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Öğe On Solution of complex equations with the homotopy perturbation method(Adiyaman University, 2024-12-31) Düz, Murat; Çamlica, ŞeydaIn this study, complex differential equations are solved using the homotopy perturbation method (HPM). Firstly, we separated the real and imaginary parts of the equation. Thus, from one unknown equation is obtained two unknown equation systems. Later, we applied HPM real and imaginary to parts of the equation. So, we have obtained real and imaginary parts of the solution.Öğe Synthesis and characterization of schiff bases and their Ag(I) complexes containing 2,5,6-trisubstituted imidazothiadiazole derivatives: molecular docking and in vitro cytotoxic effects against nonsmall lung cancer cell line(John Wiley & Sons, 2025-01-20) Mirghani, Ahmed Hamdi; Pehlivanoglu, Suray; Alici, Hakan; Tahtaci, Hakan; Uysal, SabanIn this study, four novels 2,5,6-trisubstituted imidazothiadiazole derivative ligands and their Ag(I) complexes were synthesized and characterized using various spectroscopic analysis techniques. First, imidazo[2,1-b][1,3,4]thiadiazole derivative (3) was obtained from the reaction of 5-amino-1,3,4-thiadiazole-2-thiol with benzyl bromide in the presence of KOH in an ethanolic medium. In the next step, the resultant compound reacted sequentially with four substituted phenacyl bromide derivatives (4a–4d) under refluxed ethanol for 24 h to obtain substituted 2-(benzylthio)-6-phenylimidazo[2,1-b][1,3,4]thiadiazole derivatives (5–8). Compounds (9–12) were obtained by attaching a carbonyl group to carbon number 5 of the imidazothiadiazole group in these compounds with the help of Vilsmeier–Haack reagent. The resultant compounds were reacted in an ethanolic medium to synthesize the novel (13–16) ligands by adding ethylenediamine in a 1:2 molar ratio. The Ag(I) complexes of the resultant ligands were synthesized by mixing silver acetate with the ligands in a dimethyl sulfoxide medium to obtain (17–20) complexes. All the synthesized compounds were analyzed using FTIR, 1H NMR, 13C NMR, mass spectroscopy, magnetic susceptibility, ICP-OES, and thermogravimetric analysis techniques. The study also investigates the in vitro cytotoxic effect of the ligands and complexes on A549 (nonsmall cell lung cancer) cells using the MTT assay and shows that the 13, 15, and 16 ligands, together with their complexes, exhibit potent cytotoxicity. In addition, in silico molecular docking simulations were conducted both to support the in vitro cytotoxicity experiments and to ascertain the active binding sites and interactions of the ligands and complexes on the EGFR receptor. The result indicates that ligands and complexes may serve as promising candidates for further investigation as anticancer agents.Öğe On positive integer solutions of a special diophantine equation(Palestine Polytechnic University, 2024) Emin, AhmetIn this study, the positive solutions of the Diophantine equation D: x2 −( σ2 + 4) y2 − (2σ − 2) x −(2σ4 + 8σ2) y − σ6 − 4σ4 + σ2 − 2σ − 3 = 0 on the set Z are investigated, along with some recurrence relations that provide the relationships among these solutions. In addition, solutions of the Diophantine equation D in terms of generalized Fibonacci and Lucas sequences are examined. Furthermore, we search for the solutions of this equation over finite fields Fp where p is prime and p > 5. Finally, an example is given that satisfies our results.Öğe Reduction formulas for permanents and determinants of k-tridiagonal Toeplitz matrices(Indian National Science Academy, 2024-12-25) Ahmet Zahid KüçükThis study presents some results on the permanents of k-tridiagonal matrices with the Toeplitz structure. Our investigation establishes significant connections between the permanents of this matrix family and their reduced forms in terms of bandwidth and order. We extend the investigation also to the determinants of this matrix family in this context. Moreover, we demonstrate that some subforms of k-tridiagonal Toeplitz permanents can be effectively computed using the Pascal and Lucas triangles. Finally, we make a significant contribution by revealing an integer sequence related to Fibonacci numbers, derived by analyzing the permanents of some subforms of k-tridiagonal Toeplitz matrices.Öğe Solution of Partial Differential Equations and Their Application by Three Parameters of Integral Transform(Science Research Society, 2024-11-07) Salman, Nour K.; Aldhlki, Talat Jassim; Kuffi, Emad A.; Issa, AhmadThis article explains the Nour integral transform technique and denoted by "NO transform ", it's fundamental hypothesis and its power to solve the exact solution of partial differential operator equations (PDOE's) have been introduced and shown by the exact solution of various elementary engineering partial differential operator equations such as: wave partial equation, heat partial equation, Laplace’s partial equation, telegraph partial equation, and Klein-Gordon partial equation.
