Master of Arts, The Ohio State University, 1951, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Arts, The Ohio State University, 1939, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Arts, The Ohio State University, 1934, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Arts, The Ohio State University, 1938, Graduate School

Committee: Not Provided (Other) Subjects:

Doctor of Philosophy, Case Western Reserve University, 2020, Mathematics

We will consider a variational problem arising out of the localized induction equation. We are motivated by the idea of finding “fair” splines, by considering an energy functional involving the derivative of the curvature. Among the solutions to the Euler-Lagrange equations are two elastic curves and the Kiepert Trefoil. We will introduce features and properties of the trefoil. One of the features of the trefoil is that it is an algebraic curve with a simple parametrization to handle. In addition to this, we will show that the trefoil is a model for a two-parameter spline and provide examples of how pieces of the trefoil can be cut, transformed and fitted so that the resulting curve is aesthetically “fair”.

Committee: David Singer Ph.D. (Advisor); Joel Langer Ph.D. (Committee Member); Elisabeth Werner Ph.D. (Committee Member); Colin McLarty Ph.D. (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2019, Civil Engineering

Learning the appropriate representation of objects in the real world is an ongoing area of research. Deep learning, specifically convolutional neural networks, have shown promising solutions for representation learning. In order to teach a machine to see and learn about a scene, a wide variety of information must be extracted from that scene. The extracted information can be used in many applications from medical imaging, customer behavior analysis, to worker productivity and safety in a construction site. This dissertation proposes models for extracting information from the scene through geometry and deep learning tools. We tackle the challenging problems of optimized camera placement, object contour detection and tracking, and propose a method to learn from unlabeled data. Specifically, we design a system that resembles a human. This artificial human has eyes and a brain. We model the eyes of our system as visual sensors, which can be placed anywhere in the scene, e.g., a grocery store, construction site, or on a larger scale in a smart city for traffic systems. In order to configure a network of cameras, a graph formulation is proposed. As a novel constraint, material information has been added to the more conventional constraints, such as geometric and constructive constraints, which are required for maximum coverage and observability. Material information, along with the location of the light source, provides a new perspective in the camera configuration problem as the appearance of objects changes depending on the angle that light hits their surfaces. Once the cameras are planned, the artificial brain in our system processes the sensor data streaming into the system. We use deep learning to detect, track, and locate objects in the scene. We use both tracking-by-detection and a novel temporally consistent detection and tracking algorithm. The work has been focused on learning new representations and domains in which objects live. Image-joint domain, for (open full item for complete abstract)

Committee: Alper Yilmaz (Advisor); Charles Toth (Committee Member); Rongjun Qin (Committee Member) Subjects: Civil Engineering; Computer Engineering; Computer Science; Engineering

Doctor of Philosophy, The Ohio State University, 1978, Graduate School

Committee: Not Provided (Other) Subjects: Mathematics

MS, Kent State University, 2016, College of Arts and Sciences / Department of Mathematical Sciences

Here, we prove the theorem due to Hopf that a surface with constant mean curvature that is homeomorphic to a sphere must be a sphere.

Committee: Dmitry Ryabogin PhD (Advisor) Subjects: Mathematics

PHD, Kent State University, 2015, College of Arts and Sciences / Department of Mathematical Sciences

I consider the following problems from Tomography. Suppose that the projections (sections) of two given bodies onto (by) every subspace of a fixed dimension are related by a certain condition. Does this imply that the bodies satisfy a similar condition in the ambient space? There are two major parts to this dissertation. The first one is on bodies with directly congruent projections or sections. The second part is about containment of two bodies and relations between their volumes, provided the projections (sections) of the first body can be rotated to be contained in the corresponding projection (section) of the second one.

Committee: Dmitry Ryabogin (Advisor); Artem Zvavitch (Committee Member); Joseph Diestel (Committee Member); Feodor Dragan (Committee Member); Peter Tandy (Committee Member) Subjects: Mathematics

PHD, Kent State University, 0, College of Arts and Sciences / Chemical Physics

Long range orientational order of nematic liquid crystals has been an inspiration for both theoretical works and practical applications. Using a combination of analytic calculations and numerical simulations, we investigate the interplay between orientational order and geometric constraints. In the first part of this dissertation, we concentrate on nematic order in liquid membranes, where the curvature induces non-uniformity and vice versa. Variations in nematic order, especially near topological defects, play an essential role in the interaction with curvature. In the second part, we consider the combination of the anisotropy of nematic liquid crystals with the large reversible deformations of elastomers as a mechanism for programmable deformations in soft materials.

Committee: Jonathan Selinger (Advisor); Robin Selinger (Committee Member); Antal Jakli (Committee Member); John Portman (Committee Member); Arden Ruttan (Committee Member) Subjects: Physics

Master of Science (MS), Wright State University, 2012, Physics

The nonrelativistic quantum mechanics of particles constrained to curved surfaces is studied. There is open debate as to which of several approaches is the correct one. After a review of existing literature and the required mathematics, three approaches are studied and applied to a sphere, spheroid, and triaxial ellipsoid. The first approach uses differential geometry to reduce the problem from a three dimensional problem to a two-dimensional problem. The second approach uses three dimensions and holds one of the separated wavefunctions and its associated coordinate constant. A third approach constrains the particle in a three-dimensional space between two parallel surfaces and takes the limit as the distance between the surfaces goes to zero. Analytic methods, finite element methods, and perturbation theory are applied to the approaches to determine which are in agreement. It is found that the differential geometric approach has the most agreement. Constrained quantum mechanics has application in materials science, where topological surface states are studied. It also has application as a simplified model of Carbon-60, graphene, and silicene structures. It also has application as in semiclassical quantum gravity, where spacetime is a pseudo-Riemannian manifold, to which the particles are constrained.

Committee: Lok Lew Yan Voon PhD (Advisor); Morten Willatzen PhD (Committee Member); Gary Farlow PhD (Committee Member); Doug Petkie PhD (Other) Subjects: Atoms and Subatomic Particles; Condensed Matter Physics; Mathematics; Nanoscience; Nanotechnology; Nuclear Physics; Physics; Quantum Physics; Solid State Physics; Theoretical Mathematics; Theoretical Physics

Master of Science in Mechanical Engineering, Cleveland State University, 2008, Fenn College of Engineering

A general symbolic exact analytic solution is developed for the radiation view factors including shadowing by the throat between a divergence thin gas disk between the combustion chamber and the beginning of the rocket nozzle radiating energy to the interior downstream of the nozzle contour for a class of coaxial axisymmetric converging diverging rocket nozzles. The radiation view factors presented in this thesis for the projection which are blocked or shadowed through the throat radiating downstream to the contour have never been presented before in the literature. It was found that the curvature of the function of the contour of the nozzle being either concave up or down and the slope of the first derivative being either positive or negative determined the values used for the transformation of the Stokes Theorem into terms of x, r (radius) and f(x) for the evaluation of the line integral. The analytical solutions from the view factors of, for example, the interior of a combustion chamber, or any radiating heat source to a disk may then be applied to the solution of the view factor of the disk to the interior of the rocket nozzle contour presented here. This modular building block type approach is what the author desires to allow the development of an interstellar matter antimatter rocket engine. The gases of this type of reaction shall approach those towards the speed of light, which shall involve a transport phenomena, which the author is looking forward to researching the solution.

Committee: Asuquo Ebiana PhD (Advisor); Majid Rashidi PhD (Committee Member); John Frater PhD (Committee Member); John Oprea PhD (Committee Member) Subjects: Aerospace Materials; Astrophysics; Chemical Engineering; Computer Science; Electromagnetism; Engineering; Gases; Materials Science; Mathematics; Mechanical Engineering; Nuclear Chemistry; Nuclear Physics; Radiation; Radiology; Scientific Imaging; Transportation

Master of Arts (MA), Ohio University, 2013, Philosophy (Arts and Sciences)

We attempt to clarify and evaluate what shall be called Mac Lane's thesis—the thesis that nonstandard analysis (NSA) and smooth infinitesimal analysis (SIA) are alternatives to the standard approach to the calculus. In doing so, we outline the historical approaches to the calculus, the standard approach to the calculus, and two nonstandard approaches, namely NSA and SIA; we also attempt to clarify and evaluate a set of comparisons of NSA and SIA, namely John L. Bell's 5 mathematico-philosophical contentions and Bell's historical contention.

Committee: Philip Ehrlich PhD (Advisor); Stewart Shapiro PhD (Committee Member); Todd Eisworth PhD (Committee Member) Subjects: Mathematics; Philosophy; Philosophy of Science