Duality (mathematics)In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself. For example, Desargues' theorem is self-dual in this sense under the standard duality in projective geometry. In mathematical contexts, duality has numerous meanings.
Independent set (graph theory)In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set of vertices such that for every two vertices in , there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in . A set is independent if and only if it is a clique in the graph's complement. The size of an independent set is the number of vertices it contains. Independent sets have also been called "internally stable sets", of which "stable set" is a shortening.
Beal conjectureThe Beal conjecture is the following conjecture in number theory: If where A, B, C, x, y, and z are positive integers with x, y, z ≥ 3, then A, B, and C have a common prime factor. Equivalently, The equation has no solutions in positive integers and pairwise coprime integers A, B, C if x, y, z ≥ 3. The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed proof of this conjecture or a counterexample.
Marine VHF radioMarine VHF radio is a worldwide system of two way radio transceivers on ships and watercraft used for bidirectional voice communication from ship-to-ship, ship-to-shore (for example with harbormasters), and in certain circumstances ship-to-aircraft. It uses FM channels in the very high frequency (VHF) radio band in the frequency range between 156 and 174 MHz, inclusive, designated by the International Telecommunication Union as the VHF maritime mobile band.
Leased lineA leased line is a private telecommunications circuit between two or more locations provided according to a commercial contract. It is sometimes also known as a private circuit, and as a data line in the UK. Typically, leased lines are used by businesses to connect geographically distant offices. Unlike traditional telephone lines in the public switched telephone network (PSTN) leased lines are generally not switched circuits, and therefore do not have an associated telephone number.
