Related papers: Unavoidable golden ratio
We continue the study of probabilistic and topological properties of the set of reals that are being guessed by a diamond sequence from \cite{Benhamou_Wu}. We show that the existence of sequence of a asymptotic growth $\pi$ which infinitely…
In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems…
In this paper we adopt a geometric point of view regarding a famous conjecture due to Littlewood in diophantine approximation of real numbers. Following the spirit of the geometric theory of continued fractions, we give a sufficient…
We prove in Theorem $2.2$ that the multiplicatively closed subset generated by at most two elements in the set of natural numbers $\mathbb{N}$ has arbitrarily large gaps by explicitly constructing large integer intervals with known prime…
Metallicities of both gas and stars decline toward large radii in spiral galaxies, a trend known as the radial metallicity gradient. We quantify the evolution of the metallicity gradient in the Milky Way as traced by APOGEE red giants with…
Hilbert's Foundations of Geometry was perhaps one of the most influential works of geometry in the 20th century and its axiomatics was the first systematic attempt to clear up the logical gaps of the Elements. But does it have gaps of its…
We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a complexity of natural number $n$ is…
It is still common wisdom amongst economists, politicians and lay people that economic growth is a necessity of our social systems, at least to avoid distributional conflicts. This paper challenges such belief moving from a purely physical…
The question how complex systems become more organized and efficient with time is open. Examples are, the formation of elementary particles from pure energy, the formation of atoms from particles, the formation of stars and galaxies, the…
Given a random distribution of impurities on a periodic crystal, an equivalent uniquely ergodic tiling space is built, made of aperiodic, repetitive tilings with finite local complexity, and with configurational entropy close to the entropy…
We investigate the evolution of the metallicity of the intergalactic medium (IGM) with particular emphasis on its spatial distribution. We propose that metal enrichment occurs as a two step process. First, supernova (SN) explosions eject…
Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…
We start with an ``algebraic'' RSK-correspondence due to Noumi and Yamada. Given a matrix $X$, we consider a pyramidal array of solid minors of $X$. It turns out that this array satisfies an algebraic variant of octahedron recurrence. The…
The design of crystal materials plays a critical role in areas such as new energy development, biomedical engineering, and semiconductors. Recent advances in data-driven methods have enabled the generation of diverse crystal structures.…
Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh T into hexahedra,…
After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an…
This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…
In order to investigate multiplicative structures in additively large sets, Beiglb\"{o}ck et al. raised a significant open question as to whether or not every subset of the natural numbers with bounded gaps (syndetic set) contains…
A set X of partial words over a finite alphabet A is called unavoidable if every two-sided infinite word over A has a factor compatible with an element of X. Unlike the case of a set of words without holes, the problem of deciding whether…
The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to…