For finitely generated nilpotent groups, we employ Mal'cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations for subgroups are solved using only logarithmic space and quasilinear time. Logarithmic space presentation-uniform versions of these algorithms are provided. Compressed-word versions of the same problems, in which each input word is provided as a straight-line program, are solved in polynomial time.

The paper presents an overview of the image-processing techniques. The set of basic theoretical instruments includes methods of mathematical analysis, linear algebra, probability theory and mathematical statistics, theory of digital processing of one-dimensional and multidimensional signals, wavelet-transforms and theory of information. This paper describes a methodology that aims to detect and diagnose faults, using thermographs approaches for the digital image processing technique.

A fuzzy expert system was applied to the knowledge analysis of yeast physiology in the early stage of beer fermentation, when the wort was aerated. We used ergosterol and glycogen concentration in the wort as a suitable marker of physiological state of the cell population. The amount of both compounds influences the rate of fermentation, cell growth and the final taste of beer. The concentrations of ergosterol and glycogen including the number of cells can not be measured immediately during the relatively short aeration period, and incomplete experimental data are therefore found in laboratory logbooks. We therefore suggested that the fuzzy relation between the directly measurable dissolved oxygen concentration and the rate of ergosterol or glycogen formation should be identified and a fuzzy expert system should be used to analyze the behavior of the yeast.

Recent biotechnology requires implementation of new modelling methods based on knowledge principles and learning structures, comprised in fuzzy knowledgebased systems (FKBS), neural networks (NN) and different hybrid methods. The intelligent modelling approaches solve suf®ciently a very important problem ± processing of scarce, uncertainty and incomplete numerical and linguistic information about multivariate non-linear and non-stationary systems as well as biotechnological processes. The paper deals with prediction of an enzyme oxidizing uric acid to alantoin ± the uricase, produced by Candida utilis 90-12 employing neuro-fuzzy knowledgebased approach. The implemented predictive technique exploits the fact that the fuzzy model can be seen as a network structure, similar to arti®cial NN, which on computational level assure a high model accuracy. The predictors implemented are four different by nature variables. The developed predictive model shows that best predictors of uricase production are biomass and limiting substrate concentrations.

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