Occasional white boarding : examining the effects of physics students' understanding of motion graphs

The Modeling method of teaching has demonstrated well--‐documented success in the improvement of student learning. The teacher/researcher in this study was introduced to Modeling through the use of a technique called White Boarding. Without formal training, the researcher began using the White Boarding technique for a limited number of laboratory experiences with his high school physics classes. The question that arose and was investigated in this study is “What specific aspects of the White Boarding process support student understanding?” For the purposes of this study, the White Boarding process was broken down into three aspects – the Analysis of data through the use of Logger Pro software, the Preparation of White Boards, and the Presentations each group gave about their specific lab data. The lab used in this study, an Acceleration of Gravity Lab, was chosen because of the documented difficulties students experience in the graphing of motion. In the lab, students filmed a given motion, utilized Logger Pro software to analyze the motion, prepared a White Board that described the motion with position--‐time and velocity--‐time graphs, and then presented their findings to the rest of the class. The Presentation included a class discussion with minimal contribution from the teacher. The three different aspects of the White Boarding experience – Analysis, Preparation, and Presentation – were compared through the use of student learning logs, video analysis of the Presentations, and follow--‐up interviews with participants. The information and observations gathered were used to determine the level of understanding of each participant during each phase of the lab. The researcher then looked for improvement in the level of student understanding, the number of “aha” moments students had, and the students’ perceptions about which phase was most important to their learning. The results suggest that while all three phases of the White Boarding experience play a part in the learning process for students, the Presentations provided the most significant changes. The implications for instruction are discussed.

Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.

Hamilton decompositions of 6-regular abelian Cayley graphs

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made: Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian. The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture: Alspach Conjecture: Every 2k-regular, connected Cayley graph on a finite abelian group has a Hamilton decomposition. Alspach’s conjecture is true for k = 1 and 2, but even the case k = 3 is still open. It is this case that this thesis addresses. Chapters 1–3 give introductory material and past work on the conjecture. Chapter 3 investigates the relationship between 6-regular Cayley graphs and associated quotient graphs. A proof of Alspach’s conjecture is given for the odd order case when k = 3. Chapter 4 provides a proof of the conjecture for even order graphs with 3-element connection sets that have an element generating a subgroup of index 2, and having a linear dependency among the other generators. Chapter 5 shows that if Γ = Cay(A, {s1, s2, s3}) is a connected, 6-regular, abelian Cayley graph of even order, and for some1 ≤ i ≤ 3, Δi = Cay(A/(si), {sj1 , sj2}) is 4-regular, and Δi ≄ Cay(ℤ3, {1, 1}), then Γ has a Hamilton decomposition. Alternatively stated, if Γ = Cay(A, S) is a connected, 6-regular, abelian Cayley graph of even order, then Γ has a Hamilton decomposition if S has no involutions, and for some s ∈ S, Cay(A/(s), S) is 4-regular, and of order at least 4. Finally, the Appendices give computational data resulting from C and MAGMA programs used to generate Hamilton decompositions of certain non-isomorphic Cayley graphs on low order abelian groups.

DESIGN AND SYNTHESIS OF MULTIFUNCTIONAL POLYMERIC MICELLES FOR GENE-DIRECTED ENZYME PRODRUG THERAPY

Gene-directed enzyme prodrug therapy is a form of cancer therapy in which delivery of a gene that encodes an enzyme is able to convert a prodrug, a pharmacologically inactive molecule, into a potent cytotoxin. Currently delivery of gene and prodrug is a two-step process. Here, we propose a one-step method using polymer nanocarriers to deliver prodrug, gene and cytotoxic drug simultaneously to malignant cells. Prodrugs acyclovir, ganciclovir and 5-doxifluridine were used to directly to initiate ring-opening polymerization of epsilon-caprolactone, forming a hydrophobic prodrug-tagged poly(epsilon-caprolactone) which was further grafted with hydrophilic polymers (methoxy poly(ethylene glycol), chitosan or polyethylenemine) to form amphiphilic copolymers for micelle formation. Successful synthesis of copolymers and micelle formation was confirmed by standard analytical means. Conversion of prodrugs to their cytotoxic forms was analyzed by both two-step and one-step means i.e. by first delivering gene plasmid into cell line HT29 and then challenging the cells with the prodrug-tagged micelle carriers and secondly by complexing gene plasmid onto micelle nanocarriers and delivery gene and prodrug simultaneously to parental HT29 cells. Anticancer effectiveness of prodrug-tagged micelles was further enhanced by encapsulating chemotherapy drugs doxorubicin or SN-38. Viability of colon cancer cell line HT29 was significantly reduced. Furthermore, in an effort to develop a stealth and targeted carrier, CD47-streptavidin fusion protein was attached onto the micelle surface utilizing biotin-streptavidin affinity. CD47, a marker of self on the red blood cell surface, was used for its antiphagocytic efficacy, results showed that micelles bound with CD47 showed antiphagocytic efficacy when exposed to J774A.1 macrophages. Since CD47 is not only an antiphagocytic ligand but also an integrin associated protein, it was used to target integrin alpha(v)beta(3), which is overexpressed on tumor-activated neovascular endothelial cells. Results showed that CD47-tagged micelles had enhanced uptake when treated to PC3 cells which have high expression of alpha(v)beta(3). The synthesized multifunctional polymeric micelle carriers developed could offer a new platform for an innovative cancer therapy regime.