Cvijovic's addition formula for the Lah numbers

Cereceda, José L.

doi:10.12988/ijcms.2015.511

Cited by 3 publications

(1 citation statement)

References 4 publications

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“…are the special (unsigned) Lah numbers: L(n, ℓ) is the number of ways a set of n elements can be partitioned into ℓ non-empty linearly ordered subsets. Additionally, L(0, 0) = 0, L(n, 0) = 0 for n > 0, and L(n, k) = 0 for k > n; see Lah (1955) or, e.g., Cereceda (2015) for recent research on Lah numbers.…”

Section: Alternative Representations In the Normal Casementioning

confidence: 99%

Mixture representations of noncentral distributions

Baringhaus¹,

Grübel²

2022

Preprint

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With any symmetric distribution µ on the real line we may associate a parametric family of noncentral distributions as the distributions of (X + δ) 2 , δ = 0, where X is a random variable with distribution µ. The classical case arises if µ is the standard normal distribution, leading to the noncentral chi-squared distributions. It is well-known that these may be written as Poisson mixtures of the central chi-squared distributions with odd degrees of freedom. We obtain such mixture representations for the logistic distribution and for the hyperbolic secant distribution. We also derive alternative representations for chi-squared distributions and relate these to representations of the Poisson family. While such questions originated in parametric statistics they also appear in the context of the generalized second Ray-Knight theorem, which connects Gaussian processes and local times of Markov processes.

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Section: Alternative Representations In the Normal Casementioning

confidence: 99%

Mixture representations of noncentral distributions

Baringhaus¹,

Grübel²

2022

Preprint

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The Antibacterial Applications of Graphene and Its Derivatives

Shi

Chen

Teng

et al. 2016

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120

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Graphene materials have unique structures and outstanding thermal, optical, mechanical and electronic properties. In the last decade, these materials have attracted substantial interest in the field of nanomaterials, with applications ranging from biosensors to biomedicine. Among these applications, great advances have been made in the field of antibacterial agents. Here, recent advancements in the use of graphene and its derivatives as antibacterial agents are reviewed. Graphene is used in three forms: the pristine form; mixed with other antibacterial agents, such as Ag and chitosan; or with a base material, such as poly (N-vinylcarbazole) (PVK) and poly (lactic acid) (PLA). The main mechanisms proposed to explain the antibacterial behaviors of graphene and its derivatives are the membrane stress hypothesis, the oxidative stress hypothesis, the entrapment hypothesis, the electron transfer hypothesis and the photothermal hypothesis. This review describes contributions to improving these promising materials for antibacterial applications.

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Mixture representations of noncentral distributions

Baringhaus

Grübel

2020

Communications in Statistics - Theory and Methods

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We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises-Fisher, the Watson and the angular Gaussian families. In addition to several special results we present a general approach that is based on density expansions in terms of special surface harmonics. We discuss the connections to stochastic processes on spheres, in particular random walks, discrete mixture representations derived from spherical diffusions, and the use of Markov representations for the mixing base to obtain representations for families of spherical distributions.

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Cvijovic's addition formula for the Lah numbers

Abstract: Recently, Cvijović found a new addition formula for the partial Bell polynomials B n,k. In this note, we consider the unsigned Lah numbers L(n, k) and derive algebraically Cvijović's addition formula for L(n, k). Also, we obtain a couple of vertical recurrence relations for L(n, k).

Cited by 3 publications

References 4 publications

Mixture representations of noncentral distributions

Mixture representations of noncentral distributions

The Antibacterial Applications of Graphene and Its Derivatives

Mixture representations of noncentral distributions

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