Dinamikus optimalizálás és a Leontief-modell (Dynamic optimization and the Leontief model)

A tanulmány a variációszámítás gazdasági alkalmazásaiból ismertet hármat. Mindhárom alkalmazás a Leontief-modellen alapszik. Az optimális pályák vizsgálata után arra keressük a választ, hogy az Euler–Lagrange-differenciálegyenlet rendszerrel kapott megoldások valóban optimális megoldásai-e a modelleknek. Arra a következtetésre jut a tanulmány, hogy csak pótlólagos közgazdasági feltételek bevezetésével határozhatók meg az optimális megoldások. Ugyanakkor a megfogalmazott feltételek segítségével az ismertetett modellek egy általánosabb keretbe illeszthetők. A tanulmány végső eredménye az, hogy mind a három modell optimális megoldása a Neumann-sugárnak felel meg. /===/ The study presents three economic applications of variation calculations. All three rely on the Leontief model. After examination of the optimal courses, an answer is sought to whether the solutions to the Euler–Lagrange differential equation system are really opti-mal solutions to the models. The study concludes that the optimal solutions can only be determined by introducing additional economic conditions. At the same time, the models presented can be fitted into a general framework with the help of the conditions outlined. The final conclusion of the study is that the optimal solution of all three models fits into the Neumann band.

Seasonal dynamic pattern analysis in service of climate change research. A methodical case-study - monitoring and simulation based on an aquatic insect community

Our aim was to approach an important and well-investigable phenomenon – connected to a relatively simple but real field situation – in such a way, that the results of field observations could be directly comparable with the predictions of a simulation model-system which uses a simple mathematical apparatus and to simultaneously gain such a hypothesis-system, which creates the theoretical opportunity for a later experimental series of studies. As a phenomenon of the study, we chose the seasonal coenological changes of aquatic and semiaquatic Heteroptera community. Based on the observed data, we developed such an ecological model-system, which is suitable for generating realistic patterns highly resembling to the observed temporal patterns, and by the help of which predictions can be given to alternative situations of climatic circumstances not experienced before (e.g. climate changes), and furthermore; which can simulate experimental circumstances. The stable coenological state-plane, which was constructed based on the principle of indirect ordination is suitable for unified handling of data series of monitoring and simulation, and also fits for their comparison. On the state-plane, such deviations of empirical and model-generated data can be observed and analysed, which could otherwise remain hidden.