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 ().

Sire (woreda)

Sire is one of the woredas in the Oromia Region of Ethiopia. It's part of the Arsi Zone. It is part of former Dodotana Sire woreda. The administrative center of woreda is Sire.

Demographics

The 2007 national census reported a total population for this woreda of 73,970, of whom 37,812 were men and 36,158 were women; 8,376 or 11.32% of its population were urban dwellers. The majority of the inhabitants said they practised Ethiopian Orthodox Christianity, with 51.61% of the population reporting they observed this belief, while 44.46% of the population were Muslim, and 3.76% of the population were Protestant.

Notes

Sire (novel)

Sire is a 1991 novel by the French write Jean Raspail. It tells the story of how monarchy returns to France as the 18-year-old Philippe Pharamond de Bourbon ascends the throne in 1999. The novel received the Grand prix du roman de la Ville de Paris and the Alfred de Vigny Prize.

References

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