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.

Nitrogen Oxides in the North Atlantic Troposphere: Impacts of Boreal Wildfire and Anthropogenic Emissions

Nitrogen oxides play a crucial role in the budget of tropospheric ozone (O sub(3)) and the formation of the hydroxyl radical. Anthropogenic activities and boreal wildfires are large sources of emissions in the atmosphere. However, the influence of the transport of these emissions on nitrogen oxides and O sub(3) levels at hemispheric scales is not well understood, in particular due to a lack of nitrogen oxides measurements in remote regions. In order to address these deficiencies, measurements of NO, NO sub(2) and NO sub(y) (total reactive nitrogen oxides) were made in the lower free troposphere (FT) over the central North Atlantic region (Pico Mountain station, 38 degree N 28 degree W, 2.3 km asl) from July 2002 to August 2005. These measurements reveal a well-defined seasonal cycle of nitrogen oxides (NO sub(x) = NO+NO sub(2) and NO sub(y)) in the background central North Atlantic lower FT, with higher mixing ratios during the summertime. Observed NO sub(x) and NO sub(y) levels are consistent with long-range transport of emissions, but with significant removal en-route to the measurement site. Reactive nitrogen largely exists in the form of PAN and HNO sub(3) ( similar to 80-90% of NO sub(y)) all year round. A shift in the composition of NO sub(y) from dominance of PAN to dominance of HNO sub(3) occurs from winter-spring to summer-fall, as a result of changes in temperature and photochemistry over the region. Analysis of the long-range transport of boreal wildfire emissions on nitrogen oxides provides evidence of the very large-scale impacts of boreal wildfires on the tropospheric NO sub(x) and O sub(3) budgets. Boreal wildfire emissions are responsible for significant shifts in the nitrogen oxides distributions toward higher levels during the summer, with medians of NO sub(y) (117-175 pptv) and NO sub(x) (9-30 pptv) greater in the presence of boreal wildfire emissions. Extreme levels of NO sub(x) (up to 150 pptv) and NO sub(y) (up to 1100 pptv) observed in boreal wildfire plumes suggest that decomposition of PAN to NO sub(x) is a significant source of NO sub(x), and imply that O sub(3) formation occurs during transport. Ozone levels are also significantly enhanced in boreal wildfire plumes. However, a complex behavior of O sub(3) is observed in the plumes, which varies from significant to lower O sub(3) production to O sub(3) destruction. Long-range transport of anthropogenic emissions from North America also has a significant influence on the regional NO sub(x) and O sub(3) budgets. Transport of pollution from North America causes significant enhancements on nitrogen oxides year-round. Enhancements of CO, NO sub(y) and NO sub(x) indicate that, consistent with previous studies, more than 95% of the NO sub(x) emitted over the U.S. is removed before and during export out of the U.S. boundary layer. However, about 30% of the NO sub(x) emissions exported out of the U.S. boundary layer remain in the airmasses. Since the lifetime of NO sub(x) is shorter than the transport timescale, PAN decomposition and potentially photolysis of HNO sub(3) provide a supply of NO sub(x) over the central North Atlantic lower FT. Observed Delta O sub(3)/ Delta NO sub(y) and large NO sub(y) levels remaining in the North American plumes suggest potential O sub(3) formation well downwind from North America. Finally, a comparison of the nitrogen oxides measurements with results from the global chemical transport (GCT) model GEOS-Chem identifies differences between the observations and the model. GEOS-Chem reproduces the seasonal variation of nitrogen oxides over the central North Atlantic lower FT, but does not capture the magnitude of the cycles. Improvements in our understanding of nitrogen oxides chemistry in the remote FT and emission sources are necessary for the current GCT models to adequately estimate the impacts of emissions on tropospheric NO sub(x) and the resulting impacts on the O sub(3) budget.

Biochemical Conversions of Lignocellulosic Biomass for Sustainable Fuel-Ethanol Production in the Upper Midwest

Biofuels are an increasingly important component of worldwide energy supply. This research aims to understand the pathways and impacts of biofuels production, and to improve these processes to make them more efficient. In Chapter 2, a life cycle assessment (LCA) is presented for cellulosic ethanol production from five potential feedstocks of regional importance to the upper Midwest - hybrid poplar, hybrid willow, switchgrass, diverse prairie grasses, and logging residues - according to the requirements of Renewable Fuel Standard (RFS). Direct land use change emissions are included for the conversion of abandoned agricultural land to feedstock production, and computer models of the conversion process are used in order to determine the effect of varying biomass composition on overall life cycle impacts. All scenarios analyzed here result in greater than 60% reduction in greenhouse gas emissions relative to petroleum gasoline. Land use change effects were found to contribute significantly to the overall emissions for the first 20 years after plantation establishment. Chapter 3 is an investigation of the effects of biomass mixtures on overall sugar recovery from the combined processes of dilute acid pretreatment and enzymatic hydrolysis. Biomass mixtures studied were aspen, a hardwood species well suited to biochemical processing; balsam, a high-lignin softwood species, and switchgrass, an herbaceous energy crop with high ash content. A matrix of three different dilute acid pretreatment severities and three different enzyme loading levels was used to characterize interactions between pretreatment and enzymatic hydrolysis. Maximum glucose yield for any species was 70% oftheoretical for switchgrass, and maximum xylose yield was 99.7% of theoretical for aspen. Supplemental β-glucosidase increased glucose yield from enzymatic hydrolysis by an average of 15%, and total sugar recoveries for mixtures could be predicted to within 4% by linear interpolation of the pure species results. Chapter 4 is an evaluation of the potential for producing Trichoderma reesei cellulose hydrolases in the Kluyveromyces lactis yeast expression system. The exoglucanases Cel6A and Cel7A, and the endoglucanase Cel7B were inserted separately into the K. lactis and the enzymes were analyzed for activity on various substrates. Recombinant Cel7B was found to be active on carboxymethyl cellulose and Avicel powdered cellulose substrates. Recombinant Cel6A was also found to be active on Avicel. Recombinant Cel7A was produced, but no enzymatic activity was detected on any substrate. Chapter 5 presents a new method for enzyme improvement studies using enzyme co-expression and yeast growth rate measurements as a potential high-throughput expression and screening system in K. lactis yeast. Two different K. lactis strains were evaluated for their usefulness in growth screening studies, one wild-type strain and one strain which has had the main galactose metabolic pathway disabled. Sequential transformation and co-expression of the exoglucanase Cel6A and endoglucanase Cel7B was performed, and improved hydrolysis rates on Avicel were detectable in the cell culture supernatant. Future work should focus on hydrolysis of natural substrates, developing the growth screening method, and utilizing the K. lactis expression system for directed evolution of enzymes.