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The following study utilizes data from the High School and Beyond Study in order to predict mathematics achievement using both student characteristics and school level characteristics. Utilizing Hierarchical Linear Modeling, this study extends the body of literature by exploring how race, socio-economic status, and gender, as well as the percentage of minority students in a school, whether or not the school is Catholic, the proportion of students in the academic track, and the mean socioeconomic status of the school all affect mathematics achievement. Through this methodology, it was possible to see the direct effects of both student level and school level variables on achievement, as well as the cross-level interaction of all of these variables. Findings suggest that there are discrepancies in how different types of students achieve, as well as how those students achieve in varying contexts. Many of the variables were statistically significant in their effect on mathematics achievement. Implications for this research are discussed and considerations for future research are presented.

Optimal control of general dynamic systems under realistic constraints on input signals and state variables is an important problem area in control theory. Many practical control problems can be formulated as optimization tasks, and this leads toa significant demand for efficient numerical solution algorithms. Several such algorithms have been developed, and they are typically derived from a dynamic programming view point. In this thesis a differentapproach is taken. The discretetime dynamic optimization problem is formulated as a static one, with the inputs as free variables. Newton's approach to solving such a problem with constraints, also known as Wilson's method, is then consistently pursued, anda algorithm is developed that isa true Newton algorithm for the problem, at the same time as the inherent structure is utilized for efficient calculations. An advantage with such an approach is that global and local convergence properties can be studied in a familiar framework. The algorithm is tested on several examples and comparisons to other algorithms are carried out. These show that the Newton algorithm performs well and is competitive with other methods. lt handles state variable constraints in a direct and efficient manner, and its practical convergence properties are robust. A general algorithm for !arge scale static problems is also developed in the thesis, and it is tested on a problem with load distribution in an electrical power network.

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The studies presented in this thesis explore energy transfer and relaxation in excitonic systems using two types of third-order non-linear spectroscopy, transient grating (TG) and two-dimensional photon echo (2DPE). Two major excitonic systems are studied, colloidal CdSe nanocrystals and a photosynthetic system, the light harvesting antenna protein PE545 isolated from cryptophyte algae Rhodomonas CS24. The inhomogeneous broadening present in colloidal samples has long been an obstacle to the study of the fine structure of CdSe nanocrystals. This thesis will present two studies, each using a different spectroscopy to overcome this problem and gain insight into the fine structure of the ground state exciton and biexciton. In both cases, polarization dependent measurements are used to isolate particular types of pathways through the fine structure. Polarization dependent TG measurements and a detailed kinetic model have allowed us to identify major pathways for excitonic relaxation within the fine structure of the ground state exciton, despite the inhomogeneous broadening present in the sample. Conclusions from this work include an analogy to the internal conversion and intersystem crossing transitions in molecules, concepts which are familiar to most chemists. Polarization dependent 2DPE experiments and a simulation of the resulting spectra have allowed for the direct observation of the ground state biexcitonic fine structure. The high density of states in the spectral region of the biexciton obscures these states in most spectroscopies, but the combination of polarization dependence and the use of a two-dimensional technique have revealed these elusive fine structure states. This 2DPE technique is then used to inspect light harvesting antenna protein PE545, a system of eight chromophores covalently bonded to a protein scaffold. The 2DPE measurement is capable of identifying oscillatory components of the signal which are signatures of coherent energy sharing. Using this technique, coherent energy sharing is observed throughout the spectrum of the protein at ambient temperatures, and control experiments suggest that the observed coherences are electronic, not vibrational. A short study is also presented which compares the utility of two approximations for calculations of electronic coupling and energy transfer in elongated excitonic systems.

The studies presented in this thesis explore energy transfer and relaxation in excitonic systems using two types of third-order non-linear spectroscopy, transient grating (TG) and two-dimensional photon echo (2DPE). Two major excitonic systems are studied, colloidal CdSe nanocrystals and a photosynthetic system, the light harvesting antenna protein PE545 isolated from cryptophyte algae Rhodomonas CS24. The inhomogeneous broadening present in colloidal samples has long been an obstacle to the study of the fine structure of CdSe nanocrystals. This thesis will present two studies, each using a different spectroscopy to overcome this problem and gain insight into the fine structure of the ground state exciton and biexciton. In both cases, polarization dependent measurements are used to isolate particular types of pathways through the fine structure. Polarization dependent TG measurements and a detailed kinetic model have allowed us to identify major pathways for excitonic relaxation within the fine structure of the ground state exciton, despite the inhomogeneous broadening present in the sample. Conclusions from this work include an analogy to the internal conversion and intersystem crossing transitions in molecules, concepts which are familiar to most chemists. Polarization dependent 2DPE experiments and a simulation of the resulting spectra have allowed for the direct observation of the ground state biexcitonic fine structure. The high density of states in the spectral region of the biexciton obscures these states in most spectroscopies, but the combination of polarization dependence and the use of a two-dimensional technique have revealed these elusive fine structure states. This 2DPE technique is then used to inspect light harvesting antenna protein PE545, a system of eight chromophores covalently bonded to a protein scaffold. The 2DPE measurement is capable of identifying oscillatory components of the signal which are signatures of coherent energy sharing. Using this technique, coherent energy sharing is observed throughout the spectrum of the protein at ambient temperatures, and control experiments suggest that the observed coherences are electronic, not vibrational. A short study is also presented which compares the utility of two approximations for calculations of electronic coupling and energy transfer in elongated excitonic systems.

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No description available.