Associator

In abstract algebra, the term associator is used in different ways as a measure of the nonassociativity of an algebraic structure.

Ring theory

For a nonassociative ring or algebra , the associator is the multilinear map given by

Just as the commutator measures the degree of noncommutativity, the associator measures the degree of nonassociativity of . It is identically zero for an associative ring or algebra.

The associator in any ring obeys the identity

The associator is alternating precisely when is an alternative ring.

The associator is symmetric in its two rightmost arguments when is a pre-Lie algebra.

The nucleus is the set of elements that associate with all others: that is, the n in R such that

It turns out that any two of being implies that the third is also the zero set.

Quasigroup theory

A quasigroup Q is a set with a binary operation such that for each a,b in Q, the equations and have unique solutions x,y in Q. In a quasigroup Q, the associator is the map defined by the equation

Nucleus (Anekdoten album)

Nucleus is the second full-length studio album by the Swedish progressive rock band Anekdoten. The album was released in 1995.

Track list

Personnel

Additional personnel:

References

External links

Nucleus (Sonny Rollins album)

Nucleus is an album by jazz saxophonist Sonny Rollins, released on the Milestone label in 1975, featuring performances by Rollins with George Duke, Raul de Souza, Bennie Maupin, Chuck Rainey, Eddie Moore, Mtume, Bob Cranshaw and Roy McCurdy. It was recorded at Fantasy Studios, Berkeley, CA, on September 2–5, 1975.

Reception

The Allmusic review by Scott Yanow states: "This funky date has its moments (including an updated version of "My Reverie") but falls far short of hinting at any new innovations." Music critic Robert Christgau praised the album, writing: "This is as rich an r&b saxophone record as I know, combining repetition and invention, melodies recalled and melodies unimaginable, in proportions that define the difference between selling out and reaching out.... If you really believe you don't like 'jazz,' this is as good a place to start as any."

Track listing

All compositions by Sonny Rollins except as indicated.

Indigo (Warner novel)

Indigo is a novel written by Marina Warner, published by Simon & Schuster in 1992 (ISBN 0-671-70156-8). It is a modernized and altered retelling of William Shakespeare's, The Tempest. Within the novel, Warner appropriates Shakespeare's original plot and characters to fit a dual reality, spanning the 17th and 20th Centuries, and the colonial sphere of the Caribbean alongside post-colonial London. She expands certain characters, for example, Sycorax, Shakespeare's dark witch, is given her own identity as indigo maker and village sage. The colonialist realities of 'discovery' and the conquering of 'new' lands are played out in the novel's first section. Finally, the characters of Miranda and Caliban (recreated as Dulé and George/Shaka) are unified in a shared acknowledgement of past colonial wrongs.

Further reading

Windows Communication Foundation

The Windows Communication Foundation (or WCF), previously known as "Indigo", is a runtime and a set of APIs in the .NET Framework for building connected, service-oriented applications.

The architecture

WCF is a tool often used to implement and deploy a service-oriented architecture (SOA). It is designed using service-oriented architecture principles to support distributed computing where services have remote consumers. Clients can consume multiple services; services can be consumed by multiple clients. Services are loosely coupled to each other. Services typically have a WSDL interface (Web Services Description Language) that any WCF client can use to consume the service, regardless of which platform the service is hosted on. WCF implements many advanced Web services (WS) standards such as WS-Addressing, WS-ReliableMessaging and WS-Security. With the release of .NET Framework 4.0, WCF also provides RSS Syndication Services, WS-Discovery, routing and better support for REST services.

Indigo (Never Shout Never album)

Indigo is the fourth studio album by the American pop band Never Shout Never. It was released on November 13, 2012 by Loveway Records. The album features the band recording as a whole for the second time; the first being in Time Travel. A bonus track was made available through some media outlets and also on the limited edition cassette tape. The album debuted at number 194 on the Billboard 200.

Background

"I feel like without music I really don't have any purpose in this life. [Indigo] is kind of me rediscovering that drive to make music that makes people feel good."

Recording

Christofer Ingle originally wanted to record every song with a different producer, all in different cities, to give each song a unique feel and its own style. The album would also include reworkings of "On The Brightside" and "Trouble."

For the recording of Indigo, Never Shout Never had recorded at Studio 2100 in Springfield, Missouri.

Release and promotion

Never Shout Never announced on February 8, 2012 that their then-titled Good Times would be released sometime in the summer of 2012. Ingle announced on Twitter that the album would be out by late fall. Ingle demoed the new songs through Loveway Records' Stickam page on June 4, 2012.

Tone (musical instrument)

Tone and sound are terms used by musicians and related professions to refer to the audible characteristics of a player's sound. Tone is the product of all influences on what can be heard by the listener, including the characteristics of the instrument itself, differences in playing technique (e.g. embouchure for woodwind and brass players, fretting technique or use of a slide in stringed instruments, or use of different mallets in percussion), and the physical space in which the instrument is played. In electric and electronic instruments, tone is also affected by the amplifiers, effects, and speakers used by the musician. In recorded music, tone is also influenced by the microphones, signal processors, and recording media used to record, mix, and master the final recording, as well as the listener's audio system.

Stringed instruments

The tone of a stringed instrument is influenced by factors related to construction and player technique. The instrument's shape, particularly of its resonant cavity, as well as the choice of tonewood for the body, neck, and fingerboard, are all major determinants of its tone. The material and age of the strings is also an important factor. Playing technique also influences tone, including subtle differences in the amount of pressure applied with the fretting hand, picking or bowing intensity, use of muting and/or drone techniques.