Counting zero kernel pairs over a finite field

Helmke et al. have recently given a formula for the number of reachable pairs of matrices over a finite field. We give a new and elementary proof of the same formula by solving the equivalent problem of determining the number of so called zero kernel pairs over a finite field. We show that the problem is, equivalent to certain other enumeration problems and outline a connection with some recent results of Guo and Yang on the natural density of rectangular unimodular matrices over F-qx]. We also propose a new conjecture on the density of unimodular matrix polynomials. (C) 2016 Elsevier Inc. All rights reserved.

Tuning Photoluminescence Response by Electric Field in Electrically Soft Ferroelectrics

We show that an electrically soft ferroelectric host can be used to tune the photoluminescence (PL) response of rare-earth emitter ions by external electric field. The proof of this concept is demonstrated by changing the PL response of the Eu3+ ion by electric field on a model system Eu-doped 0.94(Na1/2Bi1/2TiO3)-0.06(BaTiO3). We also show that new channels of radiative transitions, forbidden otherwise, open up due to positional disorder in the system, which can as well be tuned by electric field.