Related papers: Three classical probability problems: the Hungaria…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
Hardy conjectured that the error term arising from approximating the number of lattice points lying in a radius-$R$ disc by its area is $O(R^{1/2+o(1)})$. One source of support for this conjecture is a folklore heuristic that uses i.i.d.…
Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We…
How many fair coin tosses to choose 1 of $n$ options with uniform probability? Although a probability problem, the solution is essentially number-theoretic, with special roles for Mersenne numbers, Fermat numbers, and the haupt exponent. We…
The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by…
This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…
We establish a relationship between the two important central lines of the triangle, the Euler line and the Brocard axis, in a configuration with an arbitrary rectangle and a random point. The classical Cartesian coordinate system method…
The Eulerian triangle is a classical array of combinatorial numbers defined by a linear recursion. The associated boundary problem asks one to find all extreme nonnegative solutions to a dual recursion. Exploiting connections with random…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
This work discusses the concept of roulette, the generated curves that occur when one curve rolls without slipping along another, tracing the path of a fixed point. The coin paradox and Aristotle's wheel paradox are used as pedagogical…
We survey some ideas from the subject of Random Algebraic Geometry, a field that introduces a probabilistic perspective on classical topics in real algebraic geometry. This offers a modern approach to classical problems, such as Hilbert's…
We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically…
In this paper we overview the theory of conics and roulettes in four non-Euclidean planes. We collect the literature about these classical concepts, from the eighteenth century to the present, including papers available only on arXiv. The…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in…
In this note we present a survey on some classical and modern approaches on Pythagorean triples. Some questions are also posed in direction of some materials under review. In particular some non commutative and operator theoretical…
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
We illustrate how one can use basic combinatorial theory and computer programming technique (Python) to analyze the combinatorial game: Mahjong. The results confirm some folklore concerning the game, and expose some unexpected results.…