Related papers: Hemaka's constant
For $P$ a poset, the dimension of $P$ is defined to be the least cardinal $\kappa$ such that $P$ is embeddable in a direct product of $\kappa$ totally ordered sets. We study the behavior of this function on finite-dimensional (not…
Consider a Boolean model $\Sigma$ in $\R^d$. The centers are given by a homogeneous Poisson point process with intensity $\lambda$ and the radii of distinct balls are i.i.d.\ with common distribution $\nu$. The critical covered volume is…
Recent cosmological observations suggest the existence of a positive cosmological constant $\Lambda$ with the magnitude $\Lambda(G\hbar/c^3) \approx 10^{-123}$. This review discusses several aspects of the cosmological constant both from…
Some principles in the distribution of Centaurs and the "Scattered Disk" objects, as well as the Kuiper belt objects for its semi-major axes, eccentricities and inclinations of the orbits have been investigated. It has been established,…
In the space $\mathbb U^4$ of cubic forms of surfaces, regarded as a $G$-space and endowed with a natural invariant metric, the ratio of the volumes of those representing umbilic points with negative to those with positive indexes is…
The great development of astrometric accuracy since the observations by the Greek astronomer Hipparchus about 150 BC has often been displayed in diagrams showing the accuracy versus time. Two new diagrams are provided here, one for…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
In this article we reconsider the old mysterious relation, advocated by Dirac and Weinberg, between the mass of the pion, the fundamental physical constants, and the Hubble parameter. By introducing the cosmological density parameters, we…
"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which…
A method offering an order of magnitude sensitivity gain is described for using quasar spectra to investigate possible time or space variation in the fine structure constant, alpha. Applying the technique to a sample of 30 absorption…
We demonstrate that, in the context of the $\Lambda$CDM model, it is in principle possible to measure the value of the cosmological constant by tracing, across cosmic time, the evolution of the turnaround radius of cosmic structures. The…
Consider a Boolean model $\Sigma$ in $\R^d$. The centers are given by a homogeneous Poisson point process with intensity $\lambda$ and the radii of distinct balls are i.i.d.\ with common distribution $\nu$. The critical covered volume is…
We explore a novel link between two seemingly disparate mathematical concepts: Egyptian fractions and fractals. By examining the decomposition of rationals into sums of distinct unit fractions, a practice rooted in ancient Egyptian…
Random tilings are interesting as idealizations of atomistic models of quasicrystals and for their connection to problems in combinatorics and algorithms. Of particular interest is the tiling entropy density, which measures the relation of…
In circumstellar disks, the size of dust particles varies from submicron to several centimeters, while planetesimals have sizes of hundreds of kilometers. Therefore, various regimes for the aerodynamic drag between solid bodies and gas can…
Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…
In the context of current particle physics theories, it is quite likely that topological defects may be present in our universe. An observation of these fossils from the early universe would lead to invaluable insight into cosmology and…
We consider the quantum correlations for a S=1/2 Ising- Heisenberg model of a symmetrical diamond chain. Firstly, we compare concurrence, quantum discord and 1- norm geometric quantum discord of an ideal diamond chain in the absence of…
We study the continuum version of Sinai's problem of a random walker in a random force field in one dimension. A method of stochastic representations is used to represent various probability distributions in this problem (mean probability…
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted volume with minimum weighted perimeter. According to Chambers' recent proof of the log-convex density conjecture, for many densities on…