Combinatorial commutation properties for reordering a sequence consisting of two kinds of steps, and for separating the well-foundedness of their combination into well-foundedness of each, are investigated. A weak commutation property, called “jumping”, along with a weakened version of the lifting property, called “escaping” and requiring only an eventual lifting, are used for proving wellfound...

We provide a complete spectral characterization of the double commutation method for general Sturm-Liouville operators which inserts any finite number of prescribed eigenvalues into spectral gaps of a given background operator. Moreover, we explicitly determine the transformation operator which links the background operator to its doubly commuted version (resulting in extensions and considerabl...

A method and system are proposed for a transient-free commutation of a resonant-mode array of inductors. A single capacitor is used to tune the entire array, and triacs are used to commutate the inductors. To avoid the transients, the tuning capacitor is electrically locked when it stores the whole energy of the excited circuit. This prevents the capacitor from discharge during the fast, 0.1 ms...