Ruspoli family

The Ruspoli are an old and noble Italian family.

The origins of the family can be traced back to the Ruspoli of Florence in the 13th century and through the family's claimed direct descent from Marius Scotus in the 8th century and the Marescottis of Bologna. In the 17th century the Ruspolis moved to Rome where the last descendant, Vittoria Ruspoli, Marchioness of Cerveteri, married Sforza Vicino Marescotti Count of Vignanello, a descendant of the Farnese family on both his mother's and father's side. One of Vittoria's sons took the Ruspoli name and coat of arms to guarantee the continuity of the house.

In 1708, Vittoria's grandson, Francesco Ruspoli head of the Ruspoli Regiment fought to defend the Vatican State. In 1709 he forced the Austrians to a retreat and Pope Clement XI named Francesco first Prince of Cerveteri.

The papal title was conferred in 1721, and the Italian in 1905.

They held the post of Grand Master of the Sacred Apostolic Hospice, or Quartermaster-General of the Sacred Palaces, which was an hereditary official of the Pontifical Household. He was a Participating Privy Chamberlains and the sole lay member of the Noble Privy Antechamber, as well as a Participating Privy Chamberlains of the Sword and Cape (who were all laymen, traditionally holding hereditary posts). The post was abolished in the reforms of the Papal Curia after 1968.

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)