Quasigroup

In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that they need not be associative.

A quasigroup with an identity element is called a loop.

Definitions

There are at least two equivalent formal definitions of quasigroup. One defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. We begin with the first definition.

A quasigroup (Q, ∗) is a set, Q, with a binary operation, ∗, (that is, a magma), obeying the Latin square property. This states that, for each a and b in Q, there exist unique elements x and y in Q such that both

hold. (In other words: Each element of the set occurs exactly once in each row and exactly once in each column of the quasigroup's multiplication table, or Cayley table. This property ensures that the Cayley table of a finite quasigroup is a Latin square.)

Loop (knot)

In reference to knots, loop may refer to:

References

Turn (biochemistry)

A turn is an element of secondary structure in proteins where the polypeptide chain reverses its overall direction. For beta turns go to Beta turn.

Definition

According to one definition, a turn is a structural motif where the C^α atoms of two residues separated by few (usually 1 to 5) peptide bonds are close (< 7 Å), while the residues do not form a secondary structure element such as an alpha helix or beta sheet with regularly repeating backbone dihedral angles. Although the proximity of the terminal C^α atoms usually correlates with formation of a hydrogen bond between the corresponding residues, a hydrogen bond is not a requirement in this turn definition. That said, in many cases the H-bonding and C^α-distance definitions are equivalent.

Types of turns

Turns are classified according to the separation between the two end residues:

In an α-turn the end residues are separated by four peptide bonds ().

In a β-turn (the most common form), by three bonds ().

In a γ-turn, by two bonds ().

Saint

A saint is a person who is recognized as having an exceptional degree of holiness, or likeness to God. While the English term "saint" originated in Christianity, historians of religion now use the appellation "in a more general way to refer to the state of special holiness that many religions attribute to certain people," with the Jewish Tzadik, the Islamic Mu'min, the Hindu rishi or Sikh guru, and the Buddhist arhat or bodhisattva also being referred to as "saints". Depending on the religion, saints are recognized either by official ecclesiastical declaration/denomination or by popular acclamation (see folk saints).

In Christianity, "saint" has a wide variety of meanings, depending on the context and denomination. The original Christian denotation was any believer who is "in Christ" and in whom Christ dwells, whether in Heaven or on earth. In Eastern Orthodox and Roman Catholic doctrine, all of their faithful deceased in Heaven are considered to be saints, but some are considered worthy of greater honor, emulation, or veneration, with official ecclesiastical recognition given to some saints by canonization or glorification.

Saint (song)

"Saint", stylized as (s)AINT, is a song written by Marilyn Manson in 2003 for the album The Golden Age of Grotesque. Marilyn Manson portrays himself in the music video. The video was shot over a period of two days in November 2003 at the Sunset Tower, a hotel in Los Angeles, California. It was directed by Asia Argento, who guest stars in the video along with Eric Szmanda & former band member Gidget Gein whose "In Case of Emergency Break Heart" sculpture is featured in the video. The sculpture is an edition of three,the one in the video being owned by Asia Argento and the other is owned by artist and friend of Gidget Gein, Damian Crowley and the third version is owned by UnPOP art movement co-founder and friend Aaron Partridge.

Along with the release of the album, Lest We Forget, Manson released a single DVD with the uncut, banned from the label, original version of the music video. The only way to receive this though was to order it through Manson's website. It came also with the CD/DVD package. The explicit version of the DVD was released with the (s)AINT video in Australia and Europe. Japan required an edited version of the video due to censorship laws on showing female genitalia in media.

Saint (comics)

Saint, in comics, may refer to:

It may also refer to:

See also

References