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Let A:D(A)->H and B:D(B)->H be linear operators from domains D(A) and D(B), respectively, into a Hilbert space H. It is said that B extends A if D(A) subset D(B) and if Bv=Av ...

A broad area of mathematics connected with functional analysis, differential equations, index theory, representation theory, and mathematical physics.

The illusion illustrated above in which the bounding rectangle and inner square both appear distorted.

The orchard-planting problem (also known as the orchard problem or tree-planting problem) asks that n trees be planted so that there will be r(n,k) straight rows with k trees ...

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

A topology defined on a totally ordered set X whose open sets are all the finite intersections of subsets of the form {x in X|x>a} or {x in X|x<a}, where a in X. The order ...

The number of nondecreasing lists {a_1,a_2,...,a_n} consisting of n elements 1<=a_i<=k is given by the binomial coefficient N(n,k)=(n+k-1; n-1). For example, there are six ...

A pair of quantities (a, b) where ordering is significant, so (a, b) is considered distinct from (b, a) for a!=b.

An ambiguous term which is sometimes used to mean a partially ordered set and sometimes to mean a totally ordered set.

A rooted tree in which the order of the subtrees is significant. There is a one-to-one correspondence between ordered forests with n nodes and binary trees with n nodes.