http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7008 JAEM 2025, Vol 15, No 9 koleksiyonunu içerir. Thu, 09 Apr 2026 04:36:58 GMT 2026-04-09T04:36:58Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7027 An efficient eighth order family of iterative method for solving systems of nonlinear equations Yaseen, Saima; Zafar, Fiza In this paper, we analyse the underlying computational cost as well as applicability of the new iterative methods for real-life problems and illustrate that the new schemes produce approximations of greater numerical accuracy for solving nonlinear systems. Basins of attraction are also given for some test problems to study the convergence regions. Mon, 01 Sep 2025 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7027 2025-09-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7026 A comparative study on prime and vertex k-prime labeling of one point union of path graphs Santiago, Teresa Arockiamary; Vijayalakshmi, G. In our study, we investigate the structure of one point union of path graphs and prove that they admit a vertex k-prime labeling. Further a study on comparison between prime and vertex k-prime labeling for one point union of path graph has been analysed and applied in the field of computer science with the help of C++ programming language. Mon, 01 Sep 2025 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7026 2025-09-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7025 Availability and reliability analysis of a two-unit parallel system subject to failure and repair operating in a multi-level environment Thilaka, Balakrishnan; Hemanth Kumar, Sankaralingam; Swaminathan, Udayabaskaran In this paper, a two-unit parallel system is considered subject to failure and repair in a multi-level environment. It is assumed that there are N levels of the environment. The failure time of any operating unit in the k−th level of the environment is exponentially distributed with parameter µk, k = 1, 2, · · · , N. There is a single repair facility. The system is in down-state when both units are in the repair facility. The down-state is designated as level 0 of the environment. The repairs are done under the ‘first-come-first serve’ policy. The repair time of a failed unit in the k−th level of the environment is exponentially distributed with parameter γk, k = 0, 1, 2, · · · , N. When the system is in level 0 of the environment, one failed unit is undergoing repair and the other failed unit is waiting for repair. Upon completion of the repair of the unit, the system is immediately switched to operate in r−th level of the environment with positive probability pr, r = 1, 2, · · · , N and the repair for the other failed unit immediately starts with rate γr. Using the techniques of renewal theory and Laplace transforms, transient state probability distribution, steady-state probability distribution, availability and reliability functions and mean down-time of the system are explicitly found. A numerical illustration is provided to highlight the system performance. Mon, 01 Sep 2025 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7025 2025-09-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7024 On the generic Cut–Point detection procedure in the Binomial Group Testing Čižikovienė, Ugnė; Skorniakov, Viktor Initially announced by Dorfman in 1943 for medical screening, (Binomial) Group Testing (BGT) was quickly recognized as a useful probabilistic tool in many other fields: quality control, communications and networking, engineering, statistics, etc. To apply any particular BGT procedure effectively, one first of all needs to know an important operating characteristic, the so called Optimal Cut-Point (OCP), describing the limits of its applicability. The determination of the latter is often a complicated task. In this work, we provide a generic algorithm suitable for a wide class of the BGT procedures and demonstrate its applicability by example. The way we do it exhibits independent interest since we link the BGT to seemingly unrelated field — the bifurcation theory. Mon, 01 Sep 2025 00:00:00 GMT http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7024 2025-09-01T00:00:00Z