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K-Theory Of Quadratic Modules: A Study Of Roy's Elementary Orthogonal Group., A. A. Ambily Dr.

Doctoral Theses

This thesis discusses the K-theory of quadratic modules by studying Roys elementary orthogonal group of the quadratic space Q1H(P) over a commutative ring A. We estab- lish a set of commutator relations among the elementary generators of Roys elementary orthogonal group and use this to prove Quillens local-global principle for this elementary group. We also obtain a result on extendability of quadratic modules. We establish nor- mality of the elementary orthogonal group under certain conditions and prove stability results for the Ki group of this orthogonal group. We also prove that Roys elementary orthogonal group and Petrovs odd hyperbolic unitary …

Mathematics Teaching Efficacy, Mwakulia Emily Sau

Master of Education

The affective domain has lately drawn the attention of mathematics research community. A key finding from the research literature is that an individual’s efficacy, that is, the belief in their ability to overcome challenges and bring about the desired results can influence one’s motivation to embark on the task and invest time and resources. This study examines teachers’ beliefs about their mathematics teaching efficacy which is rarely studied in Africa including Kenya. The field work was based on a sample of primary school teachers in Voi Sub-County. The study employed a sequential mixed method approach in which a survey was …

A Comparison Of Fifth Grade Mathematics Curriculum Materials, Michael E. Starks Sr.

Dissertations

In the USA, the No Child Left Behind Act of 2001 resulted in requirements placed on school districts to show student achievement in mathematics, based on measured adequate yearly progress. This caused school districts to search for standards based programs that improve mathematics learning. A quantitative multi-year study was used to compare the state-assessed achievement levels of 1,695 fifth-grade Midwestern children in the state of Missouri, who learned mathematics from two different curriculum-delivery programs, EveryDay Mathematics and EnVision Mathematics. A 2 by 2 by 8 research design was used through the choice of two elementary schools using EveryDay Mathematics and …

Almost-Kahler Anti-Self-Dual Metrics, Inyoung Kim

Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions)

We show the existence of strictly almost-Kahler anti-self-dual metrics on certain 4-manifolds by deforming a scalar-flat Kahler metric. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of Seiberg-Witten theory. In the process, we provide a simple new proof of the fact that any almost-Kahler anti-self-dual 4-manifold must have a non-trivial Seiberg-Witten invariant. | 69 pages

Limits Of Real-Normalized Dierentials On Stable Curves, Chaya Rifka Norton

Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions)

A recent approach proposed by Grushevsky and Krichever uses real-normalized differentials, meromorphic differentials with all periods real, to study the geometry of the moduli space of curves. We describe the behavior of real-normalized differentials under degeneration of the Riemann surface, and this analysis allows us to study the limits of zeros of these differentials near the boundary of the Deligne-Mumford compactification of the moduli space of curves. Our explicit description of the behavior of real-normalized differentials near nodal curves provides a tool for understanding common zeros of such differentials which has applications for the study of plane curves. This analysis …

The Kontsevich Space Of Rational Curves On Cyclic Covers Of Projective Space, Lloyd Smith

Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions)

In this thesis we consider the space of rational curves on a smooth cyclic cover of Pn. These varieties are the simplest examples of Fano varieties beyond the classical examples of complete intersections in homogeneous spaces. We show that for a general cyclic cover, the Kontsevich moduli stack of stable curves in X is irreducible and has the expected dimension. Specifically, let X be a general smooth cyclic cover of Pn of degree r branched over a divisor of degree rd, and let M(X,e) be the Kontsevich moduli stack of stable rational curves of degree e on X. We show …

On The Local-Global Principle For Integral Apollonian, Xin Zhang

Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions)

Starting with three mutually tangent circles, in each of the two gaps we inscribe three circles, and then we inscribe three new circles into the newly generated circles, so on so forth? We obtain a packing of infinitely many circles, and we give a name Apollonian-3 packings. It turns out there exist packings of this type with curvatures (1 over radius) all integers. I will discuss what we know about the integers arising as curvatures from these packings. I will discuss the reduction theorem, the symmetry group, and a density one theorem towards the local-global conjecture. | 47 pages

Numerical Modeling And Combustion Studies Of Scramjet Problem, Ying Xu

Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions)

Physical and numerical modeling of turbulent mixing and turbulent combustion in a Scramjet combustion chamber is studied. A high-order finite volume scheme is applied to the flow, accompanied with dynamic subgrid-scale model and local averaging procedure to account for the effect of unresolved small length scales turbulent fluid behavior. The Arrhenius law kinetic mechanism is applied to describe the nonlinearity of chemical reactions. To model combustion, the finite rate chemistry is developed to characterize the combustion process inside the combustion chamber. Results are compared among the finite rate model, the flamelet model/progress variable approach adopted by Stanford PSAAP center and …

Bures Distance For Completely Positive Maps And Cp-H-Extendable Maps Between Hilbert C*- Modules., Sumesh K Dr.

Doctoral Theses

Completely positive (CP-) maps are special kinds of positivity preserving maps on C ∗ -algebras. W.F. Stinespring [Sti55] obtained a structure theorem for CP-maps showing that they are closely connected with ∗-homomorphisms. W. Arveson and other operator algebraists quickly realized the importance of these maps. Presently the role of the theory of CP-maps in our understanding of C ∗ -algebras and von Neumann algebras is well recognised. It has been argued by physicists that CPmaps are physically more meaningful than just positive maps due to their stability under ampliations. From quantum probabilistic point of view CP-maps are quantum analogues of …

Can You Solve The Navajo Sheep Problem?, Ohio University College Of Arts & Sciences

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No abstract provided.

Math Senior Seminar: Solutions & Their Bounds For The Traveling Salesman Problem, Nov. 24, Ohio University College Of Arts & Sciences

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No abstract provided.

Mathematical Biology Seminar | Features Fulbright Scholar, Nov. 20, Ohio University College Of Arts & Sciences

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No abstract provided.

Algebra Seminar | Rings Over Which Every Nonzero Cyclic Right Module Is Poor, Nov. 20, Ohio University College Of Arts & Sciences

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No abstract provided.

Learning Metrics Partnership: A Capacity Support And Policy Strengthening Initiative To Develop And Use Common Learning Metrics For Mathematics And Reading, Unesco Institute For Statistics, Acer

Monitoring Learning

The Learning Metrics Partnership (LMP) is a joint initiative of the UNESCO Institute for Statistics and the ACER Centre for Global Education Monitoring (ACER-GEM) to develop a set of nationally and internationally comparable learning metrics in mathematics and reading, and then to facilitate and support their use for monitoring purposes, in partnership with interested countries. This document outlines the LMP’s three-phase program that aims to develop and validate common learning metrics for reading and mathematics, and to support countries to report results of their assessment activities against these learning metrics. The key features of the program are fourfold: it accommodates …

The Value Of Problem Posing In Developing Creatively Gifted Mathematicians, Eric L. Mann

Faculty Presentations

The task of problem posing is often overlooked as a means to develop creatively gifted mathematicians. Silver (1997) suggested that problem posing was an instructional tactic used worldwide to develop creativity in mathematicians. More specifically, Silver advocated that deliberate instructional tactics had to be employed to precipitate creative solutions. Problem posing is often correlated with the aesthetic nature of mathematics.

In this cutting-edge session, participants’ objective is to learn about the value of problem posing through a brief presentation and have an opportunity to generate their own mathematical problem solving tasks given a mathematical concept. The intent is to encourage …

Math And Political Science Alumni Named To Foundation Board, Ohio University College Of Arts & Sciences

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No abstract provided.

John Kirby Dissertation Defense: Multiscale Copula Sampling Series And Application, Nov. 13, Ohio University College Of Arts & Sciences

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No abstract provided.

Periodic Outbreaks In Models Of Disease Transmission With A Behavioral Response, Nov. 13, Ohio University College Of Arts & Sciences

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No abstract provided.

Math Cmss Colloquia Holomorphic Stochastic Flows, Nov. 13, Ohio University College Of Arts & Sciences

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No abstract provided.

Storm Chasing Experience Open To Meteorology Students, Ohio University College Of Arts & Sciences

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Unraveling Complex Systems: What Do Brains, Internet & Ant Colonies Have In Common? Nov. 10, Ohio University College Of Arts & Sciences

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No abstract provided.

Ring Theory: Compatible Ring Structures On Injective Hulls Revisited, Nov. 7, Ohio University College Of Arts & Sciences

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No abstract provided.

Math & Microbiology Pair To Prevent Pneumonia In Hospitals, Ohio University College Of Arts & Sciences

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No abstract provided.

On Volume-Preserving Vector Fields And Finite-Type Invariants Of Knots, R. Komendarczyk, Ismar Volić

Faculty Research and Scholarship

We consider the general non-vanishing, divergence-free vector fields defined on a domain in 3-space and tangent to its boundary. Based on the theory of finite-type invariants, we define a family of invariants for such fields, in the style of Arnold’s asymptotic linking number. Our approach is based on the configuration space integrals due to Bott and Taubes.

A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan

Honors College Theses

Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.

Murphy To Discuss Collaboration With Young On Pathogens In Ventilators, Oct. 30, Ohio University College Of Arts & Sciences

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Is More Always Better: Comparing The Effects Of Single And Multiple Learning Channels On Academic Performance, Samantha Ann Spillman

USF Tampa Graduate Theses and Dissertations

Precision teaching (PT) is a measurement system used in multiple settings for all types of behavior, from driving to mathematics. The ultimate goal of PT is to develop fluent, free operant behaviors through analyzing response frequencies on a standard celeration chart. Research has found PT to be effective at improving both the speed and accuracy of academic skills. There is little research, however, in the effects of learning channels, a component of PT, as they relate to the acquisition of academic skills. The present study examined the relationship between single and multiple learning channels on the acquisition of mathematics skills …

Seminar: Designing Optimal Spraying Strategies For Controlling Re-Infestation By Chagas Vectors, Oct. 23, Ohio University College Of Arts & Sciences

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From Navajo Nation To Capitol Hill: Klein Inspires, Empowers, Advocates, Ohio University College Of Arts & Sciences

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Rich Problem Solving Tasks, Valorie L. Zonnefeld

Faculty Work Comprehensive List

No abstract provided.