The splitting number of the complete graph

If a given graphG can be obtained bys vertex identifications from a suitable planar graph ands is the minimum number for which this is possible thens is called the splitting number ofG. Here a formula for the splitting number of the complete graph is derived.     

Untersuchung eines Li-Cr-Ferrits mit Hilfe des Mößbauer-Effekts

The hyperfine-structure spectra of the 14.4 keVγ-ray of the nucleus⁵⁷Fe in the spinel type ferrite (Li ₀₅ ⁺ Fe _1.3 ³⁺ Cr _1.2 ³⁺ O ₄ ^2? ) have been measured through the use of the Mößbauer effect. These measurements were performed on powder samples at different temperatures between 88 °K and 633 °K. For the Fe³⁺ ions at both the tetrahedral (A) and octahedral (B) sites at 88 °K the effective magnetic fieldH at the Fe nuclei is the same and equal to 504±4 kG. The temperature dependence ofH _A however is different fromH _B . Application of an external magnetic field of 20 kG shows that the sign ofH _A is positive and the sign ofH _B is negative. As the temperature is increased a considerable broadening of the magnetic hfs-lines (and especially of the outer pair of lines) is observed. No theoretical discussion directly applicable to these measurements is as yet available. In the paramagnetic phase a well resolved doublet is obtained. It appears that this doublet must be interpreted as a quadrupole splitting.     

Resolution of a Coulomb reorientation ambiguity in 18O

Elastic scattering data and inelastic excitation of the lowest 2⁺ state in ¹⁸O from 120 MeV ¹⁸O incident on ²⁰⁸Pb are analyzed in coupled channels including couplings to the second 2⁺ state of ¹⁸O. This analysis favors the positive sign for the product of the four E2 matrix elements, p₄ = M₀₁₂₁,M₀₁₂₂M₂₁₂₂M₂₁₂₁ where M_ij = ?〈i∥M(E2)∥j〉. This is in agreement with shell-model calculations.