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A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

Define a valid "coloring" to occur when no two faces with a common edge share the same color. Given two colors, there is a single way to color an octahedron (Ball and Coxeter ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

Wirsing (1974) showed, among other results, that if F_n(x) is the Gauss-Kuzmin distribution, then lim_(n->infty)(F_n(x)-lg(1+x))/((-lambda)^n)=Psi(x), (1) where ...

Consider a set A_n={a_1,a_2,...,a_n} of n positive integer-denomination postage stamps sorted such that 1=a_1<a_2<...<a_n. Suppose they are to be used on an envelope with ...

An algebraic integer of the form a+bsqrt(D) where D is squarefree forms a quadratic field and is denoted Q(sqrt(D)). If D>0, the field is called a real quadratic field, and ...

An aperiodic tiling is a non-periodic tiling in which arbitrarily large periodic patches do not occur. A set of tiles is said to be aperiodic if they can form only ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

The problem of finding the number of different ways in which a product of n different ordered factors can be calculated by pairs (i.e., the number of binary bracketings of n ...

Let the probabilities of various classes in a distribution be p_1, p_2, ..., p_k, with observed frequencies m_1, m_2, ..., m_k. The quantity ...