Related papers: Counterexamples to Bloch's Principle and its Conve…
The CMI Millennium "P vs NP Problem" can be resolved e.g. if one shows at least one counterexample to the conjecture "P is equal to NP". A certain class of problems being such counterexamples is formulated. This implies the rejection of the…
In this paper, we first define two classes of holomorphic mappings defined on the unit ball $B^n$ of n-dimensional complex space $\mathbb{C}^n$ and obtain the lower estimates for Bloch's constant for these classes. Also, we derive the…
In this paper, methods of second order and higher order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroeder-Bernstein theorem. Some additional results address statements in higher order arithmetic…
Typicality has always been in the minds of the founding fathers of probability theory when probabilistic reasoning is applied to the real world. However, the role of typicality is not always appreciated. An example is the paper "Foundations…
A version of the Lebesgue differentiation theorem is offered, where the $L^p$ norm is replaced with any rearrangement-invariant norm. Necessary and sufficient conditions for a norm of this kind to support the Lebesgue differentiation…
It is shown that Bell's counterfactuals admit joint quasiprobability distributions (i.e. joint distributions exist, but may not be non-negative). A necessary and sufficient condition for the existence among them of a true probability…
In this note we give a counterexample to a conjecture proposed by Ciliberto about special linear systems of P^n through multiple base points.
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
In this short paper we show that March's criterion for the existence of a bounded non constant harmonic function on a weak model is also a necessary and sufficient condition for the solvability of the Dirichlet problem at infinity on a…
Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same…
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
In this note we elaborate on a recent counter-example to the Nelson-Seiberg theorem and to its generalizations. We provide sufficient conditions for the existence of such counter-examples, finding new ones. We claim that these…
A method is introduced for the verification of nonclassicality in terms of moments of nonclassicality quasiprobability distributions. The latter are easily obtained from experimental data and will be denoted as nonclassicality moments.…
The purpose of this article is to provide a version of Bloch-Wigner theorem over the class of rings with many units.
In this short note we give counterexamples to several results related to extension theorems published recently.
In this note we characterize when non-classical polynomials are necessary in the inverse theorem for the Gowers $U^k$-norm. We give a brief deduction of the fact that a bounded function on $\mathbb F_p^n$ with large $U^k$-norm must…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
Probabilities of causation (PoCs) are fundamental quantities for counterfactual analysis and personalized decision making. However, existing analytical results are largely confined to binary settings. This paper extends PoCs to multi-valued…
We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…