Physical Sciences and Mathematics Commons^™

A Comparison Theorem For The Topological And Algebraic Classification Of Quaternionic Toric 8-Manifolds, Piotr Runge

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating …

Testing And Estimation For Functional Data With Applications To Magnetometer Records, Inga Maslova

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The functional linear model, Y_n = ψX_n + ε_n, with functional response and explanatory variables is considered. A simple test of the nullity of ψ based on the principal component decomposition is proposed. The test statistic has asymptotic chi-squared distribution, which is also an excellent approximation in finite samples. The methodology is applied to data from terrestrial magnetic observatories.

In recent years, the interaction of the auroral substorms with the equatorial and mid-latitude currents has been the subject of extensive research. We introduce a new statistical technique that allows us to test at a specified …

Modeling The Evolution Of Insect Phenology With Particular Reference To Mountain Pine Beetle, Brian P. Yurk

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Climate change is likely to disrupt the timing of developmental events (phenology) in insect populations in which development time is largely determined by temperature. Shifting phenology puts insects at risk of being exposed to seasonal weather extremes during sensitive life stages and losing synchrony with biotic resources. Additionally, warming may result in loss of developmental synchronization within a population, making it difficult to find mates or mount mass attacks against well-defended resources at low population densities. It is unknown whether genetic evolution of development time can occur rapidly enough to moderate these effects.

The work presented here is largely motivated …

Symmetry Analysis Of General Rank-3 Pfaffian Systems In Five Variables, Francesco Strazzullo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation we applied geometric methods to study underdetermined second order scalar ordinary differential equations (called general Monge equations), nonlinear involutive systems of two scalar partial differential equations in two independent variables and one unknown and non-Monge-Ampere Goursat parabolic scalar PDE in the plane. These particular kinds of differential equations are related to general rank-3 Pfaffian systems in five variables. Cartan studied these objects in his 1910 paper. In this work Cartan provided normal forms only for some general rank-3 Pfaffian systems with 14-, 7-, and 6-dimensional symmetry algebra.

In this dissertation we provided normal forms of all general …

Simulation, Kriging, And Visualization Of Circular-Spatial Data, William James Morphet

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The circular dataimage is defined by displaying direction as the color at the same direction in a color wheel composed of a sequence of two-color gradients with color continuity between gradients. The resulting image of circular-spatial data is continuous with high resolution. Examples include ocean wind direction, Earth's main magnetic field, and rocket nozzle internal combustion flow. The cosineogram is defined as the mean cosine of the angle between random components of direction as a function of distance between observation locations. It expresses the spatial correlation of circular-spatial data. A circular kriging solution is developed based on a model fitted …