A 6-dimensional grand unified theory with the compact space having the topology of a real projective plane, i.e., a 2-sphere with opposite points identified, is considered. The space is locally flat except for two conical singularities where the curvature is concentrated. One supersymmetry is preserved in the effective 4d theory. The unified gauge symmetry, for example SU(5) , is broken only by the non-trivial global topology. In contrast to the Hosotani mechanism, no adjoint Wilson-line modulus associated with this breaking appears. Since, locally, SU(5) remains a good symmetry everywhere, no UV-sensitive threshold corrections arise and SU(5)-violating local operators are forbidden. Doublettriplet splitting can be addressed in the context of a 6d N = 2 super Yang-Mills theory with gauge group SU(6). If this symmetry is first broken to SU(5) at a fixed point and then further reduced to the standard model group in the above non-local way, the two light Higgs doublets of the MSSM are predicted by the group-theoretical and geometrical structure of the model.

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The 3C-SiC Silicon Carbide phase doped by P, Ga, and N atoms was analyzed in the framework of Density Functional Theory. The physical parameters, changing with time due to N concentration increase, were calculated. Crucial statements about the existence of the deepest level were checked. Calculations of band structures were performed using the software applications VASP and Siesta. The plane wave basis was used in the first case and the orbital basis in the frame of the virtual crystal approach in the second one.

Automation of change detection greatly enhances environmental monitoring. This study describes possibilities for automation of change detection through image processing actions that include geometric correction, classification and segmentation. The water area was photographed twice and the changes in water vegetation were under consideration. The results from image processing monitoring were compared to the on-site measurements. The correspondence between these two was satisfactory. The automation of the change detection would require both on-site actions and controlled photographing together with well defined image processing.

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