We present new functional equations connecting the counting series of plane and planar (in the sense of Harary and Palmer) dissections. Simple rigorous expressions for counting symmetric r-dissections of polygons and planar S-dissections are obtained.

In this paper we will investigate the edge-chromatic automorphism groups for two classes of graphs. Chromatic automorphism groups have been studied by a number of people, including Chvatal [4] and Baumann et al. [l, 21. Characterizations will be given for these groups. Note that all arithmetic will be done modp, p not necessarily prime. The particular p will be clear from the context. These gra...

We show that the local period at position n in a characteristic Sturmian word can be given in terms of the Ostrowski representation for n+ 1.

BACKGROUND The Neonatal Behavioral Assessment Scale (NBAS, Brazelton & Nugent, 1995) is an instrument conceived to observe the neonatal neurobehavior. Data analysis is usually performed by organizing items into groups. The most widely used data reduction for the NBAS was developed by Lester, Als, and Brazelton (1982). OBJECTIVE Examine the psychometric properties of the NBAS items in a sample...

Motivated by the work of George A. Anastassiou in [George A. Anastassiou, Ostrowski and Landau inequalities for Banach space valued functions, Mathematical and Computer Modelling, 55 (2012), 312–329], we derive some Landau type inequalities for Banach space valued functions without assuming the boundary conditions.

Here we define a Caputo like discrete nabla fractional difference and we produce discrete nabla fractional Taylor formulae for the first time. We estimate their remaiders. Then we derive related discrete nabla fractional Opial, Ostrowski, Poincaré and Sobolev type inequalities .

We present optimal upper bounds for the deviation of a fuzzy continuous function from its fuzzy average over [a, b] ⊂ R, error is measured in the D-fuzzy metric. The established fuzzy Ostrowski type inequalities are sharp, in fact attained by simple fuzzy real number valued functions. These inequalities are given for fuzzy Hölder and fuzzy differentiable functions and these facts are reflected ...