Winter

Winter is the coldest season of the year in polar and temperate climates, between autumn and spring. Winter is caused by the axis of the Earth in that hemisphere being oriented away from the Sun. Different cultures define different dates as the start of winter, and some use a definition based on weather. When it is winter in the Northern Hemisphere, it is summer in the Southern Hemisphere, and vice versa. In many regions, winter is associated with snow and freezing temperatures. The moment of winter solstice is when the sun's elevation with respect to the North or South Pole is at its most negative value (that is, the sun is at its farthest below the horizon as measured from the pole), meaning this day will have the shortest day and the longest night. The earliest sunset and latest sunrise dates outside the polar regions differ from the date of the winter solstice, however, and these depend on latitude, due to the variation in the solar day throughout the year caused by the Earth's elliptical orbit (see earliest and latest sunrise and sunset).

The Four Seasons (Vivaldi)

The Four Seasons (Italian: Le quattro stagioni) is a group of four violin concerti by Italian composer Antonio Vivaldi, each of which gives a musical expression to a season of the year. They were written about 1723 and were published in 1725 in Amsterdam, together with eight additional violin concerti, as Il cimento dell'armonia e dell'inventione ("The Contest Between Harmony and Invention").

The Four Seasons is the best known of Vivaldi's works. Unusually for the time, Vivaldi published the concerti with accompanying poems (possibly written by Vivaldi himself) that elucidated what it was about those seasons that his music was intended to evoke. It provides one of the earliest and most-detailed examples of what was later called program music—music with a narrative element.

Vivaldi took great pains to relate his music to the texts of the poems, translating the poetic lines themselves directly into the music on the page. In the middle section of the Spring concerto, where the goatherd sleeps, his barking dog can be marked in the viola section. Other natural occurrences are similarly evoked. Vivaldi separated each concerto into three movements, fast-slow-fast, and likewise each linked sonnet into three sections. His arrangement is as follows:

Winter (dolphin)

Winter (born October 5, 2005) is a bottlenose dolphin at the Clearwater Marine Aquarium in Clearwater, Florida, US, widely known for having a prosthetic tail. She is the subject of the book Dolphin Tale, and the 2011 film of the same name, a dramatization of her story, and the sequel Dolphin Tale 2. Winter was found in the coastal waters of Florida in December 2005, caught in a crab trap, which resulted in the loss of her tail. She was then taken to Clearwater Marine Aquarium. The loss of her tail caused her to swim unnaturally with her tail moving side to side instead of up and down. As a result, she was fitted with a silicone-and-plastic tail that enabled her to swim normally. She has since become a highly popular attraction at the aquarium, which led to the film's making. She lives in her pool with another dolphin, Hope, who is the subject of the 2014 sequel to Dolphin Tale, Dolphin Tale 2.

Injury and discovery

Winter was found in the ropes of a crab trap on December 10, 2005, in Mosquito Lagoon of the coastal waters of Florida. Winter received her name because she was found in December, traditionally considered a winter month, even though the exact date of her rescue (December 10) is actually within the American definition of autumn. The rope cut off the supply of blood to her tail. She was spotted and caught by a small fishing boat and a SeaWorld team (with assistance from the Harbor Branch Oceanographic Institute), who brought her to the Clearwater Marine Aquarium.

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)