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 ().

Progressive outer retinal necrosis

Progressive outer retinal necrosis, also known as Varicella zoster virus retinitis (VZVR), is an aggressive, necrotizing inflammation of the eye's retina caused by herpes varicella zoster virus. It is typically found in people with advanced AIDS, but has also been reported in those who are severely immunocompromised due to chemotherapy.

The majority of those with progressive outer retinal necrosis develop severe vision loss and blindness. Systemic antiviral drugs may improve the long-term visual outcome in those with the disease.

See also

References