Archimedes' quadrature of the parabola and minimal covers [PDF]
arXiv, 2016 The generalization of Archimedes strategy to obtain the area of a parabolic segment leads to combinatorial formulas involving minimal covers of sets. These, in turn, are conjecturally related to $q$-binomial coefficients.
arxiv
Note on the real rootedness of polynomials [PDF]
arXiv, 2017 In this paper, by the generalized Bell umbra and Rolle's theorem, we give some results on the real rootedness of polynomials. Some applications on partition polynomials and the sigma polynomials of graphs are given.
arxiv
On central Fubini-like numbers and polynomials [PDF]
arXiv, 2018 We introduce the central Fubini-like numbers and polynomials using Rota approach. Several identities and properties are established as generating functions, recurrences, explicit formulas, parity, asymptotics and determinantal representation.
arxiv
Roles of extended human papillomavirus genotyping and multiple infections in early detection of cervical precancer and cancer and HPV vaccination. [PDF]
BMC Cancer, 2022 Song F +6 more
europepmc +1 more source
Degenerate zero-truncated Poisson random variables [PDF]
arXiv, 2019 In this paper, we introduce the degenerate zero-truncated Poisson random variables whose probability mass functions are a natural extension of the zero-truncated Poisson distributions, and investigate various properties of those random variables.
arxiv
Upland rice varietal mixtures in Madagascar: evaluating the effects of varietal interaction on crop performance. [PDF]
Front Plant Sci, 2023 Rahajaharilaza K +7 more
europepmc +1 more source
Applications of the classical umbral calculus [PDF]
Algebra Universalis 49 (2003), 397-434, 2001 We describe applications of the classical umbral calculus to bilinear generating functions for polynomial sequences, identities for Bernoulli and related numbers, and Kummer congruences.
arxiv
Trends in Transcatheter Edge-to-Edge Mitral Valve Repair Over a Decade: Data From the MiTra ULM Registry. [PDF]
Front Cardiovasc Med, 2022 Nita N +6 more
europepmc +1 more source
Jordan and Smith forms of Pascal-related matrices [PDF]
arXiv, 2002 We present matrix identities which yield respectively the Jordan canonical form of the Pascal matrix P_n = (i -1 choose j -1)_{1 <= i,j <= n} modulo a prime, the eigenvectors of (i choose j)_{1 <= i,j <= n}, and the Smith normal form of powers of P_n - I_n.
arxiv
Generalizing Benford's law using power laws: application to integer sequences [PDF]
arXiv, 2006 A simple method to derive parametric analytical extensions of Benford's law for first digits of numerical data is proposed. Two generalized Benford distributions are considered, namely the two-sided power Benford distribution and the new Pareto Benford distribution. The fitting capabilities of these generalized Benford distributions are illustrated and
arxiv