Digital Commons Network^™

Extensions Of Bialgebras And Their Cohomological Description, Mark Lloyd Bochert

Doctoral Dissertations

This paper develops the theory of crossed product Hopf algebras of pairs of arbitrary Hopf algebras. The theory generalizes the crossed products of (Maj90), the Abelian crossed products of (Hof94) and the crossed product algebras of (BCM86). First, conditions are given on the structures involved that are shown to be equivalent to the existence of the crossed product. Next, a bisimplicial object is found that gives a cohomological description of the conditions. Cleft extensions of pairs of arbitrary Hopf algebras are then defined. These generalize the cleft extension algebras of (Swe68) and the Abelian cleft extensions of (By93); they are …

Orbit-Reflexivity, Michael James Mchugh

Doctoral Dissertations

Suppose $H$ is a separable, infinite dimensional Hilbert space and $T$ and $S$ are bounded linear transformations on $H$. Suppose that if $Sx\in\{x, ,Tx ,T\sp2x,...\}\sp{-}$ for every $x$ implies that $S\in\{1, T, T\sp2,...\}\sp{-SOT}$ then $T$ is orbit-reflexive. Many operators are proven to be orbit-reflexive, including analytic Toeplitz operators and subnormal operators with cyclic vectors.

Suppose that if $Sx\in\{\gamma x : x\in H, \gamma\in\doubc\}\sp{-}$ for every $x$, implies that $S\in\{\gamma T\sp{n} : n\ge0, \lambda\in\doubc\}\sp{-SOT}$ then $T$ is $\doubc$-orbit-reflexive. Many operators are shown to be $\doubc$-orbit-reflexive. $\doubc$-orbit-reflexivity is shown to be the same as reflexivity for algebraic operators.

Extending The National Council Of Teachers Of Mathematics' "Recognizing And Recording Reform In Mathematics Education" Documentation Project Through Cross-Case Analyses, Loren Phaffle Johnson

Doctoral Dissertations

The primary emphasis of this study was to broaden the understanding of data collected in the National Council of Teachers of Mathematics' (NCTM) Recognizing and Recording Reform in Mathematics Education (R$\sp3$M) project in order to more fully clarify the processes by which reform in mathematics education was occurring across five high school sites. A secondary emphasis was to develop a model of doing cross-case analyses and identifying those methodological elements and linkages that could be applied generally in large-scale studies of this sort.

R$\sp3$M documenters obtained data that resulted from interviews of mathematics teachers, administrators, and students; classroom observations; and …

Part I Synthesis, Functionalization And Metal Complexation Of Polyamine Macrocycles Part Ii Synthesis And Dynamic Nmr Studies Of Bicyclic Ureas, Daniel Cope Hill

Doctoral Dissertations

Part I. The syntheses and characterizations of novel bicyclic tetraamines (shown below) have been accomplished. The complexation of bicyclic tetraamines (R = CH$\sb3)$ with Li$\sp+$ and Na$\sp+$ have been studied by NMR spectroscopy. These tetraamines are strong bases and selective Li$\sp+$ binders. The parent "cross-bridged cyclam" (R = H; X = Y = CH$\sb2)$ was functionalized with a variety of ligating groups containing heteroatoms. Several of the ligands were investigated as possible radiopharmaceutical ($\rm\sp{99m}Tc$) imaging agent precursors.

Syntheses of non-adjacent selectively functionalized tetraazacycloalkanes have also been developed.

Part II. Synthesis and dynamic NMR studies of intramolecular transamidation of bicyclic urea …

An Investigation Into Students' Conceptual Understandings Of The Graphical Representation Of Polynomial Functions, Judith Ellen Curran

Doctoral Dissertations

Mathematics educators are realizing the impact that technology is having on the way mathematical functions can be represented and manipulated. The increased use of graphing technology in the classroom is paralleled by an increased emphasis on the role of the graphical representation of a function to solve problems. These changes together with a recognition of the significance and complexity of developing a rich understanding of the graphical representations of polynomial functions are the motivation behind this research.

The study was designed to explore students' conceptual understandings of the graphs of polynomial functions. Guided by a constructivist approach to conceptual change, …