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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...

Aim  We focus on the biogeographical role of the Balkan Peninsula as a glacial refugium and source of northward post‐glacial dispersal for many European taxa. Specifically, we analysed the genetic structure and variation of wild boar (Sus scrofa) samples primarily from Greece, a region that has repeatedly served as a glacial refugium within the Balkan Peninsula. Location  Continental Greece, the Aegean island of Samos and Bulgaria. Methods  We analysed wild boar samples from 18 localities. Samples from common domestic breeds were also examined to take into account interactions between wild and domesticated animals. Phylogenetic analyses were carried out on a 637‐bp fragment of the mitochondrial DNA control region in 200 wild boar and 27 domestic pigs. The sequences were also compared with 791 Eurasian wild boar and domestic pig D‐loop sequences obtained from GenBank. Results  Ninety‐four haplotypes were identified in the European wild boar data set, of which 68 were found in the Balkan samples and assigned to two previously described clades: the E1 European and Near Eastern clades. All of the continental samples clustered in the E1 clade and the samples from Samos fell into the Near Eastern clade, consistent with the island’s proximity to Asia Minor. Intriguingly, 62 novel haplotypes were identified and are found exclusively in the Balkans. Only six haplotypes were shared between wild boar and domestic pigs. Main conclusions  Our data reveal numerous novel and geographically restricted haplotypes in wild boar populations, suggesting the presence of separate refugia in the Balkans. Our analyses support the hypothesis of a post‐glacial wild boar expansion consistent with the leading edge model, north and west from modern day Greece, and suggest little maternal introgression of Near Eastern and domestic haplotypes into wild Balkan populations.

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Tribocorrosion of Al-Si-Cu-Mg alloys was investigated in 0.05 M NaCl and 0.1 M NaNO3 solutions under severe sliding and controlled electrochemical conditions. A simple galvanic coupling model was developed to analyze and quantitatively predict the evolution potential of the open circuit potential during tribocorrosion. According to this model and the obtained results, galvanic coupling was established in the NaNO3 solution within the wear track between passive and mechanically depassivated areas. In the NaCl solution, galvanic coupling was established between the whole depassivated wear track and the surrounding area. This difference was attributed to different mechanical properties of the passive surfaces.