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 ().

Coppélia

Coppélia is a comic ballet originally choreographed by Arthur Saint-Léon to the music of Léo Delibes, with libretto by Charles-Louis-Étienne Nuitter. Nuitter's libretto and mise-en-scène was based upon two stories by E. T. A. Hoffmann: Der Sandmann (The Sandman) and Die Puppe (The Doll). In Greek, κοπελιά means girl, young lady. Coppélia premiered on 25 May 1870 at the Théâtre Impérial l'Opéra, with the 16-year-old Giuseppina Bozzacchi in the principal role of Swanhilde. Its first flush of success was interrupted by the Franco-Prussian War and the Siege of Paris (which also led to the early death of Giuseppina Bozzacchi, on her 17th birthday), but eventually it became the most-performed ballet at the Opéra.

Modern-day productions are traditionally derived from the revivals staged by Marius Petipa for the Imperial Ballet of St. Petersburg in the late 19th century. Petipa's choreography was documented in the Stepanov method of choreographic notation at the turn of the 20th century. These notations were later used to stage the St. Petersburg version for such companies as the Vic-Wells Ballet (precursor of today's Royal Ballet).

RuneScape

RuneScape is a fantasy massively multiplayer online role-playing game (MMORPG) developed and published by Jagex, released originally in January 2001. RuneScape is a graphical browser game implemented on the client-side in Java, and incorporates 3D rendering. The game has had over 200 million accounts created and is recognised by the Guinness World Records as the world's largest free MMORPG and the most-updated game.

RuneScape takes place in the world of Gielinor, a medieval fantasy realm divided into different kingdoms, regions, and cities. Players can travel throughout Gielinor via a number of methods including on foot, magical spells, or charter ships. Each region offers different types of monsters, resources, and quests to challenge players. The game's fictional universe has also been explored through a tie-in video game on another of its maker's websites, FunOrb, Armies of Gielinor, and the novels Betrayal at Falador,Return to Canifis, and Legacy of Blood.

Players are represented in the game with customisable avatars. RuneScape does not follow a linear storyline; rather, players set their own goals and objectives. Players can choose to fight non-player character (NPC) monsters, complete quests, or increase their experience in the available skills. Players interact with each other through trading, chatting, or by participating in mini-games and activities, some of which are competitive or combative in nature, while others require cooperative or collaborative play.

Prayer for relief

A prayer for relief, in the law of civil procedure, is a portion of a complaint in which the plaintiff describes the remedies that the plaintiff seeks from the court. For example, the plaintiff may ask for an award of compensatory damages, punitive damages, attorney's fees, an injunction to make the defendant stop a certain activity, or all of these. The request for a specific amount of money may be referred to as an ad damnum clause.

References