Some Ostrowski type integral inequalities via generalized harmonic convex functions
OMS-Vol. 5 (2021), Issue 1, pp. 200 – 208 Open Access Full-Text PDF
Muhammad Tariq, Saad Ihsan Butt
Abstract: In this paper, we aim to introduce a new notion of convex functions namely the harmonic \(s\)-type convex functions. The refinements of Ostrowski type inequality are investigated which are the generalized and extended variants of the previously known results for harmonic convex functions.
Dye ability of henna dye towards cotton fabrics in comparison with reactive dye by following reactive dyeing procedure
EASL-Vol. 4 (2021), Issue 2, pp. 29 – 35 Open Access Full-Text PDF
Pranay Dutta, Md. Razaya Rabbi, Mohammad Abu Sufian, Shahnaz Mahjebin
Abstract: Although synthetic dyes are commonly used, natural dyes are still being utilized and used to improve their intrinsic aesthetic properties as the main material for the body’s beauty. For example, research results have shown that henna plant leaves comprise dye together with other additives. This provides a hint that if color from henna is properly studied, it can be used not only as body decoration but may also have fiber-substrates affinity. This paper explores the dyeing possibility-the ability to dye and the fastness qualities of henna dye extracted from henna leaves on cotton fabric compared to reactive dyeing using the same dyeing technique as reactive dyeing. Also, color fastness tests have been performed according to the ISO test methods. The implications of henna dye have been shown to have poor to moderate dyeing capability towards cotton fabrics as opposed to the reactive dyes when henna dyeing is accompanied by reactive dyeing. Similarly, henna dye demonstrated satisfactory properties of fastness as opposed to reactive dye. For henna dye with 50% shade, it gives an outstanding color tone with a good level of coloration. Taken into account the ability to dye and the fastness of color, the dyeing of matured henna leaves is equally advantageous to the dyeing of cotton fabrics.
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 \(\frac{1}{2}\).
