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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder
Electronic Theses and Dissertations
There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of different musical notes, each of which has different sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.
Decidability For Residuated Lattices And Substructural Logics, Gavin St. John
Decidability For Residuated Lattices And Substructural Logics, Gavin St. John
Electronic Theses and Dissertations
We present a number of results related to the decidability and undecidability of various varieties of residuated lattices and their corresponding substructural logics. The context of this analysis is the extension of residuated lattices by various simple equations, dually, the extension of substructural logics by simple structural rules, with the aim of classifying simple equations by the decidability properties shared by their extensions. We also prove a number of relationships among simple extensions by showing the equational theory of their idempotent semiring reducts coincides with simple extensions of idempotent semirings. On the decidability front, we develop both semantical and syntactical …
Homological Constructions Over A Ring Of Characteristic 2, Michael S. Nelson
Homological Constructions Over A Ring Of Characteristic 2, Michael S. Nelson
Electronic Theses and Dissertations
We study various homological constructions over a ring $R$ of characteristic $2$. We construct chain complexes over a field $K$ of characteristic $2$ using polynomials rings and partial derivatives. We also provide a link from the homology of these chain complexes to the simplicial homology of simplicial complexes. We end by showing how to construct all finitely-generated commutative differential graded $R$-algebras using polynomial rings and partial derivatives.
Totally Acyclic Complexes, Holly M. Zolt
Totally Acyclic Complexes, Holly M. Zolt
Electronic Theses and Dissertations
We consider the following question: when is every exact complex of injective modules a totally acyclic one? It is known, for example, that over a commutative Noetherian ring of finite Krull dimension this condition is equivalent with the ring being Iwanaga-Gorenstein. We give equivalent characterizations of the condition that every exact complex of injective modules (over arbitrary rings) is totally acyclic. We also give a dual result giving equivalent characterizations of the condition that every exact complex of flat modules is F-totally acyclic over an arbitrary ring.