Authors of this paper take under investigation the optimization of biological processes during the wastewater treatment in sequencing batch reactor (SBR) plant. A designed optimizing supervisory controller generates the dissolved oxygen (DO) trajectory for the lower level parts of the hierarchical control system. Proper adjustment of this element has an essential impact on the efficiency of the wastewater treatment process as well as on the costs generated by the plant, especially by the aeration system. The main goal of the presented solution is to reduce the plant energy consumption and to maintain the quality of effluent in compliance with the water-law permit. Since the optimization is nonlinear and includes variations of different types of variables, to solve the given problem the authors performed simulation tests and decided to implement a hybrid of two different optimization algorithms: artificial bee colony (ABC) and direct search algorithm (DSA). Simulation tests for the wastewater treatment plant case study are presented.

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We study a combinatorial problem called Minimum Maximal Matching, where we are asked to find in a general graph the smallest matching that can not be extended. We show that this problem is hard to approximate with a constant smaller than 2, assuming the Unique Games Conjecture.As a corollary we show, that Minimum Maximal Matching in bipartite graphs is hard to approximate with constant smaller than 4 3 , with the same assumption. With a stronger variant of the Unique Games Conjecture -that is Small Set Expansion Hypothesis -we are able to improve the hardness result up to the factor of 3 2 .

In recent years, the Court of Justice of the European Union has issued a number of judgments addressing the issue of consumer protection in connection with the use of unfair terms by banks in loan agreements indexed with a foreign currency exchange rate. Most of them have concerned issues of exchange rate risk and exchange rate differences between the purchase and sale rates of a given currency applied by the bank. This article analyzes the recent ruling by the Court of Justice of the European Union in the Dziubak case, which was initiated by referring questions for a preliminary ruling by a Polish court. The article’s purpose is to assess the position taken by the cjeu in this respect and its significance for consumers in Poland. Particular attention was paid to the considerations with regard to the possibility of replacing unfair provisions with general provisions and assessing the consumer’s awareness of the consequences of declaring a contract invalid. The aim is to examine the issues that were dealt with by the Court of Justice of the European Union in the Dziubak case, including – in particular – the answer to the question of whether the issues discussed by the cjeu had already been considered in its previous jurisprudence and whether it presents new, previously unknown legal consequences of the inclusion of unfair contract terms in loan agreements.

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