Q: Mac mini connection to Apple monitor with ADC connection

You need to adapt ADC to DVI and then DVI to Mini DisplayPort.

(140884)

http://www.amazon.com/Apple-DVI-ADC-Display-Adapter/dp/B00011KHT2/ref=sr_sp-atf_ title_1_1/179-1314294-8358010?ie=UTF8&qid=1402766343&sr=8-1&keywords=dvi+to+adc+ display+adapter

http://www.amazon.com/Dvi-Adc-Conversion-Box-instock/dp/B0002CZJ7A/ref=sr_sp-atf _title_1_4/179-1314294-8358010?ie=UTF8&qid=1402766343&sr=8-4&keywords=dvi+to+adc +display+adapter

http://www.amazon.com/Dr-Bott-DVIator-US-110V/dp/B000NSGIQO/ref=sr_sp-btf_title_ 1_6/179-1314294-8358010?ie=UTF8&qid=1402766343&sr=8-6&keywords=dvi+to+adc+displa y+adapter

The adopters are not cheap so likely better to get another monitor with a modern connection

Note: Only the adapter given in your 1st link will work, because the other two are not capable of powering the monitor. Apple ADC monitors get their AC power via the ADC connection.