On a class of translation planes of square order

AbstractA class of translation planes of order q2, where q = pr, p is a prime, p ⩾7, p ≠± 1 (mod 10) and r is an odd natural number is constructed and the translation complements of these planes are determined. A property shared by all these planes is that the translation complement fixes a distinguished point and divides the remaining distinguished points into two orbits of length q and q2 − q. The order of the translation complement is rq(q − 1)2 except for q = 7 and q = 13. The translation complements of these exceptional cases are also briefly studied. The class of planes considered in this paper are distinct from the classes of translation planes of S.D. Cohen and M.J. Ganley [Quart. J. Math. Oxford, 35 (1984) 101–113]

Effect of sintering temperature on electrical transport properties of La<SUB>0.67</SUB>Ca<SUB>0<SUB>.33</SUB></SUB>B>MnO<SUB>3</SUB>

A systematic investigation of lanthanum-based manganite, La0.67Ca0.33MnO3, has been undertaken with a view to understand the influence of varying crystallite size, in the nanoscale, on various physical properties. The materials were prepared by the sol-gel route by sintering at four different temperatures starting from 800 to 1100 &#176; C, with an interval of 100 &#176;C. After the usual characterization of these materials structurally by XRD, their metal-insulator transition (TP) as well as magnetic transition (TC) temperatures were determined. Surprisingly these materials are found to exhibit two different types of behaviors, viz, while TC is found to decrease from 253 to 219 K, TP is increasing from 145 to 195 K with increasing sintering temperature. A systematic study of electrical conductivity of all four materials was undertaken not only as a function of temperature (80-300 K), but also as a function of magnetic field up to 7 T mainly to understand the detailed conduction mechanism in these materials. On analyzing the data by using several theoretical models, it has been concluded that the metallic (ferromagnetic) part of the resistivity (&#961;) (below TP) fits well with the equation &#961;(T)=&#961;0+&#961;2.5T2.5, indicating the importance of grain/domain boundary effects (&#961;0) and electron-magnon scattering processes (~T2.5). On the other hand, in the high temperature (T&gt;TP) paramagnetic insulating regime, the adiabatic small polaron and VRH models fit well in different temperature regions, thereby indicating that polaron hopping might be responsible for the conduction mechanism