A central problem in approximation theory is to characterize the best approximation of a function by polynomials, or other classes of simple functions, in terms of the smoothness of the function. In this chapter, we study the characterization of the best approximation by polynomials on the sphere. In the classical setting of one variable, the smoothness of a function on 𝕊¹ is described by the modulus of smoothness, defined by the forward difference.

Just as I take the chance that your tarse is as crooked as your soul.” His mouth twitched in amusement. “'Tis straight and strong, as you will likely soon learn. However, you bargained only for my arm and my horse, not my tarse.

When such species as European larch, white pine, or black walnut are widely spaced, in order to promote the most rapid growth, it may be advisable to interspace the area with some more tolerant and slower-growing species.

The advent of rap dance is where the supposedly predominantly male performance characteristic of waack and break dance shifted to include women.