last upper and lower molars. Chumashius balchi cannot, therefore, be regarded as occurring in the direct line of development leading upward to the Recent tarsier. In lower dental formula Chumashius exhibits a closer relationship to Omomys and Hemi4codon than to Anaptomorphus and Tetonius. The character of the lower posterior premolars in Uintanius suffice to remove this Bridger genus from any c...

We study the orthogonal polynomial expansion on sparse grids for a function of d variables in a weighted L space. A fast algorithm is developed to compute the orthogonal polynomial expansion by combining the fast cosine transform, a fast transform from the Chebyshev orthogonal polynomial basis to the orthogonal polynomial basis for the weighted L space, and a fast algorithm of computing hierarc...

For a function f that is piecewise analytic on quasi-smooth arc $$\mathcal {L}$$ and any $$0<\sigma <1$$ we construct sequence of polynomials converge at rate $$e^{-n^{\sigma }}$$ each point analyticity are close to the best polynomial approximants whole . Moreover, give examples when such can be constructed for $$\sigma =1$$