395 – Later Yan is defeated by its former vassal Northern Wei at the Battle of Canhe Slope.
757 – The poet Du Fu returns to Chang'an as a member of Emperor Xuanzong's court, after having escaped the city during the An Lushan Rebellion.
877 – Louis the Stammerer (son of Charles the Bald) is crowned king of the West Frankish Kingdom at Compiègne.
1504 – Ahmad ibn Abi Jum'ah writes his Oran fatwa, arguing for the relaxation of Islamic law requirements for the forcibly converted Muslims in Spain.
1660 – A woman (either Margaret Hughes or Anne Marshall) appears on an English public stage for the first time, in the role of Desdemona in a production of Shakespeare's play Othello.
1851 – Conservative Santiago-based government troops defeat rebels at the Battle of Loncomilla, signaling the end of the 1851 Chilean Revolution.
1854 – In his Apostolic constitution Ineffabilis Deus, Pope Pius IX proclaims the dogmatic definition of Immaculate Conception, which holds that the Blessed Virgin Mary was conceived free of Original Sin.
1864 – Pope Pius IX promulgates the encyclical Quanta cura and its appendix, the Syllabus of Errors, outlining the authority of the Catholic Church and condemning various liberal ideas.
1907 – King Gustaf V of Sweden accedes to the Swedish throne.
1912 – Leaders of the German Empire hold an Imperial War Council to discuss the possibility that war might break out.
1914 – World War I: A squadron of Britain's Royal Navy defeats the Imperial German East Asia Squadron in the Battle of the Falkland Islands in the South Atlantic.
1922 – Two days after coming into existence, the Irish Free State executes four leaders of the Irish Republican Army.
1941 – World War II: U.S. President Franklin D. Roosevelt declares December 7 to be "a date which will live in infamy", after which the U.S. declares war on Japan.
1941 – World War II: Japanese forces simultaneously invade Shanghai International Settlement, Malaya, Thailand, Hong Kong, the Philippines, and the Dutch East Indies.
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The mathematical principles of communication that govern the compression and transmission of data and the design of efficient methods of doing so.
In Samoa, this was the only leap year spanned to 367 days as July 4 repeated. This means that the International Date Line was drawn from the east of the country to go west. January 1 – Ellis Island begins accommodating immigrants to the United States. February 1 – The historic Enterprise Bar and Grill is established in Rico, Colorado. February 27 – Rudolf Diesel applies for a patent, on his compression ignition engine (the Diesel engine). February 29 – St. Petersburg, Florida is incorporated as a town.
43 BC – Marcus Tullius Cicero is assassinated in Formia on orders of Marcus Antonius. 574 – Byzantine Emperor Justin II, suffering recurring seizures of insanity, adopts his general Tiberius and proclaims him as Caesar. 927 – The Sajid emir of Adharbayjan, Yusuf ibn Abi'l-Saj is defeated and captured by the Qarmatians near Kufa. 1703 – The Great Storm of 1703, the greatest windstorm ever recorded in the southern part of Great Britain, makes landfall. Winds gust up to 120 mph, and 9,000 people die.
January 1 - The Kingdom of Italy establishes Eritrea as its colony in the Horn of Africa. January 2 The steamship Persia is wrecked off Corsica; 130 lives are lost. Alice Sanger becomes the first female staffer in the White House. January 11 – 1890 British Ultimatum: The United Kingdom demands Portugal withdraw its forces from the land between the Portuguese colonies of Mozambique and Angola (most of present-day Zimbabwe and Zambia). January 15 – Ballet The Sleeping Beauty, with music by Tchaikovsky, is premiered at the Imperial Mariinsky Theatre in St.
Covers Rate-Distortion Theory, optimizing encoding and decoding for efficient data transmission.
Explores group morphisms and determinants in K-vector spaces.
Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.