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 ().

SUR

Sur may refer to:

Acronym

SUR may refer to:

In music, film and other media

Fili

A fili was a member of an elite class of poets in Ireland, up until the Renaissance, when the Irish class system was dismantled by the English.

Etymology

The word "file" is thought to derive from the Proto-Celtic *widluios, meaning "seer, one who sees" (attested on the Gaulish inscription from Larzac as "uidluias", which is the feminine genitive singular form), derived ultimately from the verb *widlu-, "to see". This may suggest that the filí were originally prophetic poets, who foretold the future in the form of verse or riddle, rather than simply poets.

Elite scholars

According to the Textbook of Irish Literature, by Eleanor Hull:

Oral tradition

The fili maintained an oral tradition that predated the Christianization of Ireland. In this tradition, poetic and musical forms are important not only for aesthetics, but also for their mnemonic value. The tradition allowed plenty of room for improvisation and personal expression, especially in regard to creative hyperbole and clever kenning. However, the culture placed great importance on the fili's ability to pass stories and information down through the generations without making changes in those elements that were considered factual rather than embellishment.