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3 articles for “probabilistic method”
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Primality Testing: A Comprehensive Analysis of Methods and Time Complexity
Abstract: This paper examines various primality testing algorithms and analyzes their time complexity. The algorithms we examine include the trial division, which is straightforward but becomes inefficient with large numbers; Fermat’s little theorem which is a probabilistic method included in Monte Carlo type of randomized algorithm; the Solovay–Strassen, based on properties from number theory, particularly those related to Euler’s criterion and Jacobi symbols; and the Miller–Rabin Probabilistic Test, which balances efficiency …
Published in International Journal of Algorithms Design and Analysis Review · Vol. 2, Issue 2, 2024 · pp. 25–31 Read article
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Study of Proximity Points and Fixed Points
Abstract: This paper explores the concepts of proximity points and fixed points, which are fundamental in mathematical analysis and nonlinear functional analysis. Fixed-point theorems play a crucial role in optimization, game theory, differential equations, and dynamic systems. Proximity points, an extension of fixed points, provide a more generalized approach, allowing near-coincidence rather than exact identity. The study discusses classical fixed-point theorems, such as Banach’s contraction principle, Brouwer’s fixed-point theorem, and Schauder’s …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 28–31 Read article
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Fracture Analysis of Functionally Graded Material (FGM) Plates Using Extended Finite Element Method: A Review.
Abstract: Functionally Graded Materials (FGMs), have drawn a lot of interest in various engineering applications due to their superior mechanical properties and ability to withstand extreme conditions. Fracture analysis in FGMs focuses on understanding how cracks initiate and propagate within these complex materials. The stress distribution becomes irregular due to spatial property variations which produces different crack paths than what occurs in homogeneous materials. The examination of FGM plates under fracture …
Published in International Journal of Fracture Mechanics and Damage Science · Vol. 4, Issue 1, 2026 · pp. 9–15 Read article