The magnetic field due to a permanent magnet of a tube-side segment as shape and of radial-oriented magnetization is considered. Such a sheet modelling a single pole of the magnet is used to express the suitable contribution to magnetic quantities. A boundary-integral approach is applied that is based on a virtual scalar quantity attributed to the magnet pole. Such an approach leads to express analytically the scalar magnetic potential and the magnetic flux density by means of the elliptic integrals. Numerical examples of the computed fields are given. The general idea of the presented approach is mainly directed towards designing the magnetic field within the air gap of electric machines with permanent magnets as an excitation source. Other technical structures with permanent magnets may be a subject of this approach as well.
This study used ISSR markers to assess the genetic diversity of a collection of 15 genotypes of Salix purpurea and 6 interspecific hybrids, employing 40 of 60 tested ISSR primers generating polymorphic amplification products. The PCR-ISSR method was adapted for S. purpurea by optimizing the annealing temperature for each primer. The polymorphism index of ISSR amplification products was 91.8% for all studied genotypes and 70.4% for S. purpurea genotypes. Nei's genetic identity statistics ranged from 0.538 to 0.958. Nei's genetic distance values were used to build a dendrogram (UPGMA) for the investigated genotypes. The dendrogram shows five clusters, and principal coordinate analysis yielded nearly the same genetic relationships among the studied genotypes. The results confirm the usefulness of ISSR markers for determining genetic diversity in S. purpurea.