Related papers: On small gaps among primes
Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod p$ and $0 \le f_g(u) \le p-1$. This map is in particular used in a…
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense…
We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of…
We examine the combined effects of winds and photoionizing radiation from O--type stars on embedded stellar clusters formed in model turbulent molecular clouds covering a range of masses and radii. We find that feedback is able to increase…
The formation of stellar clusters dictates the pace at which galaxies evolve, and solving the question of their formation will undoubtedly lead to a better understanding of the Universe as a whole. While it is well known that star clusters…
(abridged) Context: Both observations and simulations of embedded protostars have progressed rapidly in recent years. Bringing them together is an important step in advancing our knowledge about the earliest phases of star formation. Aims:…
The spontaneous generation of electrical activity underpins a number of essential physiological processes, and is observed even in tissues where specialized pacemaker cells have not been identified. The emergence of periodic oscillations in…
Stars form in dense, clustered environments, where feedback from newly formed stars eventually ejects the gas, terminating star formation and leaving behind one or more star clusters. Using the STARFORGE simulations, it is possible to…
At least 10-15% of nearby sun-like stars have known Jupiter-mass planets. In contrast, very few planets are found in mature open and globular clusters such as the Hyades and 47 Tuc. We explore here the possibility that this dichotomy is due…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
We study the formation and the evolution of galaxy groups in a critical universe, showing the importance of secondary infall for their dynamical evolution. Merging is only slightly accelerated if galaxies have massive halos, because the…
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number $n$ of generations. In two dimensions, we determine the percolation…
We make two algorithms that generate all prime numbers up to a given limit, they are a development of sieve of Eratosthenes algorithm, we use two formulas to achieve this development, where all the multiples of prime number 2 are eliminated…
Stellar clusters are critical constituents within galaxies: they are the result of highest-density star formation, and through their spatially and temporally correlated feedback they regulate their host galaxy evolution. We present a novel…
We investigate the intersection covolume of cross sections for probability preserving actions of a class of abelian groups without lattices, including $p$-adic groups and the group of finite adeles. We show that for cross sections with a…
For a prime number $p$, we consider its primorial $P:=p\#$ and $U(P):={\left(\mathbb{Z}/P\mathbb{Z}\right)}^\times$ the set of elements of the multiplicative group of integers modulo $P$ which we represent as points anticlockwise on a…
One usually thinks of a radial density profile as having a monotonically changing logarithmic slope, such as in NFW or Einasto profiles. However, in two different classes of commonly used systems, this is often not the case. These classes…
Globular clusters host complex stellar populations whose chemical signatures suggest early (3 Myr - 1 Gyr) retention and reprocessing of stellar ejecta, yet direct evidence for intracluster gas is lacking. Here we present a unified…
Connecting galaxies with their descendants (or progenitors) at different redshifts can yield strong constraints on galaxy evolution. Observational studies have historically selected samples of galaxies using a physical quantity, such as…
This paper investigates the dynamical evolution of embedded stellar clusters from the protocluster stage, through the embedded star-forming phase, and out to ages of 10 Myr -- after the gas has been removed from the cluster. The relevant…