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Full-Text Articles in Other Mathematics
Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., M. Ryan Luke
Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., M. Ryan Luke
Electronic Theses and Dissertations
In this dissertation, we will examine residuated mappings on a function lattice and how they behave with respect to the way-below relation. In particular, which residuated $\phi$ has the property that $F$ is way-below $\phi(F)$ for $F$ in appropriate sets. We show the way-below relation describes the separation of two functions and how this corresponds to contraction mappings on probabilistic metric spaces. A new definition for contractions is considered using the way-below relation.
Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King
Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King
Electronic Theses and Dissertations
In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule Mk outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. …