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We construct quark mixing matrices within a group theoretic framework which is easily applicable to any number of generations. Familiar cases are retrieved and related, and it is hoped that our viewpoint may have advantages both phenomenologically and for constructing underlying mass matrix schemes.

Materials with halide perovskite-type layer structures like K,MnF,, Rb,MnCl,, (CH,NH,),MnCI,, (C,H,NH,)MnCI, etc are of current interest for essentially three reasons:(i) These materials are nearly ideal two-deminsional magnetic materials.(ii) Materials with organic ions (C,H,, + 1NH3)i undergo several structural phase transitions due to orientation and reorientation of the organic ions.(iii) They are, as layer structures, interesting from the lattice dynamical point of view, especially with respect to the ratio of interlayer and intralayer forces.In this paper we will concentrate on (iii). on the lattice dynamics, and present a rigid-ion model calculation for the high-temperature phase of (CH,NH,),MnCl, (MAMC) with the K Z MnF, structure (Dil). The short-range forces are assumed to be axially symmetric. The 11 disposible parameters of the model are fitted to experimental data, i.e. the frequencies of IR and Raman-active phonons, and to neutron scattering data. Macroscopically, these materials are very similar to other layered materials. They crystallise in platelets and can easily be cleaved parallel to their major faces (perpendicular to the c axis). Microscopically, the layers consist of a two-dimensional array of MnCI, octahedra. The high-temperature phase of MAMC is characterised by a disorder of the orientation of the organic ions. For our model, we assume each ion to be located at the symmetrised average position. Further, the organic ions are treated as rigid bodies since we are not interested in their internal modes.The results of our model calculation confirm in MAMC the lattice dynamics are more or less three-dimensional and that the interlayer forces are of the same magnitude as the intralayer forces. Our conclusion is that the three-dimensional lattice dynamical behaviour of these layered materials is due to the importance of long-range Coulomb forces in these ionic compounds.

The far-infrared and infrared reflection spectra of TI,Ba,Ca,Cu,O,, superconducting film are reported in this paper. It is found there are three sharp reflection edges in both the superconducting and normal states, their positions being near % 150, % 350 and % 600 cm-'. We attribute these reflection spectra to the Drude free carriers and a wide mid-infrared absorption band. When the incident angle increases from 7" to 30" , some additional structures appear in the reflection spectra, which are the A,, phonon modes vibrating along c-axis. PACC: 7400; 7475; 7830Ye Hong-juan et al. Vol. 1 at zero frequency, and some mid-infrared absorption whose origin is not yet clear. There are three reflection edges in both superconducting and normal states, which do not shift. This behavior is similar to that for other oxide superconductors. How to interpret the mid-infrared absorption and lack of shift of reflection edges requires further investigation.

Two separate aspects of beams of rectangular cross section have been considered, namely the maximum space-charge-limited current which can be passed through rectangular slot apertures, and the maximum current density which can be obtained in collimated and focused beams. Both these limiting effects must be considered when attempting to maximize the current in beams of rectangular cross section. In both cases it has been found that the maximum current density is approximately the same for doubly focused rectangular beams, for singly focused ribbon beams, and for axially symmetric beams.