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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, Randy Huy Lee
Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, Randy Huy Lee
UNF Graduate Theses and Dissertations
We considered the livelihood of two prey species in the presence of a predator species. To understand this phenomenon, we developed and analyzed two mathematical models considering indirect and direct mutualism of two prey species and the influence of one predator species. Both types of mutualism are represented by an increase in the preys' carrying capacities based on direct and indirect interactions between the prey. Because of mutualism, as the death rate parameter of the predator species goes through some critical value, the model shows transcritical bifurcation. Additionally, in the direct mutualism model, as the death rate parameter decreases to …
Minimizing Reaction Systems, Matthew R. Thomas
Minimizing Reaction Systems, Matthew R. Thomas
UNF Graduate Theses and Dissertations
The theoretical model for reaction systems is a relatively new framework originally proposed as a mathematical model for biochemical processes which take place in living cells. Growing interest in this research area has lead to the abstraction of the model for non-biological purpose as well. Reaction systems, with a well understood behavior, have become important for studying transition systems. As with any mathematical model, we want to simplify a given implementation of the model as much as possible while maintaining functional equivalence. This paper discusses the formal model for reaction systems, how we can simplify them with minimization techniques, some …
The Subconstituent Algebra Of A Hypercube, Jared B. Billet
The Subconstituent Algebra Of A Hypercube, Jared B. Billet
UNF Graduate Theses and Dissertations
We study the hypercube and the associated subconstituent algebra. Let Q_D denote the hypercube with dimension D and let X denote the vertex set of Q_D. Fix a vertex x in X. We denote by A the adjacency matrix of Q_D and by A* = A*(x) the diagonal matrix with yy-entry equal to D − 2i, where i is the distance between x and y. The subconstitutent algebra T = T(x) of Q_D with respect to x is generated by A and A* . We show that A 2A* − 2AA*A + A*A 2 = 4A* A*2A − 2A*AA* + …
Maximality And Applications Of Subword-Closed Languages, Rhys Davis Jones
Maximality And Applications Of Subword-Closed Languages, Rhys Davis Jones
UNF Graduate Theses and Dissertations
Characterizing languages D that are maximal with the property that D* ⊆ S⊗ is an important problem in formal language theory with applications to coding theory and DNA codewords. Given a finite set of words of a fixed length S, the constraint, we consider its subword closure, S⊗, the set of words whose subwords of that fixed length are all in the constraint. We investigate these maximal languages and present characterizations for them. These characterizations use strongly connected components of deterministic finite automata and lead to polynomial time algorithms for generating such languages. We prove that …
Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin
Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin
UNF Graduate Theses and Dissertations
We study a problem at the intersection of harmonic morphisms and real analytic Milnor fibrations. Baird and Ou establish that a harmonic morphism from G: \mathbb{R}^m \setminus V_G \rightarrow \mathbb{R}^n\setminus \{0\} defined by homogeneous polynomials of order p retracts to a harmonic morphism \psi|: S^{m-1} \setminus K_\epsilon \rightarrow S^{n-1} that induces a Milnor fibration over the sphere. In seeking to relax the homogeneity assumption on the map G, we determine that the only harmonic morphism $\varphi: \mathbb{R}^m \setminus V_G \rightarrow S^{m-1}\K_\epsilon$ that preserves \arg G is radial projection. Due to this limitation, we confirm Baird and Ou's result, yet establish …
Self-Assembly Of Dna Graphs And Postman Tours, Katie Bakewell
Self-Assembly Of Dna Graphs And Postman Tours, Katie Bakewell
UNF Graduate Theses and Dissertations
DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and …
On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster
On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster
UNF Graduate Theses and Dissertations
In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .
The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen
The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen
UNF Graduate Theses and Dissertations
Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …
Singular Value Inequalities: New Approaches To Conjectures, Peter Chilstrom
Singular Value Inequalities: New Approaches To Conjectures, Peter Chilstrom
UNF Graduate Theses and Dissertations
Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular value inequalities, and also look at existing conjectures.