Browsing by Author "Denizler, Ismail Hakki"

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A Generalization of Robert's Result on Dimension for Artinian Modules
(King Fahd Univ Petroleum Minerals, 2010) Denizler, Ismail Hakki
In this paper, we present a generalization of Roberts' theorem on the dimension of Artinian modules over quasi-local rings (i.e., rings with only one maximal ideal) to the case where the rings are not necessarily quasi-local.
Modeling Benzene Physicochemical Properties Using Zagreb Upsilon Indices
(De Gruyter Poland Sp Z O O, 2025) Ciftci, Idris; Yamac, Kerem; Denizler, Ismail Hakki
Quantitative structure-property relationship (QSPR) frameworks leverage topological indices to model the physicochemical attributes of molecular structures. In this study, we introduce the concept of upsilon degree and define the Zagreb upsilon indices based on this concept. Our findings demonstrate that the second Zagreb upsilon index exhibits the highest predictive accuracy for the pi-electron energy of benzenes, surpassing existing degree-based topological indices with correlation coefficients exceeding 0.93. This accuracy was measured using statistical correlation analysis, and a direct comparison with the Randi & cacute; and geometric-arithmetic indices further supports the superior performance of the second Zagreb upsilon index. Furthermore, structural sensitivity and abruptness analyses, which assess the stability and variation of an index across different molecular structures, indicate that Zagreb upsilon indices offer superior performance compared to alternative indices. These results suggest that Zagreb upsilon indices have significant potential as a new and effective tool for QSPR research.
Z(S_3×c_3) İntegral Grup Halkasındaki Birimsel Elemanlar Grubu Üzerine
(2024) Denizler, Ismail Hakki; Low, Richard; Kusmus, Omer
Verilen bir sonlu grubun integral grup halkasındaki birimsel elemanların grubunu belirlemek çoğu grup için meşhur ve klasik bir açık problemdir. S_3 ve C_3 sırasıyla 6 mertebeli simetrik grup ve 3 mertebeli bir devirli grup olsun. Bu makalede, iki dereceli bir kompleks temsile göre S_3×C_3 direkt çarpım grubunun Z(S_3×C_3) integral grup halkasının birimsel elemanlarının yapısı verilmektedir. Sonuç olarak, kompleks bir tamlık bölgesi üzerinde tanımlı grup halkalarına ilişkin (Low, 2008)’ de sunulan konjektürün bir kısmı, temsil teorisi kullanılarak çözülmüştür.