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Full-Text Articles in Mathematics
Waring Rank And Apolarity Of Some Symmetric Polynomials, Max Brian Sullivan
Waring Rank And Apolarity Of Some Symmetric Polynomials, Max Brian Sullivan
Boise State University Theses and Dissertations
We examine lower bounds for the Waring rank for certain types of symmetric polynomials. The first are Schur polynomials, a symmetric polynomial indexed by integer partitions. We prove some results about the Waring rank of certain types of Schur polynomials, based on their integer partition. We also make some observations about the Waring rank in general for Schur polynomials, based on the shape of their Semistandard Young Tableaux. The second type of polynomials we refer to as a Power of a Fermat-type polynomial, or a PFT polynomial. This is a Fermat type (or power sum) polynomial over n variables with …
Zariski Geometries And Quantum Mechanics, Milan Zanussi
Zariski Geometries And Quantum Mechanics, Milan Zanussi
Boise State University Theses and Dissertations
Model theory is the study of mathematical structures in terms of the logical relationships they define between their constituent objects. The logical relationships defined by these structures can be used to define topologies on the underlying sets. These topological structures will serve as a generalization of the notion of the Zariski topology from classical algebraic geometry. We will adapt properties and theorems from classical algebraic geometry to our topological structure setting. We will isolate a specific class of structures, called Zariski geometries, and demonstrate the main classification theorem of such structures. We will construct some Zariski structures where the classification …