Edge coloring BIBDS and constructing MOELRs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well. In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic Kv into copies of Kk such that each copy of the Kk contains at most one edge from each Kv. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of examples to explain the constructions used in Chapters 3 and 4. In Chapters 3 and 4 we investigate how to properly color BIBD(v, k, λ) for k = 4, and 5. Not only will there be direct constructions of relatively small BIBDs, we also prove some generalized constructions used within. In Chapter 5 we talk about an alternate solution to Chapters 3 and 4. A purely graph theoretical solution using matchings, augmenting paths, and theorems about the edgechromatic number is used to develop a theorem that than covers all possible cases. We also discuss how this method performed compared to the methods in Chapters 3 and 4. In Chapter 6, we switch topics to Latin rectangles that have the same number of symbols and an equivalent sized matrix to Latin squares. Suppose ab = n2. We define an equitable Latin rectangle as an a × b matrix on a set of n symbols where each symbol appears either [b/n] or [b/n] times in each row of the matrix and either [a/n] or [a/n] times in each column of the matrix. Two equitable Latin rectangles are orthogonal in the usual way. Denote a set of ka × b mutually orthogonal equitable Latin rectangles as a k–MOELR(a, b; n). We show that there exists a k–MOELR(a, b; n) for all a, b, n where k is at least 3 with some exceptions.

Evaluation of the performance and cost-effectiveness of pavement sections containing open-graded base courses

Moisture induced distresses have been the prevalent distress type affecting the deterioration of both asphalt and concrete pavement sections. While various surface techniques have been employed over the years to minimize the ingress of moisture into the pavement structural sections, subsurface drainage components like open-graded base courses remain the best alternative in minimizing the time the pavement structural sections are exposed to saturated conditions. This research therefore focuses on assessing the performance and cost-effectiveness of pavement sections containing both treated and untreated open-graded aggregate base materials. Three common roadway aggregates comprising of two virgin aggregates and one recycled aggregate were investigated using four open-ended gradations and two binder types. Laboratory tests were conducted to determine the hydraulic, mechanical and durability characteristics of treated and untreated open-graded mixes made from these three aggregate types. Results of the experimental program show that for the same gradation and mix design types, limestone samples have the greatest drainage capacity, stability to traffic loads and resistance to degradation from environmental conditions like freeze-thaw. However, depending on the gradation and mix design used, all three aggregate types namely limestone, natural gravel and recycled concrete can meet the minimum coefficient of hydraulic conductivity required for good drainage in most pavements. Tests results for both asphalt and cement treated open-graded samples indicate that a percent air void content within the range of 15-25 will produce a treated open-graded base course with sufficient drainage capacity and also long term stability under both traffic and environmental loads. Using the new Mechanistic and Empirical Design Guide software, computer simulations of pavement performance were conducted on pavement sections containing these open-graded base aggregate base materials to determine how the MEPDG predicted pavement performance is sensitive to drainage. Using three truck traffic levels and four climatic regions, results of the computer simulations indicate that the predicted performance was not sensitive to the drainage characteristics of the open-graded base course. Based on the result of the MEPDG predicted pavement performance, the cost-effectiveness of the pavement sections with open-graded base was computed on the assumption that the increase service life experienced by these sections was attributed to the positive effects of subsurface drainage. The two cost analyses used gave two contrasting results with the one indicating that the inclusion of open-graded base courses can lead to substantial savings.

Tropospheric ozone and CO over North Atlantic for the past decade

We investigate how declines in US emissions of CO and O3 precursors have impacted the lower free troposphere over the North Atlantic. We use seasonal observations for O3 and CO from the PICO-NARE project for the period covering 2001 to 2010. Observations are used to verify model output generated by the GEOS-Chem 3-D global chemical transport model. Additional satellite data for CO from AIRS/Aqua and for O3 from TES/Aura were also used to provide additional comparisons; particularly for fall, winter, and spring when PICO-NARE coverage is sparse. We find GEOS-Chem captures the seasonal cycle for CO and O3 well compared to PICO-NARE data. For CO, GEOS-Chem is biased low, particularly in spring which is in agreement with findings from previous studies. GEOS-Chem is 24.7 +/- 5.2 ppbv (1-σ) low compared to PICO-NARE summer CO data while AIRS is 14.2 +/- 6.6 ppbv high. AIRS does not show nearly as much variation as seen with GEOS-Chem or the Pico data, and goes from being lower than PICO-NARE data in winter and spring, to higher in summer and fall. Both TES and GEOS-Chem match the seasonal ozone cycle well for all seasons when compared with observations. Model results for O3 show GEOS-Chem is 6.67 +/- 2.63 ppbv high compared to PICO-NARE summer measurements and TES was 3.91 +/- 4.2 ppbv higher. Pico data, model results, and AIRS all show declines in CO and O3 for the summer period from 2001 to 2010. Limited availability of TES data prevents us from using it in trend analysis. For summer CO Pico, GEOS-Chem, and AIRS results show declines of 1.32, 0.368, and 0.548 ppbv/year respectively. For summer O3, Pico and GEOS-Chem show declines of -0.726 and -0.583 ppbv/year respectively. In other seasons, both model and AIRS show declining CO, particularly in the fall. GEOS-Chem results show a fall decline of 0.798 ppbv/year and AIRS shows a decline of 0.8372 ppbv/year. Winter and spring CO declines are 0.393 and 0.307 for GEOS-Chem, and 0.455 and 0.566 for AIRS. GEOS-Chem shows declining O3 in other seasons as well; with fall being the season of greatest decrease and winter being the least. Model results for fall, winter, and spring are 0.856, 0.117, and 0.570 ppbv/year respectively. Given the availability of data we are most confident in summer results and thus find that summer CO and O3 have declined in lower free troposphere of the North Atlantic region of the Azores. Sensitivity studies for CO and O3 at Pico were conducted by turning off North American fossil fuel emissions in GEOS-Chem. Model results show that North America fossil fuel emissions contribute 8.57 ppbv CO and 4.03 ppbv O3 to Pico. The magnitude of modeled trends declines in all seasons without North American fossil fuel emissions except for summer CO. The increase in summer CO declines may be due to a decline of 5.24 ppbv/year trend in biomass burning emissions over the study period; this is higher than the 2.33 ppbv/year North American anthropogenic CO model decline. Winter O3 is the only season which goes from showing a negative trend to a positive trend.