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  Partner: UNT Libraries
 Decade: 2000-2009
 Year: 2002
 Degree Discipline: Mathematics
 Collection: UNT Theses and Dissertations
Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions

Analysis Of Sequential Barycenter Random Probability Measures via Discrete Constructions

Date: December 2002
Creator: Valdes, LeRoy I.
Description: Hill and Monticino (1998) introduced a constructive method for generating random probability measures with a prescribed mean or distribution on the mean. The method involves sequentially generating an array of barycenters that uniquely defines a probability measure. This work analyzes statistical properties of the measures generated by sequential barycenter array constructions. Specifically, this work addresses how changing the base measures of the construction affects the statististics of measures generated by the SBA construction. A relationship between statistics associated with a finite level version of the SBA construction and the full construction is developed. Monte Carlo statistical experiments are used to simulate the effect changing base measures has on the statistics associated with the finite level construction.
Contributing Partner: UNT Libraries
Dimensions in random constructions.

Dimensions in random constructions.

Date: May 2002
Creator: Berlinkov, Artemi
Description: We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
Contributing Partner: UNT Libraries
Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World

Understanding Ancient Math Through Kepler: A Few Geometric Ideas from The Harmony of the World

Date: August 2002
Creator: Arthur, Christopher
Description: Euclid's geometry is well-known for its theorems concerning triangles and circles. Less popular are the contents of the tenth book, in which geometry is a means to study quantity in general. Commensurability and rational quantities are first principles, and from them are derived at least eight species of irrationals. A recently republished work by Johannes Kepler contains examples using polygons to illustrate these species. In addition, figures having these quantities in their construction form solid shapes (polyhedra) having origins though Platonic philosophy and Archimedean works. Kepler gives two additional polyhedra, and a simple means for constructing the “divine” proportion is given.
Contributing Partner: UNT Libraries