Relationship of Algebraic Theories to Powerset Theories and Fuzzy Topological Theories for Lattice-Valued Mathematics [PDF]
International Journal of Mathematics and Mathematical Sciences, 2007 This paper deals with a broad question—to what extent is topology algebraic—using two specific questions: (1) what are the algebraic conditions on the underlying membership lattices which insure that categories for topology and fuzzy topology are indeed topological categories; and (2) what are the algebraic conditions which insure that algebraic ...
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From Music to Mathematics and Backwards: Introducing Algebra, Topology and Category Theory into Computational Musicology [PDF]
, 2018 Despite a long historical relationship between mathematics and music, the interest of mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based approaches currently employed in MIR (Music Information Research), the research project described in this paper stresses the necessity of introducing a structural ...
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‘Quasi-Boolean Algebra and Foundations of Topology:’ Chinese Mathematical Logician Hu Shihua and the Group of Münster [PDF]
History and Philosophy of LogicThis paper investigates a less well-known aspect of the history of mathematical logic as advanced by the ‘group of Münster’ in the late 1930s by analysing the work of one of their international members, Hu Shihua. By deconstructing and re-evaluating the main conceptual ingredients of Hu’s doctoral research and placing his work into the context of ...
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MathematicsThere was an omission in the original publication [...]
Ioannis Diamantis +2 more
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Properads in Algebra, Topology, Geometry and Mathematical Physics
, 2009 Ce mémoire contient un résumé de mes travaux sur le thème des propérades et de leurs applications en algèbre, topologie, géométrie et physique mathématique.
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Exploring the Applications of Algebraic Topology in Modern Mathematics and Data Analysis
Algebraic topology is a vibrant and intricate branch of mathematics that intertwines the abstract structures of algebra with the intuitive notions of topology. At its core, algebraic topology investigates topological spaces and their properties through algebraic invariants, enabling mathematicians to classify and understand spaces in a profound way ...
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Uniqueness of the Banach algebra topology for non-archimedean algebras. Special issue on the occasion of the twentieth anniversary of the Mathematics Department [PDF]
, 1980 Contains fulltext : 18______.PDF (Publisher’s version ) (Open Access)
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ALGEBRAIC TOPOLOGY AND PHYSICS (Women in Mathematics)
ALGEBRAIC TOPOLOGY AND PHYSICS (Women in Mathematics)Recently, there has been a growing interest in the relations between algebraic topology and physics. Algebraic topology is used to classify physical systems, and it can be a very powerful tool to analyze physical problems in purely mathematical ways. In this talk, I explain this idea and some of my related works.
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We resolve the century-old atomic stability paradox without quantization postulates. The electron is a static topological knot of 24 nodes in the structured vacuum V₂₃, not an orbiting particle. The key result is an exact energy hierarchy derived from x³ − x − 1 = 0: the vacuum zero-point energy E_vac = αm_ec²/2 = 1864.47 eV exceeds the ionization ...
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Fixed-point topology meets fractal memory: a Kutumba-stabilized framework for nonlocal fractal-fractional dynamics. [PDF]
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