Determine the equilibrium percentages of α-D-fructose and β-D-fructose using their specific rotations. The specific rotation of α-D-fructose is +92°, that of β-D-fructose is +18°, and the equilibrium mixture has a specific rotation of +38.5°.

Propose a mechanism for the transformation of α-D-mannopyranose to β-D-mannopyranose under basic conditions.