Inequalities approach in determination of convergence of recurrence sequences
OMS-Vol. 5 (2021), Issue 1, pp. 65 – 72 Open Access Full-Text PDF
Albert Adu-Sackey, Francis T. Oduro, Gabriel Obed Fosu
Abstract: The paper proves convergence for three uniquely defined recursive sequences, namely, arithmetico-geometric sequence, the Newton-Raphson recursive sequence, and the nested/composite recursive sequence. The three main hurdles for this prove processes are boundedness, monotonicity, and convergence. Oftentimes, these processes lie in the predominant use of prove by mathematical induction and also require some bit of creativity and inspiration drawn from the convergence monotone theorem. However, these techniques are not adopted here, rather, as a novelty, extensive use of basic manipulation of inequalities and useful equations are applied in illustrating convergence for these sequences. Moreover, we established a mathematical expression for the limit of the nested recurrence sequence in terms of its leading term which yields favorable results.
Generalized orthopair fuzzy sets based on Hamacher T-norm and T-conorm
OMS-Vol. 5 (2021), Issue 1, pp. 44 – 64 Open Access Full-Text PDF
I. Silambarasan
Abstract: The concept of q-rung orthopair fuzzy sets generalizes the notions of intuitionistic fuzzy sets and Pythagorean fuzzy sets to describe complicated uncertain information more effectively. Their most dominant attribute is that the sum of the \(q^{th}\) power of the truth-membership and the \(q^{th}\) power of the falsity-membership must be equal to or less than one, so they can broaden the space of uncertain data. This set can adjust the range of indication of decision data by changing the parameter \(q, ~q\geq 1\). In this paper, we define the Hamacher operations of q-rung orthopair fuzzy sets and proved some desirable properties of these operations, such as commutativity, idempotency, and monotonicity. Further, we proved De Morgan’s laws for these operations over complement. Furthermore, we defined the Hamacher scalar multiplication \(({n._{h}}A)\) and Hamacher exponentiation \((A^{\wedge_{h}n})\) operations on q-rung orthopair fuzzy sets and investigated their algebraic properties. Finally, we defined the necessity and possibility operators based on q-rung orthopair fuzzy sets and some properties of Hamacher operations that are considered.
Dominator Chromatic numbers of orientations of trees
ODAM-Vol. 4 (2021), Issue 1, pp. 4 – 11 Open Access Full-Text PDF
Michael Cary
Abstract: In this paper we prove that the dominator chromatic number of every oriented tree is invariant under reversal of orientation. In addition to this marquee result, we also prove the exact dominator chromatic number for arborescences and anti-arborescences as well as bounds on other orientations of oft studied tree topologies including generalized stars and caterpillars.
Variation of radiofrequency intensities from the DTTV-transmitter in Kampala Metropolitan; Uganda
EASL-Vol. 4 (2021), Issue 1, pp. 21 – 29 Open Access Full-Text PDF
Peter Opio, Akisophel Kisolo, Willy Okullo, Tumps. W. Ireeta
Abstract: This paper presents the variation of radiofrequencies intensities from the DTTV-transmitter in Kampala Metropolitan for the sub 700 MHz (470-694 MHz) and the 700 MHz (694-790 MHz) frequency bands. The results of this study showed that though all the measurement locations from the transmitter have a good reception of DTTV signals, their radiofrequency intensities varied at the different points on the same measurement location at a constant distance from the DTTV transmitter. The study further showed that there is a general decrease in the radiofrequency intensities for the sub 700 MHz frequency band and a slight general increase in the radiofrequency intensities for the 700 MHz frequency band. This research revealed that the measured Reference Signal Received Power (RSRP) values for all the measurement locations where within the IEEE and FCC recommended values for any DTTV signal reception.
A variety of uncertainty principles for the Hankel-Stockwell transform
OMA-Vol. 5 (2021), Issue 1, pp. 22 – 34 Open Access Full-Text PDF
Khaled Hleili
Abstract: In this work, we establish \(L^p\) local uncertainty principle for the Hankel-Stockwell transform and we deduce \(L^p\) version of Heisenberg-Pauli-Weyl uncertainty principle. Next, By combining these principles and the techniques of Donoho-Stark we present uncertainty principles of concentration type in the \(L^p\) theory, when \(1\)<\(p\leqslant2\). Finally, Pitt's inequality and Beckner's uncertainty principle are proved for this transform.
Convergence analysis for a fast class of multi-step Chebyshev-Halley-type methods under weak conditions
OMS-Vol. 5 (2021), Issue 1, pp. 34 – 43 Open Access Full-Text PDF
Samundra Regmi, Ioannis K. Argyros, Santhosh George
Abstract: In this study a convergence analysis for a fast multi-step Chebyshe-Halley-type method for solving nonlinear equations involving Banach space valued operator is presented. We introduce a more precise convergence region containing the iterates leading to tighter Lipschitz constants and functions. This way advantages are obtained in both the local as well as the semi-local convergence case under the same computational cost such as: extended convergence domain, tighter error bounds on the distances involved and a more precise information on the location of the solution. The new technique can be used to extend the applicability of other iterative methods. The numerical examples further validate the theoretical results.
