The Distribution of Minimum of Ratios of Two Random Variables and Its Application in Analysis of Multi-hop Systems

The distributions of random variables are of interest in many areas of science. In this paper, ascertaining on the importance of multi-hop transmission in contemporary wireless communications systems operating over fading channels in the presence of cochannel interference, the probability density functions (PDFs) of minimum of arbitrary number of ratios of Rayleigh, Rician, Nakagami-m, Weibull and α-µ random variables are derived. These expressions can be used to study the outage probability as an important multi-hop system performance measure. Various numerical results complement the proposed mathematical analysis

First evidence for charge ordering in NaV2_2O5_5 from Raman spectroscopy

We argue on the basis of symmetry selection rules and Raman scattering spectra that NaV$_2$O$_5$ undergoes a charge ordering phase transition at T$_c$=34 K. Such a transition is characterized by the redistribution of the charges at the phase transition and corresponds to the change of the vanadium ions, from uniform V$^{4.5+}$ to two different V$^{4+}$ and V$^{5+}$ states. In the low temperature phase the V$^{4+}$ ions are forming a "zig-zag" ladder structure along the {\bf b}-axis, consistent with the symmetry of the P2/b space group.Comment: to be published in solid state communication