2-connected outerplanar graphs have a unique minimal cycle basis with length 2|E|-|V|. They are the only Hamiltonian graphs with a cycle basis of this length. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

A phonological disorder is a communication disorder of the speech sound system characterized by an impaired ability to use developmentally expected speech sounds and sound patterns to communicate with others (Bauman-Waengler, 2004). This impairment affects the clarity of a child's speech and how easily a child's speech can be understood. As stated in the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV) (American Psychiatric Association, 1994), difficulties with speech sound production may interfere with academic achievement, social communication, or future occupational achievement. Children with phonological impairments are generally viewed as being at risk for reading difficulties (American Speech-Language-Hearing Association, 2001).Clinicians and researchers in speech-language pathology agree that efficient treatment of children who have moderate to severe phonological disorders is critical. Although imitation and structured practice are primary strategies employed by speech- language pathologists for practicing speech production, using communicative tasks to facilitate generalization during phonological intervention has been suggested in the literature.The purpose of this study was to determine if communication-centered phonological intervention would be effective in improving speech production in preschool children with moderate to severe phonological disorders. A single subject multiple probe across subjects research design (Horner andamp; Baer, 1978) was used to assess the effectiveness of communication-centered phonological intervention with three preschool children. The communication-centered phonological intervention in this investigation consisted of the combined application of focused stimulation of key words during joint storybook reading and interactive practice of key words using communicative feedback.All three subjects demonstrated some type of phonological improvement following the communication-centered intervention. Two out of the three subjects demonstrated improvement in the use of the target phonological patterns during theintervention sessions with one of these participants demonstrating generalization of the target phonological pattern to conversational speech. Although the third subject did not demonstrate improvement during the intervention period, follow-up testing revealed some system-wide changes in his phonology that may be attributed to the intervention. Further investigation of communication-centered phonological intervention is warranted.

This project investigates the apparent contradiction of a female artist who prioritises embodied presence in her art works, but produces Minimalist installations. It does this by describing in detail and analysing, and thus re-evaluating the significance of, the full range of actions and processes that are performed to produce the work. It further proposes that, in the actions of crafting the individual elements and in designing, planning and installing the work in Modernist gallery spaces, conditions are set up for viewers of the finished work to experience a physical awareness that echoes that of the artist in those actions and processes.

Since it arose in the 1960s, the minimalist aesthetic has increasingly influenced composers of art and popular music around the world and, in turn, minimalist composers have drawn on the compositional ideas of Western popular music and several non-Western musics. Educationally, minimal music offers much potential for music in the classroom as it embodies a number of musical characteristics known to, and preferred by, students aged 9-18 years at primary, secondary and first year tertiary level. Socially, it offers teachers an opportunity to engage students, through composing activities, with contemporary society. The study aims, firstly, to analyse compositions by students aged 9, 12, 15 and 18 years and their teachers, seeking pastiche development of, and compositional expansion beyond, the musical concepts presented in a resource booklet of projects, The Pulse Music Album. Secondly, this study aims to investigate how nineteen participating teachers in three countries engage their students with minimalist composing activities stimulated through the resource booklet. The study attempts to determine why teachers adopt their particular roles and strategies by examining music qualifications, preferences and experience, teaching perspectives and teaching environments. It also seeks to identify reasons why one group of teachers submitted pieces which were pastiches of those presented in the projects and another group submitted compositions which moved well beyond pastiche into an expansion of these same musical concepts and argues for this as evidence of dialogue with contemporary society. Conclusions drawn from the findings note that while there are many commonalities between the backgrounds and approaches of both groups of teachers, there are clearly observed differences. These differences suggest approaches to classroom composition for consideration by practising classroom teachers, in-service instructors and teacher training institutions.

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.

Thesis (Ph. D.)--University of Washington. / Bibliography: leaves [120]-123.

München, Techn. University, Diss., 2007.

Zugl.: Rostock, Hochsch. für Musik und Theater, Diss., 2005

Zugl.: Aachen, Techn. Hochsch., Diss., 2008

Zugl.: Karlsruhe, Univ., Diss., 2009 / Hergestellt on demand