These generating functions depend in a fundamental way on the generating functions of random permutation statistics.

While these two albedos are correlated, the numerical factor between them depends in a very nontrivial way on the surface properties.

The resulting definition, although it involves the choice of basis f, does not actually depend on f in an essential way.

The Cayley graph depends in an essential way on the choice of the set of generators.

But I could not have done so if my life had depended on it-which in a way it did.

This architecture, the "tertiary structure" of molecules, depends in a complicated way on the molecules' basic composition, or "primary structures."

In the SA algorithm, the relaxation time also depends on the candidate generator, in a very complicated way.

The strength of the uncertainty relations depend in a known way on the particular system and the measurements performed on it.

Unlike most theorems in geometry, this result depends in a critical way on the choice of axioms for set theory.

The properties of the spin representations depend, in a subtle way, on the dimension and signature of the orthogonal group.