A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

The linguistic situation in Kirkuk:a sociolinguistic study

This study is concerned with the linguistic situation in the town of Kirkuk in north eastern Iraq. In this town there are three main ethnic groups: Kurds, Arabs and Turkmana with some very smell minorities such as Chaldeene, Assyrians and Armenians. The languages spoken by these three ethnic groups belong to different language Family groups. In the First cart of the study the historical background of the population, a review of the literature, both of the present linguistic situation in Kirkuk end of relevant sociolinguistics in general, and the theoretical Framework, have been discussed in detail in order to provide background to this study which is mainly concerned with the Following areas: 1. The relationships existing between ethnic background and language usage and language loyalty in Kirkuk. 2. The attitudes of Kirkukiane towards language maintenance and language shift in Kirkuk. 3. Bilingual, multilingual individual communicative competence of Kurds, Arabs and Turkmans in the languages concerned, including the degree to which such a speaker is bilingual or multilingual and the nature of bilingualism or multilingualism in different domains and situations in Kirkuk. To throw light a these areas a situationally-oriented language survey was conducted; the relevant data was collected by randomly distributed questionnaire, by parsonal interview, by personal observation of language use and language attitudes in this town. The data subjected to commuter analysis and the results proved that the were no significant and substantial correlations between the language use, attitudes and competence based on the socio-economic status of respondents in this town, on the other hand, the correlations between the ethnic backgrounds and the language, use, attitudes and competence are indisoutable.