http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7076 JAEM 2025, Vol 15, No 11 koleksiyonunu içerir. 2026-04-08T18:48:32Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7087 Realization algorithm for defining fractional order in oscillating systems with liquid damper Nazile, Hajiyeva; Irade, Aliyeva; Aliev, Fikret Akhmedali In the paper the problem of defining the fractional order in oscillating systems with liquid damper. Firstly, the equation of the object is reduced to the Volterra integral equation of the second kind with respect to the second order derivative of the phase coordinate. Based on the statistical data the quadratic functional has been constructed. Using the method of successive approximations the obtained Volterra integral equation has been solved and its solution has the form of the Neumann series. By means of the least squares method, we ensure that the theoretical results coincide with the statistical data, and as a result, a more effective fractional order is determined. Then, an effective algorithm is proposed. Since some steps of this algorithm need explanation, the issue of the implementation of the algorithm is considered. 2025-11-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7086 More on continuous and irresolute maps in Pythagorean fuzzy topological spaces Vadivel, Appachi; Gavaskar, Guru; Sundar, C. John The new dimension of non-standard fuzzy sets called Pythagorean fuzzy sets which can handle the inaccurate data very strongly has been established in recent days. Even though intuitionistic fuzzy sets were generously used in decision making to handle the imprecise data the novelty and the voluminous of Pythagorean fuzzy environment gives motivation to use it in decision making process. The Pythagorean fuzzy topological spaces are the novel generalization of fuzzy topological spaces. In this paper, we develop the concept of Pythagorean fuzzy δ continuity which is stronger than Pythagorean fuzzy continuous function in Pythagorean fuzzy topological spaces and specialize some of their basic properties with examples. Also, we introduce and discuss about properties and characterization of Pythagorean fuzzy δ irresolute maps. Interrelations have been studied elaborately for the defined functions using various examples. 2025-11-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7085 Wiener and Harary indices of Mycielskian graphs Goyal, Shanu; Tanya Let G = (V(G), E(G)) be a graph, where V = {v1, v2, . . . vn}. Let V′ = {v′1, v′2, . . . , v′n} be the twin of the vertex set V(G). The Mycielskian graph M(G) of G is defined as the graph whose vertex set is V(G) ∪ V′(G) ∪ {w} and the edge set is E(G) ∪ {viv′j : vivj ∈ E(G)} ∪ {v′iw ∈ V′(G)}. The vertex v′i is the twin of the vertex vi (or vi is twin of the vertex v′i) and the vertex w is the root of M(G). The closed Mycielskian graph M[G] of G is defined as the graph whose vertex set is V(G) ∪ V′(G) ∪ {w} and the edge set is E(G)∪ {viv′j : vivj ∈ E(G)} ∪ {viv′i : i = 1, 2, . . . , n}∪ {v′iw ∈ V′(G)}. The vertex v′i is the twin of the vertex vi (or vi is twin of the vertex v′i) and the vertex w is the root of M[G]. In this paper, we study the Wiener and Harary indices of the Mycielskian and closed Mycielskian graphs. 2025-11-01T00:00:00Z http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/7084 On some families of linear diophantine graphs Salama, Omar Mohamed; Seoud, Mohammed Abdel Azim; Anwar, Mohamed; Elsonbaty, Ahmed Diophantine labeling of graphs is an extension of the prime labeling of graphs. In this manuscript, we introduce some necessary conditions for determining whether a given graph admits Diophantine labeling or not, and if yes, we will find such a Diophantine labeling. We also study specific families of graphs, including the Complete graphs Kn, Wheel graphs Wn and Wn,n, Circulant graphs Cn(j), Path graphs Pn(j), Cartesian product graphs C3 × Cm, Normal Product graphs Pn ◦ Pn, Corona graphs G ⊙ H, Double Fan graphs gn = Pn + K2, Power graphs P2n and P3n, to ascertain their Diophantine nature. 2025-11-01T00:00:00Z