We consider the problem of bounding the maximum possible number fk,d(n) of k-simplices that are spanned by a set of n pointsin Rd and are similar to a given simplex. We first show that f2,3(n) = O(n13/6), and then tacklethe general case, and show that fd-2, d(n) = O(nd-8/5) and fd-1,d(n) = O*(nd-72/55), for any d.Our technique extends to derive bounds for other valuesof k and d, and we illustrate this by showing that f2,5(n)=O(n8/3).

A binary algorithm for division of an (M + N)-bit integer by an N-bit integer is presented. The algorithm produces the (M + 1)-bit quotient and the N-bit remainder in time O(M + N). Two hardware implementations, one using combinational logic in cellular arrays, and one employing systolic arrays, are given. These implementations are designed for modularity and regularity, and thus are suitable for VLSI systems. An important property of these implementations is that decisions are based on only one bit of the operands. Thus, fan-in and length of connecting wires are bounded independently of operand size. In addition, the systolic implementation has area O + N), which is the best possible.

We discuss a technological means of protecting software from unauthorized duplication and use, which does not at the same time limit its sale or distribution on rely on a trusted authority.