A method for separating a lead radioisotope from a mixture comprising the lead radioisotope and a radioisotope of radium or thorium is provided, along with a system comprising a plurality of chromatographic columns. The system can include a first cartridge having a lead-complexing media that preferentially binds the lead radioisotope over radioisotopes of radium or thorium, and a second cartridge having a weak cationic exchange media, where a pH of a loading solution used to load the second cartridge is pH.sup.2L, and a pH of an eluent used to elute the lead radioisotope from the second cartridge is pH.sup.2E, and pH.sup.2L is greater than pH.sup.2E. The system can also comprise further third and fourth cartridges with chromatographic media to extract and purify the lead radioisotope, to provide a purified solution of lead radioisotope that can be used for medical and other purposes, such as in the labeling of radiopharmaceutical compounds.

A method for direct current (DC)-DC conversion. The method includes converting an input voltage to a set of output voltages by selecting a first output capacitor in a set of output capacitors of a DC-DC converter, charging an inductor of the DC-DC converter, and discharging an electric current passing through the inductor into the first output capacitor. The first output capacitor is selected responsive to a voltage level of the first output capacitor being less than a first reference voltage in a set of reference voltages. The inductor is charged by applying the input voltage to the inductor. The first output capacitor maintains a first output voltage in the set of output voltages.

Parametric Differential Moving Bed named as PDMB, characterizes by obtaining target separation system's elution profile via optimized chromatography's separation parameters between selected solid sorbent and mobile phase; such generalized process employ an apparatus transforming such profile for mass production purpose, wherein disclosed apparatus bypassing imperfections observed in chromatography via new mass transfer equilibrium contact method, differential set-up between two phases, eliminating displacement zone via maintaining installed resin/adsorbent in semi-dry status thus enhancing maximum mass transfer efficiency. Through implementing aforesaid methods, disclosed apparatus further employs single stage recycle procedures to simulate moving beds operation in confined closed loop in differential protocols; which comprise multiple modules sequentially connected, yet each functions independently and simultaneously feeding feed solution, isolating at least one desired component, recycling mobile phase, concentrating multiple isolated components, regenerating adsorbent, washing and sanitizing; apparatus further integrate additional sequential unit operation installing other type solid phase material within.