Related papers: Real analytic counterexample to the freeness conje…
A classical result of Malgrange says that for a polynomial P and an open subset $\Omega$ of $\R^d$ the differential operator $P(D)$ is surjective on $C^\infty(\Omega)$ if and only if $\Omega$ is P-convex. H\"ormander showed that $P(D)$ is…
In this short note we give counterexamples to several results related to extension theorems published recently.
We prove that if Q is a nw-nep forcing then it cannot add a dominating real. We also prove that Amoeba forcing cannot be P(X)/I if I is an aleph_1-complete ideal.
This work investigates the combinatorial structures underlying cyclic conditional freeness and introduces cumulants that serve to linearize the cyclic conditional additive convolution. In the process, we establish the notion of "cyclic…
We study the formalized v statement by allowing the occurrence of different arrays of quantifiers in it. We prove that for some specific arrays of quantifiers we get consistency statements that are S-equivalent to the original…
We show that some results of L. Makar-Limanov, P. Malcolmson and Z. Reichstein on the existence of free associative algebras are valid in the more general context of varieties of algebras.
We give a very short proof that a subgroup of a free group that is positively generated cannot be part of a counterexample to the Generalized Hanna Neumann Conjecture.
We give an alternative description of the top algebra of the free crossed square of algebras on 2-construction data in terms of tensors and coproducts of crossed modules of commutative algebras.
Recent results on finite open group transformations are reviewed.
We disprove the characterisation of graphs with equal independence and annihilation number by Larson and Pepper (2011). Series of counterexamples with arbitrary number of vertices, arbitrary number of components, arbitrary large…
We give a counterexample to a conjecture of S.E. Morris by showing that there is a compact plane set X such that R(X) has no non-zero, bounded point derivations but such that R(X) is not weakly amenable. We also give an example of a…
The wrapping transformation $W$ is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measures on the circle, with the multiplicative convolution…
Crawley-Boevey introduced the definition of a noncommutative Poisson structure on an associative algebra A that extends the notion of the usual Poisson bracket. Let V be a symplectic manifold and G be a finite group of symplectimorphisms of…
This note provides an alternate account of Calegari's rationality theorem for stable commutator length in free groups.
We continue to discuss the example presented in \cite{JarPfl2015}. In particular, we clarify some gaps and complete the description of the Shilov boundary.
In this paper we present an explicit counterexample of degree $n=7$, which shows that the conjecture proposed by Li et al. \cite{Li2013} regarding the first derivative bounds for rational B\'ezier curves is generally false. We further…
We introduce the notion of $\lambda$-double Lie algebra, which coincides with usual double Lie algebra when $\lambda = 0$. We state that every $\lambda$-double Lie algebra for $\lambda\neq0$ provides the structure of modified double Poisson…
It is shown that if $\alpha ,\zeta $ are ordinals such that $1\leq \zeta <\alpha <\zeta \omega ,$ then there is an operator from $C(\omega ^{\omega ^\alpha })$ onto itself such that if $Y$ is a subspace of $C(\omega ^{\omega ^\alpha })$…
We introduce the $\omega$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a structural way without using techniques from higher recursion…
We show that the naive adaptation of Malle's conjecture to fair counting functions is not true in general.