When you are immobilizing an enzyme, there are several things to consider. First is how much enzyme you loaded. Second is how much enzyme leaches from the nanoparticle and is therefore not useful even though it was briefly immobilized. Finally, the activity of the remaining enzyme. Frequently, enzymes lose some activity during immobilization.

I think activity yield is probably a measure of how much substrate is converted per amount of enzyme loaded per volume per period of time (M substrate/(M enzyme*volume*time)). With that in mind, I think activity recovery is a comparison between the activty yield of the immobilized enzyme and the activiy yield of the free enzyme. As Shelley Minteer^ says, many immobilization processes result in a reduction of enzyme activity.

yes yield =recovery

you can calculate this parameter by dividing the total activity after purification over the total activity before (*100). sure some enzyme molecules will lost during purification thus always yield or recovery decreases.as you proceed in further purification steps.