JAEM 2025, Vol 15, No 12JAEM 2025, Vol 15, No 12 koleksiyonunu içerir.http://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/71102026-04-14T21:33:30Z2026-04-14T21:33:30ZComputation of some degree-based topological indices of [n]circulenes according to the size of their central polygonRajabinejad, ZohrehSemnani, Saeed Mohammadianihttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/71212025-12-02T06:32:09Z2025-12-01T00:00:00ZComputation of some degree-based topological indices of [n]circulenes according to the size of their central polygon
Rajabinejad, Zohreh; Semnani, Saeed Mohammadiani
In this paper, several degree-based topological indices are computed for the family of [n]circulenes, a class of polycyclic hydrocarbons, using the M-polynomial method, which eliminates edge counting. Closed-form formulas depending only on the central polygon size n are derived for indices including the First and Second Zagreb, Modified Zagreb, Harmonic, Symmetric Division Degree, Inverse Sum, and Sigma indices. Numerical and graphical analyses for n = 3 to 10 reveal increasing trends, reflecting growing structural complexity. Additionally, an asymptotic analysis explores the behavior of these indices as n → ∞. These results offer a unified and scalable computational framework that fills a theoretical gap and aids quantitative structure–property relationship modeling of complex polycyclic systems.
2025-12-01T00:00:00ZAn investigation of the fractional Dirac operator using Laplace transformShahriari, MohammadMohammadalipour, BaharehBazm, SohrabMirzaei, Hanifhttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/71202025-12-02T06:15:59Z2025-12-01T00:00:00ZAn investigation of the fractional Dirac operator using Laplace transform
Shahriari, Mohammad; Mohammadalipour, Bahareh; Bazm, Sohrab; Mirzaei, Hanif
In this paper, the fractional Dirac operator with Caputo’s fractional derivative is considered. By using Laplace transform, the fractional Dirac operator reduces to an algebraic equation. Then by applying the inverse Laplace transform, we obtain the closed form of the characteristic function according to the two–parameters Mittag–Leffler function. By truncating the series of Mittag–Leffler function, the eigenvalues and the corresponding eigenfunctions are approximated. A convergence analysis for the proposed procedure is given. Finally, the efficiency and simplicity of the method are shown with some examples.
2025-12-01T00:00:00ZWeighted reproducing Kernel Property on Banach SpacesSababe, Saeed HashemiBiranvand, Naderhttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/71192025-12-01T12:40:20Z2025-12-01T00:00:00ZWeighted reproducing Kernel Property on Banach Spaces
Sababe, Saeed Hashemi; Biranvand, Nader
Weighted Reproducing Kernel Banach Spaces (WRKBS) extend kernel theory by incorporating weights to enhance modeling flexibility. This paper defines WRKBS, explores their theoretical foundations, and demonstrates their effectiveness in regression, classification, and clustering. Numerical experiments validate their advantages in structured data modeling and symmetry-aware learning. Applications span computer vision, physics-based modeling, and graph-based learning, with future directions in scalable algorithms and deep learning integration.
2025-12-01T00:00:00ZComplex rays and applicationsHasanoğlu, Elmanhttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/71182025-12-01T12:16:43Z2025-12-01T00:00:00ZComplex rays and applications
Hasanoğlu, Elman
Complex rays are a fascinating aspect of modern diffraction theory, typically sought as complex solutions to the eikonal equation. Traditionally, these solutions are obtained by analytically continuing real rays into the complex domain. However, this approach demands the analyticity of initial data, significantly limiting its applicability to many practical problems. Additionally, unlike real rays, complex rays cannot be visualized in space, presenting another drawback. In this paper, we present an alternative interpretation of complex rays, as introduced in [1], and describe a novel approach to two model diffraction problems and Gaussian beams.
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