Search
6 articles for “Linear Algebra”
-
A Review Paper on The Mathematical Foundations of Artificial Intelligence
Abstract: Artificial Intelligence (AI) is deeply rooted in various branches of mathematics, which provide the theoretical foundation and practical tools for developing intelligent systems. This paper explores the crucial role of mathematics in AI, focusing on key areas such as Linear Algebra, Probability and Statistics, Optimization Techniques, Calculus, Graph Theory, and Fourier and Wavelet Transforms. Linear Algebra is fundamental for representing and manipulating data, with applications in dimensionality reduction and neural …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 7–14 Read article
-
Algebraic Foundations of AES (Advanced Encryption Standard): Group Theory and Finite Field Applications in Symmetric Cryptography
Abstract: This paper presents a mathematical study of symmetric cryptographic algorithms, with a particular emphasis on the Advanced Encryption Standard (AES), which is one of the most widely used encryption schemes in modern security applications. The study highlights how abstract mathematical frameworks such as group theory, finite fields, and vector space concepts provide the foundation for the design, implementation, and analysis of AES. By approaching the algorithm from a mathematical perspective, …
Published in Recent Trends in Mathematics · Vol. 2, Issue 1, 2025 · pp. 12–16 Read article
-
Comparing Results of a Study on Mathematics Instruction in English at Diploma College in Solapur District
Abstract: Study programmes at the Diploma College in Solapur include mathematics courses, which are instructed in English. Comparing the educational outcomes in the Mathematics study course with the English language of instruction is the primary objective of the paper. We concentrated on the students' proficiency in solving specific linear algebra and mathematical analysis problems. The first-year students in the Diploma study programme in Diploma College, Solapur made up the research sample. …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 12–18 Read article
-
Parameter Identification of Vibrating MIMO Mass-Spring-Damper Mechanical Systems with Coulomb Friction
Abstract: This study presents a time-domain method for identifying parameters in multi-degree-of-freedom (DOF) linear mass-spring-damper systems that include Coulomb friction, where the friction coefficient varies within a limited range, using measurements of position and control force. For mass identification in single-degree-of-freedom (DOF) vibrating mechanical systems with stiffness and no damping but Coulomb friction, the friction term is eliminated by first derivative processing. In addition, the identification of the coefficient of friction …
Published in International Journal of Mechanical Dynamics and Systems Analysis · Vol. 3, Issue 1, 2025 · pp. 20–34 Read article
-
Intuitionistic Fuzzy Hypergraph Laplacians and Dominating Transversals for Resilient Discrete Network Design
Abstract: This manuscript develops a discrete mathematical framework for resilience analysis on networks whose interactions are polyadic, uncertain, and partially conflicting. Classical graphs compress multi-way coordination into pairwise edges, while ordinary fuzzy graphs often ignore the non-membership information that becomes critical in emergency logistics, infrastructure interdependence, and cyberphysical coordination. We therefore formulate an intuitionistic fuzzy hypergraph in which each vertex hyperedge incidence carries membership, non-membership, and hesitation, and we construct a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 2, 2026 · pp. 15–21 Read article
-
Animated Transient Response of High Voltage Power Line Towers Equipped with Nonlinear Footing Resistances
Abstract: This study focuses, among other objectives, on the use of animation techniques for visualizing the electromagnetic transients in high voltage power line towers. The model includes parameters such as the tower’s footing resistance and its location-dependent surge impedance. It describes the governing algebraic/partial differential equations expressed in terms of the current and voltage distributions as functions of time and location. The transients are assumed initiated by a lightning discharge of …
Published in Trends in Electrical Engineering · Vol. 14, Issue 1, 2024 · pp. 44–52 Read article