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K-Theory Of Quadratic Modules: A Study Of Roy's Elementary Orthogonal Group., A. A. Ambily Dr.
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 …
Bures Distance For Completely Positive Maps And Cp-H-Extendable Maps Between Hilbert C*- Modules., Sumesh K Dr.
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 …
A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan
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.
Proximinality Properties Of Subspaces And Intersection Properties Of Balls In Banach Spaces., Jayanarayanan C. R. Dr.
Proximinality Properties Of Subspaces And Intersection Properties Of Balls In Banach Spaces., Jayanarayanan C. R. Dr.
Doctoral Theses
In this chapter, we explain the background and the main theme of this thesis and provide a chapter-wise summary of its principal results. We introduce some notations and preliminaries that will be used in the subsequent chapters.Study of proximinality related properties and ball intersection related properties of Banach spaces have been an active area of research in the field of geometry of Banach spaces. In this thesis, we mainly study these two classes of Banach space theoretic properties.We consider only Banach spaces over the real field R and all subspaces we consider are assumed to be closed.1.1 PreliminariesFor a Banach …
On The Group Of Transvections Of Ade-Diagrams, Marvin Jones
On The Group Of Transvections Of Ade-Diagrams, Marvin Jones
Theses and Dissertations
In this thesis we examine symplectic spaces with forms generated by the ADEdiagrams. Specifically, we determine the generators of the group of transvections for each space under the standard basis, S, of Kn (where K is a field with characteristic 0) and the hyperbolic basis, H, we get from the classification theorem of symplectic spaces. Further, we examine how the generators of these groups are related via g : Gf,S ! SL(Z)n where g(X) = P−1XP where P is the change of basis matrix for S to H.
A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson
A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson
Undergraduate Honors Thesis Collection
The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …
Teachers' Beliefs And Practices Regarding Homework: An Examination Of The Cognitive Domain Embedded In Third Grade Mathematics Homework, Pandora Dell Bedford
Teachers' Beliefs And Practices Regarding Homework: An Examination Of The Cognitive Domain Embedded In Third Grade Mathematics Homework, Pandora Dell Bedford
Theses and Dissertations
The purpose of this phenomenological study was to gain a better understanding of third grade math teachers''beliefs and practices regarding homework, to explain how teachers''beliefs and practices regarding homework aligned to the framework of the Revised Bloom's'Taxonomy Cognitive Domain, and to determine the administrative influences on homework practices. The data were collected during October and November 2013. Six third grade math teachers (primary unit of analysis) and four principals (secondary unit of analysis) were interviewed from Dell School District. Each participant (teacher and principal) was interviewed for approximately one hour. A second meeting was set at a later time with …
Calculator Usage In Secondary Level Classrooms: The Ongoing Debate, Nicole Plummer
Calculator Usage In Secondary Level Classrooms: The Ongoing Debate, Nicole Plummer
Honors College Theses
With technology becoming more prevalent every day, it is imperative that students gain enough experience with different technological tools in order to be successful in the “real-world”. This thesis will discuss the debate and overall support for an increased usage of calculators as tools in the secondary level classroom. When the idea of calculators in the classroom first came to life, many educators were very apprehensive and quite hesitant of this change. Unfortunately, more than 40 years later, there is still hesitation for their usage; and rightfully so. While there are plenty of advantages of calculator use in the classroom, …
Convexity Properties Of The Diestel-Leader Group Γ_3(2), Peter J. Davids
Convexity Properties Of The Diestel-Leader Group Γ_3(2), Peter J. Davids
Honors Projects
The Diestel-Leader groups are a family of groups first introduced in 2001 by Diestel and Leader in [7]. In this paper, we demonstrate that the Diestel-Leader group Γ3(2) is not almost convex with respect to a particular generating set S. Almost convexity is a geometric property that has been shown by Cannon [3] to guarantee a solvable word problem (that is, in any almost convex group there is a finite-step algorithm to determine if two strings of generators, or “words”, represent the same group element). Our proof relies on the word length formula given by Stein and Taback …
Inversion Of The Broken Ray Transform, Roman Krylov
Inversion Of The Broken Ray Transform, Roman Krylov
Electronic Theses and Dissertations
The broken ray transform (BRT) is an integral of a function along a union of two rays with a common vertex. Consider an X-ray beam scanning an object of interest. The ray undergoes attenuation and scatters in all directions inside the object. This phenomena may happen repeatedly until the photons either exit the object or are completely absorbed. In our work we assume the single scattering approximation when the intensity of the rays scattered more than once is negligibly small. Among all paths that the scattered rays travel inside the object we pick the one that is a union of …
Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder
Keeping Your Options Open: An Introduction To Pricing Options, Ryan F. Snyder
Senior Independent Study Theses
An option is a contract which gives the holder of the option the right, but not the obligation, to buy or sell a given security at a given price, which is called the strike price. For example, suppose Yahoo stock is currently trading at $10 per share. A person could buy an option that gives him or her the ability to purchase shares of Yahoo stock for $12 in one year. If the price of Yahoo stock is greater than $12 in one year, the holder of the option will make money. However, he or she will not use the …
The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen
The Analytic Hierarchy Process: A Mathematical Model For Decision Making Problems, Giang Huong Nguyen
Senior Independent Study Theses
The ability to make the right decision is an asset in many areas and lines of profession including social work, business, national economics, and international security. However, decision makers often have difficulty choosing the best option since they might not have a full understanding of their preferences, or lack a systematic approach to solve the decision making problems at hand. The Analytic Hierarchy Process (AHP) provides a mathematical model that helps the decision makers arrive at the most logical choice, based on their preferences. We investigate the theory of positive, reciprocal matrices, which provides the theoretical justification of the method …