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Full-Text Articles in Physical Sciences and Mathematics
On The Discrete Differential Geometry Of Surfaces In S4, George Shapiro
On The Discrete Differential Geometry Of Surfaces In S4, George Shapiro
Open Access Dissertations
The Grassmannian space GC(2, 4) embedded in CP5 as the Klein quadric of twistor theory has a natural interpretation in terms of the geometry of “round” 2-spheres in S4. The incidence of two lines in CP3 corresponds to the contact properties of two 2- spheres, where contact is generalized from tangency to include “half-tangency:” 2-spheres may be in contact at two isolated points. There is a connection between the contact properties of 2-spheres and soliton geometry through the classical Ribaucour and Darboux transformations. The transformation theory of surfaces in S4 is investigated using the recently developed theory of “Discrete Differential …
Class Numbers Of Ray Class Fields Of Imaginary Quadratic Fields, Omer Kucuksakalli
Class Numbers Of Ray Class Fields Of Imaginary Quadratic Fields, Omer Kucuksakalli
Open Access Dissertations
Let K be an imaginary quadratic field with class number one and let [Special characters omitted.] be a degree one prime ideal of norm p not dividing 6 d K . In this thesis we generalize an algorithm of Schoof to compute the class number of ray class fields [Special characters omitted.] heuristically. We achieve this by using elliptic units analytically constructed by Stark and the Galois action on them given by Shimura's reciprocity law. We have discovered a very interesting phenomena where p divides the class number of [Special characters omitted.] . This is a counterexample to the elliptic …
Correction Methods, Approximate Biases, And Inference For Misclassified Data, Meng-Shiou Shieh
Correction Methods, Approximate Biases, And Inference For Misclassified Data, Meng-Shiou Shieh
Open Access Dissertations
When categorical data are misplaced into the wrong category, we say the data is affected by misclassification. This is common for data collection. It is well-known that naive estimators of category probabilities and coefficients for regression that ignore misclassification can be biased. In this dissertation, we develop methods to provide improved estimators and confidence intervals for a proportion when only a misclassified proxy is observed, and provide improved estimators and confidence intervals for regression coefficients when only misclassified covariates are observed. Following the introduction and literature review, we develop two estimators for a proportion , one which reduces the bias, …