Int. J. Quantum Chem. 106 (2006)] is unsatisfactory.
This paper examines Chwistek's claim that with Principia's definition of a class "Richard's paradox can be formulated". It is shown that the demonstration fails since it requires an incorrect elimination of a defined term and use of a…
We formulate a conjecture which generalizes Darmon's "refined class number formula". We discuss relations between our conjecture and the equivariant leading term conjecture of Burns. As an application, we give another proof of the "except…
This paper has been withdrawn by the authors, due to a flaw in the proof of Theorem 1. This preprint is superseded by quant-ph/0610027, where a correct proof can be found. Thanks to Rainer Siegmund-Schultze for spotting the error.
We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also…
The paper was withdrawn because of its significant overlap with a paper appeared recently.
In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].
This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…
This is a paper for a special issue of the journal "Studia Semiotyczne" devoted to Stanislaw Krajewski's paper [30]. This paper gives some supplementary notes to Krajewski's [30] on the Anti-Mechanist Arguments based on G\"{o}del's…
We give a counterexample to the most optimistic analogue (due to Kleshchev and Ram) of the James conjecture for Khovanov-Lauda-Rouquier algebras associated to simply-laced Dynkin diagrams. The first counterexample occurs in type A_5 for p =…