Related papers: On Two Recent Approaches to the Born Rule
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: 1. Some…
This manuscript contains a small portion of the algebraic theory of orthogonal polynomials developed by Maroni and their applicability to the study and characterization of the classical families, namely Hermite, Laguerre, Jacobi, and Bessel…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of extensor fields is present using algebraic and analytical tools developed in previous papers. Several important formulas are derived.
This paper examines the concept of a combination rule for belief functions. It is shown that two fairly simple and apparently reasonable assumptions determine Dempster's rule, giving a new justification for it.
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
We present an elementary proof of a conjecture proposed by I. Rasa in 2017 which is an inequality involving Bernstein basis polynomials and convex functions. It was affirmed in positive by A. Komisarski and T. Rajba very recently by the use…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We have shown in previous work that the equivalence of the Heisenberg and Schr\"odinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work, we give further evidence that the…
Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it…
In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results
A physical experiment comprises along the time trajectory a start, a time evolution (duration), and an end, which is the measurement. In non relativistic quantum mechanics the start of the experiment is defined by the wave function at time…
Quantum mechanics has lacked a widely recognized interpretation since its birth. Many of these are still under consideration because interpretations are tough or impossible to disprove experimentally. We show how to distinguish…
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
New results on comparison of distributions of Gaussian quadratic forms are presented
The possibility to recover the which-way information, for example in the two slit experiment, is based on a natural but implicit assumption about the position of a particle {\it before} a position measurement is performed on it. This…
Discussion of "Bayesian Model Selection Based on Proper Scoring Rules" by Dawid and Musio [arXiv:1409.5291].
Discussion of "Bayesian Model Selection Based on Proper Scoring Rules" by Dawid and Musio [arXiv:1409.5291].
Simple natural proofs of all known results regarding the aerodynamic Newton problem are obtained. Additional new theorems and new promising formulas in terms of Hessian measures are found. We would like to express our deep gratitude to Gerd…
In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…
Gott has promulgated a rule for making probabilistic predictions of the future duration of a phenomenon based on the phenomenon's present age [Nature, Vol. 363, 315 (1993)]. I show that the two usual methods for deriving Gott's rule are…