Trends in research on the possible effects of climate change concerning aquatic ecosystems with special emphasis on the modelling approach

Knowledge on the expected effects of climate change on aquatic ecosystems is defined by three ways. On the one hand, long-term observation in the field serves as a basis for the possible changes; on the other hand, the experimental approach may bring valuable pieces of information to the research field. The expected effects of climate change cannot be studied by empirical approach; rather mathematical models are useful tools for this purpose. Within this study, the main findings of field observations and their implications for future were summarized; moreover, the modelling approaches were discussed in a more detailed way. Some models try to describe the variation of physical parameters in a given aquatic habitat, thus our knowledge on their biota is confined to the findings based on our present observations. Others are destined for answering special issues related to the given water body. Complex ecosystem models are the keys of our better understanding of the possible effects of climate change. Basically, these models were not created for testing the influence of global warming, rather focused on the description of a complex system (e. g. a lake) involving environmental variables, nutrients. However, such models are capable of studying climatic changes as well by taking into consideration a large set of environmental variables. Mostly, the outputs are consistent with the assumptions based on the findings in the field. Since synthetized models are rather difficult to handle and require quite large series of data, the authors proposed a more simple modelling approach, which is capable of examining the effects of global warming. This approach includes weather dependent simulation modelling of the seasonal dynamics of aquatic organisms within a simplified framework.

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.