https://www.ajol.info/index.php/qm/issue/feed Quaestiones Mathematicae 2021-06-29T15:18:59+00:00 Publishing Manager publishing@nisc.co.za Open Journal Systems <p><em>Quaestiones Mathematicae</em> is devoted to research articles from a wide range of mathematical areas. Longer expository papers of exceptional quality are also considered. Published in English, the journal receives contributions from authors around the globe and serves as an important reference source for anyone interested in mathematics.</p><p>Read more about the journal <a href="http://www.nisc.co.za/products/12/journals/quaestiones-mathematicae" target="_blank">here</a>. </p> https://www.ajol.info/index.php/qm/article/view/209667 Strongly primary ideals in rings with zero-divisors 2021-06-29T13:16:08+00:00 Abdelhaq El Khalfi abdelhaq.elkhalfi@usmba.ac.ma Najib Mahdou mahdou@hotmail.com Najib Mahdou mahdou@hotmail.com <p>Let A be an integral domain with quotient field K. A. Badawi and E. Houston called a strongly primary ideal I of A if whenever x; y ∈ K and xy ∈ I, we have x ∈ I or yn ∈ I for some n ≥ 1. In this note, we study the generalization of strongly primary ideal to the context of arbitrary&nbsp; commutative rings. We de ne a primary ideal P of A to be strongly primary if for each a; b ∈ A, we have aP⊆ bA or b<sup>n</sup>A ⊆ a<sup>n</sup>P for some n ≥ 1.<br><br><strong>Key words:</strong> Primary, strongly primary, trivial ring extension, amalgamated duplication.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209668 Some information measures in concomitants of generalized order statistics under iterated Farlie-Gumbel-Morgenstern Bivariate type 2021-06-29T13:54:13+00:00 H.M. Barakat hmbarakat@hotmail.com I.A. Husseiny hmbarakat@hotmail.com <p>In this paper, we study the concomitants of generalized order statistics from iterated Farlie-Gumbel-Morgenstern (FGM) bivariate&nbsp; distribution. Three information measures, the Shannon entropy, the Kullback-Leibler distance and the Fisher information number, are derived and studied for this model. For each of these information measures, a computational study is conducted, in which we compare the<br>model of order statistics and model of sequential order statistics.</p> <p><br><strong>Key words</strong>: Concomitants, generalized order statistics, iterated FGM family, Shannon's entropy, Kullback-Leibler distance, Fisher information number.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209670 Some inequalities for the (p; q)-mixed affine surface areas 2021-06-29T14:05:04+00:00 Weidong Wang wangwd722@163.com Xia Zhao wangwd722@163.com <p>The notion of (p; q)-mixed volume was rst introduced by Lutwak, Yang and Zhang in 2018. According to this concept, Li, Wang and Zhou de ned the (p; q)- mixed affine surface areas in 2019. In this paper, we establish some inequalities including cyclic inequality, monotonous inequality and product inequality for the (p; q)-mixed affine surface areas.</p> <p><br><strong>Key words</strong>: (p; q)-mixed volume, (p; q)-mixed affine surface area, cyclic inequality, mo- notonous inequality, product inequality.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209672 Recurrence relation associated with the sums of square binomial coefficients 2021-06-29T14:10:40+00:00 Hac`ene Belbachir hacenebelbachir@gmail.com Abdelghani Mehdaoui hacenebelbachir@gmail.com <p>Our purpose is to describe the recurrence relation associated to the sums of diagonal elements lying along a finite ray of square binomial triangle. We also give the generating function. As consequences of the main theorem we prove some recurrence relations conjectured in Sloane’s OEIS, furthermore we also give some combinatorial identities.<br><br><strong>Key words:</strong> Recurrence relation, generating function, square binomials.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209674 A note on Aupetit's perturbation theorem 2021-06-29T14:17:41+00:00 Sonja Mouton smo@sun.ac.za <p>We investigate the different forms of Aupetit's perturbation theorem and its variants, and provide some generalisations.<br><br><strong>Key words</strong>: Spectrum, inessential ideal, Riesz and strong Riesz properties.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209675 Riemann Soliton within the framework of contact geometry 2021-06-29T14:23:49+00:00 M.N. Devaraja devarajamaths@gmail.com H. Aruna Kumara devarajamaths@gmail.com V. Venkatesha devarajamaths@gmail.com <p>In this paper, we study contact metric manifold whose metric is a Riemann soliton. First, we consider Riemann soliton (g; V ) with V as&nbsp; contact vector eld on a Sasakian manifold (M; g) and in this case we prove that M is either of constant curvature +1 (and V is Killing) or D-homothetically xed -Einstein manifold (and V leaves the structure tensor φ invariant). Next, we prove that if a compact K-contact manifold whose metric g is a gradient almost Riemann soliton, then it is Sasakian and isometric to a unit sphere S<sup>2n+1</sup>. Further, we study H-contact&nbsp; manifold admitting a Riemann soliton (g; V ) where V is pointwise collinear with .<br><br><strong>Key words</strong>: Contact metric manifold, Riemann soliton, gradient almost Riemann soliton.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209676 A new factor theorem on generalized absolute Cesaro summability 2021-06-29T14:38:18+00:00 Huseyin Bor hbor33@gmail.com <p>In this paper, we have proved a general theorem dealing with the φ -l C;α ;β l k summability factors of in nite series. Also, some new and known results are deduced.<br><br><strong>Key words</strong>: Cesaro mean, absolute summability, almost increasing sequence, in nite series, Holder's inequality, Minkowski's inequality.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209679 General multiplicative Zagreb indices of trees with given independence number 2021-06-29T14:53:30+00:00 Selvaraj Balachandran bala_maths@rediffmail.com Tomas Vetrik bala_maths@rediffmail.com <p>We obtain lower and upper bounds on general multiplicative Zagreb indices for trees with given independence number and order. Bounds on basic multiplicative Zagreb indices follow from our results. We also show that the bounds are best possible.<br><br><strong>Key words</strong>: Independence number, multiplicative Zagreb index, tree.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209681 On some new Gaussian hypergeometric summation formulae with applications 2021-06-29T15:02:10+00:00 T.K. Pogany poganj@pfri.hr Arjun K. Rathie akrathie@gmail.com <p>The aim of this note is to provide some new Gaussian hypergeometric summation formulae. These are further used to obtain certain new&nbsp; expressions for the product of hypergeometric series. Already obtained results by Bailey, Choi and Rathie and Qureshi et al. follow special cases of our main ndings.<br><br><strong>Key words:</strong> Bailey's results, Gaussian hypergeometric function 2F1, summation formulae.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209682 Positioned numerical semigroups 2021-06-29T15:10:45+00:00 M.B. Branco mbb@uevora.pt M.C. Faria mfaria@adf.isel.ipl.pt J.C. Rosales mfaria@adf.isel.ipl.pt <p>No Abstract.</p> 2021-06-29T00:00:00+00:00 Copyright (c) https://www.ajol.info/index.php/qm/article/view/209684 Generating integer polynomials from X<sup>2</sup> and X<sup>3</sup> using function composition: A study of subnearrings of (z[x];+; ◦) 2021-06-29T15:17:43+00:00 Erhard Aichinger erhard@algebra.uni-linz.ac.at Sebastian Kreinecker erhard@algebra.uni-linz.ac.at <p>Which integer polynomials can we write down if the only exponent to be used is 3? Such problems can be considered as instances of the subnearring generation problem. We show that the nearring (Z[x];+; ◦) of integer polynomials, where the nearring multiplication is the composition of polynomials, has uncountably many subnearrings, and we give an explicit description of those nearrings that are generated by subsets of {1; x; x<sup>2</sup>; x<sup>3</sup>}.<br><br><strong>Key words</strong>: Nearrings, integer polynomials, subnearring membership problem.</p> 2021-06-29T00:00:00+00:00 Copyright (c)