相关论文: A counterexample to the Arakelyan Conjecture

We construct an entire function $f$ with only three singular values whose order of growth can change under a quasiconformal equivalence. This is a counterexample to the Order Conjecture in the Speiser class ${\mathcal S}$ of entire…

In [2] the author claims to provide a counterexample to a result in a recent paper [1]. In this note, we prove that the details of his example is false and this example is compatible with our result in [1] and so is not a countreexample.

In this paper we give a counterexample to the conjecture: Let $S\in{\rm SInn}$. Then $z\cdot S$ is onto $U$.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

Arakelian's classical approximation theorem \cite{Ar} gives necessary and sufficient conditions such that functions can be uniformly approximated in (unbounded) closed sets $F\subset \mathbb{C}$ by entire functions. The conditions are…

Another counter-example to Dirac's Conjecture is presented, which resembles the Cawley model but is so modified as to include second class constraints. The arbitrary function in the general solution to the defining equations of momenta…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

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…

We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…

An example of a cocomplete abelian category that is not complete is constructed.

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

We show that the natural directed analogues of the KKL theorem [KKL88] and the Eldan--Gross inequality [EG20] from the analysis of Boolean functions fail to hold. This is in contrast to several other isoperimetric inequalities on the…

The paper presents a counterexample to the Hodge conjecture.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

In this note, we discuss recently discovered counterexamples to Mordell's Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the counterexample to Mordell's Pellian Equation Conjecture that can…

We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.

In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.

We construct the counter-example for polynomial version of Sarnak's conjecture for minimal systems, which assets that the M\"obius function is linearly disjoint from subsequences along polynomials of deterministic sequences realized in…