Synthesis of a terminal Ce(iv) oxo complex by photolysis of a Ce(iii) nitrate complex.

Reaction of [Ce(NR2)3] (R = SiMe3) with LiNO3 in THF, in the presence of 2,2,2-cryptand, results in the formation of the Ce(iii) "ate" complex, [Li(2,2,2-cryptand)][Ce(κ2-O2NO)(NR2)3] (1) in 38% yield. Photolysis of 1 at 380 nm affords [Li(2,2,2-cryptand)][Ce(O)(NR2)3] (2), in 33% isolated yield after reaction work-up. Complex 2 is the first reported example of a Ce(iv) oxo complex where the oxo ligand is not supported by hydrogen bonding or alkali metal coordination. Also formed during photolysis are [Li(2,2,2-cryptand)]2[(μ3-O){Ce(μ-O)(NR2)2}3] (3) and [Li(2,2,2-cryptand)][Ce(OSiMe3)(NR2)3] (4). Their identities were confirmed by X-ray crystallography. Complex 4 can also be prepared via reaction of [Ce(NR2)3] with LiOSiMe3 in THF, in the presence of 2,2,2-cryptand. When synthesized in this fashion, 4 can be isolated in 47% yield. To rationalize the presence of 2, 3, and 4 in the reaction mixture, we propose that photolysis of 1 first generates 2 and NO2, via homolytic cleavage of the N-O bond in its nitrate co-ligand. Complex 2 then undergoes decomposition via two separate routes: (1) ligand scrambling and oligomerization to form 3; and, (2) abstraction of a trimethylsilyl cation to form a transient Ce(iv) silyloxide, [CeIV(OSiMe3)(NR2)3], followed by 1e- reduction to form 4. Alternatively, complex 4 could form directly via ·SiMe3 abstraction by 2

Combinatorial Games on Graphs

Combinatorial games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games along with some educational tools were developed in the pursuit of the solution of these games. The game of Nim is at least centuries old, possibly originating in China, but noted in the 16th century in European countries. It consists of several stacks of tokens, and two players alternate taking one or more tokens from one of the stacks, and the player who cannot make a move loses. The formal and intense study of Nim culminated in the celebrated Sprague-Grundy Theorem, which is now one of the centerpieces in the theory of impartial combinatorial games. We study a variation on Nim, played on a graph. Graph Nim, for which the theory of Sprague-Grundy does not provide a clear strategy, was originally developed at the University of Colorado Denver. Graph Nim was first played on graphs of three vertices. The winning strategy, and losing position, of three vertex Graph Nim has been discovered, but we will expand the game to four vertices and develop the winning strategies for four vertex Graph Nim. Graph Theory is a markedly visual field of mathematics. It is extremely useful for graph theorists and students to visualize the graphs they are studying. There exists software to visualize and analyze graphs, such as SAGE, but it is often extremely difficult to learn how use such programs. The tools in GeoGebra make pretty graphs, but there is no automated way to make a graph or analyze a graph that has been built. Fortunately GeoGebra allows the use of JavaScript in the creation of buttons which allow us to build useful Graph Theory tools in GeoGebra. We will discuss two applets we have created that can be used to help students learn some of the basics of Graph Theory. The game of thrones is a two-player impartial combinatorial game played on an oriented complete graph (or tournament) named after the popular fantasy book and TV series. The game of thrones relies on a special type of vertex called a king. A king is a vertex, k, in a tournament, T, which for all x in T either k beats x or there exists a vertex y such that k beats y and y beats x. Players take turns removing vertices from a given tournament until there is only one king left in the resulting tournament. The winning player is the one which makes the final move. We develop a winning position and classify those tournaments that are optimal for the first or second-moving player

Concrete Bridge Girders with Exposed Flexural Reinforcement

Reinforced concrete highway bridge girders are regularly repaired by replacing deteriorated concrete with new concrete, temporarily exposing the flexural reinforcement. The absence of bond between the concrete and steel at this stage makes it difficult to compute the flexural capacity and the current code criteria provide no guidance to assist practitioners. The research reported in this thesis rectifies this knowledge gap. A thorough examination is presented of experimental and analytical investigations by others to determine the typical behaviour, including probable failure modes, of reinforced concrete specimens with exposed flexural reinforcement. Based on these findings, two analytical approaches are developed to predict the longest length of flexural reinforcement that could be exposed that ensures a girder will still exhibit a ductile failure with no reduction in yield capacity. The Strain Compatibility Analysis derived by Harris was enhanced to involve realistic concrete stress-strain relationships and was validated experimentally using five 4-metre T-section specimens subjected to simultaneous point and uniformly distributed loading. A Strut-and Tie Analysis was also derived for this generic loading condition that could only be indirectly validated experimentally. The ratios of the test failure load to the failure load predicted using the Strain Compatibility Analysis had a mean value of 1.00 and a standard deviation of 0.068

Master of Science

thesisGlass fiber reinforced polymer (GFRP) composites offer several advantages over welded steel plate connections when used in the connection of vertical joints between concrete wall panels. These advantages include resistance to corrosion, higher tensile strength, and ability to conform to uneven surfaces. In the present research, push-off tests and wall tests were carried out to understand the behavior of GFRP composite connections between concrete elements. Push-off tests were performed to understand direct shear transfer capability when using different concrete surface preparation methods. Wall tests were performed to understand the behavior of different GFRP composite connections under simulated seismic loads, or cyclic shear. Ultimately, the GFRP composite connections displayed little ductility, but demonstrated outstanding displacement and load capacity. Push-off tests were performed for a GFRP composite connection between two L-shaped concrete elements. Each of the six groups of surface preparation included three specimens each, resulting in eighteen push-off specimens. A compressive load at the top and bottom of the specimen introduced direct shear in the GFRP composite connections. Specimens with concrete surface preparation using only a high-pressure wash demonstrated superior load and displacement capacities. Wall tests were performed for GFRP composite connections between two concrete panels, with the connection only applied on one side of the joint. A lateral load was applied at the top of the wall pair, while restraining the horizontal movement at the base and the vertical movement of each panel, inducing shear in the connection. Tests from group one (using unidirectional lamina) included eight specimens and concluded that the use of application pressure and CFRP anchors significantly increased load, displacement, and shear capacity of the GFRP composite connection. Also, fewer layers and CFRP anchor use increased the amount of energy dissipated during simulated seismic loads. Tests from group two (using bidirectional lamina) included six specimens and concluded that the use of GFRP anchors significantly increased load, displacement, and shear capacity of the GFRP composite connection. Also, the use of epoxy-putty adhesive had a significant effect on the load capacity; and full seam coverage and GFRP anchor use increased the amount of energy dissipated during simulated seismic loads

An inquiry into the development of expert systems in legal reasoning

The first goal of this paper is to review some of the steps necessary in developing a system that reasons effectively in some domain of law. The paper will begin by addressing the issues of domain selection, domain analysis and knowledge acquisition, knowledge representation, and selection of an inference method. After presenting a brief argument against using rule-based reasoning as the primary mode of inference, the paper will go on to expound the virtues of Kevin Ashley\u27s HYPO, a software model of case based legal argument. It will conclude with a short description of my experience implementing part of a software model of legal reasoning