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| Title | Abstract | Action(s) |
|---|---|---|
| An Efficient Encryption Technique Based on Coupled Map Lattices | This study introduces a highly secure image encryption technique based on coupled map lattices (CMLs), a class of chaotic systems known for their sensitivity to initial conditions and spatiotemporal complexity. The CMLs offer an ideal foundation for encryption due to its ability to generate unpredictable and nonlinear transformations. Although several chaos-based encryption methods have been explored in the past, many suffer from narrow parameter ranges, limited key spaces, or insufficient resistance to modern cryptographic attacks. To address these issues, we propose a novel two-parameter wide-range CMLs model that enhances key generation and improves chaotic behavior across a broader parameter space. The encryption process employs a dynamic key schedule, pixel permutation, and modular diffusion using CMLs-generated sequences. Comprehensive experimental evaluations demonstrate that the proposed method ensures high entropy, minimal pixel correlation, and strong resistance to brute-force, occlusion, noise, and differential attacks. It also outperforms existing techniques in both computational efficiency and encryption strength. |
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| A New Multiple Image Encryption Scheme Based on Chaotic Systems | Due to rapid developments in communication networks, the transferring of data through these networks has increased the risk. To protect this information, data encryption plays a significant role. This work extends a single chaotic map (SC3) to encrypt batches of images concurrently while maintaining high security standards. A new multiple-image encryption scheme based on the chaotic systems is designed to encrypt batches of images more efficiently and securely. By leveraging the complex dynamics and sensitivity to initial conditions inherent in chaotic maps, the scheme achieves a high level of confusion and diffusion across multiple images. The proposed multiple-image encryption scheme provides an effective and scalable solution for secure multimedia transmission. |
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| On Hankel Determinant of the inverse of q-Bounded Turning Functions. | The aim of this thesis is to investigate the Hankel determinants of the inverse functions of a subclass of univalent functions known as ˇq-bounded turning functions. This class, which generalizes classical bounded turning functions by incorporating the parameter ˇq, has attracted attention due to its connections with fractional analysis and ˇq-calculus. In this work, we focus on estimating the third Hankel determinant for the inverse functions associated with this class. By leveraging the analytical properties of ˇq-Carathéodory functions and the relationships between a function’s coefficients and those of its inverse, we derive an exact inequality for the determinant. Using tools from ˇq-calculus, subordination theory, and coefficient bounds, we obtain new sharp bounds that explicitly illustrate how the parameter ˇq influences the determinant’s value. The results not only generalize known outcomes for classical bounded turning functions but also provide new insights into the analytic structure and geometric behavior of inverse ˇqbounded turning functions in the open unit disc. Furthermore, we discuss geometric properties of the inverses and explore applications to extremal problems, thereby extending the understanding of coefficient problems in Geometric Function Theory. A minor graphical analysis is also performed to validate the new results against the classical literature. |
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| A Study of Spin Precession Effects of Axisymmetric Black Holes | Recent advances in gravitational theory and cosmology have emphasized the need to explore black hole structures within extended frameworks beyond general relativity. This thesis investigates the spin precession effects induced by both spacetime rotation and curvature in two distinct black hole models: a rotating black hole in Brans–Dicke (BD) gravity, which includes a dynamical scalar field, and a rotating black hole surrounded by a string cloud in the presence of dark energy. The study aims to understand how spin precession behaves in these modified gravitational settings and how it can serve as a tool to distinguish between black holes and naked singularities. By analyzing the precession of a test gyroscope near the central object, it is found that divergent precession frequencies are indicative of black hole horizons, while finite precession rates point toward naked singularities. This establishes spin precession as a potential observational criterion for differentiating these two types of compact objects. Furthermore, the influence of scalar fields and exotic matter components, such as dark energy and string clouds, on the precession behavior is explored, offering new insights into how such fields affect the spacetime geometry and the motion of spinning test particles. Overall, the results contribute to a deeper theoretical understanding of compact object classification in alternative gravity theories through physically measurable quantities. |
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