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Articles 1 - 2 of 2
Full-Text Articles in Number Theory
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces, A. A. Salama, Florentin Smarandache, Valeri Kroumov
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces, A. A. Salama, Florentin Smarandache, Valeri Kroumov
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we generalize the crisp topological space to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the definitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.
Finding Zeros Of Rational Quadratic Forms, John F. Shaughnessy
Finding Zeros Of Rational Quadratic Forms, John F. Shaughnessy
CMC Senior Theses
In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.