Browsing by Subject "Applied and computational mathematics"

Now showing 1 - 4 of 4
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    Dodgson's determinant: a qualitative analysis
    (2011-07) Schmidt, Amy Dannielle
    Condensation, developed by Charles Dodgson, is an uncommon method for calculating the determinant of a matrix. It is generally considered to be numerically unstable due to its iterative nature. While we do not attempt to prove whether or not the algorithm is stable, we conduct a qualitative stability analysis. We compare the algorithm's performance to that of row reduction on contrived and random matrices. We test two modified condensation algorithms for 3#2;3 and 4#2;4 matrices, which we include in our comparisons as well. We also briefly investigate the relationship between the condition number of a matrix and the performance of these algorithms when used to calculate its determinant.
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    Stoichiometric modeling of nutrient and biomass flux in the Gulf of Mexico.
    (2012-07) Pollesch, Nathan L.
    The purpose of this thesis is to explore the connections between agricultural runoff influx, oil influx, and oxygen levels in a near-coastal marine environment. The creation of oxygen deficient conditions is investigated through the use of a stoichiometric modeling approach that utilizes a system of ordinary differential equations. Agricultural runoff is modeled as a source of a limiting nutrient for algae. Oil influx is modeled as a carbon source for bacterial consumption. The investigation is motivated by the Gulf of Mexico-ecosystem in the wake of the Deepwater Horizon oil rig incident of 2010, which contributed large amounts of oil (carbon) to the Gulf system. The model consists of an algal class with flexible stoichiometry that utilizes the nutrient for growth and a bacterial class with fixed stoichiometry that assimilates the carbon. A consumer class with fixed stoichiometry that is dependent upon the oxygen present in the system is modeled and is used to indicate oxygen deficient conditions. Equilibrium, time series, and stability analysis of this five-dimensional system are presented. Through the analyses presented and simulations, it is found that this model reproduces the behavior of the biological processes associated with nutrient enrichment and the creation hypoxic areas, or ‘dead zones'.
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    Symmetric chain decompositions of partially ordered sets
    (2014-07) Zjevik, Ondrej
    A partially ordered set, or poset, is a set of elements and a binary relation which determines an order within elements. Various combinatorial properties of finite and ordered posets have been extensively studied during the last 4 decades. The Sperner property states that the size of the largest subset of pairwise incomparable elements does not exceed the size of the largest level set in an ordered poset. Since a symmetric chain decomposition is a sufficient condition for the Sperner property, we may prove the Sperner property by finding a symmetric chain decomposition for a poset.In this paper we focus on three types of posets: the Boolean algebra, inversion poset and the Young's lattice. An explicit construction for a symmetric chain decomposition is known only for Boolean algebras. No explicit construction has been found for inversion posets and Young's lattices, a symmetric chain decomposition was found only for a small subset of these posets. Using a maximal flow, we introduce an algorithm for finding this decomposition. We present our results and discuss two implementations of this algorithm.