Related papers: When Euler met Brun
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
Pre-main sequence and main-sequence binary systems are observed to have periods, P, ranging from one day to 10^(10) days and eccentricities, e, ranging from 0 to 1. We pose the problem if stellar-dynamical interactions in very young and…
We discuss recent advances on weak forms of the Prime $k$-tuple Conjecture, and its role in proving new estimates for the existence of small gaps between primes and the existence of large gaps between primes.
Let $p_n$ is the $n$-th prime. With help of the Cram\'er-like model, we prove that the set of intervals of the form $(2p_n,\enskip2p_{n+1})$ containing at list 3 primes has a positive density with respect to the set of all intervals of such…
Granular flows through pipes show interesting phenomena, e.g. clogging and density waves, 1/f-noise. These things are fairly good studied by computer-experiments, but there is a lack in theoretical and analytical consideration. We introduce…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
We study the transport of many partially distinguishable and possibly interacting particles under the action of repeated projective measurements on a target space and investigate how the particles' interference affects the mean first…
This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs…
The eccentricity distribution of exoplanets is known from radial velocity surveys to be divergent from circular orbits beyond 0.1 AU. This is particularly the case for large planets where the radial velocity technique is most sensitive. The…
A number of properties of the Uehling potential are investigated. In particular, we determine the Fourier spatial resolution of the Uehling potential. The lowest-order correction on vacuum polarisation is re-written in terms of the electron…
Planets on eccentric orbits have a higher geometric probability of transiting their host star. By application of Bayes' theorem, we reverse this logic to show that the eccentricity distribution of transiting planets is positively biased.…
We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the…
In financial time series there are periods in which the value increases or decreases monotonically. We call those periods elemental trends and study the probability distribution of their duration for the indices DJIA, NASDAQ and IPC. It is…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
We derive the initial spin period distribution of neutron stars by studying the population of young pulsars associated with supernova remnants. Our hierarchical Bayesian approach accounts for the measurement uncertainties of individual…
A class of Emergent Universe (EU) model is studied in the light of recent observational data. Significant constraints on model parameters are obtained from the observational data. Density parameter for a class of model is evaluated. Some of…
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
We consider the use of random walks as an approach to obtain connection coefficients for higher-order Bernoulli and Euler polynomials. In particular, we consider the cases of a $1$-dimensional linear reflected Brownian motion and of a…
Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and…