A mathematical model of a plane, steady state biofilm, with the use of a single substrate kinetics, was proposed. A set of differential equations was solved. In order to analyse the biofilm’s behaviour, a number of simulations were performed. The simulations included varying process parameters such as detachment coefficient and substrate loading. Two detachment models were taken into consideration: one describing the detachment ratio as proportional to the thickness of the biofilm, and the other one proportional to the thickness of the biofilm squared. The results provided information about substrate and live cell distribution in biofilm and the influence of certain parameters on biofilm behaviour.

A method of parameters fitting to the experimental vapour - liquid - liquid equilibrium (VLLE) data is presented for the NRTL and the Uniquac equations for six quaternary mixtures. The same equations but with coefficients taken from the simulator Chemcad database were also used for calculation of the VLLE for the same mixtures. The calculated equilibrium temperatures and compositions for all the three phases were compared with the experimental data for these four cases. The investigated models were also applied for calculation of the compositions and temperatures of ternary azeotropes occurring in the considered quaternary mixtures. The computed values were compared with the experimental ones to appreciate the model's accuracy and to confirm whether the model correctly predicts the presence of homo- or heteroazeotrope. The NRTL equation with coefficients fitted to the VLLE data proved to be the most accurate model. For the mixtures containing water, ethanol and two different hydrocarbons this model shows particularly high accuracy. In three cases the mean deviations between the calculated and measured temperatures do not exceed 0.25 K, and for the fourth mixture the difference equals 0.33. Besides, the mean deviations between the calculated and the measured concentrations in the gas and liquid phases, with one exception do not exceed 1 mole %.

W transcendentalnej dedukcji kategorii, w drugim wydaniu Krytyki czystego rozumu, Kant wprowadza termin „formalna naoczność” (formale Anschauung), ukazując w ten sposób, że określenie to zawiera bogatszą treść niż „forma naoczności” (Form der Anschauung). Wiąże się to z określaniem, tj. determinowaniem czystej formy naoczności, które dokonuje się za sprawą syntezy postaciowej, będącej wytworem wyobraźni, ale przy współudziale kategorii. Rozważam m.in. kwestię, jak należy rozumieć jedność przestrzeni i co jest źródłem owej jedności. Przy okazji analizuję ważne i trudne pojęcie różnorodności (Mannigfaltigkeit), które – jak się wydaje – leży u podstaw różnicy między dwoma sposobami ujęcia przestrzeni jako czystej naoczności.

This paper proposes a novel method for digital image watermarking, in which watermarks are embedded in the domain of fast para-metric transforms based on known spread spectrum approaches. Fast parametric transforms have the ability to adapt the forms of base vectors, which enables automatic selection of the domain of watermarking in relation to the pair: a marked image – a watermarking attack. The process of adapting the forms of fast parametric transforms is carried out with aid of the classical genetic algorithm with the fitting function based on the known measure of separability of watermarks. The effectiveness of the proposed method has been verified experimentally on the basis of the images of two classes, i.e. natural images and technical diagrams. The results taking into account both the efficiency of watermark embedding and the generated distortions in the marked images are summarized in tables and accompanied by an appropriate commentary.