Family Π

Family Π is a group of New Testament manuscripts. Belonging to the Byzantine text-type, it is one of the textual families of this group. The name of the family, "Π" (pronounced in English as "pie"), is drawn from the symbol used for the Codex Petropolitanus. One of the most distinct of the Byzantine sub-groups, it is very old and the third largest. The oldest Byzantine manuscripts belong to this family.

Hermann von Soden designated this group by the symbol "K^a". According to him, its text is not purely Byzantine.

Codices and manuscripts

Soden included the following in this group of codices: Cyprius (K), Petropolitanus (Π), 72, 114, 116, 178, 265, 389, 1008, 1009, 1079, 1154, 1200, 1219, 1346, and 1398. Lake added to this group of manuscripts: 489, 537, 652, 775, 796, 904, 1478, 1500, 1546, 1561, 1781, 1816. Soden also associated Codex Alexandrinus with this group. Wisse lists about 150 witnesses of the family, but the majority of them belong to this family only in some parts of their text. The Peshitta, in the Gospels, represents this family.

Index set

In mathematics, an index set is a set whose members label (or index) members of another set. For instance, if the elements of a set A may be indexed or labeled by means of a set J, then J is an index set. The indexing consists of a surjective function from J onto A and the indexed collection is typically called an (indexed) family, often written as (A_j)_j∈J.

Examples

An enumeration of a set S gives an index set , where f : J → S is the particular enumeration of S.

Any countably infinite set can be indexed by .

For , the indicator function on r is the function given by

The set of all the functions is an uncountable set indexed by .

Other uses

In computational complexity theory and cryptography, an index set is a set for which there exists an algorithm I that can sample the set efficiently; i.e., on input 1ⁿ, I can efficiently select a poly(n)-bit long element from the set.

See also

References

Family (Spanish band)

Family was a cult band from Spain in the 1990s. Although initially unsuccessful, Family gradually acquired a fanbase and is now highly recognised in the Spanish underground pop scene. Their only album, Un Soplo en el Corazón has been praised for its poetic lyrics, inspired music and elegant artwork.

Family - Un Soplo en el Corazón (Tracklist)

1. La Noche Inventada (2:24)

2. Nadadora (2:57)

3. Como un Aviador (3:19)

4. En el Rascacielos (2:32)

5. El Bello Verano (2:19)

6. Portugal (2:10)

7. El Buen Vigía (2:05)

8. Viaje a los Sueños Polares (2:53)

9. Al Otro Lado (2:02)

10. Carlos Baila (2:49)

11. Yo TePerdí una Tarde de Abril (3:01)

12. Dame Estrellas O Limones (2:24)

13. El mapa (2:20)

14. Martín se ha ido para siempre (3:09)

Sugar

Sugar is the generalized name for sweet, short-chain, soluble carbohydrates, many of which are used in food. They are carbohydrates, composed of carbon, hydrogen, and oxygen. There are various types of sugar derived from different sources. Simple sugars are called monosaccharides and include glucose (also known as dextrose), fructose and galactose. The table or granulated sugar most customarily used as food is sucrose, a disaccharide. (In the body, sucrose hydrolyses into fructose and glucose.) Other disaccharides include maltose and lactose. Longer chains of sugars are called oligosaccharides. Chemically-different substances may also have a sweet taste, but are not classified as sugars. Some are used as lower-calorie food substitutes for sugar described as artificial sweeteners.

Sugars are found in the tissues of most plants, but are present in sufficient concentrations for efficient extraction only in sugarcane and sugar beet. Sugarcane refers to any of several species of giant grass in the genus Saccharum that have been cultivated in tropical climates in South Asia and Southeast Asia since ancient times. A great expansion in its production took place in the 18th century with the establishment of sugar plantations in the West Indies and Americas. This was the first time that sugar became available to the common people, who had previously had to rely on honey to sweeten foods. Sugar beet, a cultivated variety of Beta vulgaris, is grown as a root crop in cooler climates and became a major source of sugar in the 19th century when methods for extracting the sugar became available. Sugar production and trade have changed the course of human history in many ways, influencing the formation of colonies, the perpetuation of slavery, the transition to indentured labour, the migration of peoples, wars between sugar-trade–controlling nations in the 19th century, and the ethnic composition and political structure of the New World.

Sugar (musical)

Sugar is a musical with a book by Peter Stone, music by Jule Styne, and lyrics by Bob Merrill. It is based on the film Some Like It Hot, which was adapted by Billy Wilder and I.A.L. Diamond from a story by Robert Thoeren and Michael Logan. It premiered on Broadway in 1972 and was staged in the West End twenty years later.

Synopsis

Two unemployed musicians, bass player Jerry and saxophone player Joe, witness the St. Valentine's Day Massacre in Chicago. In order to escape gangster Spats Palazzo and his henchmen, they dress as women and join Sweet Sue and Her Society Syncopaters, an all-female band about to leave town for an engagement at a Miami Beach hotel.

Complications arise when Joe, now known as Josephine, falls in love with beautiful band singer Sugar Kane, who has a slight drinking problem that tends to interfere with her ability to choose a romantic partner wisely. More than anything, Sugar wants to marry a millionaire, prompting Joe to disguise himself as the man of her dreams.

Sugar (Tokio album)

Sugar is the eleventh studio album by Japanese band Tokio. It was released on February 20, 2008. The album peaked at sixth place on the Oricon weekly charts and charted for six weeks.

Track listing

References