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🔗 Mathematics

In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The proof is an extension of Szemerédi's theorem. The problem can be traced back to investigations of Lagrange and Waring from around 1770.

🔗 Chess 🔗 Books 🔗 Board and table games

The Libro de los Juegos (Spanish: "Book of games"), or Libro de axedrez, dados e tablas ("Book of chess, dice and tables", in Old Spanish), was a Spanish translation of Arabic texts on chess, dice and tables (backgammon forebears) games, commissioned by Alfonso X of Castile, Galicia and León and completed in his scriptorium in Toledo in 1283. It contains the earliest European treatise on chess as well as being the oldest document on European tables games, and is an exemplary piece of the literary legacy of the Toledo School of Translators.

🔗 Biography 🔗 Russia 🔗 Russia/technology and engineering in Russia 🔗 Russia/demographics and ethnography of Russia 🔗 African diaspora 🔗 Russia/Russian, Soviet, and CIS military history 🔗 Russia/history of Russia

Abram Petrovich Gannibal, also Hannibal or Ganibal, or Abram Hannibal or Abram Petrov (Russian: Абра́м Петро́вич Ганниба́л; c. 1696 – 14 May 1781), was a Russian military engineer, major-general, and nobleman of African origin. Kidnapped as a child, Gannibal was taken to Russia and presented as a gift to Peter the Great, where he was freed, adopted and raised in the Emperor's court household as his godson.

Gannibal eventually rose to become a prominent member of the imperial court in the reign of Peter's daughter Elizabeth. He had 11 children, most of whom became members of the Russian nobility; he was a great-grandfather of the author and poet Alexander Pushkin.

🔗 Mathematics

In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics. The question was solved in 1980 by Alex Wilkie, who showed that such unprovable identities do exist.

🔗 Computing 🔗 Time 🔗 Linux

Unix time (also known as Epoch time, POSIX time, seconds since the Epoch, or UNIX Epoch time) is a system for describing a point in time. It is the number of seconds that have elapsed since the Unix epoch, that is the time 00:00:00 UTC on 1 January 1970, minus leap seconds. Leap seconds are ignored, with a leap second having the same Unix time as the second before it, and every day is treated as if it contains exactly 86400 seconds. Due to this treatment, Unix time is not a true representation of UTC.

Unix time is widely used in operating systems and file formats. In Unix-like operating systems, date is a command which will print or set the current time; by default, it prints or sets the time in the system time zone, but with the -u flag, it prints or sets the time in UTC and, with the TZ environment variable set to refer to a particular time zone, prints or sets the time in that time zone.

🔗 History 🔗 Military history 🔗 Military history/Early Modern warfare 🔗 European history

The "General Crisis" is the term used by some historians to describe the period of widespread conflict and instability that occurred from the early 17th century to the early 18th century in Europe and in more recent historiography in the world at large. The concept is much debated by historians; there is no consensus.

The term was coined by Eric Hobsbawm in his pair of 1954 articles entitled "The Crisis of the Seventeenth Century" published in Past and Present.

🔗 Geology 🔗 Marine life 🔗 Algae

Diatoms (diá-tom-os 'cut in half', from diá, 'through' or 'apart'; and the root of tém-n-ō, 'I cut'.) are a major group of algae, specifically microalgae, found in the oceans, waterways and soils of the world. Living diatoms make up a significant portion of the Earth's biomass: they generate about 20 to 50 percent of the oxygen produced on the planet each year, take in over 6.7 billion metric tons of silicon each year from the waters in which they live, and contribute nearly half of the organic material found in the oceans. The shells of dead diatoms can reach as much as a half-mile (800m) deep on the ocean floor, and the entire Amazon basin is fertilized annually by 27 million tons of diatom shell dust transported by transatlantic winds from the African Sahara, much of it from the Bodélé Depression, which was once made up a system of fresh-water lakes.

Diatoms are unicellular: they occur either as solitary cells or in colonies, which can take the shape of ribbons, fans, zigzags, or stars. Individual cells range in size from 2 to 200 micrometers. In the presence of adequate nutrients and sunlight, an assemblage of living diatoms doubles approximately every 24 hours by asexual multiple fission; the maximum life span of individual cells is about six days. Diatoms have two distinct shapes: a few (centric diatoms) are radially symmetric, while most (pennate diatoms) are broadly bilaterally symmetric. A unique feature of diatom anatomy is that they are surrounded by a cell wall made of silica (hydrated silicon dioxide), called a frustule. These frustules have structural coloration due to their photonic nanostructure, prompting them to be described as "jewels of the sea" and "living opals". Movement in diatoms primarily occurs passively as a result of both water currents and wind-induced water turbulence; however, male gametes of centric diatoms have flagella, permitting active movement for seeking female gametes. Similar to plants, diatoms convert light energy to chemical energy by photosynthesis, although this shared autotrophy evolved independently in both lineages. Unusually for autotrophic organisms, diatoms possess a urea cycle, a feature that they share with animals, although this cycle is used to different metabolic ends in diatoms. The family Rhopalodiaceae also possess a cyanobacterial endosymbiont called a spheroid body. This endosymbiont has lost its photosynthetic properties, but has kept its ability to perform nitrogen fixation, allowing the diatom to fix atmospheric nitrogen.

The study of diatoms is a branch of phycology. Diatoms are classified as eukaryotes, organisms with a membrane-bound cell nucleus, that separates them from the prokaryotes archaea and bacteria. Diatoms are a type of plankton called phytoplankton, the most common of the plankton types. Diatoms also grow attached to benthic substrates, floating debris, and on macrophytes. They comprise an integral component of the periphyton community. Another classification divides plankton into eight types based on size: in this scheme, diatoms are classed as microalgae. Several systems for classifying the individual diatom species exist. Fossil evidence suggests that diatoms originated during or before the early Jurassic period, which was about 150 to 200 million years ago.

Diatoms are used to monitor past and present environmental conditions, and are commonly used in studies of water quality. Diatomaceous earth (diatomite) is a collection of diatom shells found in the earth's crust. They are soft, silica-containing sedimentary rocks which are easily crumbled into a fine powder and typically have a particle size of 10 to 200 μm. Diatomaceous earth is used for a variety of purposes including for water filtration, as a mild abrasive, in cat litter, and as a dynamite stabilizer.

🔗 Soviet Union 🔗 Firearms

The TP-82 (Russian: ТП-82) was a triple-barrelled Soviet pistol that was carried by cosmonauts on space missions.

It was intended as a survival aid to be used after landings and before recovery in the Siberian wilderness. The TP-82 was the result of cosmonaut Alexei Leonov's concerns after being stranded in the Siberian wilderness when his Voskhod capsule malfunctioned. He feared that the 9mm pistol that was provided in the survival kit would be ineffective against the Siberian wildlife, namely bears and wolves.

The upper two shotgun barrels used 12.5×70 mm ammunition (40 gauge), and the lower rifled barrel used 5.45×39mm ammunition developed for the AK-74 assault rifle. The TP-82 has a large lever on the left side of the receiver that opens the action and a small grip-safety under the trigger-guard that resembles a secondary trigger.

The pistol could be used for hunting, to defend against predators and for visible and audible distress signals. The detachable buttstock was also a machete that came with a canvas sheath. TP-82s were carried regularly on Soviet and Russian space missions from 1986 to 2007. They were part of the Soyuz Portable Emergency-Survival Kit (Носимый аварийный запас, Nosimyi Avariynyi Zapas, NAZ). In 2007, the media reported that the remaining ammunition for the TP-82 had become unusable and that a regular semi-automatic pistol would be used on future missions.

🔗 China 🔗 Ethnic groups 🔗 Gender Studies

The Mosuo (Chinese: 摩梭; pinyin: Mósuō) are a small ethnic group living in Yunnan and Sichuan provinces in China, close to the border with Tibet. Dubbed the 'Kingdom of Women' by the Chinese, the Mosuo population of about 50,000 live near Lugu Lake in the Tibetan Himalayas 27°42′35.30″N 100°47′4.04″E.

Scholars use diverse terms and spellings to designate the Mosuo culture. Most prefer 'Mosuo' some spell it 'Moso', while a minority use neither term, but refer to them as the Na people.

The Mosuo people are known as the 'Kingdom of Women' because the Na are a matrilineal society: heterosexual activity occurs only by mutual consent and mostly through the custom of the secret nocturnal 'visit'; men and women are free to have multiple partners, and to initiate or break off relationships when they please.