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.)
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 Cα 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 Cα 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 Cα-distance definitions are equivalent.
Types of turns
Turns are classified according to the separation between the two end residues:
).
).
).Torched
Torched may refer to:
See also
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