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 ().

List of The Hunger Games characters

The following is a list of characters in The Hunger Games trilogy, a series of young adult science fiction novels by Suzanne Collins that were later adapted into a series of four feature films.

Main characters

Stono Rebellion

The Stono Rebellion (sometimes called Cato's Conspiracy or Cato's Rebellion) was a slave rebellion that began on 9 September 1739, in the colony of South Carolina. It was the largest slave uprising in the British mainland colonies, with 42-47 whites and 44 blacks killed. The uprising was led by native Africans who were likely from the Central African Kingdom of Kongo. Some of the rebels spoke Portuguese. Their leader Jemmy was a literate slave; in some reports he is referred to as "Cato", and likely was held by the Cato, or Cater, family who lived near the Ashley River and north of the Stono River. He led 20 other enslaved Kongolese, who may have been former soldiers, in an armed march south from the Stono River (for which the rebellion is named). They were bound for Spanish Florida. In an effort to destabilize British rule, the Spanish had promised freedom and land at St. Augustine to slaves who escaped from the British colonies.

Jemmy and his group recruited nearly 60 other slaves and killed some whites before being intercepted and defeated by South Carolina militia near the Edisto River. A group of slaves escaped and traveled another 30 miles (50 km) before battling a week later with the militia. Most of the captured slaves were executed; the surviving few were sold to markets in the West Indies.

Cato (spy)

Cato was an African-American slave who served as an American Patriot spy and courier during the American Revolutionary War. His owner, Hercules Mulligan, was a "sub-agent of the Culper Ring" in New York City. Mulligan's activities began before the Ring was formed and he operated both independently and in connection with the Ring. Cato was a vital associate in Mulligan's activities, often acting as a courier, in part through British-held territory. Historian Paul R. Misencik has written that Cato was a "faithful accomplice" of Mulligan.

An article in the Daughters of the American Revolution Magazine in 1985 stated: "Every estimate of the number of minorities who participated in the American Revolution has been deceptively low...." Cato is among those whose contributions have been mostly overlooked. Other than his intelligence activities with Mulligan, no definite information about him or his life is available.

American Revolution

Early activities

Mulligan had a fashionable clothing business, which, along with his marriage to Elizabeth Sanders, daughter of a Royal Navy admiral, gave him access to officers who would talk to him about military matters. Mulligan was an active member of the Sons of Liberty, and took in Washington's aide Alexander Hamilton when he arrived in New York as a young man in 1773 to attend King's College, later Columbia University. Mulligan later helped Hamilton obtain a commission in the army. Although Mulligan tried to flee New York City after the British occupied it in September 1776, the popular tailor was caught and returned to the city after a brief period of time in detention.