Partitioning the edges of a graph

For any integer m (≥2), it is known that there are simple graphs of maximum valence m whose edges cannot be coloured with m colours in such a way that adjacent edges shall have different colours. We find those values of m and k for which it is true that every simple graph whose maximum valence does not exceed mk can be coloured with m colours in such a way that no colour appears more than k times at any vertex.     

Reversible hypergroups

Using the properties of the characters of a finite group as a prototype, a new notion of a reversible hypergroupH is introduced which takes account of degrees and multiplicities. Many properties of finite abelian groups have analogues for reversible hypergroups. For example, the hypergroup algebra CH is defined by analogy with a group algebra. Using the representations of this algebra, reversible hypergroups are shown to be in one-to-one correspondence with abstract «character tables» (of which Brauer’s «pseudo groups» are examples). These possess the usual orthogonality relations, whether or not they are character tables of groups. Examples are given of reversible hypergroups which are not isomorphic with the set of characters of any finite group.     

Operational features and microwave characteristics of the VircatorII experiment

The Vircator II oscillating virtual-cathode microwave source operates with diode voltages between 600 and 800 kV and diode current between 50 and 120 kA. Maximal microwave output power between 200 and 500 MW is achieved when the diode aspect ratio, cathode surface, charge voltage, and extraction coupling are arranged to simultaneously (1) maximize diode voltage, (2) satisfy magnetic insulation criteria, (3) avoid nonuniform or unstable electron emission, and (4) optimize microwave transmission from the virtual cathode to the launching antenna. Broadband radiation between 0.4 and 5.5 GHz is generated. The central frequency follows the beam plasma frequency. It is tuned by varying the current density with anode-cathode gap adjustments     

Heterolayer mobility in the Bloch-Grüneisen range

It is shown that, for two-dimensional heterolayer conduction at low temperatures, the phonon-scattering contribution to the reciprocal of the ohmic mobility has a Bloch-Grüneisen regime, for low enough temperatures T, in which the deformation coupling gives a term proportional to T⁷ and (for polar semiconductors) piezoelectric coupling gives a term proportional to T⁵. It is pointed out that there could be an intermediate temperature range with a slower T dependence.     

Neutral K1(890) and ρ0 meson production in e+e− annihilation at ;s=29GeV

The production of neutral K¹(890) and ρ⁰ mesons was studied in e⁺e^? annihilation at $\text{s}\text{=29}\text{GeV}$ using the High Resolution Spectrometer at PEP. Differential cross sections are presented as a function of the scaled energy variable z and compared to π⁰ and K⁰ production. The measured multiplicities are 0.84±0.08 ?⁰ mesons and $\text{0.57±0.09 K}{}^{10}\text{(890)}$ mesons per event for a meson momentum greater than 725 MeV/c. The ratios of vector meson to pseudoscalar meson production for (u,d), s and c quark are compared to predictions of the Lund model.     

An interpretation of structural sorting diagrams for AB type compounds using molecular orbital ideas

The factors governing the structure adopted by a particular AB compound are investigated by deriving two parameters reflecting aspects of the interaction between A and B, using simple molecular orbital ideas, which can be quantified by use of atomic parameters derived from pseudopotential theory. A plot of the values of these two parameters, for a large database of compounds, produces a remarkable topological clustering of AB compounds with the same structure. This structural sorting can also be effected for nonoctet AB compounds if the number of electrons is taken into account. These parameters are related to other indices, R_σ, R_π, previously used by Bloch, Zunger, Phillips et al. to construct structural sorting diagrams. Hence we find a justification for the success of such displays, and shed light on the reasons underpinning structural preference, in terms of the number of valence electrons, and the relative positions of the energy levels of the constituent atoms. There appear to be strong similarities between the electronic reasons behind atomic site preferences in molecules and this site preference or coordination number problem in solids.