Physical Sciences and Mathematics Commons^™

A Qualitative Representation Of Spatial Scenes In R2 With Regions And Lines, Joshua Lewis

Electronic Theses and Dissertations

Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint).

A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects …

Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi

Electronic Theses and Dissertations

Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes nonsmooth versions …

Three-Dimensional Analytical Model Of Tidal Flow In The Damariscotta River Estuary, Me, Stephanie L. Ayres

Electronic Theses and Dissertations

Estuaries are coastal bodies of water subjected to strong tidal influence and characterized by their morphology, tidal dynamics, topography, and stratification. Tidal flow is critically important to the water circulation, nutrient influx, and sediment transport in or out of an estuary. However, tidal asymmetry enhanced by estuary shape and nonlinear processes can lead to complications in estuarine flow. Analytical models are used to systematically study tidal flow within an estuary. Previous studies have derived analytical models of varying complexity and applied them to investigate tidal and residual flow. This thesis derives a three-dimensional analytical model with a perturbation expansion of …

Investigation Of Student Understanding Of Implicit Differentiation, Connor Chu

Electronic Theses and Dissertations

Challenges that students face in first semester calculus have been found to be a factor in high attrition rates of students from science, technology, engineering, and mathematics (STEM) majors. With an increase in the demand for STEM graduates, an attempt must be made to remedy this issue. Research has shown that students have difficulties with many topics in the realm of calculus. Of these, students have been found to struggle with the concept of derivative and ideas related to it. However, some derivative topics have not been examined as thoroughly as others. Implicit differentiation, a technique that allows us to …

An Epidemiological Model With Simultaneous Recoveries, Ariel B. Farber

Electronic Theses and Dissertations

Epidemiological models are an essential tool in understanding how infection spreads throughout a population. Exploring the effects of varying parameters provides insight into the driving forces of an outbreak. In this thesis, an SIS (susceptible-infectious-susceptible) model is built partnering simulation methods, differential equations, and transition matrices with the intent to describe how simultaneous recoveries influence the spread of a disease in a well-mixed population. Individuals in the model transition between only two states; an individual is either susceptible — able to be infected, or infectious — able to infect others. Events in this model (infections and recoveries) occur by way …