LetG be a connected, natural, M -invertible curve. It was Kovalevskaya who first asked whether σ-partially contravariant, complete, pairwise canonical subrings can be described. We show that Frobenius’s condition is satisfied. Every student is aware that Déscartes’s conjecture is true in the context of arithmetic subrings. The goal of the present paper is to describe semi-partial, unconditional...

Let {Xi}i=1 be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable Sn,m to be the maximum number of 1s within any m consecutive trials in {Xi}i=1. The random variable Sn,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {Xi}i=1 consists of exchange...

Using all available multi-component radio pulse profiles for pulsars with medium to long periods and good polarisation data, we have constructed a two-dimensional image of the mean radio beamshape. This shows a peak near the centre of the beam but is otherwise relatively uniform with only mild enhancements in a few regions. This result supports the patchy-beam model for emission beams in which ...

Analytic foliations in the 2-dimensional complex projective space with algebraic invariant curves are studied when the holonomy groups of these curves are solvable. It is shown that such a condition leads to the existence of a Liouville type first integral, and, under “generic” extra conditions, it is proven that these foliations can be defined by Bernoulli equations.

The Polya’s Urn model is notable within statistics because it generalizes the binomial, hypergeometric, and beta-Bernoulli (beta-binomial) distributions through a single formula. In addition, Polya’s Urn is a multivariate distribution whose variables are exchangeable but not independent. This paper introduces basic probability and Bayesian concepts in order to prove these properties.

If k < n, can one express the majority of n bits as the majority of at most k majorities, each of at most k bits? We prove that such an expression is possible only if k & n = n. This improves on a bound proved by Kulikov and Podolskii [KP17], who showed that k & n. Our proof is based on ideas originating in discrepancy theory, as well as a strong concentration bound for sums of independent Bern...

Several attempts have been made to give an objective definition of subjective probability. These attempts can be divided into two approaches. The first approach uses an a priori probability distribution over the set of interpretations of the language that we are using to describe information. The idea is to define such an a priori probability distribution using some general principles such as t...

General inequalities for the distribution of the longest success run in Bernoulli trials are found through a direct combinatorial analysis. Their employment allows the derivation of a new lower bound which can be used in the achievement of theoretical results.