Distance-regular graphs with intersection arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} do not exist

We prove that the arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} cannot be realized as the intersection arrays of distance-regular graphs. In the proof we use some inequalities bounding the size of substructures (cliques, cocliques) in a distance-regular graph.     

On automorphisms of the generalized hexagon of order (3,27)

Possible orders and fixed-point subgraphs for automorphisms of the generalized hexagon S of order (3,27) are found. It is proved that, if the automorphism group of S acts transitively on points, then S is isomorphic to the classical generalized hexagon corresponding to the building of the Steinberg group ³ D ₄(3).     

Magnetooptical,optical, and magnetotransport properties of Co/Cu superlattices with ultrathin cobalt layers

We investigated the field dependences of the magnetization and magnetoresistance of superlattices [Co(t _x, Å)/Cu(9.6 Å)]30 prepared by magnetron sputtering, differing in the thickness of cobalt layers (0.3 Å ≤ t _Co ≤ 15 Å). The optical and magnetooptical properties of these objects were studied by ellipsometry in the spectral region of hω= 0.09–6.2 eV and with the help of the transverse Kerr effect (hω= 0.5–6.2 eV). In the curves of an off-diagonal component of the tensor of the optical conductivity of superlattices with t _Co = 3–15 Å, a structure of oscillatory type (“loop”) was detected in the ultraviolet region, resulting from the exchange splitting of the 3d band in the energy spectrum of the face-centered cubic structure of cobalt (fcc Co). Based on magnetic experiments and measurements of the transverse Kerr effect, we found the presence of a superparamagnetic phase in Co/Cu superlattices with a thickness of the cobalt layers of 3 and 2 Å. The transition from superlattices with solid ferromagnetic layers to superparamagnetic cluster-layered nanostructures and further to the structures based on Co and Cu (t _Co = 0.3–1 Å) with a Kondo-like characteristics of the electrical resistivity at low temperatures is analyzed.     

GQ(4, 2)-extensions, strongly regular case

A strongly regular locallyGQ(4, 2)-graph is a graph with parameters either (126, 45, 12, 8) or (190, 45, 12, 10). The existence and the uniqueness of the corresponding locallyGQ(4, 2)-graph in the first case are well known. We prove that theGQ(4, 2)-hyperoval on ten vertices either is the Petersen graph, or is the Möbius 5-prism, or consists of two (2, 3)-subgraphs connected by three edges. We obtain homogeneousGQ(4, 2)-solutions with a strongly regular point graph; in particular, this implies the negative answer to the question of F. Buekenhout concerning the existence of a locallyGQ(4, 2)-graph with the parameters (190, 45, 12, 10).     

Triterpenoids in leaves of Urals and Altai birches and questions of their chemotaxonomy

Pacific Ocean Institute of Bioorganic Chemistry, Far Eastern Branch, USSR Academy of Sciences, Vladivostok. Wood Institute, Urals Branch, USSR Academy of Sciences, Sverdlovsk. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 278–279, March–April, 1990.     

Optical properties and electronic structure of BiTeCl and BiTeBr compounds

Optical properties of BiTeCl and BiTeBr compounds with a strong Rashba spin–orbit coupling are studied in the 0.08–5.0 eV range using the optical ellipsometry method. Fundamental characteristics of the electronic structure are obtained. Similarly to BiTeI, spectra of the imaginary part of dielectric permittivity constant ε₂(E) in the energy interval between the plasma edge and the threshold of an intense interband absorption (0.7 eV in BiTeCl and 0.6 eV in BiTeBr) display a fine structure of electronic transitions at 0.25 and 0.55 eV in BiTeCl and 0.20 and 0.50 eV in BiTeBr. These features are assigned to electronic transitions between the bulk conduction zones split by the Rashba spin–orbit interaction. The parameters of the electronic structure of BiTeCl and BiTeBr are compared with the BiTeI compound that was studied earlier. In the BiTeCl–BiTeBr–BiTeI row, the absorption edge and main features of the fundamental absorption exhibit a shift to low energies.