Index Catalog // ScholarsArchive@OSU

Collision probabilities of convex polygons in spherical two-space

Creator:: Treuden, Mark Richard
Resource Type:: Dissertation

On the Structure of the Orbit Spaces of Almost Torus Manifolds with Non-negative Curvature

Creator:: Dong, Zheting
Abstract:: An almost torus manifold $M$ is a closed $(2n+1)$-dimensional orientable Riemannian manifold with an effective, isometric $n$-torus action such that the fixed point set $M^T$ is non-empty. Almost torus manifolds are analogues of torus manifolds in odd dimension and share many of the characteristics of torus manifolds. For example, both...
Resource Type:: Dissertation

Triangular billiards surfaces and translation covers

Creator:: Schmurr, Jason Peter
Abstract:: We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers.
Resource Type:: Dissertation
Full Text:: translation overs among triangular billiards surfa es. Our main toolsare the J-invariant of Kenyon and

Notions of complexity in substitution dynamical systems

Creator:: Wing, David Josiah
Abstract:: There has been a lot of work done in recent decades in the field of symbolic dynamics. Much attention has been paid to the so-called "complexity" function, which gives a sense of the rate at which the number of words in the system grow. In this paper, we explore this...
Resource Type:: Dissertation
Full Text:: to thank Dennis Garity for his generous patience and guidance. There are of course many other

Classifying seven dimensional manifolds of fixed cohomology type

Creator:: Montagantirud, Pongdate
Abstract:: Finding new examples of compact simply connected spaces admitting a Riemannian metric of positive sectional curvature is a fundamental problem in differential geometry. Likewise, studying topological properties of families of manifolds is very interesting to topologists. The Eschenburg spaces combine both of those interests: they are positively curved Riemannian manifolds...
Resource Type:: Dissertation
Full Text:: them. One year later, in 1982 J. H. Eschenburg [Esb82] was looking for further spaces of positive

A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

Creator:: Rockwell, Daniel Luke
Abstract:: The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the...
Resource Type:: Dissertation
Full Text:: following way: let #N(Bj, b, α) be the number of k, 1 ≤ k ≤ N − j + 1, such that ak+j−1 = bk for 1 ≤ k ≤ j

Rigidity of Vertex-Regular Actions on Fuchsian Buildings

Creator:: Smith, Samantha T.
Abstract:: We present a method by which torsion-free groups of automorphisms of a 2-dimensional hyperbolic building which act simply transitively on the vertex set can be constructed, and prove that any such group can be obtained by this construction. The method produces groups defined by finite presentations with strong small cancellation...
Resource Type:: Dissertation
Full Text:: will be called positive if �1 = �2 = · · · = �k = 1. It will be called reduced if x �j ij 6= x−�j+1ij

Local indicability and relative presentations of groups

Creator:: Fredericks, Julia D.
Resource Type:: Dissertation
Full Text:: would also like to thank my committee, Dennis Garity, Bob Burton, Burt Fein and Juha Pohjanpelto, all

Asphericity of length 6 equations over torsion free groups

Creator:: Kim, Seong Kun
Resource Type:: Dissertation

Rigidity for a class of Coxeter groups

Creator:: Kaul, Anton
Resource Type:: Dissertation

ScholarsArchive@OSU

Collision probabilities of convex polygons in spherical two-space

On the Structure of the Orbit Spaces of Almost Torus Manifolds with Non-negative Curvature

Triangular billiards surfaces and translation covers

Notions of complexity in substitution dynamical systems

Classifying seven dimensional manifolds of fixed cohomology type

A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

Rigidity of Vertex-Regular Actions on Fuchsian Buildings

Local indicability and relative presentations of groups

Asphericity of length 6 equations over torsion free groups

Rigidity for a class of Coxeter groups

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