On parametric equivalence, isomorphism and uniqueness: Cycle related graphs
ODAM-Vol. 4 (2021), Issue 1, pp. 45 – 51 Open Access Full-Text PDF
J. Kok, J. Shiny
Abstract: This furthers the notions of parametric equivalence, isomorphism and uniqueness in graphs. Results for certain cycle related graphs are presented. Avenues for further research are also suggested.
Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling
OMS-Vol. 5 (2021), Issue 1, pp. 192 – 199 Open Access Full-Text PDF
Ronald Onyango, Brian Oduor, Francis Odundo
Abstract: The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.
Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integrals
EASL-Vol. 4 (2021), Issue 2, pp. 12 – 28 Open Access Full-Text PDF
Naila Mehreen, Matloob Anwar
Abstract: The aim of this paper is to establish the Hermite-Hadamard-Fejér type inequalities for co-ordinated harmonically convex functions via Katugampola fractional integral. We provide Hermite-Hadamard-Fej\’er inequalities for harmonically convex functions via Katugampola fractional integral in one dimension.
Kolakoski sequence: links between recurrence, symmetry and limit density
ODAM-Vol. 4 (2021), Issue 1, pp. 29 – 44 Open Access Full-Text PDF
Alessandro Della Corte
Abstract: The Kolakoski sequence \(S\) is the unique element of \(\left\lbrace 1,2 \right\rbrace^{\omega}\) starting with 1 and coinciding with its own run length encoding. We use the parity of the lengths of particular subclasses of initial words of \(S\) as a unifying tool to address the links between the main open questions – recurrence, mirror/reversal invariance and asymptotic density of digits. In particular we prove that recurrence implies reversal invariance, and give sufficient conditions which would imply that the density of 1s is \(\frac{1}{2}\).
Rate of convergence in total variation for the generalized inverse Gaussian and the Kummer distributions
OMS-Vol. 5 (2021), Issue 1, pp. 182 – 191 Open Access Full-Text PDF
Essomanda KONZOU
Abstract: The generalized inverse Gaussian distribution converges in law to the inverse gamma or the gamma distribution under certain conditions on the parameters. It is the same for the Kummer’s distribution to the gamma or beta distribution. We provide explicit upper bounds for the total variation distance between such generalized inverse Gaussian distribution and its gamma or inverse gamma limit laws, on the one hand, and between Kummer’s distribution and its gamma or beta limit laws on the other hand.
Prime and irreducible filters in strong quasi-ordered residuated systems
OMS-Vol. 5 (2021), Issue 1, pp. 172 – 181 Open Access Full-Text PDF
Daniel A. Romano
Abstract: In this article, we continue our research on quasi-ordered residuated systems introduced in 2018 by S. Bonzio and I. Chajda and various types of filters in them. Some fundamental properties of strong quasi-ordered residuated systems are given in this article. In addition, the concepts of prime and irreducible filters in such systems are introduced and analyzed.
