Related papers: The Two-Piece Normal, Binormal, or Double Gaussian…
We study a bijective map from integer partitions to the prime factorizations of integers that we call the "supernorm" of a partition, in which the multiplicities of the parts of partitions are mapped to the multiplicities of prime factors…
We study the notion of formal duality introduced by Cohn, Kumar, and Sch\"urmann in their computational study of energy-minimizing particle configurations in Euclidean space. In particular, using the Poisson summation formula we reformulate…
The regular logistic map was introduced in 1960s, served as an example of a complex system, and was used as an instrument to demonstrate and investigate the period doubling cascade of bifurcations scenario of transition to chaos. In this…
We investigate Maxwell's attempt to justify the mathematical assumptions behind his 1860 Proposition IV according to which the velocity components of colliding particles follow the normal distribution. Contrary to the commonly held view we…
The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters, and…
In 1853 J. Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these…
Initially proposed by Martin Gardner in the 1950s, the famous two-children problem is often presented as a paradox in probability theory. A relatively recent variant of this paradox states that, while in a two-children family for which at…
Ritt's Second Theorem deals with composition collisions g o h = g* o h* of univariate polynomials over a field, where deg g = deg h*. Joseph Fels Ritt (1922) presented two types of such decompositions. His main result here is that these…
The aim of this article is to introduce a new family of distributions, which generalizes the skew normal distribution (SN). This new family, called Beta skew-normal (BSN), arises naturally when we consider the distributions of order…
A new three parameter natural extension of the Conway-Maxwell-Poisson (COM-Poisson) distribution is proposed. This distribution includes the recently proposed COM-Poisson type negative binomial (COM-NB) distribution [Chakraborty, S. and…
In a recent issue of the Bulletin of the Korean Mathematical Society, Qi and Zhang discovered an interesting integral representation for the Bernoulli numbers of the second kind (also known as Gregory's coefficients, Cauchy numbers of the…
The idea of graph compositions, which was introduced by A. Knopfmacher and M. E. Mays, generalizes both ordinary compositions of positive integers and partitions of finite sets. In their original paper they developed formulas, generating…
In order to provide a local description of a regular function in a small neighbourhood of a point $x$, it is sufficient by Taylor's theorem to know the value of the function as well as all of its derivatives up to the required order at the…
Baxter permutations arose in the study of fixed points of the composite of commuting functions by Glen Baxter in 1964. This type of permutations are counted by Baxter numbers $B_n$. It turns out that $B_n$ enumerate a lot of discrete…
We study consequences and applications of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences…
The Teissier distribution, originally proposed by Teissier [31], was designed to model mortality due to aging in domestic animals. More recently, Krishna et al. [19] introduced the Unit Teissier (UT) distribution on the interval (0, 1)…
Double hard scattering can play an important role for producing multiparticle final states in hadron-hadron collisions. The associated cross sections depend on double parton distributions, which at present are only weakly constrained by…
The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some…
In this article we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be described by relations which is similar to the conditional…
Physical and mathematical applications of fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we…