For a function from the unit interval to itself with constant slope and one discontinuity, the itineraries of the point of discontinuity are called the critical itineraries. These critical itineraries play a significant role in the study of β-expansions (with positive or negative β) and fractal transformations. A combinatorial characterization of the critical itineraries of such functions is pr...

Recent high-pressure experiments have led to the conclusion that water release from subducted sediments lying under continents in subduction regions occurs at about 220 km depth. This dehydration reaction is in good agreement with the seismological signature of the discontinuity indicating that sediment dehydration causes the Lehmann discontinuity in