Related papers: Estimating constellations among primes - I. Unifor…
According to the hierarchical model, small galaxies form first and merge together to form bigger objects. In parallel, galaxies assemble their mass through accretion from cosmic filaments. Recently, the increased spatial resolution of the…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
It is shown that the first $n$ prime numbers $p_1,...,p_n$ determine the next one by the recursion equation $$ p_{n+1} =\lim\limits_{s\to +\infty} [\prod\limits^n_{k=1} (1-\frac{1}{p^s_k}) \sum\limits^\infty_{j=1} \frac{1}{j^s} -1]^{-1/s}.…
Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations…
This paper proposes, and demonstrates the efficacy of, an elementary method for establishing a lower bound for cardinalities of selected sets of twin primes, and shows that the proof employed may be modified for selected sets of Goldbach…
Our unified chemical and spectrophotometric evolution code allows to simultaneously study the ISM abundances of a series of elements and the spectral properties of the stellar population in our model galaxies. We use stellar evolutionary…
Nested Archimedean copulas recently gained interest since they generalize the well-known class of Archimedean copulas to allow for partial asymmetry. Sampling algorithms and strategies have been well investigated for nested Archimedean…
We show how to obtain a Bayesian estimate of the rates or numbers of signal and background events from a set of events when the shapes of the signal and background distributions are known, can be estimated, or approximated; our method works…
A central challenge in observational studies of galaxy formation is how to associate progenitor galaxies with their descendants at lower redshifts. One promising approach is to link galaxies at fixed number density, rather than fixed…
We aim to study how the orbits of galaxies in clusters depend on the prominence of the corresponding central galaxies. We divided our data set of $\sim$ 100 clusters and groups into four samples based on their magnitude gap between the two…
We study the surprising discrepancy between the number of primes corresponding, respectively, to the two letters of an infinite word engendered by one of the simplest Lindenmayer systems. We formulate a conjecture concerning the rate of…
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…
New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…
Observations suggest that star formation occurs in only one or two crossing times for a range of scales spanning a factor of 1000. These observations include (1) measurements of embedded cluster ages in comparison with the cloud core…
Probability of coincidental clustering among the orbits of comets, asteroids and meteoroids depends on many factors like: the size of the orbital sample searched for clusters or the size of the identified group, it is different for groups…
The method of Murty and Cioab\u{a} shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids the search for perfect matchings and thus…
We present an algorithm analogous to the sieve of Eratosthenes that produces the list of twin primes. Next, we count the number of twin primes resulting from the construction with two different heuristic arguments. The first method is…
Star clusters are studied widely both as benchmarks for stellar evolution models and in their own right. Cluster age and mass distributions within galaxies are probes of star formation histories, and of cluster formation and disruption…