Related papers: Hemaka's constant
We propose and study a mathematical model that qualitatively reproduces several ancient ornamental designs than one can see in historical museums of Crete and Athens. The designs contain several rings that circumscribe a fixed number of…
Let $M^n$ be a complete, open Riemannian manifold with $\Ric \geq 0$. In 1994, Grigori Perelman showed that there exists a constant $\delta_{n}>0$, depending only on the dimension of the manifold, such that if the volume growth satisfies…
In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent)…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
We consider the following measure of symmetry of a convex n-dimensional body K: $\rho(K)$ is the smallest constant for which there is a point x in K such that for partitions of K by an n-1-dimensional hyperplane passing through x the ratio…
For h=3 or 4, Egyptian decompositions into h unit fractions, like 2/D = 1/D1 + ... +1/Dh, were given by using (h-1) divisors (di) of D1. This ancient modus operandi, well recognized today, provides Di=DD1/di for i greater than 1.…
Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction…
We are going to show that new star product was found by Mebaraki for noncommutative curved space time has some properties when $\triangle$ (it has appeared in new multiplication) is a constant.
We have fitted the surface brightness of a sample of 79 elliptical galaxies pertaining to the Coma cluster of galaxies using the Sersic profile. This model is defined through three primary parameters: scale length (a), intensity (\Sigma_0),…
Recent work by J.~Prades and myself on $K\to\pi\pi$ is described. The first part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme…
We analyzed the archival data of the continuum emission at six wavelengths from 3 to 0.4 mm and 13CO and C18O (1-0, 2-1, and 3-2) lines in the protoplanetary disk around HD 142527 obtained with the Atacama Large Millimeter/submillimeter…
We use the classical definitions (i) $\pi$ is the ratio of area to the square of the radius of a circle; (ii) $\pi$ is the ratio of circumference to the diameter of a circle, to prove $\pi$'s existence within the purview of Euclidean…
There are many homological dimensions which are closely related to ring theoretic properties. The notion of a AB ring has been introduced by Huneke and Jorgensen. It has nice homological properties. In this paper, we shall define a…
Even the most classical states are still governed by quantum theory. A number of physical systems can be described by their Majorana constellations of points on the surface of a sphere, where concentrated constellations and highly symmetric…
It is demonstrated that iterative repeating of some simple geometric construction leads unavoidably in the limit to the golden ratio. The procedure appears to be quickly convergent regardless of a ratio of initial elements sizes. This could…
We introduce a measure of ''quantumness'' for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a…
We study the mappings of the first resolvable class defined by G. Koumoullis as a valuable tool to address the point of continuity property in the non-metrizable setting. First, we investigate the distance of a general mapping to the family…
Inside a fixed bounded domain $\Omega$ of the plane, we look for the best compact connected set $K$, of given perimeter, in order to maximize the first Dirichlet eigenvalue $\lambda_1(\Omega\setminus K)$. We discuss some of the qualitative…
This article studies three-dimensional objects and their volumes in Elamite mathematics, particularly those found in the Susa Mathematical Tablet No.\,14 (\textbf{SMT No.\,14}). In our discussion, we identify some basic solids whose volumes…
In this paper we use and extend the results present in \cite{1,2,3,4} and in particular in \cite{4} to obtain a statistical description of the cosmological constant in a cosmological de Sitter universe in terms of massless excitations with…