Island

An island /ˈaɪlənd/ or isle /ˈaɪl/ is any piece of sub-continental land that is surrounded by water. Very small islands such as emergent land features on atolls can be called islets, skerries, cays or keys. An island in a river or a lake island may be called an eyot or ait, or a holm. A grouping of geographically or geologically related islands is called an archipelago, e.g. the Philippines.

An island may be described as such despite the presence of an artificial land bridge, for example Singapore and its causeway, or the various Dutch delta islands, such as IJsselmonde. Some places may even retain "island" in their names for historical reasons after being connected to a larger landmass by a wide land bridge, such as Coney Island or Coronado Island. Conversely, when a piece of land is separated from the mainland by a man-made canal, for example the Peloponnese by the Corinth Canal, it is generally not considered an island.

There are two main types of islands: continental islands and oceanic islands. There are also artificial islands.

Islands (Mike Oldfield album)

Islands is the 11th album by Mike Oldfield, released in 1987 by Virgin. Guest singers on the album are Bonnie Tyler, Kevin Ayers, Anita Hegerland and Jim Price. A different track list and cover was used for the American edition.

Music videos, producers and singers

Islands was also released as a full-length VHS video album. For each track a video was made and released, often mixing state of the art (for the time) computer-generated images with real life images. This was released as part of The Wind Chimes.

The album boasts the largest number of co-producers out of all of Oldfield's work; production was handled by Michael Cretu (later of Enigma fame), Geoffrey Downes, Tom Newman, Simon Phillips, Alan Shacklock and Oldfield himself. Singers on the album are Bonnie Tyler, Kevin Ayers, Anita Hegerland and Jim Price.

Album artwork

The UK front cover artwork was of a tropical island, and hidden in the surrounding sea is a large number of hand shapes. The hand images are based on a still frame from the longform video released at the same time as the album; a couple of scenes in the video, which was mainly filmed in Bali, feature a group of natives performing a ritualistic dance which involves hand-waving movements. The American cover is completely different; it displays two cube shapes. The photography on the back of the US version was by Jerry Uelsmann.

Islands (King Crimson album)

Islands is the fourth studio album by King Crimson, released December 1971. Islands would be the last King Crimson studio album before the group's trilogy of Larks' Tongues in Aspic, Starless and Bible Black and Red. It's also the last to feature the lyrics of Peter Sinfield.

Production & Release

The harmonic basis for the tune "The Letters" is derived from the Giles, Giles and Fripp song "Why Don't You Just Drop In," available on The Brondesbury Tapes compilation. The bridge section is also taken from the King Crimson version of the song, performed by the original line-up, titled simply "Drop In" and later released on the live-album Epitaph. The original basis for the song "Prelude: Song of the Gulls" is derived from the Giles, Giles and Fripp song "Suite No. 1". The first vinyl release of the album features a hidden track. At the end of side two there is a recording of studio chatter followed by Fripp saying, among other things, "...What we're going to do, umm... do it twice more, once with the oboe, once without it, and then... we finish." This was included on the initial CD release but was accidentally left off the first pressings of the 1989 Definitive Edition CD remaster. It was restored on all subsequent reissues.

*-algebra

In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.

Terminology

*-ring

In mathematics, a *-ring is a ring with a map * : A → A that is an antiautomorphism and an involution.

More precisely, * is required to satisfy the following properties:

for all x, y in A.

This is also called an involutive ring, involutory ring, and ring with involution. Note that the third axiom is actually redundant, because the second and fourth axioms imply 1* is also a multiplicative identity, and identities are unique.

Ringtone

A ringtone or ring tone is the sound made by a telephone to indicate an incoming call or text message. Not literally a tone nor an actual (bell-like) ring any more, the term is most often used today to refer to customizable sounds used on mobile phones.

Background

A phone “rings” when its network indicates an incoming call and the phone thus alerts the recipient. For landline telephones, the call signal can be an electric current generated by the switch or exchange to which the telephone is connected, which originally drove an electric bell. For mobile phones, the network sends the phone a message indicating an incoming call. The sound the caller hears is called the ringback tone, which is not necessarily directly related.

The electromagnetic bell system is still in widespread use. The ringing signal sent to a customer's telephone is 90 volts AC at a frequency of 20 hertz in North America. In Europe it is around 60-90 volts AC at a frequency of 25 hertz. Some non-Bell Company system party lines in the US used multiple frequencies (20/30/40 Hz, 22/33/44 Hz, etc.) to allow "selective" ringing.

Sigma-ring

In mathematics, a nonempty collection of sets is called a σ-ring (pronounced sigma-ring) if it is closed under countable union and relative complementation.

Formal definition

Let be a nonempty collection of sets. Then is a σ-ring if:

if for all

if

Properties

From these two properties we immediately see that

This is simply because .

Similar concepts

If the first property is weakened to closure under finite union (i.e., whenever ) but not countable union, then is a ring but not a σ-ring.

Uses

σ-rings can be used instead of σ-fields (σ-algebras) in the development of measure and integration theory, if one does not wish to require that the universal set be measurable. Every σ-field is also a σ-ring, but a σ-ring need not be a σ-field.

A σ-ring that is a collection of subsets of induces a σ-field for . Define to be the collection of all subsets of that are elements of or whose complements are elements of . Then is a σ-field over the set . In fact is the minimal σ-field containing since it must be contained in every σ-field containing .

Interlude

Interlude may refer to:

Film

Music