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Trees and Ordinal Indices in C(K) Spaces for K Countable Compact

Description: In the dissertation we study the C(K) spaces focusing on the case when K is countable compact and more specifically, the structure of C() spaces for < ω1 via special type of trees that they contain. The dissertation is composed of three major sections. In the first section we give a detailed proof of the theorem of Bessaga and Pelczynski on the isomorphic classification of C() spaces. In due time, we describe the standard bases for C(ω) and prove that the bases are monotone. In the second section we consider the lattice-trees introduced by Bourgain, Rosenthal and Schechtman in C() spaces, and define rerooting and restriction of trees. The last section is devoted to the main results. We give some lower estimates of the ordinal-indices in C(ω). We prove that if the tree in C(ω) has large order with small constant then each function in the root must have infinitely many big coordinates. Along the way we deduce some upper estimates for c0 and C(ω), and give a simple proof of Cambern's result that the Banach-Mazur distance between c0 and c = C(ω) is equal to 3.
Date: August 2015
Creator: Dahal, Koshal Raj
Partner: UNT Libraries

The Effects of Organic Surface Amendments on Soil Nutrients and Initial Tree Establishment

Description: This study examined the effects of replicating woodland soil surface horizonation on the nutrient status of underlying soils and the initial establishment and growth of trees. A total of 283 container grown trees were planted in a bufferzone around a future landfill site. Control amendments consisted of an 8 cm layer (0.5 m3) of wood chips applied in a circular area of 4.6 m2 around the trees' planting pit. For the treatment, a 2.5 cm layer of composted biosolids (0.15 m3 or 80 Mg/ha) was applied in a circular area of 4.6 m2 around the trees' planting pit followed by an 8 cm layer (0.5 m3) of wood chips. The results indicate that the replication of woodland soil surface attributes using composted biosolids can significantly improve the nutrient status of underlying soil. Some significant effects were seen under control conditions, too. However, the effects on tree establishment and growth parameters were, for the most part, not statistically significant.
Date: May 1999
Creator: Thuesen, Kevin (Kevin Andrew)
Partner: UNT Libraries