History.

Cast iron has been found in China dating to the 5th century BC, but the earliest extant blast furnaces in China date to the 1st century AD and in the West from the High Middle Ages. They spread from the region around Namur in Wallonia (Belgium) in the late 15th century, being introduced to England in 1491. The fuel used in these was invariably charcoal. The successful substitution of coke for charcoal is widely attributed to English inventor Abraham Darby in 1709. The efficiency of the process was further enhanced by the practice of preheating the combustion air (hot blast), patented by Scottish inventor James Beaumont Neilson in 1828.

China.

Archaeological evidence shows that bloomeries appeared in China around 800 BC. Originally it was thought that the Chinese started casting iron right from the beginning, but this theory has since been debunked by the discovery of'more than ten' iron digging implements found in the tomb of Duke Jing of Qin (d. 537 BC), whose tomb is located in Fengxiang County, Shaanxi (a museum exists on the site today). There is however no evidence of the bloomery in China after the appearance of the blast furnace and cast iron. In China, blast furnaces produced cast iron, which was then either converted into finished implements in a cupola furnace, or turned into wrought iron in a fining hearth.  Although cast iron farm tools and weapons were widespread in China by the 5th century BC, employing workforces of over 200 men in iron smelters from the 3rd century onward, the earliest blast furnaces constructed were attributed to the Han Dynasty in the 1st century AD. These early furnaces had clay walls and used phosphorus-containing minerals as a flux. Chinese blast furnaces ranged from around two to ten meters in height, depending on the region. The largest ones were found in modern Sichuan and Guangdong, while the 'dwarf" blast furnaces were found in Dabieshan. In construction, they are both around the same level of technological sophistication  The effectiveness of the Chinese human and horse powered blast furnaces was enhanced during this period by the engineer Du Shi (c. AD 31), who applied the power of waterwheels to piston-bellows in forging cast iron. Early water-driven reciprocators for operating blast furnaces were built according to the structure of horse powered reciprocators that already existed. That is, the circular motion of the wheel, be it horse driven or water driven, was transferred by the combination of a belt drive, a crank-and-connecting-rod, other connecting rods, and various shafts, into the reciprocal motion necessary to operate a push bellow. Donald Wagner suggests that early blast furnace and cast iron production evolved from furnaces used to melt bronze. Certainly, though, iron was essential to military success by the time the State of Qin had unified China (221 BC). Usage of the blast and cupola furnace remained widespread during the Song and Tang Dynasties. By the 11th century, the Song Dynasty Chinese iron industry made a switch of resources from charcoal to coke in casting iron and steel, sparing thousands of acres of woodland from felling. This may have happened as early as the 4th century AD.  The primary advantage of the early blast furnace was in large scale production and making iron implements more readily available to peasants. Cast iron is more brittle than wrought iron or steel, which required additional fining and then cementation or co-fusion to produce, but for menial activities such as farming it sufficed. By using the blast furnace, it was possible to produce larger quantities of tools such as ploughshares more efficiently than the bloomery. In areas where quality was important, such as warfare, wrought iron and steel were preferred. Nearly all Han period weapons are made of wrought iron or steel, with the exception of axe-heads, of which many are made of cast iron.  Blast furnaces were also later used to produce gunpowder weapons such as cast iron bomb shells and cast iron cannons during the Song dynasty.

Medieval Europe.

The simplest forge, known as the Corsican, was used prior to the advent of Christianity. Examples of improved bloomeries are the (sometimes called wolf-furnace), which remained until the beginning of the 19th century. Instead of using natural draught, air was pumped in by a "trompe", resulting in better quality iron and an increased capacity. This pumping of airstream in with bellows is known as "cold blast", and it increases the fuel efficiency of the bloomery and improves yield. They can also be built bigger than natural draught bloomeries.

Oldest European blast furnaces.

The oldest known blast furnaces in the West were built in Dürstel in Switzerland, the Märkische Sauerland in Germany, and at Lapphyttan in Sweden, where the complex was active between 1205 and 1300. At Noraskog in the Swedish parish of Järnboås, there has also been found traces of blast furnaces dating even earlier, possibly to around 1100. These early blast furnaces, like the Chinese examples, were very inefficient compared to those used today. The iron from the Lapphyttan complex was used to produce balls of wrought iron known as osmonds, and these were traded internationally – a possible reference occurs in a treaty with Novgorod from 1203 and several certain references in accounts of English customs from the 1250s and 1320s. Other furnaces of the 13th to 15th centuries have been identified in Westphalia.  The technology required for blast furnaces may have either been transferred from China, or may have been an indigenous innovation. Al-Qazvini in the 13th century and other travellers subsequently noted an iron industry in the Alburz Mountains to the south of the Caspian Sea. This is close to the silk route, so that the use of technology derived from China is conceivable. Much later descriptions record blast furnaces about three metres high. As the Varangian Rus' people from Scandinavia traded with the Caspian (using their Volga trade route), it is possible that the technology reached Sweden by this means. The step from bloomery to true blast furnace is not big. Simply just building a bigger furnace and using bigger bellows to increase the volume of the blast and hence the amount of oxygen leads inevitably into higher temperatures, bloom melting into liquid iron, and cast iron flowing from the smelters. Already the Vikings are known to have used double bellows, which greatly increases the volumetric flow of the blast.  The Caspian region may also have been the source for the design of the furnace at Ferriere, described by Filarete, involving a water-powered bellows at in Valdidentro in northern Italy in 1226 in a two-stage process. With this process, the molten iron was tapped twice a day into water, thereby granulating it.

Cistercian contributions.

One means by which certain technological advances were spread within Europe was a result of the General Chapter of the Cistercian monks. This may have included the blast furnace, as the Cistercians are known to have been skilled metallurgists. According to Jean Gimpel, their high level of industrial technology facilitated the diffusion of new techniques: "Every monastery had a model factory, often as large as the church and only several feet away, and waterpower drove the machinery of the various industries located on its floor." Iron ore deposits were often donated to the monks along with forges to extract the iron, and within time surpluses were being offered for sale. The Cistercians became the leading iron producers in Champagne, France, from the mid-13th century to the 17th century, also using the phosphate-rich slag from their furnaces as an agricultural fertilizer.  Archaeologists are still discovering the extent of Cistercian technology. At Laskill, an outstation of Rievaulx Abbey and the only medieval blast furnace so far identified in Britain, the slag produced was low in iron content. Slag from other furnaces of the time contained a substantial concentration of iron, whereas Laskill is believed to have produced cast iron quite efficiently. Its date is not yet clear, but it probably did not survive until Henry VIII's Dissolution of the Monasteries in the late 1530s, as an agreement (immediately after that) concerning the "smythes" with the Earl of Rutland in 1541 refers to blooms. Nevertheless, the means by which the blast furnace spread in medieval Europe has not finally been determined.

Origin and spread of early modern blast furnaces.

Due to the casting of cannon, the blast furnace came into widespread use in France in the mid 15th century.  The direct ancestor of these used in France and England was in the Namur region in what is now Wallonia (Belgium). From there, they spread first to the Pays de Bray on the eastern boundary of Normandy and from there to the Weald of Sussex, where the first furnace (called Queenstock) in Buxted was built in about 1491, followed by one at Newbridge in Ashdown Forest in 1496. They remained few in number until about 1530 but many were built in the following decades in the Weald, where the iron industry perhaps reached its peak about 1590. Most of the pig iron from these furnaces was taken to finery forges for the production of bar iron.  The first British furnaces outside the Weald appeared during the 1550s, and many were built in the remainder of that century and the following ones. The output of the industry probably peaked about 1620, and was followed by a slow decline until the early 18th century. This was apparently because it was more economic to import iron from Sweden and elsewhere than to make it in some more remote British locations. Charcoal that was economically available to the industry was probably being consumed as fast as the wood to make it grew. The Backbarrow blast furnace built in Cumbria in 1711 has been described as the first efficient example.  The first blast furnace in Russia opened in 1637 near Tula and was called the Gorodishche Works. The blast furnace spread from here to central Russia and then finally to the Urals.

Coke blast furnaces.

In 1709, at Coalbrookdale in Shropshire, England, Abraham Darby began to fuel a blast furnace with coke instead of charcoal. Coke's initial advantage was its lower cost, mainly because making coke required much less labor than cutting trees and making charcoal, but using coke also overcame localized shortages of wood, especially in Britain and on the Continent. Metallurgical grade coke will bear heavier weight than charcoal, allowing larger furnaces. A disadvantage is that coke contains more impurities than charcoal, with sulfur being especially detrimental to the iron's quality. Coke's impurities were more of a problem before hot blast reduced the amount of coke required and before furnace temperatures were hot enough to make slag from limestone free flowing. (Limestone ties up sulfur. Manganese may also be added to tie up sulfur).  Coke iron was initially only used for foundry work, making pots and other cast iron goods. Foundry work was a minor branch of the industry, but Darby's son built a new furnace at nearby Horsehay, and began to supply the owners of finery forges with coke pig iron for the production of bar iron. Coke pig iron was by this time cheaper to produce than charcoal pig iron. The use of a coal-derived fuel in the iron industry was a key factor in the British Industrial Revolution. Darby's original blast furnace has been archaeologically excavated and can be seen in situ at Coalbrookdale, part of the Ironbridge Gorge Museums. Cast iron from the furnace was used to make girders for the world's first iron bridge in 1779. The Iron Bridge crosses the River Severn at Coalbrookdale and remains in use for pedestrians.

Steam-powered blast.

The steam engine was applied to power blast air, overcoming a shortage of water power in areas where coal and iron ore were located. The cast iron blowing cylinder was developed in 1768 to replace the leather bellows, which wore out quickly. The steam engine and cast iron blowing cylinder led to a large increase in British iron production in the late 18th century.

Hot blast.

Hot blast was the single most important advance in fuel efficiency of the blast furnace and was one of the most important technologies developed during the Industrial Revolution. Hot blast was patented by James Beaumont Neilson at Wilsontown Ironworks in Scotland in 1828. Within a few years of the introduction, hot blast was developed to the point where fuel consumption was cut by one-third using coke or two-thirds using coal, while furnace capacity was also significantly increased. Within a few decades, the practice was to have a "stove" as large as the furnace next to it into which the waste gas (containing CO) from the furnace was directed and burnt. The resultant heat was used to preheat the air blown into the furnace.  Hot blast enabled the use of raw anthracite coal, which was difficult to light, to the blast furnace. Anthracite was first tried successfully by George Crane at Ynyscedwyn Ironworks in south Wales in 1837. It was taken up in America by the Lehigh Crane Iron Company at Catasauqua, Pennsylvania, in 1839. Anthracite use declined when very high capacity blast furnaces requiring coke were built in the 1870s.

Modern furnaces.

Iron blast furnaces.

The blast furnace remains an important part of modern iron production. Modern furnaces are highly efficient, including Cowper stoves to pre-heat the blast air and employ recovery systems to extract the heat from the hot gases exiting the furnace. Competition in industry drives higher production rates. The largest blast furnace in the world is in South Korea, with a volume around. It can produce around of iron per year.  This is a great increase from the typical 18th-century furnaces, which averaged about per year. Variations of the blast furnace, such as the Swedish electric blast furnace, have been developed in countries which have no native coal resources.

Lead blast furnaces.

Blast furnaces are currently rarely used in copper smelting, but modern lead smelting blast furnaces are much shorter than iron blast furnaces and are rectangular in shape. The overall shaft height is around 5 to 6 m. Modern lead blast furnaces are constructed using water-cooled steel or copper jackets for the walls, and have no refractory linings in the side walls. The base of the furnace is a hearth of refractory material (bricks or castable refractory). Lead blast furnaces are often open-topped rather than having the charging bell used in iron blast furnaces.  The blast furnace used at the Nyrstar Port Pirie lead smelter differs from most other lead blast furnaces in that it has a double row of tuyeres rather than the single row normally used. The lower shaft of the furnace has a chair shape with the lower part of the shaft being narrower than the upper. The lower row of tuyeres being located in the narrow part of the shaft. This allows the upper part of the shaft to be wider than the standard.

Zinc blast furnaces (Imperial Smelting Furnaces).

The blast furnaces used in the Imperial Smelting Process ("ISP") were developed from the standard lead blast furnace, but are fully sealed. This is because the zinc produced by these furnaces is recovered as metal from the vapor phase, and the presence of oxygen in the off-gas would result in the formation of zinc oxide.  Blast furnaces used in the ISP have a more intense operation than standard lead blast furnaces, with higher air blast rates per m of hearth area and a higher coke consumption.  Zinc production with the ISP is more expensive than with electrolytic zinc plants, so several smelters operating this technology have closed in recent years. However, ISP furnaces have the advantage of being able to treat zinc concentrates containing higher levels of lead than can electrolytic zinc plants.

Modern process.

Modern furnaces are equipped with an array of supporting facilities to increase efficiency, such as ore storage yards where barges are unloaded. The raw materials are transferred to the stockhouse complex by ore bridges, or rail hoppers and ore transfer cars. Rail-mounted scale cars or computer controlled weight hoppers weigh out the various raw materials to yield the desired hot metal and slag chemistry. The raw materials are brought to the top of the blast furnace via a skip car powered by winches or conveyor belts.  There are different ways in which the raw materials are charged into the blast furnace. Some blast furnaces use a "double bell" system where two "bells" are used to control the entry of raw material into the blast furnace. The purpose of the two bells is to minimize the loss of hot gases in the blast furnace. First, the raw materials are emptied into the upper or small bell which then opens to empty the charge into the large bell. The small bell then closes, to seal the blast furnace, while the large bell rotates to provide specific distribution of materials before dispensing the charge into the blast furnace. A more recent design is to use a "bell-less" system. These systems use multiple hoppers to contain each raw material, which is then discharged into the blast furnace through valves. These valves are more accurate at controlling how much of each constituent is added, as compared to the skip or conveyor system, thereby increasing the efficiency of the furnace. Some of these bell-less systems also implement a discharge chute in the throat of the furnace (as with the Paul Wurth top) in order to precisely control where the charge is placed.  The iron making blast furnace itself is built in the form of a tall structure, lined with refractory brick, and profiled to allow for expansion of the charged materials as they heat during their descent, and subsequent reduction in size as melting starts to occur. Coke, limestone flux, and iron ore (iron oxide) are charged into the top of the furnace in a precise filling order which helps control gas flow and the chemical reactions inside the furnace. Four "uptakes" allow the hot, dirty gas high in carbon monoxide content to exit the furnace throat, while "bleeder valves" protect the top of the furnace from sudden gas pressure surges. The coarse particles in the exhaust gas settle in the "dust catcher" and are dumped into a railroad car or truck for disposal, while the gas itself flows through a venturi scrubber and/or electrostatic precipitators and a gas cooler to reduce the temperature of the cleaned gas.  The "casthouse" at the bottom half of the furnace contains the bustle pipe, water cooled copper tuyeres and the equipment for casting the liquid iron and slag. Once a "taphole" is drilled through the refractory clay plug, liquid iron and slag flow down a trough through a "skimmer" opening, separating the iron and slag. Modern, larger blast furnaces may have as many as four tapholes and two casthouses. Once the pig iron and slag has been tapped, the taphole is again plugged with refractory clay.  The tuyeres are used to implement a hot blast, which is used to increase the efficiency of the blast furnace. The hot blast is directed into the furnace through water-cooled copper nozzles called tuyeres near the base. The hot blast temperature can be from 900 °C to 1300 °C (1600 °F to 2300 °F) depending on the stove design and condition. The temperatures they deal with may be 2000 °C to 2300 °C (3600 °F to 4200 °F). Oil, tar, natural gas, powdered coal and oxygen can also be injected into the furnace at tuyere level to combine with the coke to release additional energy and increase the percentage of reducing gases present which is necessary to increase productivity.

Process engineering and chemistry.

Blast furnaces operate on the principle of chemical reduction whereby carbon monoxide, having a stronger affinity for the oxygen in iron ore than iron does, reduces the iron to its elemental form. Blast furnaces differ from bloomeries and reverberatory furnaces in that in a blast furnace, flue gas is in direct contact with the ore and iron, allowing carbon monoxide to diffuse into the ore and reduce the iron oxide to elemental iron mixed with carbon. The blast furnace operates as a countercurrent exchange process whereas a bloomery does not. Another difference is that bloomeries operate as a batch process while blast furnaces operate continuously for long periods because they are difficult to start up and shut down. (See: Continuous production) Also, the carbon in pig iron lowers the melting point below that of steel or pure iron; in contrast, iron does not melt in a bloomery.  Silica has to be removed from the pig iron. It reacts with calcium oxide (burned limestone) and forms a silicate which floats to the surface of the molten pig iron as "slag". Historically, to prevent contamination from sulfur, the best quality iron was produced with charcoal.  The downward moving column of ore, flux, coke or charcoal and reaction products must be porous enough for the flue gas to pass through. This requires the coke or charcoal to be in large enough particles to be permeable, meaning there cannot be an excess of fine particles. Therefore, the coke must be strong enough so it will not be crushed by the weight of the material above it. Besides physical strength of the coke, it must also be low in sulfur, phosphorus, and ash. This necessitates the use of metallurgical coal, which is a premium grade due to its relative scarcity.  The main chemical reaction producing the molten iron is:  This reaction might be divided into multiple steps, with the first being that preheated blast air blown into the furnace reacts with the carbon in the form of coke to produce carbon monoxide and heat:  The hot carbon monoxide is the reducing agent for the iron ore and reacts with the iron oxide to produce molten iron and carbon dioxide. Depending on the temperature in the different parts of the furnace (warmest at the bottom) the iron is reduced in several steps. At the top, where the temperature usually is in the range between 200 °C and 700 °C, the iron oxide is partially reduced to iron(II,III) oxide, FeO.  At temperatures around 850 °C, further down in the furnace, the iron(II,III) is reduced further to iron(II) oxide:  Hot carbon dioxide, unreacted carbon monoxide, and nitrogen from the air pass up through the furnace as fresh feed material travels down into the reaction zone. As the material travels downward, the counter-current gases both preheat the feed charge and decompose the limestone to calcium oxide and carbon dioxide:  The calcium oxide formed by decomposition reacts with various acidic impurities in the iron (notably silica), to form a fayalitic slag which is essentially calcium silicate, :  As the iron(II) oxide moves down to the area with higher temperatures, ranging up to 1200 °C degrees, it is reduced further to iron metal:  The carbon dioxide formed in this process is re-reduced to carbon monoxide by the coke:  The temperature-dependent equilibrium controlling the gas atmosphere in the furnace is called the Boudouard reaction:  The "pig iron" produced by the blast furnace has a relatively high carbon content of around 4–5% and usually contains too much sulphur, making it very brittle, and of limited immediate commercial use. Some pig iron is used to make cast iron. The majority of pig iron produced by blast furnaces undergoes further processing to reduce the carbon and sulphur content and produce various grades of steel used for construction materials, automobiles, ships and machinery. Desulphurisation usually takes place during the transport of the liquid steel to the steelworks. This is done by adding "calcium oxide", which reacts with the "iron sulfide" contained in the pig iron to form "calcium sulfide" (called "lime desulfurization"). In a further process step, the so-called basic oxygen steelmaking, the carbon is oxidized by blowing oxygen onto the liquid pig iron to form "crude steel".  Although the efficiency of blast furnaces is constantly evolving, the chemical process inside the blast furnace remains the same. According to the American Iron and Steel Institute: "Blast furnaces will survive into the next millennium because the larger, efficient furnaces can produce hot metal at costs competitive with other iron making technologies." One of the biggest drawbacks of the blast furnaces is the inevitable carbon dioxide production as iron is reduced from iron oxides by carbon and as of 2016, there is no economical substitute – steelmaking is one of the largest industrial contributors of the CO emissions in the world (see greenhouse gases).  The challenge set by the greenhouse gas emissions of the blast furnace is being addressed in an ongoing European Program called ULCOS (Ultra Low CO Steelmaking). Several new process routes have been proposed and investigated in depth to cut specific emissions ( per ton of steel) by at least 50%. Some rely on the capture and further storage (CCS) of, while others choose decarbonizing iron and steel production, by turning to hydrogen, electricity and biomass. In the nearer term, a technology that incorporates CCS into the blast furnace process itself and is called the Top-Gas Recycling Blast Furnace is under development, with a scale-up to a commercial size blast furnace under way. The technology should be fully demonstrated by the end of the 2010s, in line with the timeline set, for example, by the EU to cut emissions significantly. Broad deployment could take place from 2020 on.

Manufacture of stone wool.

Stone wool or rock wool is a spun mineral fibre used as an insulation product and in hydroponics. It is manufactured in a blast furnace fed with diabase rock which contains very low levels of metal oxides. The resultant slag is drawn off and spun to form the rock wool product. Very small amounts of metals are also produced which are an unwanted by-product.

Decommissioned blast furnaces as museum sites.

For a long time, it was normal procedure for a decommissioned blast furnace to be demolished and either be replaced with a newer, improved one, or to have the entire site demolished to make room for follow-up use of the area. In recent decades, several countries have realized the value of blast furnaces as a part of their industrial history. Rather than being demolished, abandoned steel mills were turned into museums or integrated into multi-purpose parks. The largest number of preserved historic blast furnaces exists in Germany; other such sites exist in Spain, France, the Czech Republic, Japan, Luxembourg, Poland, Romania, Mexico, Russia and the United States.

Gas cleaning systems.

The blast furnace gas can be used to generate heat. So by reducing the constituents in blast furnace gas we can increase the calorific value and can be used to generate heat and rise the temperature in any furnace.  The gas cleaning system contains two stages, the coarse cleaning system and the fine cleaning system.  In the coarse cleaning system a dust catcher is used. A dust catcher is a cylindrical steel structure with conical top and bottom sections. It is also lined with refractory bricks.  The principle of the dust catcher is that the dust-laden gas is given a sudden reverse in speed and direction. Because of their mass, the coarse dust particles cannot change their velocity easily, and hence settle to the bottom.

A Blast Furnace is a type of metallurgical furnace used for smelting to produce industrial metals, generally pig iron, but also others such as lead or copper. "Blast" refers to the combustion air being "forced" or supplied above atmospheric pressure.

高炉是炼铁的一种设施,也是目前最具有规模经济的炼铁法。


Origin.

The Evenks or Ewenki are sometimes conjectured to be connected to the Shiwei people who inhabited the Greater Khingan Range in the 5th to 9th centuries, although the native land of the majority of Evenki people is in the vast regions of Siberia between Lake Baikal and the Amur River. The Ewenki language forms the northern branch of the Manchu-Tungusic language group and is closely related to Even and Negidal in Siberia. By 1600 the Evenks or Ewenki of the Lena and Yenisey river valleys were successful reindeer herders. By contrast the Solons (ancestors of the Evenkis in China) and the Khamnigans (Ewenkis of Transbaikalia) had picked up horse breeding and the Mongolian deel from the Mongols. The Solons nomadized along the Amur River. They were closely related to the Daur people. To the west the Khamnigan were another group of horse-breeding Evenks in the Transbaikalia area. Also in the Amur valley a body of Siberian Evenki-speaking people were called Orochen by the Manchus.

Historical distribution.

The ancestors of the south-eastern Evenks have most likely been in the Baikal region of Southern Siberia (near the modern-day Mongolian border) since the Neolithic era.  Considering the north-western Evenks Vasilevich claims: "The origin of the Evenks is the result of complex processes, different in time, involving the mixing of different ancient aboriginal tribes from the north of Siberia with tribes related in language to the Turks and Mongols. The language of these tribes took precedence over the languages of the aboriginal population". Elements of more modern Evenk culture, including conical tent dwellings, bone fish-lures, and birch-bark boats, were all present in sites that are believed to be Neolithic. From Lake Baikal, “they spread to the Amur and Okhotsk Sea...the Lena Basin...and the Yenisey Basin”.

Contact with Russians.

In the 17th century, the Russian empire made contact with the Evenks. Cossacks, who served as a kind of “border-guard” for the tsarist government, imposed a fur tax on the Siberian tribes. The Cossacks exploited the Evenk clan hierarchy and took hostages from the highest members in order to ensure payment of the tax. Although there was some rebellion against local officials, the Evenks generally recognized the need for peaceful cultural relations with the Russians (Vasilevich, 624). Contact with the Russians and constant demand for fur taxes pushed the Evenks east all the way to Sakhalin island, where some still live today (Cassells). In the 19th century some groups migrated south and east into Mongolia and Manchuria (Vasilevich, 625). Today there are still Evenk populations in Sakhalin, Mongolia, and Manchuria (Ethnologue), and to a lesser extent, their traditional Baikal region (Janhunen). Russian invasion of the Evenks (and other indigenous peoples) resulted in language erosion, traditional decline, identity loss, among others, of thereof. This was especially the case during the Soviet regime. Soviet policies of collectivization, forced sedentarization (or sometimes refer to as Sedentism), "unpromising villages", and Russification of the education system compromised social, cultural, and mental well-being of the Evenks. Today, few people can speak the Evenki language, reindeer herding is in significant decline, the suicide rate is extremely high, and alcoholism is a serious issue.

Traditional life.

Traditionally they were a mixture of pastoralists and hunter-gatherers—they relied on their domesticated reindeer for milk and transport and hunted other large game for meat (Vasilevich, 620-1). Today “[t]he Evenks are divided into two large groups...engaging in different types of economy. These are the hunting and reindeer-breeding Evenks...and the horse and cattle pastoral Evenks as well as some farming Evenks” (620). The Evenks lived mostly in areas of what is called a taiga, or boreal forest. They lived in conical tents made from birch bark or reindeer skin tied to birch poles. When they moved camp, the Evenks would leave these frameworks and carry only the more portable coverings. During winter, the hunting season, most camps consisted of one or two tents while the spring encampments had up to 10 households (Vasilevich, 637).  Their skill of riding the domesticated reindeer allowed the Evenks to “colonize vast areas of the eastern taiga which had previously been impenetrable” (Vitebsky, 31). The Evenks used a saddle unique to their culture which is placed on the shoulders of the reindeer so as to lessen the strain on the animal, and used not stirrups but a stick to balance (31-32). Evenks did not develop reindeer sledges until comparatively recent times (32). They instead used their reindeer as pack animals and often traversed great distances on foot, using snowshoes or skis (Vasilevich, 627). The Evenki people did not eat their domesticated reindeer (although they did hunt and eat wild reindeer) but kept them for milk. (Forsyth, 49-50). Large herds of reindeer were very uncommon. Most Evenks had around 25 head of reindeer because they were generally bred for transportation. Unlike in several other neighboring tribes Evenk reindeer-breeding did not include “herding of reindeer by dogs nor any other specific features” (Vasilevich, 629). Very early in the spring season, the winter camps broke up and moved to places suitable for calving. Several households pastured their animals together throughout the summer, being careful to keep “[s]pecial areas...fenced off...to guard the newborn calves against being trampled on in a large herd” (629).

Clothing.

The Evenks wore a characteristic garb “adapted to the cold but rather dry climate of Central Siberia and to a life of mobility...they wore brief garments of soft reindeer or elk skin around their hips, along with leggings and moccasins, or else long supple boots reaching to the thigh” (49). They also wore a deerskin coat that did not close in front but was instead covered with an apron-like cloth. Some Evenkis decorated their clothing with fringes or embroidery (50). The Evenki traditional costume always consisted of these elements: the loincloth made of animal hide, leggings, and boots of varying lengths (Vasilevich, 641). Facial tattooing was also very common.

Hunting.

The traditional Evenk economy was a mix of pastoralism (of horses or reindeer), fishing, and hunting. The Evenk who lived near the Okhotsk Sea hunted seal, but for most of the taiga-dwellers, elk, wild reindeer, and fowl were the most important game animals. Other animals included “roe deer, bear, wolverine, lynx, wolf, Siberian marmot, fox, and sable” (Vasilevich, 626). Trapping did not become important until the imposition of the fur tax by the tsarist government. Before acquiring guns in the 18th century, Evenks used steel bows and arrows. Along with their main hunting implements, hunters always carried a “pike”—“which was a large knife on a long handle used instead of an axe when passing through the thick taiga or as a spear when hunting bear” (626). The Evenks have deep respect for animals and all elements of nature: "It is forbidden to torment an animal, bird, or insect, and a wounded animal must be finished off immediately. It is forbidden to spill the blood of a killed animal or defile it. It is forbidden to kill animals or birds that were saved from pursuit by predators or came to a person for help in a natural disaster." (Sirina, 24).

Evenks of Russia.

The Evenks were formerly known as "tungus". This designation was spread by the Russians, who acquired it from the Yakuts and the Siberian Tatars (in the Yakut language "tongus") in the 17th century. The Evenks have several self-designations, of which the best known is "evenk". This became the official designation for the people in 1931. Some groups call themselves "orochen" ('an inhabitant of the River Oro'), "orochon" ('a rearer of reindeer'), "ile" ('a human being'), etc. At one time or another tribal designations and place names have also been used as self-designations, for instance "manjagir", "birachen", "solon", etc. Several of these have even been taken for separate ethnic entities.  There is also a similarly named Siberian group called the Evens (formerly known as "Lamuts"). Although related to the Evenks, the Evens are now considered to be a separate ethnic group. The Evenks are spread over a huge territory of the Siberian taiga from the River Ob in the west to the Okhotsk Sea in the east, and from the Arctic Ocean in the north to Manchuria and Sakhalin in the south. The total area of their habitat is about 2,500,000 km2. In all of Russia only the Russians inhabit a larger territory. According to the administrative structure, the Evenks live, from west to east, in Tyumen and Tomsk Oblasts, Krasnoyarsk Krai with Evenk Autonomous Okrug, Irkutsk, Chita, and Amur Oblasts, the Buryat and the Sakha Republics, Khabarovsk Krai, and Sakhalin Oblast. However, the territory where they are a titular nation is confined solely to Evenk Autonomous Okrug, where 3,802 of the 35,527 Evenks live (according to the 2002 Census). More than 18,200 Evenks live in the Sakha Republic.  Evenki is the largest of the northern group of the Manchu-Tungus languages, a group which also includes Even and Negidal.  Many Evenks in Russia still engage in a traditional lifestyle of raising reindeer, fishing, and hunting.

Russian Federation.

According to the 2002 census 35,527 Evenki lived in Russia.

Evenks of China.

According to the 2000 Census, there are 30,505 Evenks in China mainly made up of the Solons and the Khamnigans. 88.8% of China's Evenks live in the Hulunbuir region in the north of the Inner Mongolia Province, near the city of Hailar. The Evenk Autonomous Banner is also located near Hulunbuir. There are also around 3,000 Evenks in neighbouring Heilongjiang Province.  The Manchu Emperor Hong Taiji conquered the Evenks in 1640, and executed their leader Bombogor. After the Manchu conquest, the Evenks were incorporated into the Eight Banners.  In 1763, the Qing government moved 500 Solon Evenk and 500 Daur families to the Tacheng and Ghulja areas of Xinjiang, in order to strengthen the empire's western border. 1020 Xibe families (some 4000 persons) followed the next year. Since then, however, the Solons of Xinjiang have assimilated into other ethnic groups, and are not identified as such anymore.  Some Evenkis fled to Soviet Siberia across the Amur river after murdering a Japanese officer to avoid punishment from the Japanese. The Japanese occuation led to many murders of Evenkis and Evenki men were conscripted as scouts and rangers by the Japanese secret service in 1942.  The Evenks of China today tend to be settled pastoralists and farmers.

Evenks of Ukraine.

According to the 2001 census, there were 48 Evenks living in Ukraine. The majority (35) stated that their native language was Russian; four indicated Evenk as their native language, and three that it was Ukrainian.

Religion.

Prior to contact with the Russians, the belief system of the Evenks was animistic. Many have adopted Tibetan Buddhism.  The Evenki, like most nomadic, pastoral, and subsistence agrarian peoples, spend most of their lives in very close contact with nature. Because of this, they develop what A. A. Sirina calls an "ecological ethic". By this she means "a system of responsibility of people to nature and her spirit masters, and of nature to people"(9). Sirina interviewed many Evenks who until very recently spent much of their time as reindeer herders in the taiga, just like their ancestors. The Evenki people also spoke along the same lines: their respect for nature and their belief that nature is a living being.  This idea, "[t]he embodiment, animation, and personification of nature—what is still called the animistic worldview—is the key component of the traditional worldview of hunter-gatherers" (Sirina, 13). Although most of the Evenkis have been "sedentarized"—that is, made to live in settled communities instead of following their traditional nomadic way of life (Fondahl, 5)—"[m]any scholars think that the worldview characteristic of hunter-gatherer societies is preserved, even if they make the transition to new economic models (Sirina, 30, quoting Barnard 1998, Lee 1999, Peterson 1999).  Although nominally Christianized in the 18th century, the Evenki people maintain many of their historical beliefs—especially shamanism (Vasilevich, 624). The Christian traditions were "confined to the formal performance of Orthodox rites which were usually timed for the arrival of the priest in the taiga" (647).  The religious beliefs and practices of the Evenks are of great historical interest since these retain some archaic forms of belief. Among the most ancient ideas are spiritualization and personification of all natural phenomena, belief in an upper, middle, and lower world, belief in the soul ("omi") and certain totemistic concepts. There were also various magical rituals associated with hunting and guarding herds. Later on, these rituals were conducted by shamans. Shamanism brought about the development of the views of spirit-masters (Vasilevich 647).  There are few sources on the shamanism of the Evenki peoples below the Amur/Helongkiang river in Northern China. There is a brief report of fieldwork conducted by Richard Noll and Kun Shi in 1994 of the life of the shamaness Dula'r (Evenki name), also known as Ao Yun Hua (her Han Chinese name). She was born in 1920 and was living in the village of Yiming Gatsa in the Evenki Banner (county) of the Hulunbuir Prefecture, in the Inner Mongolian Autonomous Region. While not a particularly good informant, she described her initiatory illness, her multiyear apprenticeship with a Mongol shaman before being allowed to heal at the age of 25 or 26, and the torments she experienced during the Cultural Revolution in the 1960s when most of her shamanic paraphernalia was destroyed. Mongol and Buddhist Lamaist influences on her indigenous practice of shamansim were evident. She hid her prize possession—an Abagaldi (bear spirit) shaman mask, which has also been documented among the Mongols and Dauer peoples in the region. The field report and color photographs of this shaman are available online.  Olga Kudrina (c. 1890–1944) was a shaman among the Reindeer Evenki of northern Inner Mongolia along the Amur River's Great Bend (today under the jurisdiction of Genhe, Hulunbuir).

The Evenks (also spelled Ewenki or Evenki based on their endonym "Ewenkī(l)") are a Tungusic people of Northern Asia. In Russia, the Evenks are recognised as one of the indigenous peoples of the Russian North, with a population of 38,396 (2010 census). In China, the Evenki form one of the 56 ethnic groups officially recognised by the People's Republic of China, with a population of 30,875 (2010 census). There are 537 Evenks in Mongolia (2015 census) called "Khamnigan" in Mongolian language.

鄂温克族(俄语:,旧称通古斯或索伦)是东北亚地区的一个民族,主要居住于俄罗斯西伯利亚以及中国内蒙古和黑龙江两省区,蒙古国也有少量分布。中国鄂温克人主要信仰萨满教,俄罗斯鄂温克人除少数信仰萨满教外,主要为东正教信徒。鄂温克人讲鄂温克语,属于阿尔泰语系—满-通古斯语族—通古斯语支, 无文字。历史上曾使用满文。


Life.

Sorghaghtani was the daughter of Jakha Gambhu, the younger brother of the powerful Keraite leader Toghrul, also known as Ong Khan. According to "The Secret History of the Mongols", around 1203, when Toghrul was a more powerful leader than Temüjin, Temüjin proposed to Toghrul that Temüjin's eldest son Jochi might marry Toghrul's daughter or granddaughter, thus binding the two groups. However, Toghrul refused this alliance, and later attempted to kill the increasingly powerful Temüjin through an invitation to discuss this proposal. However, Temüjin discovered this plan and they escaped at the last moment. Eventually, the Keraites were routed in the ensuing war and Toghrul was killed, possibly by the Naimans.  Unlike his brother, Jakha usually supported Temüjin and gave his two daughters to him and one more daughter to Genghis Khan's oldest son Jochi. Genghis married the elder of the daughters (later handed over to another general), and gave young Sorghaghtani, who was still a teenager, to his son Tolui. Sorghaghtani's father Jakha was probably killed when the Keraites revolted against Genghis Khan in 1204.  Like most Mongol women of the time, Sorghaghtani wielded great authority at home. Mongol women had far more rights than in many other cultures at the time, especially since the men were often away and they were the ones responsible for the home. Although she herself was illiterate, she recognized the value of literacy in running such a far-flung empire. Each of her sons learned a different language for different regions. Sorghaghtani, a Nestorian Christian, respected other religions. Her sons, like Genghis, were all very tolerant in matters of religion, and the Mongol Empire promulgated the notion of state above religion while supporting all major religions of the time. Sorghaghtani also financed the construction of a madrasa in Bukhara and gave alms to both Christians and Muslims.  Soghoghtani's husband Tolui, whose appanages included eastern Mongolia, parts of Iran and North China, died at the age of 41 in 1232. Ögedei Khan, Genghis's third son who had succeeded his father, gave her enduring authority to handle Tolui's estates. The "Secret History" suggests that Ögedei may have consulted Sorghaghtani on various matters, and he always held her in high regard. Ogedei appointed her in charge of the Empire's administration, which meant she played a pivotal role in securing the lands won under Genghis Khan.  Ögedei sought to link her realm to his and proposed marriage, which she declined; he then proposed that she marry his son Güyük (widows often married again within the family among Mongols), but she refused, claiming that her four sons needed her attention. This decision later turned out to be one of the most important ones in the formation of the Mongol Empire, as all four of Sorghaghtani's sons (grandsons of Genghis) became leaders in their own right.  When Sorghaghtani asked for part of Hebei province as her appanage in 1236 after the end of the Mongol conquest of the Jin dynasty, Ögedei hesitated, but not for long. She shunned him into compliance by pointing out that the place was hers by right anyway, because her husband had conquered it. However, Ögedei also expanded his personal appanage, seizing some territories of Tolui and took most of Sorghaghtani's soldiers.  After Ögedei Khan's death in 1241, his wife Töregene Khatun ruled as regent until 1246, when she managed to get her son Güyük elected as the Khagan at a large kurultai. However, he immediately set out to undermine his mother's power as well as that of Sorghaghtani, Alaqai Beki (the Ongud ruler and daughter of Genghis Khan) and Ebuskun (the wife of Chagatai Khan, regent for the Central Asian Empire).  Meanwhile, the ambitious Sorghaghtani had secretly teamed up with Güyük's cousin Batu Khan, the senior male in the Borjigin and ruler of the Golden Horde (north of Caspian Sea to Bulgaria). In 1248, when Güyük was setting out on a campaign to the Middle East (ostensibly for conquest, but possibly to defeat Batu Khan), he died under somewhat suspicious circumstances; some have speculated that Sorghaghtani may have taken "direct action against Güyük".  After Güyük's death, Sorghaghtani sent her eldest son Möngke to Batu Khan. Batu and Sorghaghtani championed the name of Möngke, who had fought along with Batu in the European campaign, as Khagan. Möngke was named Great Khan at a "kurultai" organized by Batu in Siberia some time before 1250, but this was contested as not being properly in Mongolia. However, the ancient Mongol homeland where Genghis was born was in her regency, so she organized a "kurultai" here which was attended by Batu's brother Berke. Möngke was formally named the Great Khan. The Ögedei and Güyük families attempted to overthrow him, but failed. Möngke arrested and drowned Güyük's widow Oghul Qaimish, and many other members of Ögedei's family.  Sorghaghtani fell ill and died in February or March 1252 around Tsagaan Sar, the Mongol New Year festival, a few months after Möngke's accession ceremony. She was buried in a Christian church in Gansu.

Children.

Sorghaghtani bore Tolui at least four children. They included:

Legacy.

In 1310, she was regarded as "Empress" in a ceremony that included a Nestorian mass. Sorghaghtani was enshrined in a Christian church in Ganzhou in 1335, and sacrifices were ordered to be offered here. By 1480 a cult had been conducted for her memory at the orda that was kept by the Chahars. This ordo moved to Ordos City (in modern Inner Mongolia) in the 17th century.  She is spoken of very highly both in the "Secret History", as well as by Muslim, Chinese and Christian historians.

Prester John.

Sorghaghtani was the niece of the powerful Keraite leader of the Mongols, Ong Khan (often known simply as Toghrul). To Europeans, Toghrul was one of the distant Eastern rulers who was sometimes associated with the legend of "Prester John". During Mongol-European diplomacy, the Mongols sometimes played upon this perception by the Europeans, describing Mongol princesses such as Sorghaghtani and Doquz Khatun as being "daughters of Prester John".

Sorghaghtani Beki () or Bekhi ("Bek(h)i" is a title), also written Sorkaktani, Sorkhokhtani, Sorkhogtani, Siyurkuktiti (c. 1190–1252; posthumous name: ) was a Keraite princess and daughter-in-law of Genghis Khan. Married to Tolui, Genghis' youngest son, Sorghaghtani Beki became one of the most powerful and competent people in the Mongol Empire. She made policy decisions at a pivotal moment that led to the transition of the Mongol Empire towards a more cosmopolitan and sophisticated style of administration. She raised her sons to be leaders, and maneuvered the family politics so that all four of her sons, Möngke Khan, Hulagu Khan, Ariq Böke, and Kublai Khan, went on to inherit the legacy of their grandfather.

唆鲁禾帖尼(;1190年-1252年),大蒙古国(蒙古帝国)皇太后,克烈氏,是拖雷的正妻,蒙哥、忽必烈、旭烈兀、阿里不哥的生母。蒙哥和忽必烈都做过大元(大蒙古国)的帝王,旭烈兀在西亚开创了伊儿汗国,阿里不哥1260年在蒙古本土被部分宗王贵族推举即位,并和忽必烈争位达四年之久,最终忽必烈胜利。由于她的这四个杰出的儿子都做过帝王,所以她被后世史学家称为“四帝之母”。


Definitions.

Probability mass function.

In general, if the random variable "X" follows the binomial distribution with parameters "n" ∈ N and "p" ∈ [0,1], we write "X" ~ B("n", "p"). The probability of getting exactly "k" successes in "n" independent Bernoulli trials is given by the probability mass function:  for "k" = 0, 1, 2,..., "n", where  is the binomial coefficient, hence the name of the distribution. The formula can be understood as follows. "k" successes occur with probability "p" and "n" − "k" failures occur with probability (1 − "p"). However, the "k" successes can occur anywhere among the "n" trials, and there are formula_10 different ways of distributing "k" successes in a sequence of "n" trials.  In creating reference tables for binomial distribution probability, usually the table is filled in up to "n"/2 values. This is because for "k" > "n"/2, the probability can be calculated by its complement as  Looking at the expression "f"("k", "n", "p") as a function of "k", there is a "k" value that maximizes it. This "k" value can be found by calculating and comparing it to 1. There is always an integer "M" that satisfies  "f"("k", "n", "p") is monotone increasing for "k" < "M" and monotone decreasing for "k" > "M", with the exception of the case where ("n" + 1)"p" is an integer. In this case, there are two values for which "f" is maximal: ("n" + 1)"p" and ("n" + 1)"p" − 1. "M" is the "most probable" outcome (that is, the most likely, although this can still be unlikely overall) of the Bernoulli trials and is called the mode.

Example.

Suppose a biased coin comes up heads with probability 0.3 when tossed. The probability of seeing exactly 4 heads in 6 tosses is

Cumulative distribution function.

The cumulative distribution function can be expressed as:  where formula_16 is the "floor" under "k", i.e. the greatest integer less than or equal to "k".  It can also be represented in terms of the regularized incomplete beta function, as follows:  which is equivalent to the cumulative distribution function of the -distribution:  Some closed-form bounds for the cumulative distribution function are given below.

Properties.

Expected value and variance.

If "X" ~ "B"("n", "p"), that is, "X" is a binomially distributed random variable, n being the total number of experiments and p the probability of each experiment yielding a successful result, then the expected value of "X" is:  This follows from the linearity of the expected value along with fact that is the sum of identical Bernoulli random variables, each with expected value. In other words, if formula_20 are identical (and independent) Bernoulli random variables with parameter, then formula_21 and  The variance is:  This similarly follows from the fact that the variance of a sum of independent random variables is the sum of the variances.

Higher moments.

The first 6 central moments are given by

Mode.

Usually the mode of a binomial "B"("n", "p") distribution is equal to formula_25, where formula_26 is the floor function. However, when ("n" + 1)"p" is an integer and "p" is neither 0 nor 1, then the distribution has two modes: ("n" + 1)"p" and ("n" + 1)"p" − 1. When "p" is equal to 0 or 1, the mode will be 0 and "n" correspondingly. These cases can be summarized as follows:  Proof: Let  For formula_29 only formula_30 has a nonzero value with formula_31. For formula_32 we find formula_33 and formula_34 for formula_35. This proves that the mode is 0 for formula_29 and formula_7 for formula_32.  Let formula_39. We find  From this follows  So when formula_42 is an integer, then formula_42 and formula_44 is a mode. In the case that formula_45, then only formula_46 is a mode.

Median.

In general, there is no single formula to find the median for a binomial distribution, and it may even be non-unique. However several special results have been established:

Tail bounds.

For "k" ≤ "np", upper bounds can be derived for the lower tail of the cumulative distribution function formula_47, the probability that there are at most "k" successes. Since formula_48, these bounds can also be seen as bounds for the upper tail of the cumulative distribution function for "k" ≥ "np".  Hoeffding's inequality yields the simple bound  which is however not very tight. In particular, for "p" = 1, we have that "F"("k";"n","p") = 0 (for fixed "k", "n" with "k" < "n"), but Hoeffding's bound evaluates to a positive constant.  A sharper bound can be obtained from the Chernoff bound:  where "D"("a" || "p") is the relative entropy between an "a"-coin and a "p"-coin (i.e. between the Bernoulli("a") and Bernoulli("p") distribution):  Asymptotically, this bound is reasonably tight; see for details.  One can also obtain "lower" bounds on the tail formula_52, known as anti-concentration bounds. By approximating the binomial coefficient with Stirling's formula it can be shown that which implies the simpler but looser bound  For "p" = 1/2 and "k" ≥ 3"n"/8 for even "n", it is possible to make the denominator constant:

Statistical Inference.

Estimation of parameters.

When "n" is known, the parameter "p" can be estimated using the proportion of successes: formula_56 This estimator is found using maximum likelihood estimator and also the method of moments. This estimator is unbiased and uniformly with minimum variance, proven using Lehmann–Scheffé theorem, since it is based on a minimal sufficient and complete statistic (i.e.: "x"). It is also consistent both in probability and in MSE.  A closed form Bayes estimator for "p" also exists when using the Beta distribution as a conjugate prior distribution. When using a general formula_57 as a prior, the posterior mean estimator is: formula_58. The Bayes estimator is asymptoticly efficient and as the sample size approaches infinity ("n" → ∞), it approaches the MLE solution. The Bayes estimator is biased (how much depends on the priors), admissible and consistent in probability.  For the special case of using the standard uniform distribution as a non-informative prior (formula_59), the posterior mean estimator becomes formula_60 (a posterior mode should just lead to the standard estimator). This method is called the rule of succession, which was introduced in the 18th century by Pierre-Simon Laplace.  When estimating "p" with very rare events and a small "n" (e.g.: if x=0), then using the standard estimator leads to formula_61 which sometimes is unrealistic and undesirable. In such cases there are various alternative estimators. One way is to use the Bayes estimator, leading to: formula_62). Another method is to use the upper bound of the confidence interval obtained using the rule of three: formula_63)

Confidence intervals.

Even for quite large values of "n", the actual distribution of the mean is significantly nonnormal. Because of this problem several methods to estimate confidence intervals have been proposed.  In the equations for confidence intervals below, the variables have the following meaning:

Wilson (score) method.

The notation in the formula below differs from the previous formulas in two respects:

Comparison.

The exact (Clopper–Pearson) method is the most conservative.  The Wald method, although commonly recommended in textbooks, is the most biased.

Related distributions.

Sums of binomials.

If "X" ~ B("n", "p") and "Y" ~ B("m", "p") are independent binomial variables with the same probability "p", then "X" + "Y" is again a binomial variable; its distribution is "Z=X+Y" ~ B("n+m", "p"):  However, if "X" and "Y" do not have the same probability "p", then the variance of the sum will be smaller than the variance of a binomial variable distributed as formula_82

Ratio of two binomial distributions.

This result was first derived by Katz et al. in 1978.  Let "X" ~ B("n","p") and "Y" ~ B("m","p") be independent. Let "T" = ("X"/"n")/("Y"/"m").  Then log("T") is approximately normally distributed with mean log("p"/"p") and variance ((1/"p") − 1)/"n" + ((1/"p") − 1)/"m".

Conditional binomials.

If "X" ~ B("n", "p") and "Y" | "X" ~ B("X", "q") (the conditional distribution of "Y", given "X"), then "Y" is a simple binomial random variable with distribution "Y" ~ B("n", "pq").  For example, imagine throwing "n" balls to a basket "U" and taking the balls that hit and throwing them to another basket "U". If "p" is the probability to hit "U" then "X" ~ B("n", "p") is the number of balls that hit "U". If "q" is the probability to hit "U" then the number of balls that hit "U" is "Y" ~ B("X", "q") and therefore "Y" ~ B("n", "pq"). Since formula_83 and formula_84, by the law of total probability, Since formula_86 the equation above can be expressed as Factoring formula_88 and pulling all the terms that don't depend on formula_89 out of the sum now yields After substituting formula_91 in the expression above, we get Notice that the sum (in the parentheses) above equals formula_93 by the binomial theorem. Substituting this in finally yields and thus formula_95 as desired.

Bernoulli distribution.

The Bernoulli distribution is a special case of the binomial distribution, where "n" = 1. Symbolically, "X" ~ B(1, "p") has the same meaning as "X" ~ Bernoulli("p"). Conversely, any binomial distribution, B("n", "p"), is the distribution of the sum of "n" Bernoulli trials, Bernoulli("p"), each with the same probability "p".

Poisson binomial distribution.

The binomial distribution is a special case of the Poisson binomial distribution, or general binomial distribution, which is the distribution of a sum of "n" independent non-identical Bernoulli trials B("p").

Normal approximation.

If "n" is large enough, then the skew of the distribution is not too great. In this case a reasonable approximation to B("n", "p") is given by the normal distribution  and this basic approximation can be improved in a simple way by using a suitable continuity correction. The basic approximation generally improves as "n" increases (at least 20) and is better when "p" is not near to 0 or 1. Various rules of thumb may be used to decide whether "n" is large enough, and "p" is far enough from the extremes of zero or one:  The rule formula_100 is totally equivalent to request that Moving terms around yields: Since formula_103 and formula_104, to obtain the desired conditions: Notice that these conditions automatically imply that formula_106. On the other hand, apply again the square root and divide by 3, Subtracting the second set of inequalities from the first one yields: and so, the desired first rule is satisfied,  Assume that both values formula_110 and formula_111 are greater than 9. Since formula_114, we easily have that We only have to divide now by the respective factors formula_116 and formula_117, to deduce the alternative form of the 3-standard-deviation rule: The following is an example of applying a continuity correction. Suppose one wishes to calculate Pr("X" ≤ 8) for a binomial random variable "X". If "Y" has a distribution given by the normal approximation, then Pr("X" ≤ 8) is approximated by Pr("Y" ≤ 8.5). The addition of 0.5 is the continuity correction; the uncorrected normal approximation gives considerably less accurate results.  This approximation, known as de Moivre–Laplace theorem, is a huge time-saver when undertaking calculations by hand (exact calculations with large "n" are very onerous); historically, it was the first use of the normal distribution, introduced in Abraham de Moivre's book "The Doctrine of Chances" in 1738. Nowadays, it can be seen as a consequence of the central limit theorem since B("n", "p") is a sum of "n" independent, identically distributed Bernoulli variables with parameter "p". This fact is the basis of a hypothesis test, a "proportion z-test", for the value of "p" using "x/n", the sample proportion and estimator of "p", in a common test statistic.  For example, suppose one randomly samples "n" people out of a large population and ask them whether they agree with a certain statement. The proportion of people who agree will of course depend on the sample. If groups of "n" people were sampled repeatedly and truly randomly, the proportions would follow an approximate normal distribution with mean equal to the true proportion "p" of agreement in the population and with standard deviation formula_119

Poisson approximation.

The binomial distribution converges towards the Poisson distribution as the number of trials goes to infinity while the product "np" remains fixed or at least "p" tends to zero. Therefore, the Poisson distribution with parameter "λ" = "np" can be used as an approximation to B("n", "p") of the binomial distribution if "n" is sufficiently large and "p" is sufficiently small. According to two rules of thumb, this approximation is good if "n" ≥ 20 and "p" ≤ 0.05, or if "n" ≥ 100 and "np" ≤ 10.  Concerning the accuracy of Poisson approximation, see Novak, ch. 4, and references therein.

Beta distribution.

The binomial distribution and beta distribution are different views of the same model of repeated Bernoulli trials. The binomial distribution is the PMF of successes given independent events each with a probability of success. Mathematically, when and, the beta distribution and the binomial distribution are related by a factor of :  Beta distributions also provide a family of prior probability distributions for binomial distributions in Bayesian inference: Given a uniform prior, the posterior distribution for the probability of success given independent events with observed successes is a beta distribution.

Computational methods.

Generating binomial random variates.

Methods for random number generation where the marginal distribution is a binomial distribution are well-established.  One way to generate random samples from a binomial distribution is to use an inversion algorithm. To do so, one must calculate the probability that for all values from through. (These probabilities should sum to a value close to one, in order to encompass the entire sample space.) Then by using a pseudorandom number generator to generate samples uniformly between 0 and 1, one can transform the calculated samples into discrete numbers by using the probabilities calculated in the first step.

History.

This distribution was derived by James Bernoulli. He considered the case where "p" = "r"/("r" + "s") where "p" is the probability of success and "r" and "s" are positive integers. Blaise Pascal had earlier considered the case where "p" = 1/2.

In probability theory and statistics, the binomial distribution with parameters "n" and "p" is the discrete probability distribution of the number of successes in a sequence of "n" independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: success/yes/true/one (with probability "p") or failure/no/false/zero (with probability "q" = 1 − "p"). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., "n" = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

\! 在概率论和统计学中,二项分布(英语:Binomial Distribution)是"n"个独立的是/非试验中成功的次数的离散概率分布,其中每次试验的成功概率为"p"。这样的单次成功/失败试验又称为伯努利试验。实际上,当"n" = 1时,二项分布就是伯努利分布。二项分布是显著性差异的二项试验的基础。


History.

1968–1977.

SDAJ was formed on May 5, 1968, the 150th birthday of Karl Marx. The SDAJ participated in social movements that arose from 1968's student movement. It became one of the leading left-wing youth organizations in West Germany and enjoyed a high political profile – for example, in actions against fare increases ("Red Dot Actions"). The SDAJ claimed over 35,000 members.

1978–1987.

From 1978 to 1988, the SDAJ organized the Festival of Youth biannually together with the Marxist Student Association Spartacus (MSB). The Festival was held mid-May on the grounds of the Dortmund exhibition. Internationally known artists attended. For example, the 1978 festival included figures such as Jutta Weinhold, Snowball, Udo Lindenberg, Pudys and the Titi Winterstein Quintet. Political debates were a common feature. According to the SDAJ, more than 100,000 visitors attended.  Until the fall of the GDR, the SDAJ maintained contact with Free German Youth (FDJ), a sibling organization.  In the 1980s, the SDAJ played a major role in the West German peace movement.

1988–1997.

In 1988, conflicts emerged in SDAJ and DKP as reformist tendencies gained strength. At the SDAJ Federal Congress of 1989 the organization split, as the majority of the delegates voted for a proposal that would keep the SDAJ as a Marxist working class youth organization. The defeated faction grouped around then national chairman Birgit Radow and left the Congress. The Radow group failed to create a nationwide organization. Many former leading members switched to the youth structures of the PDS.  The fall of the GDR and the reunification of Germany, produced a crisis in SDAJ and DKP. Funding from GDR was discontinued and employees were laid off. Until about 1993, the SDAJ remained virtually without functioning central coordination. In 1994 the reorganization and reactivation of district and local associations began. As of the late 1990s local groups stabilized and new groups established in areas including Leipzig, Dresden, Gera, Potsdam, Rostock, Gadebusch and Berlin.

1998-.

Due to the slight increase in membership, the bi-annual Festival of Youth was refounded in 2008 in Jugendpark of Cologne.  In October 2011, the SDAJ held its 20th national congress of Hanover.

Socialist German Workers Youth (, abbreviated SDAJ) is a political youth organization in Germany. It is a Marxist–Leninist organization and related to the Deutsche Kommunistische Partei (German Communist Party). SDAJ is a member of World Federation of Democratic Youth.

社会主义德国工人青年(,缩写为SDAJ)是德国的一个青年组织,与德国的共产党相关,被视为该党的青年翼。该组织成立于1968年5月5日(卡尔·马克思诞辰150周年纪念日)。该组织以马克思列宁主义为指导思想。该组织的总部位于埃森。该组织的主席是Lena Kreymann。该组织是世界民主青年联盟的成员。该组织曾派代表参加欧洲共产主义青年组织会议。2014年,该组织有500名成员。


Supported dialects.

Initially, Free Pascal adopted the "de facto" standard dialect of Pascal programmers Borland Pascal but later on adopted Delphi. From version 2.0 on, Delphi compatibility has been continuously implemented or improved.  The project has a "compilation mode" concept, and the developers made it clear that they would incorporate working patches for the standardized dialects of the American National Standards Institute (ANSI) and International Organization for Standardization (ISO) to create a standards-compliant mode.  A small effort has been made to support some of the Apple Pascal syntax to ease interfacing to the Classic Mac OS and macOS. Since the Apple dialect implements some standard Pascal features that Turbo Pascal and Delphi omit, Free Pascal is a bit more ISO-compatible than these.  The 2.2."x" release series did not significantly change the dialect objectives beyond roughly Delphi 7 level syntax, instead aiming for closer compatibility. A notable exception to this was the addition of support for generics to Free Pascal in version 2.2.0, several years before they were supported in any capacity by Delphi. , several Delphi 2006-specific features were added in the development branch, and some of the starting work for the features new in Delphi 2009 (most notably the addition of the codice_1 type) was completed. The development branch also features an "Objective-Pascal" extension for Objective-C (Cocoa) interfacing.  As of version 2.7.1, Free Pascal implemented basic ISO Pascal mode, though many things such as codice_2 and codice_3 procedure and file-buffer variable concept for file handling were still absent.  As of version 3.0.0, ISO Pascal mode is fairly complete, with one remaining bug that has since been fixed in the trunk branch. It has been able to compile standardpascal.org's P5 ISO Pascal compiler with no changes.

History.

Early years.

Free Pascal was created when Borland clarified that Borland Pascal development for DOS would stop with version 7, to be replaced by a Windows-only product, which later became Delphi.  Student Florian Paul Klämpfl began developing his own compiler written in the Turbo Pascal dialect and produced 32-bit code for the GO32v1 DOS extender, which was used and developed by the DJ's GNU Programming Platform (DJGPP) project at that time.  Originally, the compiler was a 16-bit DOS executable compiled by Turbo Pascal. After two years, the compiler was able to compile itself and became a 32-bit executable.

Expansion.

The initial 32-bit compiler was published on the Internet, and the first contributors joined the project. Later, a Linux port was created by Michael van Canneyt, five years before the Borland Kylix compiler became available.  The DOS port was adapted for use in OS/2 using the Eberhard Mattes eXtender (EMX) which made OS/2 the second supported compiling target. As well as Florian Klämpfl the original author, Daniël Mantione also contributed significantly to make this happen, providing the original port of the run-time library to OS/2 and EMX. The compiler improved gradually, and the DOS version migrated to the GO32v2 extender. This culminated in release 0.99.5, which was much more widely used than prior versions, and was the last release aiming only for Turbo Pascal compliance; later releases added a Delphi compatibility mode. This release was also ported to systems using Motorola 68000 family (m68k) processors.  With release 0.99.8 the Win32 target was added, and a start was made with incorporating some Delphi features. Stabilizing for a non-beta release began, and version 1.0 was released in July 2000. The 1.0."x" series was widely used, in business and education. For the 1.0."x" releases, the port to 68k CPU was redone, and the compiler produced stable code for several 68k Unix-like and AmigaOS operating systems.

Version 2.

During the stabilization of what would become 1.0."x", and also when porting to the Motorola 68k systems, it was clear that the design of the code generator was far too limited in many aspects. The principal problems were that adding processors meant rewriting the code generator, and that the register allocation was based on the principle of always keeping three free registers between building blocks, which was inflexible and difficult to maintain.  For these reasons, the 1.1."x" series branched off from the 1.0."x" main branch in December 1999. At first, changes were mostly clean-ups and rewrite-redesigns to all parts of the compiler. The code generator and register allocator were also rewritten. Any remaining missing Delphi compatibility was added.  The work on 1.1.x continued slowly but steadily. In late 2003, a working PowerPC port became available, followed by an ARM port in summer 2004, a SPARC port in fall 2004, and an x86-64-AMD64 port in early 2004, which made the compiler available for a 64-bit platform.  In November 2003, a first beta release of the 1.1."x" branch was packaged and numbered 1.9.0. These were quickly followed by versions 1.9.2 and 1.9.4; the latter introduced OS X support. The work continued with version 1.9.6 (January 2005), 1.9.8 (late February 2005), 2.0.0 (May 2005), 2.0.2 (December 2005), and 2.0.4 (August 2006).

Version 2.2.x.

In 2006, some of the major reworks planned for 2.2, such as the rewrite of the unit system, had still not begun, and it was decided to instead start stabilizing the already implemented features.  Some of the motives for this roadmap change were the needs of the Lazarus integrated development environment project, particularly the internal linker, support for Win64, Windows CE, and OS X on x86, and related features like DWARF. After betas 2.1.2 and 2.1.4, version 2.2.0 was released in September 2007, followed by version 2.2.2 in August 2008 and version 2.2.4 in March 2009.  The 2.2."x" series vastly improved support for the ActiveX and Component Object Model (COM) interface, and Object Linking and Embedding (OLE), though bugs were still being found. The delegation to interface using the codice_4 keyword was partly implemented, but was not complete. Library support for ActiveX was also improved.  Another major feature was the internal linker for Win32, Win64, and Windows CE, which greatly improved linking time and memory use, and make the compile-link-run cycle in Lazarus much faster. The efficiency for smart-linking, or dead code elimination, was also improved.  Minor new features included improved DWARF (2/3) debug format support, and optimizations such as tail recursion, omission of unneeded stack frames and register-based common subexpression elimination (CSE) optimization. A first implementation of generic programming (generics) support also became available, but only experimentally.

Version 2.4.x.

The 2.4.x release series had a less clear set of goals than earlier releases. The unit system rewrite was postponed again, and the branch that became 2.4 was created to keep risky commits from 2.2 to stabilize it. Mostly these risky commits were more involved improvements to the new platforms, Mac PowerPC 64, Mac x86-64, iPhone, and many fixes to the ARM and x86-64 architectures in general, as well as DWARF.  Other compiler improvements included whole program optimization (WPO) and devirtualization and ARM embedded-application binary interface (EABI) support.  Later, during the 2.2 cycle, a more Delphi-like resource support (based on special sections in the binary instead of Pascal constants) was added. This feature, direly needed by Lazarus, became the main highlight of the branch.  Other more minor additions were a memory manager that improved heap manager performance in threaded environments, small improvements in Delphi compatibility such as codice_5, and improvements in interface delegation.  On January 1, 2010, Free Pascal 2.4.0 was released, followed on November 13, 2010, by bug fix release 2.4.2, with support for codice_6 loops, codice_7 and codice_8 classes, and other changes.

Version 2.6.x.

In January 2012, Free Pascal 2.6 was released. This first version from the 2.6 release series also supported Objective Pascal on OS X and iOS targets and implemented many small improvements and bug fixes. In February 2013, FPC 2.6.2 was released. It contained NetBSD and OpenBSD releases for the first time since 1.0.10, based on fresh ports. In March 2014, the last point release in the 2.6 series, 2.6.4, was launched, featuring mostly database (fcl-db) updates.

Version 3.0.x.

Version 3.0.0 was released on November 25, 2015 and was the first major release since January 1, 2012. It contains many new language features: FPC New Features 3.0  Version 3.0.2 was released on February 15, 2017 and includes bug fixes and minor compiler updates.
 Version 3.0.4 was released on November 28, 2017.
 It includes many language improvements over previous versions like an internal linker for Executable and Linkable Format (ELF), Arm AARCH64 for iOS and Linux, a revived i8086 platform, extended libraries and much more.

Version 3.2.x.

The next major release, version 3.2.0, was published on June 19, 2020. It introduced a plethora of new language features including generic routines, standard namespaces, managed records and expanded functionality for dynamic arrays, in addition to the advent of new standard units and the support of additional platforms.

Targets.

Free Pascal also supports byte code generation for the Java Virtual Machine as of version 3.0.0 and targets both Oracle's Java and Google's Android JVM, although Object Pascal syntax is not fully supported. Free Pascal 3.0.0 also supports ARMHF platforms like the Raspberry Pi, including ARMV6-EABIHF running on Raspbian. Work on 64-bit ARM has resulted in support for iOS in 3.0.0 as well. A native ARM Android target has been added, ending the formerly hacked ARM Linux target to generate native ARM libraries for Android. This makes porting Lazarus applications to Android (using Custom Drawn Interface) easier. Since FPC 2.6.2, OpenBSD and NetBSD are supported on IA32 and X86_64 architectures. A new target "embedded" has been added for usage without OS (ARM Cortex M and MIPS mainly). With InstantFPC it is possible to run Pascal programs, which are translated just in time, as Unix scripts or CGI back-end.

Integrated development environments.

Like most modern compilers, Free Pascal can be used with an integrated development environment (IDE). Besides independent IDEs there are also plugins to various existing IDEs

Bundled libraries.

Apart from a compiler and an IDE Free Pascal provides the following libraries:

Free Pascal Compiler (FPC) is a compiler for the closely related programming-language dialects Pascal and Object Pascal. It is free software released under the GNU General Public License, with exception clauses that allow static linking against its runtime libraries and packages for any purpose in combination with any other software license.

Free Pascal (简称 FPC,原名为 FPK Pascal),是一个支持16位,32位和64位处理器的专业 Pascal 语言编译器,支持多种处理器架构,包括:Intel x86(也支持8086)、AMD64/x86-64、PowerPC及其64位架构、SPARC、ARM、AArch64、MIPS 以及 JVM。Free Pascal 支持多种操作系统,包括:GNU/Linux、FreeBSD、Haiku、Mac OS X/iOS/Darwin、DOS、Win32/64、WinCE、OS/2、MorphOS、Nintendo GBA、Nintendo DS、Nintendo Wii、Android、AIX and AROS,对 Motorola 68k 的支持也在开发中。


Signs and symptoms.

Those with nightmares experience abnormal sleep architecture and that the results of having a nightmare during the night were very similar to those of people who have insomnia. This is thought to be caused by frequent nocturnal awakenings and fear of falling asleep.

Classification.

According to the International Classification of Sleep Disorders-Third Edition (ICSD-3) the nightmare disorder, together with REM sleep behaviour disorder (RBD) and recurrent isolated sleep paralysis form the REM-related parasomnias subcategory of the Parasomnias cluster. Nightmares may be idiopathic without any signs of psychopathology or associated with disorders like stress, anxiety, substance abuse, psychiatric illness or PTSD (>80% of PTSD patients report nightmares). As regarding the dream content of the dreams they are usually imprinting negative emotions like sadness, fear or rage. According to the clinical studies the content can range from being chased, injury or death of others, falling, natural disasters or accidents. Typical dreams or recurrent dreams may also have some of these topics.

Cause.

Scientific research shows that nightmares may have many causes. In a study focusing on children, researchers were able to conclude that nightmares directly correlate with the stress in children’s lives. Children who experienced the death of a family member or a close friend or know someone with a chronic illness have more frequent nightmares than those who are only faced with stress from school or stress from social aspects of daily life. A study researching the causes of nightmares focuses on patients who have sleep apnea. The study was conducted to determine whether or not nightmares may be caused by sleep apnea, or being unable to breathe. In the nineteenth century, authors believed that nightmares were caused by not having enough oxygen, therefore it was believed that those with sleep apnea had more frequent nightmares than those without it. The results actually showed that healthy people have more nightmares than the sleep apnea patients. Another study supports the hypothesis. In this study, 48 patients (aged 20–85 yrs) with obstructive airways disease (OAD), including 21 with and 27 without asthma, were compared with 149 sex- and age-matched controls without respiratory disease. OAD subjects with asthma reported approximately 3 times as many nightmares as controls or OAD subjects without asthma. The evolutionary purpose of nightmares then could be a mechanism to awaken a person who is in danger.  Lucid-dreaming advocate Stephen LaBerge has outlined a possible reason for how dreams are formulated and why nightmares occur with a high frequency. To LaBerge, a dream starts with an individual thought or scene, such as walking down a dimly lit street. Since dreams are not predetermined, the brain responds to the situation by either thinking a good thought or a bad thought, and the dream framework follows from there. Since the prominence of bad thoughts in dreams is higher than good, the dream will proceed to be a nightmare.

Nightmare myths.

There is a view, possibly featured in the story "A Christmas Carol", that eating cheese before sleep can cause nightmares, but there is little scientific evidence for this phenomenon.

Treatment.

Sigmund Freud and Carl Jung seemed to have shared a belief that people frequently distressed by nightmares could be re-experiencing some stressful event from the past. Both perspectives on dreams suggest that therapy can provide relief from the dilemma of the nightmarish experience.  Halliday (1987), grouped treatment techniques into four classes. Direct nightmare interventions that combine compatible techniques from one or more of these classes may enhance overall treatment effectiveness:

Posttraumatic stress disorder.

Recurring posttraumatic stress disorder nightmares in which traumas are re-experienced respond well to a technique called imagery rehearsal. This involves dreamers coming up with alternative, mastery outcomes to the nightmares, mentally rehearsing those outcomes while awake, and then reminding themselves at bedtime that they wish these alternate outcomes should the nightmares reoccur. Research has found that this technique not only reduces the occurrence of nightmares and insomnia, but also improves other daytime PTSD symptoms. The most common variations of Imagery Rehearsal Therapy (IRT) "relate to the number of sessions, duration of treatment, and the degree to which exposure therapy is included in the protocol". The medication prazosin appears useful in decreasing the number of nightmares and the distress caused by them in people with PTSD.

Epidemiology.

The prevalence in children (5–12 years old) is between 20 and 30%, and in adults 8 to 30%.

Etymology.

The word "nightmare" is derived from the Old English "mare", a mythological demon or goblin who torments others with frightening dreams. The term has no connection with the word for "female horse." Subsequently, the prefix "night-" was added to stress the dream aspect. The word "nightmare" is cognate with the Dutch term "nachtmerrie" and German "Nachtmahr" (dated).

A nightmare, also called a bad dream, is an unpleasant dream that can cause a strong emotional response from the mind, typically fear but also despair, anxiety and great sadness. However, psychological nomenclature differentiates between nightmares and bad dreams, specifically, people remain asleep during bad dreams whereas nightmares awaken individuals. Further, the process of psychological homeostasis employs bad dreams to protect an individual's Homeostatically Protected Mood (HPMood) from the impact of elevated anxiety levels. During sleep, nightmares indicate the failure of the homeostatic system employing bad dreams to extinguish anxiety accumulated throughout the day. The dream may contain situations of discomfort, psychological or physical terror or panic. After a nightmare, a person will often awaken in a state of distress and may be unable to return to sleep for a short period of time.

恶梦(nightmare),亦称噩梦或梦魇,指人在睡眠时做的令人感到恐惧的梦,有时伴有胸闷气短等难受的感觉。恶梦主要有梦魇、被追杀和人悬空、人下落三大类型,这三大类型的恶梦分别是因可怕的晕厥、可怕的似乎被追杀的心悸感和可怕的心悬空、心下落的心悸感这三大心血管病的症状引起的。