Group action

In mathematics, a symmetry group is an abstraction used to describe the symmetries of an object. A group action formalizes the relationship between the group and the symmetries of the object. It relates each element of the group to a particular transformation of the object.

In this case, the group is also called a permutation group (especially if the set is finite or not a vector space) or transformation group (especially if the set is a vector space and the group acts like linear transformations of the set). A permutation representation of a group G is a representation of G as a group of permutations of the set (usually if the set is finite), and may be described as a group representation of G by permutation matrices. It is the same as a group action of G on an ordered basis of a vector space.

A group action is an extension to the notion of a symmetry group in which every element of the group "acts" like a bijective transformation (or "symmetry") of some set, without being identified with that transformation. This allows for a more comprehensive description of the symmetries of an object, such as a polyhedron, by allowing the same group to act on several different sets of features, such as the set of vertices, the set of edges and the set of faces of the polyhedron.

Orbit (horse)

Orbit (foaled 1885) was a Thoroughbred racehorse. He was trained at Kingsclere by John Porter for the 1st Duke of Westminster. As a three-year-old he won the Eclipse Stakes.

Breeding

Orbit was the son of Epsom Derby and Champion Stakes winner Bend Or. His dam was Fair Alice, a daughter of July Stakes winner Cambuscan.

Racing career

Orbit won three races as a two-year-old; the Criterion Nursery Handicap at Newmarket, the Kempton Park Champion Nursery Handicap and the Daveridge Stakes. Orbit started his three-year-old career by winning the Craven Stakes at Newmarket by ¾ length from Cotillon. His next race came in the 2000 Guineas at Newmarket. Friar's Balsam started as the 1/3 favourite for the race, with Ayrshire at 100/12 and Orbit at 100/8. Orbit ran on well in the closing stages to finish in third place. Ayrshire won the race by two lengths from Johnny Morgan, who was a head in front of Orbit. After winning the 2000 Guineas win Ayrshire started as the 5/6 favourite for the Epsom Derby and Orbit was second favourite at 11/2. Orbit could only finish in fifth place, over seven lengths behind winner Ayrshire. He then finished second in the Triennial Stakes at Ascot. Orbit started as the 9/4 favourite for the Eclipse Stakes and in the final 100 yards of the race Orbit gradually edged away from stablemate Ossory and beat him by a length.

Orbit (band)

Orbit is a Boston, Massachusetts-based power trio. Formed in 1994, the band went on hiatus in late 2001. Their initial releases were on drummer Buckley's own Lunch Records label before the band moved to major label A&M Records. They completed recording their second major label album, "Guide To Better Living", but it was never released by A&M. The band then moved back to Lunch Records for the rest of their releases.

Perhaps the high point of the band's career was the hit, "Medicine", and their presence on the 1997 Lollapalooza tour. They also had the song, "XLR8R", included on the soundtrack of the PlayStation 2 game, FreQuency.

Orbit played two reunion shows on December 28 and 29, 2007, at the Paradise Rock Club in Boston, MA. They performed with also defunct Boston indie rock group The Sheila Divine.

Orbit performed a show on January 14, 2011, at the Paradise Rock Club in Boston, MA with The Sheila Divine.

Members

Success!

Success! is a musical by Bernard J. Taylor that was first recorded in 1993 as a studio concept album featuring various West End performers including Lon Satton (who created the role of Poppa in Andrew Lloyd Webber's Starlight Express), Claire Moore, Kathryn Evans, Jessica Martin and Maurice Clarke. It had its world premiere stage production in Rotherham, Yorkshire, in 1995.

Following are extracts of some of the reviews:

"Great writers of stage music have always proved themselves to be versatile. In the light of the favourable reaction it received it would have been more than easy for Taylor to follow Wuthering Heights with another show in that same grand scale, but instead he quickly showed his credentials by heading in a totally different direction and in doing so comes up with another admirable piece of work. "Success!" is full of splendid material and is loads of fun." - Mike Gibb, Masquerade, Issue 13, 1993

"An adaptation of the Faust legend, I enjoyed this one very much, and it has some bright, breezy and catchy numbers. I will be surprised if anyone who buys it is disappointed with the standard of the songs." - Terry Wardrope, Words and Music, Issue 17, January 1994.

Success (The Weather Girls album)

Success is a 1983 studio album originally released by American singing duo The Weather Girls. The album includes the group's biggest hit, "It's Raining Men", which peaked at #1 on the U.S. Dance chart, #46 on the U.S. Pop chart, & #34 on the U.S. R&B chart.

Track listing

Production

Personnel

The Weather Girls

Additional personnel

Statlanta

Statlanta is the debut studio album by Atlanta rapper Stat Quo. First recorded and set to be released in 2003, under Shady Records, Aftermath Records and Interscope Records with mentors Eminem and Dr. Dre as executive producers, it was reworked in 7 years not featuring any of the original material recordings, it was released on July 13, 2010 under Sha Money XL's Dream Big Ventures label after many push-backs.

Statlanta debuted at #85 on Billboard's Top R&B/Hip-Hop Albums chart.

Production and guests

Statlanta features production from Sha Money XL, Needlz, S1, Boi-1da, Stat Quo himself, among others. Featured guests include Marsha Ambrosius, Antonio McLendon, Brevi, Esthero, Raheem DeVaughn, Devin the Dude, and Talib Kweli. Former mentor Dr. Dre was involved since the recording process, and served as production consultant-supervisor, he helped Stat Quo along with Aftermath producer Mike Chav to materialize the album.

A leftover recorded track, entitled "Atlanta on Fire" that features Eminem, does not appear on the album. It has been leaked on the internet before the album was released years later.