Note: The title symbol UVS represents the mathematical expression U=f(V,S). In each case presented, the three-dimensional function is derived by scaling the higher-dimensional precursor using a particular extensive variable. For example, __U__=f(__V__,__S__,N) is scaled by N to give the molar-based function U=f(V,S). The binary second transform __A__´=f(T,*µ*,N_{2},__V__) is scaled by the volume and plotted at a fixed temperature to give the density-based function

but the mathematical expressions usually show the transformed independent variables (*µ*_{i},T,P) first in the argument list.