Işık Üniversitesi YayınlarıIşık University Publicationshttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/23842026-06-15T07:40:14Z2026-06-15T07:40:14ZOktay Veliev, Multidimensional Periodic Schrödinger Operator (Perturbation Theories in High Energy Regions and Their Applications)Hasanoğlu, Elmanhttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/72942026-06-11T10:56:33Z2026-06-01T00:00:00ZOktay Veliev, Multidimensional Periodic Schrödinger Operator (Perturbation Theories in High Energy Regions and Their Applications)
Hasanoğlu, Elman
Book Review: Oktay Veliev, Multidimensional Periodic Schrödinger Operator (Perturbation Theories in High Energy Regions and Their Applications). Springer, Switzerland, 424 pp., 2024, Springer Tracts in Modern Physics, STMP, Vol. 291.
2026-06-01T00:00:00ZA unified spectral filter framework for ill-posed linear operator equations in Hilbert spacesReddy, B. BhaskarKumari Chilukuri, RajaTummala, Anil ChowdaryRao Musala, VenkateswaraKakarla, Hari KishoreManoharan, Kavithahttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/72932026-06-11T06:21:08Z2026-06-01T00:00:00ZA unified spectral filter framework for ill-posed linear operator equations in Hilbert spaces
Reddy, B. Bhaskar; Kumari Chilukuri, Raja; Tummala, Anil Chowdary; Rao Musala, Venkateswara; Kakarla, Hari Kishore; Manoharan, Kavitha
Regularization is useful for stable recovery in inverse problems with ill-posed linear operator equations in Hilbert spaces because small perturbations in data can make problems highly unstable. Tikhonov regularization, truncated singular value decomposition, and iterative polynomial filtering, classical methods, have been understood from singular value decay and the Picard condition. However, most literature analyses convergence, parameter choice, and saturation from separate perspectives. This study fills the gap by constructing a unified spectral filter framework that integrates bias–variance decomposition, polynomial and exponential decay, convergence rate analysis, and stabilityconsistent parameter choice frameworks, including the discrepancy principle and the Lcurve criterion. To enhance saturation control and qualification, we propose extensions to fractional and generalized spectral filters. In the severely ill-posed setting, we identify logarithmic convergence barriers with the inductive method, thereby exposing accuracy limits that exist independently from filter design. The findings are directly applicable to stable inversion and are operator theoretically sound for real-world applications, including medical imaging, geophysical reconstruction, signal processing, and data-driven recovery of ill-conditioned systems.
2026-06-01T00:00:00ZPicture fuzzy characteristic and picture fuzzy divisor of zero in a ring along with their applications in real life situationsDogra, ShovanPal, Madhumangalhttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/72922026-06-11T05:58:51Z2026-06-01T00:00:00ZPicture fuzzy characteristic and picture fuzzy divisor of zero in a ring along with their applications in real life situations
Dogra, Shovan; Pal, Madhumangal
The paper provides the concept of a picture fuzzy ideal over a ring and illustrates it with example. Additionally, it introduces the notions of picture fuzzy characteristic and picture fuzzy divisor of zero in a ring with respect to some picture fuzzy subring, investigating their related properties. The conditions under which picture fuzzy characteristic and picture fuzzy divisor of zero coincide with ordinary characteristic and ordinary divisor of zero are explicitly stated. It is demonstrated that the unit element in a ring, under some certain conditions, is not a picture fuzzy divisor of zero. Moreover, the picture fuzzy characteristic of the Cartesian product of two rings over the Cartesian product of two picture fuzzy subrings is calculated. Lastly, applications of PFCh and PFD of zero in Customers’ feedback and Customers’ sentiment analysis are presented Significant note of the work: Characteristic and divisor of zero are two foundational concepts in Abstract Algebra, playing a pivotal role in understanding the structure and behavior of rings. In this paper, these classical notions are extended and explored within the picture fuzzy environment, an advanced framework that builds upon fuzzy sets and intuitionistic fuzzy sets. By generalizing these concepts, the study bridges the gap between abstract algebraic theory and the flexible, nuanced reasoning enabled by Picture fuzziness. Key properties of picture fuzzy characteristic and picture fuzzy divisor of zero are thoroughly investigated, revealing how these concepts retain their essence while adapting to the picture fuzzy context. Furthermore, the abstract notions of characteristic and divisor of zero are connected to real-world scenarios, demonstrating their relevance and applicability when interpreted through the lens of picture fuzziness. This work not only advances the theoretical understanding of algebraic structures but also opens new avenues for applying fuzzy algebra in solving practical problems, thereby inspiring innovative research in both mathematics and interdisciplinary fields.
2026-06-01T00:00:00ZAn investigation of Pythagorean fuzzy digital convexityPreethi, N.Revathi, Govindasamy Krishnamoorthyhttp://belgelik.isikun.edu.tr/xmlui/handleiubelgelik/72912026-06-11T05:04:51Z2026-06-01T00:00:00ZAn investigation of Pythagorean fuzzy digital convexity
Preethi, N.; Revathi, Govindasamy Krishnamoorthy
The aim of this study is to introduce Pythagorean fuzzy digital convex sets, Pythagorean fuzzy digital cut sets, Pythagorean fuzzy digital topological spaces, Pythagorean fuzzy digital generalized closed sets, and Pythagorean fuzzy digital generalized open sets. Furthermore, to enrich the theory of Pythagorean fuzzy digital topological concepts, certain applications of Pythagorean fuzzy digital generalized closed sets, particularly the notion of Pythagorean fuzzy digital generalized T ½ spaces, are discussed and explored in detail.
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