Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2004. / Includes bibliographical references.

Münster (Westfalen), Universiẗat, Diss., 2002. / Dateiformat: PS.

Let KO(X) be the real and KSP(X) be the quaternionic K-theory of a finite CW-complex X . The tensor product and the exterior powers of vector bundles induce on L(X) = KO(X) ⊕ KSP(X) the structure of Z₂ -graded λ-ring. In this thesis it is shown, that the Adams operations Ѱk : L(X) → L(X) , k = l, 2, 3,..., which are associated to this λ-ring, are ring homomorphisms and satisfy the composition law Ѱk ₀ Ѱℓ = Ѱℓk = Ѱℓ ₀ Ѱk , k, ℓ = 1, 2, 3,... Finally, the ring L(X) together with its Ѱ-operations is explicitely determined for the quaternionic and complex projective spaces. / Science, Faculty of / Mathematics, Department of / Graduate

For T the circle group, we construct a differential refinement of T-equivariant K-theory. We first construct a de Rham model for delocalized equivariant cohomology and a delocalized equivariant Chern character based on [19] and [14]. We show that the delocalized equivariant Chern character induces a complex isomorphism. We then construct a geometric model for differential T-equivariant K-theory analogous to the model of differential K-theory in [27] and deduce its basic properties. / text

Let G be a simple connected graph on 2n vertices with a perfect matching. For 1 ≤ k ≤ n - 1, G is said to be k-extendable if for every matching M of size k in G there is a perfect matching in G containing all the edges of M. A k-extendable graph G is said to be k-critical (k-minimal) if G+uv (G-uv) is not k-extendable for every non-adjacent (adjacent) pair of vertices u and v of G. The problem that arises is that of characterizing k-extendable, k-critical and k-minimal graphs.In Chapter 2, we establish that δ(G) ≥ 1/2(n + k) is a sufficient condition for a bipartite graph G on 2n vertices to be k-extendable. For a graph G on 2n vertices with δ(G) ≥ n + k 1, n - k even and n/2 ≤ k ≤ n - 2, we prove that a necessary and sufficient condition for G to be k-extendable is that its independence number is at most n - k. We also establish that a k-extendable graph G of order 2n has k + 1 ≤ δ(G) n or δ(G) ≥ 2k + 1, 1 ≤ k ≤ n - 1. Further, we establish the existence of a k-extendable graph G on 2n vertices with δ(G) = j for each integer j Є [k + 1, n] u [2k + 1, 2n 1]. For k = n - 1 and n - 2, we completely characterize k-extendable graphs on 2n vertices. We conclude Chapter 2 with a variation of the concept of extendability to odd order graphs.In Chapter 3, we establish a number of properties of k-critical graphs. These results include sufficient conditions for k-extendable graphs to be k-critical. More specifically, we prove that for a k-extendable graph G ≠ K2n on 2n vertices, 2 ≤ k ≤ n - 1, if for every pair of non-adjacent vertices u and v of G there exists a dependent set S ( a subset S of V (G) is dependent if the induced subgraph G[S] has at least one edge) of G-u-v such that o(G-(S u {u,v})) = S, then G is k-critical. Moreover, for k = 2 this sufficient condition is also a necessary condition for non-bipartite graphs. We also establish a ++ / necessary condition, in terms of the minimum degree, for k-critical graphs.We conclude Chapter 3 by completely characterizing k-critical graphs on 2n vertices for k = 1, n - 1 and n - 2.Chapter 4 contains results on k-minimal graphs. These results include necessary and sufficient conditions for k-extendable graphs to be k-minimal. More specifically, we prove that for a k-extendable graph G on 2n vertices, 1 ≤ k ≤ n - 1, the following are equivalent:G is minimalfor every edge e = uv of G there exists a matching M of size k in G-e such that V(M) n {u,v} = ø and for every perfect matching F in G containing M, e Є F.for every edge e = uv of G there exists a vertex set S of G-u-v such that: M(S) ≥ k; o(G-e-S) = S - 2k + 2; and u and v belong to different odd components of G-e-S, where M(S) denotes a maximum matching in G[S].We also establish a necessary condition, in terms of minimum degree, for k-minimal and k-minimal bipartite graphs. In fact, we prove that a k-minimal graph G ≠ K2n on 2n vertices, 1 ≤ k ≤ n - 1, has minimum degree at most n + k - 1. For a k-minimal bipartite graph G ≠ Kn,n , 1 ≤ k ≤ n - 3, we show that δ(G) < ½(n + k).Chapter 1 provides the notation, terminology, general concepts and the problems concerning extendability graphs and (k,t)-critical graphs.

Στην παρούσα διπλωματική εργασία γίνεται μία (όσο το δυνατόν καλύτερη) καταγραφή των γνωστών αποτελεσμάτων, καθώς επίσης και αποτελεσμάτων που αφορούν τις k -ζήτα συναρτήσεις και k -υπεργεωμετρικές. Επιπλέον δίνουμε και νέες ανισότητες για τις Γk(x) και Bk(x, y) συναρτήσεις. / --

The single aim of this thesis can be stated clearly: to argue for the use and usefulness of thick and thin concepts within law. The distinction between thick and thin concepts - recently popularized in analytic philosophy - has in the last two decades migrated from its point of origin in meta-ethics to other areas of philosophy and now law. My contention is that whilst use of the distinction within law is welcome, legal deployment of the distinction has been haphazard, with the idea left vague and ambiguous. Although the lack of clarity within the legal literature could be explained by the infancy of these ideas within legal discourse, the imprecision and ambiguity that results has undermined the juristic value of the central distinction for law. In particular I note the lack of any attention at all within the legal literature to the question of whether normative and descriptive aspects of thick concepts are capable of being separated - even though this controversy has dominated the philosophical literature. However, my criticism of the legal deployment of thick and thin is not restricted to this idea alone. Failure to investigate (or mention) the several issues I identify has, I argue, seen opportunities missed for the gainful use of the distinction in law, with my thesis focusing, in illustration, on the value to be gained through such analysis in the areas of jurisprudence and legal education. I select these two areas because they ably demonstrate the opportunities that I contend exist, and also because their scope, from theoretical analysis to educational practice, serves notice that these insights might reasonably range over a wider field in law too.

Thèse d'exercice : Médecine : Nancy 1 : 2009. / Titre provenant de l'écran-titre.

Thesis (Ph.D.)--Baylor University, 2007. / Includes bibliographical references (p. 188-201).

Thesis (M.A. (African Languages)) -- University of Pretoria, 2007.