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3 articles for “polynomial algebras”
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Algebraic Foundations of Generalized Signal Processing: A Unified Approach Across Domains
Abstract: Using the techniques of algebra, notably polynomial algebras and modules, algebraic signal processing (ASP) is a contemporary, abstract framework that generalizes conventional signal processing— including Fourier analysis, filtering, and convolution. The notion is to use algebraic structures to explain signals, systems, and transformations such that ideas may be understood and generalized across many domains, including time, space, graph, or group. A unifying theoretical framework called ASP generalizes classical signal processing …
Published in Current Trends in Signal Processing · Vol. 15, Issue 3, 2025 · pp. 33–44 Read article
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Algebraic Geometry and Mathematical Physics: An Interdisciplinary Exploration
Abstract: Algebraic geometry, a branch of mathematics that studies solutions to systems of polynomial equations, has profound implications in mathematical physics. This paper delves into the intersection of algebraic geometry and mathematical physics, exploring how concepts from algebraic geometry illuminate various physical phenomena. We examine applications in string theory, quantum field theory, and positive geometry, highlighting the role of algebraic structures in understanding the fabric of the universe.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 12, Issue 3, 2025 · pp. 26–29 Read article
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Study of Algebraic Structures in Discrete Mathematics and Its Applications
Abstract: Algebraic structures such as groups, rings, fields, semi groups, and lattices form the foundational framework of discrete mathematics. These structures are defined by specific sets and operations that follow algebraic laws, enabling a systematic approach to problem-solving in various domains. This paper explores the theoretical principles of these algebraic systems and highlights their vital role in computer science, cryptography, automata theory, coding theory, and software engineering. By examining their properties …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 35–40 Read article