Inverse, ill-posed problems, essentially different solutions and explicit formulas for solutions

A request for an inverse problem, as well as for an incorrect problem produces tens of millions of answers in the Internet. In the past few decades, hundreds of international conferences on these topics have been held annually. Problems of this kind are quite involved, and their numerical analysis requires the development of special methods and numerical algorithms. Explicit formulas provide the main tool for testing these methods and numerical algorithms. The Cauchy problem for an elliptic equation is a classical ill-posed problem, which serves as a model for many inverse and incorrect problems. In the present paper we give a numerically realizable explicit formula for solving the Cauchy problem in a two-dimensional domain for a general second-order linear elliptic equation with analytic coefficients and the Cauchy analytic data on the analytic boundary.

Exploring the Decision-Making Process of Pre-Service Teachers in Solving Mathematics Literacy Problems

Students’ lack of mathematical literacy skills is also accompanied by the lack of mathematical literacy skills of most pre-service teachers. The purpose of this study is to investigate the decision-making process conducted by pre-service teachers in solving mathematical literacy problems. This qualitative descriptive study involved two subjects taken from 42 pre-service mathematics teacher students. Each subject was identified based on their pattern in solving mathematical literacy problems correctly and inappropriately. Data were collected through tests of mathematical literacy problems and test-based interviews. The results showed that there were differences in the decision-making process done by the students with correct and incorrect problem solving, namely: (1) building ideas, having three vs. two solution ideas, formulating and employing correctly vs. formulating correctly and employing inappropriately; (2) clarifying ideas, giving reasons for each idea vs. having wrong reasons due to calculation errors, interpreting correctly vs. interpreting incorrectly; and (3) assessing the reasonableness of an idea, providing logical reasons with one choice vs. logical reasons with one choice but less sure. Based on the findings, it can be concluded that the creativity of prospective teacher students in building ideas is still low and reasoning in expressing and choosing ideas is still weak, causing immature decision making. The finding of this study provides suggestions for educators to provide structured assignments and for other researchers to find factors influencing pre-service teachers’ decision-making in mathematics problem-solving to improve pre-service teachers’ decision-making skills.

PROSES KEBIJAKAN PERSUTERAAN ALAM DI SULAWESI SELATAN

Production of cocoon and raw silk in South Sulawesi have decreased in recent years. One of the problem is misleading policy formulation and implementation. The purpose of this studies is to know the policy of sericulture that have implemented in South Sulawesi. The method of analyses are discourse analysis/narrative, actors/network, and politics/interest. The result indicated that three factors ie. narrative, actors and interests among stakeholder in sericulture development disturb the policy implementation so it wouldn’t achieve the goal. Incorrect problem formulation also disrupt the sericulture development so it didn’t increase cocoon and raw silk production in South Sulawesi. Key words: policy, process, sericulture, South Sulawesi

Light Impurity Depth Profiling in the Nuclear Reaction AnalysiS

The general problem in the analysis of a sample by non-destructive techniques such as nuclear microanalysis, ellipsometry, etc. is the interpretation of the measured data. The impurity depth profile obtained may noticeable non-physical fluctuations. From the mathematical point of view this could be explain by the fact that while interpreting the results we have to solve an incorrect problem to which routine computational methods are not applicable.