Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.

A synchronic lexical study of the Ede language continuum of West Africa: The effects of different similarity judgment criteria

In the context of a synchronic lexical study of the Ede varieties of West Africa, this paper investigates whether the use of different criteria sets to judge the similarity of lexical features in different language varieties yields matching conclusions regarding the relative relationships and clustering of the investigated varieties and thus leads to similar recommendations for further sociolinguistic research. Word lists elicited in 28 Ede varieties were analyzed with the inspection method. To explore the effects of different similarity judgment criteria, two different similarity judgment criteria sets were applied to the elicited data to identify similar lexical items. The quantification of these similarity decisions led to the computation of two similarity matrices which were subsequently analyzed by means of correlation analysis and multidimensional scaling. The findings of this analysis suggest compatible conclusions regarding the relative relationships and clustering of the investigated Ede varieties. However, the matching clustering results do not necessarily lead to the same recommendations for more in-depth sociolinguistic research, when interpreted in terms of an absolute lexical similarity threshold. The indicated ambiguities suggest the usefulness of focusing on the relative, rather than absolute in establishing recommendations for further sociolinguistic research.

XSAMPL3D: An Action Description Language for the Animation of Virtual Characters

In this paper we present XSAMPL3D, a novel language for the high-level representation of actions performed on objects by (virtual) humans. XSAMPL3D was designed to serve as action representation language in an imitation-based approach to character animation: First, a human demonstrates a sequence of object manipulations in an immersive Virtual Reality (VR) environment. From this demonstration, an XSAMPL3D description is automatically derived that represents the actions in terms of high-level action types and involved objects. The XSAMPL3D action description can then be used for the synthesis of animations where virtual humans of different body sizes and proportions reproduce the demonstrated action. Actions are encoded in a compact and human-readable XML-format. Thus, XSAMPL3D describtions are also amenable to manual authoring, e.g. for rapid prototyping of animations when no immersive VR environment is at the animator's disposal. However, when XSAMPL3D descriptions are derived from VR interactions, they can accomodate many details of the demonstrated action, such as motion trajectiories,hand shapes and other hand-object relations during grasping. Such detail would be hard to specify with manual motion authoring techniques only. Through the inclusion of language features that allow the representation of all relevant aspects of demonstrated object manipulations, XSAMPL3D is a suitable action representation language for the imitation-based approach to character animation.

The sociolinguistic situation of ǂHoan, a moribund 'Khoisan' language of Botswana

In 2010, we conducted a sociolinguistic survey on the moribund 'Khoisan' language ǂHoan (Ju-ǂHoan), spoken in Botswana at the fringe of the Kalahari Desert. The survey aimed at investigating language use, degrees of multilingualism and language attitude among the ǂHoan speakers. Data collection was done on the basis of a questionnaire. We found that the positive language attitude of individuals towards ǂHoan often conflicts with the community's attitude towards this language, resulting in a split of actual language use between the family and more formal situations. All ǂHoan speakers are at least bilingual speaking the local lingua franca Kgalagadi (Bantu) besides ǂHoan. Most of them are in fact even trilingual, speaking Gǀui (Khoe-Kwadi) in addition to ǂHoan and Kgalagadi. Most of our results stand in line with an earlier sociolinguistic survey on ǂHoan by Batibo (2005a) which was carried out in 2003. In comparing Batibo's results to ours, changes in the sociolinguistic situation of ǂHoan as well as differences between the different villages will be pointed out.

Caregiver Responses to the Language Mixing of a Young Trilingual

The situation once described by Hoffmann (1985), in which children grow up exposed to three languages from an early age, is a reality for an increasing number of families. In Europe – as elsewhere – greater mobility is leading to greater numbers of mixed-language couples (Piller 2002), and, by extension, multilingual families. For such families, questions concerning the acquisition and maintenance of three or more languages in a natural environment are of direct relevance. Researchers in bilingualism have already pointed out the importance of social context for the acquisition of two languages in childhood, focusing in particular on the quantity and quality of exposure to the languages (De Houwer 1990; Döpke 1992; Okita 2002; Lanza 2004) or the prestige of the languages (Lambert 1977). In this paper, I will make use of the insights gained by such researchers and test them in a trilingual setting. The paper will focus mainly on one aspect, namely the conversational style of parents and caretakers. The data come from research being carried out in Switzerland and consist of 33 interviews with multilingual families, as well as case studies of two trilingual children. The findings attest to the importance of conversational style, but at the same time indicate that a number of further factors are also of great significance.