let f, g and h be all entire functions of several complex variables. in this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

There is considerable controversy surrounding the nature of the paramagnetic to ferromagnetic phase transition in La(0.7)Ca(0.3)MnO3. We have used transmission electron microscopy to determine whether the phase transition is first or second order. On warming through the transition point, the ferromagnetic phase retreats from the sample surface as it is replaced by the paramagnetic phase. This c...

The nature of phase separation in Pr(0.5)Sr(0.5)MnO(3) has been probed by linear, as well as nonlinear, magnetic susceptibilities and resistivity measurements across the second order paramagnetic to ferromagnetic transition (T(C)) and first order ferromagnetic to antiferromagnetic transition (T(N)). We found that the ferromagnetic (metallic) clusters, which form at T(C), continuously decrease t...

We consider a mean-field continuum model of classical particles in Rd with Ising or Heisenberg spins. The interaction has two ingredients, a ferromagnetic spin coupling and a spin-independent molecular force. We show that a feedback between these forces gives rise to a first-order phase transition with simultaneous jumps of particle density and magnetization per particle, either at the threshol...

Single phase Eu doped GdMnO3 ceramics were prepared using solid state reaction route. Several different characterization techniques were used to investigate the structural and magnetic properties of the samples, including X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM), Energy Dispersive Spectroscopy (EDX) and Vibrating Sample Magnetometer (VSM). All samples indicated single p...