The research revealed in the paper considers the improvement of secondary treatment of wastewater in the aerobic reactor to provide removal of organics and nutrients. There were five types of polymer biofilm carriers taken into account initially; however, two of them were decided not to apply due to technological reasons. The main part of the research was divided into three substages to investigate each type of biofilm carrier. According to the literature review, the optimal efficiency may be reached if the carrier filling ratio is 10 to 30% of reactor volume. On this basis, there were three benches launched at each sub-stage with a corresponding filling ratio of 10, 20, and 30%. The fourth reactor at each sub-stage had no floating carrier to control the experiment. The research of all three types of carriers showed the effect of BOD removal in the range of 95–96% for benches equipped with a floating carrier, which can be considered similar to the control bench with the efficiency of 92%. In the case of ammonia nitrogen, the removal control bench showed only 55% of efficiency, while floating carriers helped to increase the efficiency up to 70–86%. Despite obtaining relatively positive results, the research has to be continued to achieve regulation requirements in treatment quality.
LAUGHLIN STATES ON THE SPHERE AS REPRESENTATIONS OF ${\mathcal U}_q({\rm sl}2))$
