相关论文: A counterexample to the "composition conjecture"

The Polynomial Abel differential equations are considered a model problem for the classical Poincar\'e center--focus problem for planar polynomial systems of ordinary differential equations. Last decades several works pointed out that all…

This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

We study the analogue of the classical infinitesimal center problem in the plane, but for zero cycles. We define the displacement function in this context and prove that it is identically zero if and only if the deformation has a…

We present a counter-example to the recent claim that supermultiplets of N-extended supersymmetry with no central charge and in 1-dimension are specified unambiguously by providing the numbers of component fields in all available…

A class of bilinear permutation polynomials over a finite field of characteristic 2 was constructed in a recursive manner recently which involved some other constructions as special cases. We determine the compositional inverses of them…

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

In this short note we present a family of counterexamples to the King's conjecture.

The paper presents a counterexample to the Hodge conjecture.

We give an explicit counterexample to an entanglement inequality suggested in a recent paper [quant-ph/0005126] by Benatti and Narnhofer. The inequality would have had far-reaching consequences, including the additivity of the entanglement…

The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.

Recently, G. Mason has produced a counterexample of order 128 to a conjecture in conformal field theory and tensor category theory in [Ma]. Here we easily produce an infinite family of counterexamples, the smallest of which has order 72.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We study the integral Hodge conjecture in complex codimension $2$ and $3$ for approximations to the classifying space of groups of type A. In degree two, we prove a conjecture of Ben Antieau, extending his two counterexamples to a general…

We describe in some details an idea of M. Kontsevich how one can try to find a counterexample to the Hodge conjecture using tropical geometry.

We study the compositional inverses of some general classes of permutation polynomials over finite fields. We show that we can write these inverses in terms of the inverses of two other polynomials bijecting subspaces of the finite field,…

In an earlier work [K. Castillo et al., J. Math. Anal. Appl., 514 (2022) 126358], we give positive answer to the first, and apparently more easy, part of a conjecture of M. Ismail concerning the characterization of the continuous $q$-Jacobi…

Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.

We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…