Related papers: A note on Cybenko's Universal Approximation Theore…
That gravitation can be understood as purely metric phenomenon depends crucially on the validity of a number of hypotheses which are summarised by the Einstein Equivalence Principle, the least well tested part of which being the…
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work to cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation…
It is argued that recent claims by A. Hobson that standard quantum theory has no measurement problem cannot be sustained. Moreover, it is pointed out that taking the reduced density operator of a component system as an epistemic…
In [Compositio Math. 155 (2019)] Kleinbock and Wadleigh proved a "zero-one law" for uniform inhomogeneous Diophantine approximations. We generalize this statement with arbitrary weight functions and establish a new and simple proof of this…
The measurement problem is seen as an ambiguity of quantum mechanics, or, beyond that, as a contradiction within the theory: Quantum mechanics offers two conflicting descriptions of the Wigner's-friend experiment. As we argue in this note…
Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental…
When a physicist says that a theory is fine-tuned, they mean that it must make a suspiciously precise assumption in order to explain a certain observation. This is evidence that the theory is deficient or incomplete. One particular case of…
Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The…
Grounded on the quantum measurement riddle, a general argument against the universal validity of the superposition principle was recently put forward by Bassi and Ghirardi. It is pointed out that this argument is valid only within the realm…
An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and…
Quantum-mechanical interpretation-related implications of the theory of unitary premeasurement [1] on complete measurement (objectification or collapse included) are investigated in the present article with a view to give an affirmative…
The quantum measurement problem is formulated in the form of an insolubility theorem that states the impossibility of obtaining, for all available object preparations, a mixture of states of the compound object and apparatus system that…
This paper goes back to a famous problem of Mahler in metrical Diophantine approximation. The problem has been settled by Sprindzuk and subsequently improved by Alan Baker and Vasili Bernik. In particular, Bernik's result establishes a…
Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…
In introductions to the subject for a general audience of mathematicians or logicians, the univalence axiom is typically explained by handwaving. This gives rise to several misconceptions, which cannot be properly addressed in the absence…
With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
\footnotesize B\"{o}r\"{o}czky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We establish this inequality…
Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…
We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John- Nirenberg inequality and of related inequalities due to John and to Wik.…