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5 articles for “Euclidean metric”
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Galois Theory and Ricci Flow Curvature Applications for Generating the Mandelbrot Set
Abstract: In this paper, an application of Galois theory is presented through Ricci flow curvature in Mandelbrot set. The Mandelbrot set is analyzed over Ricci flow equation for generating the fractal set simply. Although, the fractal set is generated as the points in the complex plane connected to the Julia set and approaches to infinity. This paper proposes an efficient method of fractal set generation based on onto-one correspondence between Ricci …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 9, Issue 3, 2022 · pp. 24–29 Read article
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Examining the Crowd in Real-time with Deep Learning
Abstract: In this research, a model is proposed that can be used to estimate crowd density in a specific region and to establish social distances in accordance with predetermined rules. This is accomplished utilizing a multi-source model-based approach. In a small public gathering where hand counting is impossible, this technique conducts a survey. To do this, input video frames are extracted, each frame is processed, and then passed to the model …
Published in Journal of Computer Technology & Applications · Vol. 14, Issue 1, 2023 · pp. 41–45 Read article
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Comparative Analysis of Distance Metrics using Face Recognition
Abstract: Researchers are using various distance metric standards in evaluation of face recognition methods. In past decades, the Eigenfaces and Fisherfaces face recognition methods were generally evaluated using the Euclidean distance (ED) metric that have shown better performance in cooperative environments, but poorly performed in non-cooperative environments. This paper presents a comparative analysis of distance metrics through face recognition methods i.e., Eigenfaces and Fisherfaces in both cooperative environments and non-cooperative environments. …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 8, Issue 1, 2021 · pp. 1–7 Read article
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Multicriteria Decision Making using SR-Fuzzy Sets
Abstract: In this study, we introduce and explore square-root fuzzy sets (SR-Fuzzy sets), a novel extension within the realm of fuzzy set theory. We begin by establishing a comparative analysis between SR-Fuzzy sets and two well-known fuzzy set models: Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS). This comparison highlights the unique characteristics and mathematical structure of SR-Fuzzy sets. A particular focus is placed on the complement operator, which plays …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 12–20 Read article
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A Novel Mathematical Exploration of Fractal Dynamics in Hyperbolic Spaces
Abstract: This research paper presents an original study on the behavior, generation, and properties of fractal structures within hyperbolic geometry. Unlike classical Euclidean fractals, hyperbolic fractals demonstrate accelerated boundary complexity and distinct scaling symmetries due to the curvature of the underlying space. The paper proposes new iterative models, analyzes geometric invariants, and explores potential applications in data visualization, network science, and theoretical physics. This research paper conducts an in-depth investigation into …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 1–7 Read article