Related papers: A counterexample of two Romanov type conjectures
The said paper entitled "A Proof Of The Plane Jacobian Conjecture" is not true.
The article presents the proof of Casas-Alvero conjecture.
We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions.
The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3].
By extending Lv-Xin-Zhou's first layer formulas of the $q$-Dyson product, we prove Kadell's conjecture for the Dyson product and show the error of his $q$-analogous conjecture. With the extended formulas we establish a $q$-analog of…
This paper is withdrawn. We found a mistake in Lemma 4.1
A generalized skew information is defined and a generalized uncertainty relation is established with the help of a trace inequality which was recently proven by J.I.Fujii. In addition, we prove the trace inequality conjectured by S.Luo and…
We prove a Khintchine type inequality under the assumption that the sum of Rademacher random variables equals zero. As an application we show a new tail-bound for a hypergeometric random variable.
We construct two Frechet algebras admitting countably many mutually inequivalent Frechet algebra topologies. The second example is a modification of the maiden (and first) example of a non-Banach Frechet algebra with two inequivalent…
We show that a conjecture of Einsiedler, Kapranov, and Lind on adelic amoebas of subvarieties of tori and their intersections with open halfspaces of complementary dimension is false for subvarieties of codimension greater than one that…
Error in proof of theorem 10.
We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal…
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
We provide a counterexample to P.~Olver's freeness conjecture for $C^\omega$ transformations.
We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.
We show the Williams Conjecture is false for irreducible shifts of finite type by examining relative sign-gyration numbers of conjugacies between shifts with no points of period one or two.
The main purpose of this note is to give a counterexample to the following conjecture, raised by Florian Frick [\textit{Int. Math. Res. Not. IMRN 2020 (13), 4037-4061 (2020)}]. Conjecture. Let $r\geq 3$ and let $\mathcal{F}$ be a set…
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
We present a proof of the full Mari\~no-Vafa Conjecture that identifies certain open string invariants of the resolved conifold with the Chern-Simons knot invariant of the unknot, i.e. the quantum dimensions.