Related papers: On small gaps among primes
Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy…
Multiplicity is common in field stars and among protostellar systems. Models suggest two paths of formation: turbulent fragmentation and protostellar disk fragmentation. We attempt to find whether or not the coevality frequency of multiple…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
The substructures observed in protoplanetary disks may be the signposts of embedded planets carving gaps or creating vortices. The inferred masses of these planets often fall in the Jovian regime despite their low abundance compared to…
In this work we study the properties of protoclusters of galaxies by employing the MUSIC set of hydrodynamical simulations, featuring a mass-limited sample of 282 resimulated clusters with available merger trees up to high redshift, and we…
We propose the formula for the number of pairs of consecutive primes $p_n, p_{n+1}<x$ separated by gap $d=p_{n+1}-p_n$ expressed directly by the number of all primes $<x$, i.e. by $\pi(x)$. As the application of this formula we formulate 7…
Artificial broadcasts from extraterrestrial intelligences (ETIs) are a hypothetical class of celestial phenomena. Unlike known astrophysical objects, the societies that generate them may be able to replicate on galactic scales through…
We study the first occurrences of gaps between primes in the arithmetic progression (P): $r$, $r+q$, $r+2q$, $r+3q,\ldots,$ where $q$ and $r$ are coprime integers, $q>r\ge1$. The growth trend and distribution of the first-occurrence gap…
I set the stage for discussion of the stellar populations in interacting galaxies by looking back over the slow development of our understanding of these systems. From early anecdotal collections, to systematic cataloging, and finally to…
The connection between some features of the metallicity gradient in the Galactic disk, best revealed by Open Clusters and Cepheids, and the spiral structure, is explored. The step-like abrupt decrease in metallicity at 8.5 kpc (with R_0=…
The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally characterized at the boundary by the notable Proth-Glibreath…
Localized contractile configurations or asters spontaneously appear and disappear as emergent structures in the collective stochastic dynamics of active polar actomyosin filaments. Passive parti- cles which (un)bind to the active filaments…
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…
Bertrand's Postulate ensures existence of prime $p$ between $n$ and $2n$, $n$ an integer $\geq 2$ and the sieve of Eratosthenes, a very simple ancient algorithm, generates all prime numbers up to any given limit. Combining the above two, in…
We use N-body integration to follow the evolution of clusters of 200 binary systems with different initial half mass radii $R_{0.5}$. We also simulate single-star clusters. All clusters evolve according to the same $n(t)$ curve, where…
Consider a smooth point O of a complex analytic surface S. A constellation based at O is a set of infinitely near points of O, centers of a sequence of blow-ups above O. Finite constellations are usually encoded in two ways: either using an…
Based on a simple object, an i.i.d. sequence of positive integer-valued random variables, $\{a_n\}_{n\in \mathbb{Z}}$, we introduce and study two random structures and their connections. First, a population dynamics, in which each…
When a massive object crosses a star stream velocity changes are induced both along and transverse to the stream which can lead to the development of a visible gap. For a stream narrow relative to its orbital radius the time of stream…
We define the excedance number on the complex reflection groups and compute its multidistribution with the number of fixed points on the set of involutions in these groups. We use some recurrence formulas and generating functions…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…