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Acta Technologica Agriculturae 1/2016Dušan Páleš et al.The most effective way for determination of curves for practical use is to use a set of control points. These control points can be accompanied by other restriction for the curve, for example boundary conditions or conditions for curve continuity (Sederberg, 2012). When a smooth curve runs only through some control points, we refer to curve approximation. The B-spline curve is one of such approximation curves and is addressed in this contribution. A special case of the B-spline curve is the Bézier curve Rédl et al., 2014). The B-spline curve is applied to a set of control points in a space, which were obtained by measurement of real vehicle movement on a slope (Rédl, 2007(Rédl, , 2008. Data were processed into the resulting trajectory (Rédl, 2012;Rédl and Kučera, 2008). Except for this, the movement of the vehicle was simulated using motion equations (Rédl, 2003;Rédl and Kročko, 2007). B-spline basis functionsBézier basis functions known as Bernstein polynomials are used in a formula as a weighting function for parametric representation of the curve (Shene, 2014). B-spline basis functions are applied similarly, although they are more complicated. They have two different properties in comparison with Bézier basis functions and these are: 1) solitary curve is divided by knots, 2) basis functions are not nonzero on the whole area. Every B-spline basis function is nonzero only on several neighbouring subintervals and thereby it is changed only locally, so the change of one control point influences only the near region around it and not the whole curve.These numbers are called knots, the set U is called the knot vector, and the half-opened interval 〈u i , u i + 1 ) is the i-th knot span. Seeing that knots u i may be equal, some knot spans may not exist, thus they are zero. If the knot u i appears p times, hence u i = u i + 1 = ... = u i + p -1 , where p >1, u i is a multiple knot of multiplicity p, written as u i (p). If u i is only a solitary knot, it is also called a simple knot. If the knots are equally spaced, i.e. (u i + 1 -u i ) = constant, for every 0 ≤ i ≤ (m -1), the knot vector or knot sequence is said uniform, otherwise it is non-uniform.Knots can be considered as division points that subdivide the interval 〈u 0 , u m 〉 into knot spans. All B-spline basis functions are supposed to have their domain on 〈u 0 , u m 〉. We will use u 0 = 0 and u m = 1.To define B-spline basis functions, we need one more parameter k, which gives the degree of these basis functions. Recursive formula is defined as follows:This definition is usually referred to as the Cox-de Boor recursion formula. If the degree is zero, i.e. k = 0, these basis functions are all step functions that follows from Eq. (1). N i, 0 (u) = 1 is only in the i-th knot span 〈u i , u i + 1 ). For example, if we have four knots u 0 = 0, u 1 = 1, u 2 = 2 and u 3 = 3, knot spans 0, 1 and 2 are 〈0, 1), 〈1, 2) and 〈2, 3), and the basis functions of degree 0 are N 0, 0 (u) = 1 on interval 〈0, 1) Acta In this co...

Cyanobacterial blooms are tightly related to increasing trophic conditions of lakes and climate warming. Abiotic and biotic parameters were studied in a shallow lake, in which the island with the largest cormorants colony in north-eastern Poland is situated. We hypothesized that the strongest cyanobacterial blooms will persist near the cormorant’s island and will decrease with an increasing distance from it. Filamentous cyanobacteria (Pseudanabaena, Planktolyngbya, Limnothrix, Planktothrix) were the main phytoplankton components during summer and autumn. Their strongest blooms (up to 66 mg L−1) were recorded near the roosting area. The content of nutrients and chlorophyll a, and the biomass of phytoplankton (primarily cyanobacteria) and zooplankton, decreased gradually with the increasing distance from the island. The changes from hypertrophic to eutrophic conditions were confirmed by a decrease in values of the trophic state index from 72 (site 1) to 58 (site 5). This all suggests that cormorants might have a significant impact on the deterioration of water quality (at distance to 1.6 km) and can contribute to faster water eutrophication. Our results suggest that protection of breeding sites for many waterbirds, such as cormorants, becomes a real threat for the functioning of aquatic ecosystems due to a large load of nutrients.

Interaction between juvenile narrow-claw crayfish, Astacus leptodactylus (Eschscholtz), and common water frog, Rana esculenta (L.), tadpoles or common blue damselfly, Enallagma cyathigerum (Charpentier), larvae during rearing under controlled conditions Dariusz Ulikowski, Iwona Piotrowska, £ucjan Chybowski, Tadeusz Krzywosz, Piotr Traczuk Received -07 July 2014/Accepted -06 October 2014. Published online: 31 December 2014 ©Inland Fisheries Institute in Olsztyn, Poland Citation: Ulikowski D., Piotrowska I., Chybowski £., Krzywosz T., Traczuk P. 2014 -Interaction between juvenile narrow-claw crayfish, Astacus leptodactylus (Eschscholtz), and common water frog, Rana esculenta (L.), tadpoles or common blue damselfly, Enallagma cyathigerum (Charpentier), larvae during rearing under controlled conditions -Arch. Pol. Fish. 22: 257-264.Abstract. Interactions were studied among juvenile narrow-claw crayfish, Astacus leptodactylus (Eschscholtz), and common water frog, Rana esculenta (L.), tadpoles and common blue damselfly, Enallagma cyathigerum (Charpentier), larvae during rearing under controlled conditions. Interactions among the species studied had a positive impact on the survival of the crayfish, but the differences were not statistically significant (P ³ 0.5). The juvenile crayfish attacked and consumed the frog tadpoles and damselflies, but the juvenile crayfish very rarely fell prey to them. Only in the initial stage of life and during molting did larval damselflies prey upon juvenile crayfish. After 30 days of the experiment the interaction between crayfish-tadpoles and crayfish-larval damselflies was not noted to have had a statistically significant (P ³ 0.05) impact on crayfish growth. Juvenile crayfish aggression toward tadpoles and larval damselflies was often offset by the loss of even both chelipeds. In the crayfish-larval damselfly interaction the loss of both chelipeds was three-fold more common than it was in the crayfish-tadpole interaction; however, these differences were not statistically significant (P ³ 0.5). The effect of intraspecific interaction (crayfish-crayfish) was more a threat in terms of mortality from cannibalism than were interspecific interactions (crayfish-tadpole and crayfish-larval damselfly).

High content of humic substances and low pH values are factors limiting the species richness and abundance of some organisms in dystrophic lakes. Unfavourable winter conditions (i.e. low water temperature, poor light conditions, ice/snow cover) may additionally restrict their development. The aim of this study was to compare ice-on (winter) and ice-off (summer) abiotic (organic carbon, total phosphorus and nitrogen) and biotic (chlorophyll a, phytoplankton, ciliates, rotifers, crustaceans, fish) parameters in five dystrophic lakes of the Wigry National Park (north-east Poland). We tested the hypothesis that the abundance and diversity of planktonic organisms in dystrophic lakes could be lower in winter than in summer. Our results showed that the winter period, with ice and snow cover, was characterised by clearly higher oxygen concentrations, pH values and conductivity, but lower total phosphorus concentrations, species richness of phytoplankton, ciliates, rotifers and crustaceans, and phytoplankton to zooplankton biomass ratios in comparison to the summer. All of the studied groups of organisms, except rotifers, reached relatively high abundances and biomasses in both seasons and, in some lakes, they were higher in winter than in summer. Our results suggest that fish composition and abundance did not play an important role in structuring plankton communities. The small dystrophic lakes, although located close to one another, differed in terms of abiotic parameters and had specific species compositions of phyto-and zooplankton. Warmer winters, which are the result of climate change, may favour the intensive development of planktonic communities under the ice in dystrophic lakes of temperate climatic zones.