Related papers: A note on Cybenko's Universal Approximation Theore…

One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…

This note is a comment on the "quantum interferometry" section of Reference [1]. It points out that the methods of that section can be applied to more general states than the ones that are discussed in Ref. [1].

This paper deals with the problem of quantifying the approximation a probability measure by means of an empirical (in a wide sense) random probability measure, depending on the first n terms of a sequence of random elements. In Section 2,…

For a simple electromagnetic model of a clock introduced by Jefimenko (clock $\#$ 1 in 1996 {\it Am. J. Phys.} {\bf 64} 812), a change of the rate of the clock when it is set in uniform motion is calculated exactly, employing the correct…

The generalized uncertainty principle (GUP) is a gravitational correction of Heisenberg's uncertainty principle, which allows us to probe some features of quantum gravity even without the full theory. We are used to working with metric…

We show how information on the uniformity properties of a point set employed in numerical multidimensional integration can be used to improve the error estimate over the usual Monte Carlo one. We introduce a new measure of (non-)uniformity…

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…

A solution is given to a conjecture proposed by Y. Wigderson and A. Wigderson concerning a "Heisenberg-like" uncertainty principle. This is an old article already published in 2022.

We discuss several open problems in Diophantine approximation. Among them there are famous Littlewood's and Zaremba's conjectures as well as some new and not so famous problems.

We consist of first presenting Zeckendorf Theorem with these two versions Fibonacci and Luca. In this document we obtain results on the generalized of the Zeckendorf theorem for Fibonacci numbers (multibonacci). Such results find…

In this paper we present a short and elementary proof for the error in Simpson's rule.

As it is known, universal codes, which estimate the entropy rate consistently, exist for stationary ergodic sources over finite alphabets but not over countably infinite ones. We generalize universal coding as the problem of universal…

We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.

A short proof to a recent theorem of Giambruno and Mishchenko is given in this note.

This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…

In this paper we address the question of whether it is possible to obtain evidence that we are in a superposition of different worlds, as suggested by the relative state interpretation of quantum mechanics. We find that it is impossible to…

I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…

There are reasons to believe that implications of a certain paradox introduced by Ginzburg and related problems have not been fully recognized. Pertinent issues remain open and unresolved. There are instances when the current widely used…

The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In…