oh...I used jump wire to hook the (+) from a 12V battery to 7805 input, and the battery (-) to 7805 ground, and have BNC hooked up the the device that will be driven by uno. This setting seems to be fine with a very brief charge.
btw, what would be the potential harm by missing capacities?? I really have to think about it seriously, given the power source is very expensive. And do you think it's necessary to add another capacitor between 7805 ground and -28V??