Abstract Horizontal and vertical generating functions recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal log-concavity of sequences assigned to polynomials which show up in combinatorics, number theory physics. This includes Laguerre polynomials, Pochhammer D’Arcais Nekrasov–Okounkov polynomials.

OBJECTIVE To investigate the correlation between different radiographic methods in the evaluation of the lumbosacral concavity. METHODS The sample consisted of 52 individuals with ages ranging from 18 to 28 years old. The procedures related to radiographic image collection were carried out in collaboration with a diagnostic imaging center of a hospital in Curitiba, PR, Brazil. The angles of t...

The generalized trigonometric functions which have a short history, were introduced by Lindqvist two decades ago. Since 2010, many mathematician began to study their classical inequalities, general convexity and concavity, multiple-angle formulas and parameter convexity and concavity. A number of results have been obtained. This is a survey. Some new refinements, generalizations, applications, ...

In this paper, we discuss the properties of the hyperfibonacci numbers F [r] n and hyperlucas numbers L [r] n . We investigate the log-concavity (log-convexity) of hyperfibonacci numbers and hyperlucas numbers. For example, we prove that {F [r] n }n≥1 is log-concave. In addition, we also study the log-concavity (log-convexity) of generalized hyperfibonacci numbers and hyperlucas numbers.

PURPOSE To assess the diagnostic power of the Corneal Visualization Scheimpflug Technology (Corvis ST) provided corneal biomechanical parameters in keratoconic corneas. METHODS The following biomechanical parameters of 48 keratoconic eyes were compared with the corresponding ones in 50 normal eyes: time of the first applanation and time from start to the second applanation [applanation-1 time...

This is a small observation concerning scale mixtures and their log-concavity. A function f(x) ≥ 0, x ∈ Rn is called log-concave if f (λx + (1− λ)y) ≥ f(x)f(y) (1) for all x,y ∈ Rn, λ ∈ [0, 1]. Log-concavity is important in applied Bayesian Statistics, since a distribution with a log-concave density is easy to treat with many different approximate inference techniques. For example, log-concavit...

This study introduces a novel technique to identify foot outline characteristics and to classify feet into groups using turning functions and clustering techniques so that shape can complement anthropometry in producing good fitting shoes. The digital 3D foot scans, obtained from 50 Hong Kong Chinese subjects (25males and 25 females)were processed to generate the foot outlines at heights of 2mm...