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We derive Sobolev-type inner products with respect to which hat functions on arbitrary triangulations of domains in R are orthogonal. Compared with linear interpolation, the resulting approximation schemes yield superior accuracy at little extra cost.

We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be ∗-autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. The theory is extremely rich with numerous connections to classical Domain Theory, complete dist...

qi = 1, pA ≥ v ≥ Aq. The number v is known as the value of game. The pair (p, q) is known as an equilibrium for the matrix game. As usual, x ≥ 0 means that every entry of the vector x is ≥ 0. We write y ≤ t for a vector y and a number t if every entry of y is ≤ t. We go even further in abusing notation, denoting by y− t the vector obtaining from y by subtracting t from every entry. Similarly we...