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For all integers n and nonnegative integers t, the harmonic logarithms lambda_n^((t))(x) of order t and degree n are defined as the unique functions satisfying 1. ...

The construction of polyhedra using identical building blocks. The illustrations above show such constructions for the cuboctahedron, octahedron rhombic dodecahedron, and ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

Extend Hilbert's inequality by letting p,q>1 and 1/p+1/q>=1, (1) so that 0<lambda=2-1/p-1/q<=1. (2) Levin (1937) and Stečkin (1949) showed that (3) and ...

Define F(1)=1 and S(1)=2 and write F(n)=F(n-1)+S(n-1), where the sequence {S(n)} consists of those integers not already contained in {F(n)}. For example, F(2)=F(1)+S(1)=3, so ...

The pair of sequences defined by F(0)=1, M(0)=0, and F(n) = n-M(F(n-1)) (1) M(n) = n-F(M(n-1)). (2) The first few terms of the "male" sequence M(n) for n=0, 1, ... are 0, 0, ...

There are two possible definitions: 1. Possessing similarity of form, 2. Continuous, one-to-one, in surjection, and having a continuous inverse. The most common meaning is ...

Given a sum and a set of weights, find the weights which were used to generate the sum. The values of the weights are then encrypted in the sum. This system relies on the ...

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

Informally, an L^2-function is a function f:X->R that is square integrable, i.e., |f|^2=int_X|f|^2dmu with respect to the measure mu, exists (and is finite), in which case ...