Infima and complements in the lattice of quasi-uniformities

We show that the infimum of any family of proximally symmetric quasi-uniformities is proximally symmetric, while the supremum of two proximally symmetric quasi-uniformities need not be proximally symmetric. On the other hand, the supremum of any family of transitive quasi-uniformities is transitive, while there are transitive quasi-uniformities whose infimum with their conjugate quasi-uniformity is not transitive. Moreover we present two examples that show that neither the supremum topology nor the infimum topology of two transitive topologies need be transitive. Finally, we prove that several operations one can perform on and between quasi-uniformities preserve the property of having a complement.     

Optimized Pump Power Ratio on 2nd Order Pumping Discrete Raman Amplifier

By optimizing pump power ratio between 1st order backward pump and 2nd order forward pump on discrete Raman amplifier, we demonstrated over 2dB noise figure improvement without excessive non-linearity degradation.