Large deviations for random walks in a random environment on a strip

We consider a random walk in a random environment (RWRE) on the strip of finite width $\mathbb{Z} \times \{1,2,\ldots,d\}$. We prove both quenched and averaged large deviation principles for the position and the hitting times of the RWRE. Moreover, we prove a variational formula that relates the quenched and averaged rate functions, thus extending a result of Comets, Gantert, and Zeitouni for nearest-neighbor RWRE on $\mathbb{Z}

Strict monotonicity properties in one-dimensional excited random walks

We consider one-dimensional excited random walks with finitely many cookies at each site. There are certain natural monotonicity results that are known for the excited random walk under some partial orderings of the cookie environments. We improve these monotonicity results to be strictly monotone under a partial ordering of cookie environments introduced by Holmes and Salisbury. While the self-interacting nature of the excited random walk makes a direct coupling proof difficult, we show that there is a very natural coupling of the associated branching process from which the monotonicity results follow

Crystal engineering with 2,2':6',2"- terpyridine derivatives and their metal complexes : from simple building blocks to coordination polymers and networks

This thesis concerns the design of ligands for use in the construction of larger supramolecular systems, with emphasis on the application of 4'-substitured 2,2',6',2''- terpyridine ligands and their iron(II) and ruthenium(II) complexes in crystal engineering. The first section considers 4'-hydrazone functionalized 2,2',6',2''-terpyridines and their dynamic behaviour in solution and structural characteristics in the solid state, with respect to protonation. Neutral, mono- and di-protonated ligands are considered. The iron(II) and ruthenium(II) complexes of these ligands are reported and their properties studied by variable temperature NMR, UV-visible spectroscopy and single crystal X-ray crystallography. Subtle changes in substituents were found to have dramatic effects on crystal packing and some common packing arrangements were identified. A range of potential ‘expanded ligands’ (complexes which can themselves act as ligands for additional metal centres), are introduced in the next section. These can be potentially used to bridge metal centres to form both discrete and infinite structures, in particular in the solid state. In a systematic study of single crystal X-ray crystal structures of these complexes many were found to be more flexible than they first appear, and that the crystal packing arrangements were often sensitive to solvent. The next section describes the first crystallographically characterized coordination polymers and networks which include metal bis(terpyridine) units. Self-complementary hydrogen bonding was also found to be a stabilizing motif, with a number of such structures prepared. The final chapter blends the ideas of previous sections: 4'-(x-pyridyl) functionalized 2,2',6',2''-terpyridine ligands are used to form ‘expanded ligands’ with iron(II) and ruthenium(II) centres. These were characterized in solution, with protonation of the distant pendant pyridyl ring found to significantly influence the MLCT absorption of the complexes. These complexes were incorporated into two larger structures and characterised by single crystal X-ray crystallography. A selfcomplementary hydrogen bonded polymer which possesses nanopores through the crystal lattice is reported. Iron bis(thiocyanate) was also used to form a bridged coordination polymer

Funding for the Future

This research paper touches on the fundamental issues surrounding inequality in the American educational system, specifically between race and class. Prior research has indicated that minorities and lower class families experience far less ideal and adequate educations than white families with higher incomes. This paper brings together work done by Jonathon Kozol and the Civil Rights Project while using examples from New Hampshire schools in order to emphasize the disparate treatment of children in American schools