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Articles 1 - 5 of 5
Full-Text Articles in Mathematics
The Examination Of The Arithmetic Surface (3, 5) Over Q, Rachel J. Arguelles
The Examination Of The Arithmetic Surface (3, 5) Over Q, Rachel J. Arguelles
Electronic Theses, Projects, and Dissertations
This thesis is centered around the construction and analysis of the principal arithmetic surface (3, 5) over Q. By adjoining the two symbols i,j, where i2 = 3, j2 = 5, such that ij = -ji, I can produce a quaternion algebra over Q. I use this quaternion algebra to find a discrete subgroup of SL2(R), which I identify with isometries of the hyperbolic plane. From this quaternion algebra, I produce a large list of matrices and apply them via Mobius transformations to the point (0, 2), which is the center of my Dirichlet domain. This …
Symmetric Generation, Ana Gonzalez
Symmetric Generation, Ana Gonzalez
Electronic Theses, Projects, and Dissertations
We will examine progenitors. We start with progenitors of the form $m^{*n} : N$ where $m^{*n}$ is a free group and $N$ is a permutation group of degree $n$. But, $m^{*n} : N$ is a group of infinite order so we will factor by the necessary relations to get finite homomorphic images. These groups are constructed through the manual double coset enumeration method. We will examine how to construct progenitors for wreath products.
Lattice Reduction Algorithms, Juan Ortega
Lattice Reduction Algorithms, Juan Ortega
Electronic Theses, Projects, and Dissertations
The purpose of this thesis is to propose and analyze an algorithm that follows
similar steps of Guassian Lattice Reduction Algorithm in two-dimensions and applying
them to three-dimensions. We start off by discussing the importance of cryptography in
our day to day lives. Then we dive into some linear algebra and discuss specific topics that
will later help us in understanding lattice reduction algorithms. We discuss two lattice
problems: the shortest vector problem and the closest vector problem. Then we introduce
two types of lattice reduction algorithms: Guassian Lattice Reduction in two-dimensions
and the LLL Algortihm. We illustrate how both …
The Decomposition Of The Space Of Algebraic Curvature Tensors, Katelyn Sage Risinger
The Decomposition Of The Space Of Algebraic Curvature Tensors, Katelyn Sage Risinger
Electronic Theses, Projects, and Dissertations
We decompose the space of algebraic curvature tensors (ACTs) on a finite dimensional, real inner product space under the action of the orthogonal group into three inequivalent and irreducible subspaces: the real numbers, the space of trace-free symmetric bilinear forms, and the space of Weyl tensors. First, we decompose the space of ACTs using two short exact sequences and a key result, Lemma 3.5, which allows us to express one vector space as the direct sum of the others. This gives us a decomposition of the space of ACTs as the direct sum of three subspaces, which at this point …
Homomorphic Images And Related Topics, Alejandro Martinez
Homomorphic Images And Related Topics, Alejandro Martinez
Electronic Theses, Projects, and Dissertations
In this thesis, we have demonstrated our method of writing symmetric presentations of permutation progenitors, finding monomial representations and symmetric presentations of monomial progenitors. We have also explained how various types of additional relations are found. We have discovered original symmetric presentations and original constructions of numerous groups.