Isotope

Isotopes are variants of a particular chemical element which differ in neutron number, although all isotopes of a given element have the same number of protons in each atom. The term isotope is formed from the Greek roots isos (ἴσος "equal") and topos (τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table. The number of protons within the atom's nucleus is called atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic number identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number of neutrons. The number of nucleons (both protons and neutrons) in the nucleus is the atom's mass number, and each isotope of a given element has a different mass number.

For example, carbon-12, carbon-13 and carbon-14 are three isotopes of the element carbon with mass numbers 12, 13 and 14 respectively. The atomic number of carbon is 6, which means that every carbon atom has 6 protons, so that the neutron numbers of these isotopes are 6, 7 and 8 respectively.

Mutation (Jordan algebra)

In mathematics, a mutation, also called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and only if the given element is invertible, in which case the mutation is called a proper mutation or an isotope. Mutations were first introduced by Max Koecher in his Jordan algebraic approach to Hermitian symmetric spaces and bounded symmetric domains of tube type. Their functorial properties allow an explicit construction of the corresponding Hermitian symmetric space of compact type as a compactification of a finite-dimensional complex semisimple Jordan algebra. The automorphism group of the compactification becomes a complex subgroup, the complexification of its maximal compact subgroup. Both groups act transitively on the compactification. The theory has been extended to cover all Hermitian symmetric spaces using the theory of Jordan pairs or Jordan triple systems. Koecher obtained the results in the more general case directly from the Jordan algebra case using the fact that only Jordan pairs associated with period two automorphisms of Jordan algebras are required.

Isotope (band)

Isotope was a British jazz-rock band fronted by guitarist Gary Boyle.

Boyle founded the band in June 1972 and a first album, Isotope, was largely composed by keyboardist Brian Miller. Jeff Clyne played bass and Nigel Morris played drums. Clyne and Miller left in 1974, however, and were replaced by Hugh Hopper and Laurence Scott (b. 7 Feb 1946) respectively. After touring, this new line-up recorded the band's second album Illusion. In late 1974 the band appeared on film on BBC 2's The Old Grey Whistle Test playing "Spanish Sun" from the album.

Further touring followed and there were various personnel changes. Deep End was recorded in 1976 with two keyboardists Zoe Kronberger and Frank Roberts. Hopper played on one track, but the bass was otherwise played by Dan K. Brown. Morris Pert also played percussion.

Boyle subsequently focused on a solo career.

Discography