Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

‘Neutral, native-like or authentic’ : Investigating attitudes and beliefs of expanding circle speakers of English

The status of English as the language of international communication is by now well-established. However, in the past 16 years, research has tried to emphasize the fact that the English spoken in international contact situations and between people with other first languages than English has different needs than the English spoken locally amongst native speakers, resulting in the emergence of English as a lingua franca (ELF) as a scholarly field. However, the impact of findings in ELF has so far only led to a moderate shift in English language teaching. Especially in expanding circle countries, where ELF should have the biggest impact, change is only gradually becoming palpable. Accent and pronunciation, as one of the biggest factors on both identity and mutual intelligibility (Jenkins 2000; 2007) are at the root of discussion. The scope of this study is therefore to examine accent choices and the extent to which native speaker ideology informs the preferences of ten speakers of ELF and 27 German natives with experience in international communication. Both ethnographical and sociolinguistic methods, as well as auditory analysis have been applied and conducted. The auditory analysis of six variables in the recorded speech production of the ten speakers suggests that there is no significant preference of one norm-giving variety over the other. Rather, speakers tend to mix-and-match General American- and Standard Southern British English-like features in their pronunciation. When reporting their accent ideals, the idea of a ‘neutral’ English accent is mentioned by four participants. Neutral accents seem to have been understood as ‘unmarked accents’. Expressed beliefs on their own English pronunciation show a comparatively high level of reflection on and confidence in their own production. Results from a rating task and a survey given to 27 German participants reveal attitudes that are more negatively stacked. While Germans reported openness towards NNS (non-native speaker) accents and showed awareness of the priority of intelligibility over accent choice in both their own and others’ pronunciation, they still largely reported NS accent preference. The ratings of the production from ten ELF speakers confirmed this and showed that ‘neutral’ is equated with native-like. In the light of these findings, issues are discussed that ultimately relate to the influence of NS Englishes, identity and the development of English as an international language.

Deictic Demonstratives in Japanese, Finnish and Swedish : First and Third Language Perspectives

The goal of this thesis is twofold. Firstly, it investigates the actual, native use of spatial-deictic demonstratives in Japanese, Finnish and Swedish. Secondly, it investigates and elucidates the interlanguage of Finnish-speaking and Swedish-speaking learners of Japanese regarding their use of Japanese spatial-deictic demonstratives in the light of respective native use and, in comparison to the descriptions of demonstratives in the teaching materials used. Thus, the present study deals with analyses of two sets of empirical data: data produced by native-speaking informants (L1 data) and data produced by language learners (L2 data). These were elicited by Discourse Completion Tasks (DCTs) designed, collected and analyzed using both quantitative and qualitative methods by the author. The results showed that the actual use of demonstratives by the native informants was not always in accordance with the way described in grammars. The typological similarities between Japanese and Finnish were in this study not reflected in the native use of demonstratives, and some uses were not solely based on the spatial relations between the referent, the speaker and the addressee, but rather on social-interactional factors. The main findings regarding the learner data revealed some differences in the usage rate of the demonstratives between the two Finnish-speaking groups and the one Swedish-speaking learner group studied. There were, however, no particular differences found between them regarding the type of demonstrative used. It is suggested that these differences are first and foremost connected both with the teaching materials used and the more or less heterogeneous linguistic environment in which the learners reside, and only thereafter with the typological similarities or differences between their respective native languages, Finnish and Swedish, and the target language, Japanese. It is further argued that the learners’ use of the different Japanese demonstratives, that is the type of demonstrative used, could be explained in terms of familiarity with the grammar. That is, when the situations used in the DCTs were exemplified in teaching materials and were familiar to them, the learners seemed to use Japanese demonstratives as they are described in the teaching materials and as the native Japanese speakers use them. When the situations used in the DCTs were not exemplified in the teaching materials, the learners seem to rely more on their native language. The results, thus, suggest that the learners’ interlanguage is influenced by the grammar of the target language known to the learners, but also by the number of languages (or varieties) that the learners have contact with at the time of learning. The results of the present study have implications for the teaching of Japanese in at least two ways. Firstly, the importance of grammar instruction must be emphasized since its effect on the learners’ language is apparent. Secondly, the contents of teaching materials should be revised on the basis of the native speakers’ actual use of the grammar.