The paper considers the technique of modeling and formation educational components of the planned training of CDIO Syllabus, realized in the form of the educational adaptive environment of engineering education. The following key concepts of the methodology have been accepted: competence models of the stages of the CDIO initiative, the method of project training, syntax for describing the concepts of the domain, models for mapping support concepts in the form of expressions of knowledge and ontological engineering.

The use of environmentally friendly inorganic binders and new technologies for cores production is widely discussed topic in recent years. This paper contains information about new hot curing process for core making with alumina-silicate based inorganic binders – geopolymers. Main differences between hot cured geopolymers and hot cured alkali silicate based inorganic binders are discussed. The main objective of this research paper was to investigate basic technological properties of geopolymer binder system such as strength, compaction, storage ability and knock-out properties. For this purpose, three mixtures with different powder additives were prepared and tested in laboratory conditions using specific methods. Strength properties evaluation showed sufficient levels as well as knock-out properties measurement, even with additives B and C originally designed for the use with alkali silicate based two component binder systems. Additives B and C were considered compatible with geopolymer binders after casting production trial results. Storage ability of geopolymers seems to be more sensitive than of alkali silicate based binders in the same tested conditions. Mixtures with geopolymer binder showed 20% more decrease of strength compared to alkali silicate binders after 24 hours in conditions of 25 °C and 65 %RH.

The paper presents some problems of heat conduction in a semi-infinite periodically stratified layer. The layer is subjected to acting a constant temperature on the part of boundary, normal to the layering. The free heat exchange with surroundings is assumed on the remaining part of the boundary. The composite layer is supposed to be composed of n periodically repeated two-component lamina. The problem is solved in two ways: (10) directly as a heat conduction problem, (20) by using model with microlocal parameters [1,2]. The main aim of the paper is a comparison of the obtained results and to conclude possibilities of applications of the homogenized model with microlocal parameters.