title: Dora Richter

text: Dora "Dorchen" Richter (16 April 1891 – presumed 1933) was the first known person to undergo complete male-to-female gender reassignment surgery. She was one of a number of transgender people in the care of sex-research pioneer Magnus Hirschfeld at Berlin's Institute for Sexual Research during the 1920s and early 1930s. She underwent surgical removal of the testicles in 1922, followed in 1931 by removal of the penis and vaginoplasty.


title: Dora Richter

text: Richter was born as the oldest child of six to a poor farming family in Bohemian Ore Mountains region in 1891. Early in childhood, Richter displayed a "tendency to act and carry on in a feminine way". At the age of 6 years, she apparently tried to remove her penis with a tourniquet.


title: Dora Richter

text: In 1909, after a baker apprenticeship she left her small town and moved to a bigger one, where she continued to dress as a girl in her free time. She joined a wandering theater troupe and got to Leipzig, where she stayed for two years. In 1916 she got drafted to the army, but got discarded in just two weeks. From Leipzig she came back to her hometown, where she was encouraged by a friend to go to Hirschfeld's practice in Berlin. From May 1923, Richter worked with other transgender people as a domestic servant at the Institute for Sexual Research, one of the few places where a trans person could be employed, where she was affectionately known as Dorchen. In 1922, she underwent an orchiectomy. In 1931 , a psychiatrist working at the institute, published a paper about Richter's (and Toni Ebel's) gender confirming surgeries as a case study in "Zeitschrift für Sexualwissenschaft und Sexualpolitik": "Her castration had the effect – albeit not very extensive – of making her body become fuller, restricting her beard growth, making visible the first signs of breast development, and giving the pelvic fat pad... a more feminine shape."


title: Dora Richter

text: In early 1931, Richter had a penectomy performed by institute physician Ludwig Levy-Lenz, and in June that year an artificial vagina was surgically grafted by Berlin surgeon , making her the first transgender woman of whom records remain to undergo vaginoplasty. Late 1931 she was working as a cook in Restaurant Kempinski (modern Hotel Bristol) at Kurfürstendamm 27.


title: Dora Richter

text: In 1933 footage of Dora and two other Hirschfeld trans patients, Toni Ebel and Charlotte Charlaque (all anonymously/uncredited) was used as a documentary segment in an Austrian movie "Mysterium des Geschlechtes" ("Mystery of Sex") about contemporary sexology.


title: Dora Richter

text: In May 1933, with growing Nazi influence in Germany (Hirschfeld had fled the country), a mob of students attacked the institute, and the state authorities then burned its records. Richter's fate after this attack is not known. Nowadays it is presumed that she was either killed in the attack or was arrested after it and died in custody. However, in 1955, Charlotte Charlaque, who fled Germany to Karlsbad in 1933, wrote in a pseudonymized article about Hirschfeld "sex change" patients, that Dora Richter, "[...] born in Karlsbad, Bohemia[...] soon became an owner of a small restaurant in the city of her birth".


title: Margaret, Maid of Norway

text: Margaret (, ; March or April 1283 – September 1290), known as the Maid of Norway, was the queen-designate of Scotland from 1286 until her death. As she was never inaugurated, her status as monarch is uncertain and has been debated by historians.


title: Margaret, Maid of Norway

text: Margaret was the daughter of King Eric II of Norway and Margaret of Scotland. By the end of the reign of her maternal grandfather, King Alexander III of Scotland, she was his only surviving descendant and recognized heir presumptive. Alexander III died in 1286, his posthumous child was stillborn, and Margaret inherited the crown. Owing to her young age, she remained in Norway rather than going to Scotland. Her father and the Scottish leaders negotiated her marriage to Edward of Caernarfon, son of King Edward I of England. She was finally sent to Great Britain in September 1290, but died in Orkney, sparking off the succession dispute between thirteen competitors for the crown of Scotland.


title: Margaret, Maid of Norway

text: Margaret, Maid of Norway, was the only child of King Eric II of Norway and his first wife, Margaret, daughter of King Alexander III of Scotland. She was born in Tønsberg, a coastal town in southeastern Norway, between March and 9 April 1283, when her mother died, apparently from the complications of childbirth. Aged fifteen and possessing little royal authority, King Eric did not have much say about his daughter's future. The infant Margaret was instead in the custody of the leading Norwegian magnate, Narve, Bishop of Bergen. Margaret's upbringing in the city of Bergen shows that her future marriage was expected to be important to the kingdom's foreign policy. The 1281 treaty arranging the marriage of Eric of Norway and Margaret of Scotland specified that the Scottish princess and her children would succeed to the throne of Scotland if King Alexander died leaving no legitimate sons and if no legitimate son of King Alexander left legitimate children. It also stated that the couple's daughters could inherit the Norwegian throne "if it is the custom". The Scottish party seems to have been deceived because the succession law of Norway, codified in 1280, provided only for succession by males, meaning that the Maid could not have succeeded to her father's kingdom.


title: Margaret, Maid of Norway

text: Alexander, brother of Margaret's mother and the last surviving child of the King of Scotland, died on 28 January 1284. The Maid was left as the only living descendant of Alexander III. The King did not wait to discover whether his son's widow, Margaret of Flanders, was pregnant. Already on 5 February he had all thirteen earls, twenty-four barons, and three clan chiefs come to Scone and swear to recognize his granddaughter as his successor if he died leaving neither son nor daughter and if no posthumous child was born to his son. By April it had presumably become clear that the young Alexander's widow was not expecting a child and that Margaret was the heir presumptive.


title: Margaret, Maid of Norway

text: Alexander III's wife, another Margaret, sister of King Edward I of England, had died in 1275, and the oath he exacted strongly implied that he now intended to remarry. When Edward expressed his condolence to Alexander III that month for the death of his son, the latter responded that "much good may come to pass yet through your kinswoman, the daughter of your niece ... who is now our heir", suggesting that the two kings may have already been discussing a suitable marriage for Margaret. Alexander and his magnates may have hoped for an English match. The King took a new wife, Yolanda of Dreux, on 14 October 1285, hoping to father another child. On the evening of 18 March 1286, he set out to meet with Queen Yolanda, only to be found dead with a broken neck the next day.


title: Margaret, Maid of Norway

text: Following the unexpected death of King Alexander, Scottish magnates gathered to discuss the future of the kingdom. They swore to preserve the throne for the right heir and chose six regents, known as guardians of Scotland, to govern the country. Although the succession had been laid out by the time King Alexander III died, Margaret's accession was not yet assured: Her stepgrandmother, Queen Yolanda, was pregnant and the child was expected to succeed to the throne. There was a dispute in parliament in April involving Robert Bruce, 5th Lord of Annandale, and John Balliol, Lord of Galloway. Bruce may have opposed the Maid's succession, or the two men may have both claimed to be next in line to the throne after Yolanda's child and Margaret. Queen Yolanda delivered a stillborn child in November, and within a few months King Eric's most prominent councilor, Bjarne Erlingsson, arrived in Scotland to claim the kingdom for Margaret. Bruce raised a rebellion with his son, Robert, Earl of Carrick, but was defeated in early 1287. The precariousness of the situation made King Eric reluctant to see his three-year-old daughter leave Norway for Scotland.


title: Margaret, Maid of Norway

text: In May 1289, Eric II sent envoys to Edward I as part of the kings' unfolding discussion about the future of Margaret, whom they called "lady and queen". As Margaret was still with her father, the Scots could only observe the negotiations between the two kings. Eric was indebted to Edward, and Edward was determined to make the most of the situation. The guardians, accompanied by Bruce, finally met with English and Norwegian envoys at Salisbury in October. The Treaty of Salisbury was drawn up on 6 November 1289, stating that Eric and Margaret, "queen and heir of the kingdom", asked Edward to intervene on behalf of his grandniece so "that she could ordain and enjoy therein as other kings do in their kingdoms". Margaret was to be sent, by 1 November 1290, to England directly or via Scotland. Once the Scots could assure Edward that Scotland was peaceful and safe, he would send her to them. Edward was allowed to choose her husband, though her father retained the right to veto the choice. At Edward's request, a papal dispensation permitting Margaret to marry her granduncle's son, Edward of Caernarfon, was issued on 16 November 1289. The guardians and other prelates and magnates wrote that they were firmly in favour of the English match for "the lady Margaret queen of Scotland, our lady". It was strongly implied that Margaret's husband would be king, and Edward insisted on referring to Margaret as queen in order to speed up the accession of his own son, though the Scots themselves normally described her only as their lady.


title: Margaret, Maid of Norway

text: Negotiations about Margaret's marriage, dower, succession, and the nature of the intended personal union between England and Scotland continued into 1290. A lavishly provisioned ship failed to fetch the Maid in May because of diplomatic difficulties. The Treaty of Birgham, agreed on 18 July, provided that Scotland was to remain fully independent despite the personal union and that Margaret alone would be inaugurated as monarch at Scone. By late August 1290, Margaret was preparing to sail from Bergen to the island of Great Britain or was already at sea. The ship was her father's but he did not accompany her; the most prominent men in her entourage were Bishop Narve and Baron Tore Haakonsson. She must have embarked in good health, but became ill during her journey. The ship landed in Orkney, a Norwegian archipelago off the coast of Scotland, on about 23 September. Having suffered there for up to a week from either food poisoning or, less likely, motion sickness, Margaret died between 26 and 29 September 1290 in the arms of Bishop Narve. The Scottish magnates, who had assembled at Scone for the child queen's inauguration, learned about her death in October. Her body was returned to Bergen, where King Eric insisted on having the coffin opened to confirm his daughter's identity. He then had it buried in the north wall of the chancel of Christ Church, now destroyed.


title: Margaret, Maid of Norway

text: Margaret was the last legitimate scion of the line of King William the Lion. Thirteen men laid claim to succession, most notably Bruce and Balliol. King Eric half-heartedly claimed the Scottish crown as well, and died in 1299. In 1301 she was impersonated by a German woman, False Margaret, who was burned at the stake.


title: Margaret, Maid of Norway

text: Historians debate whether Margaret should be considered a queen and included in the list of Scottish monarchs. She was never inaugurated, and her contemporaries in Scotland described her as queen very rarely, referring to her instead as their "lady". She was called Scotland's "lady", "heir", or "lady and heir" during the deliberations of the Great Cause after her death. On the other hand, documents issued from late 1286 no longer refer to the "king whosoever he may be", indicating that the throne may have been regarded as already occupied by Margaret. Pope Nicholas IV considered Margaret to be the monarch of Scotland and treated her as such, sending to her a bull regarding the episcopal election of Matthew the Scot. In modern historiography she is nearly unanimously called "queen", and reference books give 19 March 1286, the date of Alexander III's death, as the start of her reign.


title: Margaret, Maid of Norway

text: Margaret's family ties resulted from the marital diplomacy that sought to ensure peace among the three kingdoms on the North Sea – Norway, Scotland, and England, and placed her at the centre of the Scottish succession intrigues.


title: Uncertainty

text: Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.


title: Uncertainty

text: Although the terms are used in various ways among the general public, many specialists in decision theory, statistics and other quantitative fields have defined uncertainty, risk, and their measurement as:


title: Uncertainty

text: The lack of certainty, a state of limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome.


title: Uncertainty

text: There is a difference between uncertainty and variability. Uncertainty is quantified by a probability distribution which depends upon our state of information about the likelihood of what the single, true value of the uncertain quantity is. Variability is quantified by a distribution of frequencies of multiple instances of the quantity, derived from observed data.


title: Uncertainty

text: In economics, in 1921 Frank Knight distinguished uncertainty from risk with uncertainty being lack of knowledge which is immeasurable and impossible to calculate. Because of the absence of clearly defined statistics in most economic decisions where people face uncertainty, he believed that we cannot measure probabilities in such cases; this is now referred to as Knightian uncertainty.


title: Uncertainty

text: Knight pointed out that the unfavorable outcome of known risks can be insured during the decision-making process because it has a clearly defined expected probability distribution. Unknown risks have no known expected probability distribution, which can lead to extremely risky company decisions.


title: Uncertainty

text: Other taxonomies of uncertainties and decisions include a broader sense of uncertainty and how it should be approached from an ethics perspective:


title: Uncertainty

text: For example, if it is unknown whether or not it will rain tomorrow, then there is a state of uncertainty. If probabilities are applied to the possible outcomes using weather forecasts or even just a calibrated probability assessment, the uncertainty has been quantified. Suppose it is quantified as a 90% chance of sunshine. If there is a major, costly, outdoor event planned for tomorrow then there is a risk since there is a 10% chance of rain, and rain would be undesirable. Furthermore, if this is a business event and $100,000 would be lost if it rains, then the risk has been quantified (a 10% chance of losing $100,000). These situations can be made even more realistic by quantifying light rain vs. heavy rain, the cost of delays vs. outright cancellation, etc.


title: Uncertainty

text: Some may represent the risk in this example as the "expected opportunity loss" (EOL) or the chance of the loss multiplied by the amount of the loss (10% × $100,000 = $10,000). That is useful if the organizer of the event is "risk neutral", which most people are not. Most would be willing to pay a premium to avoid the loss. An insurance company, for example, would compute an EOL as a minimum for any insurance coverage, then add onto that other operating costs and profit. Since many people are willing to buy insurance for many reasons, then clearly the EOL alone is not the perceived value of avoiding the risk.


title: Uncertainty

text: Quantitative uses of the terms uncertainty and risk are fairly consistent from fields such as probability theory, actuarial science, and information theory. Some also create new terms without substantially changing the definitions of uncertainty or risk. For example, surprisal is a variation on uncertainty sometimes used in information theory. But outside of the more mathematical uses of the term, usage may vary widely. In cognitive psychology, uncertainty can be real, or just a matter of perception, such as expectations, threats, etc.


title: Uncertainty

text: Vagueness is a form of uncertainty where the analyst is unable to clearly differentiate between two different classes, such as 'person of average height.' and 'tall person'. This form of vagueness can be modelled by some variation on Zadeh's fuzzy logic or subjective logic.


title: Uncertainty

text: Ambiguity is a form of uncertainty where even the possible outcomes have unclear meanings and interpretations. The statement ""He returns from the bank"" is ambiguous because its interpretation depends on whether the word 'bank' is meant as ""the side of a river"" or ""a financial institution"". Ambiguity typically arises in situations where multiple analysts or observers have different interpretations of the same statements.


title: Uncertainty

text: Uncertainty may be a consequence of a lack of knowledge of obtainable facts. That is, there may be uncertainty about whether a new rocket design will work, but this uncertainty can be removed with further analysis and experimentation.


title: Uncertainty

text: At the subatomic level, uncertainty may be a fundamental and unavoidable property of the universe. In quantum mechanics, the Heisenberg uncertainty principle puts limits on how much an observer can ever know about the position and velocity of a particle. This may not just be ignorance of potentially obtainable facts but that there is no fact to be found. There is some controversy in physics as to whether such uncertainty is an irreducible property of nature or if there are "hidden variables" that would describe the state of a particle even more exactly than Heisenberg's uncertainty principle allows.


title: Uncertainty

text: The most commonly used procedure for calculating measurement uncertainty is described in the "Guide to the Expression of Uncertainty in Measurement" (GUM) published by ISO. A derived work is for example the National Institute of Standards and Technology (NIST) Technical Note 1297, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results", and the Eurachem/Citac publication "Quantifying Uncertainty in Analytical Measurement". The uncertainty of the result of a measurement generally consists of several components. The components are regarded as random variables, and may be grouped into two categories according to the method used to estimate their numerical values:


title: Uncertainty

text: By propagating the variances of the components through a function relating the components to the measurement result, the combined measurement uncertainty is given as the square root of the resulting variance. The simplest form is the standard deviation of a repeated observation.


title: Uncertainty

text: In metrology, physics, and engineering, the uncertainty or margin of error of a measurement, when explicitly stated, is given by a range of values likely to enclose the true value. This may be denoted by error bars on a graph, or by the following notations:


title: Uncertainty

text: In the last notation, parentheses are the concise notation for the ± notation. For example, applying 10 meters in a scientific or engineering application, it could be written or , by convention meaning accurate to "within" one tenth of a meter, or one hundredth. The precision is symmetric around the last digit. In this case it's half a tenth up and half a tenth down, so 10.5 means between 10.45 and 10.55. Thus it is "understood" that 10.5 means , and 10.50 means , also written and respectively. But if the accuracy is within two tenths, the uncertainty is ± one tenth, and it is "required" to be explicit: and or and . The numbers in parentheses "apply" to the numeral left of themselves, and are not part of that number, but part of a notation of uncertainty. They apply to the least significant digits. For instance, stands for , while stands for . This concise notation is used for example by IUPAC in stating the atomic mass of elements.


title: Uncertainty

text: The middle notation is used when the error is not symmetrical about the value – for example . This can occur when using a logarithmic scale, for example.


title: Uncertainty

text: Uncertainty of a measurement can be determined by repeating a measurement to arrive at an estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation. However, if the values are averaged, then the mean measurement value has a much smaller uncertainty, equal to the standard error of the mean, which is the standard deviation divided by the square root of the number of measurements. This procedure neglects systematic errors, however.


title: Uncertainty

text: When the uncertainty represents the standard error of the measurement, then about 68.3% of the time, the true value of the measured quantity falls within the stated uncertainty range. For example, it is likely that for 31.7% of the atomic mass values given on the list of elements by atomic mass, the true value lies outside of the stated range. If the width of the interval is doubled, then probably only 4.6% of the true values lie outside the doubled interval, and if the width is tripled, probably only 0.3% lie outside. These values follow from the properties of the normal distribution, and they apply only if the measurement process produces normally distributed errors. In that case, the quoted standard errors are easily converted to 68.3% ("one sigma"), 95.4% ("two sigma"), or 99.7% ("three sigma") confidence intervals.


title: Uncertainty

text: In this context, uncertainty depends on both the accuracy and precision of the measurement instrument. The lower the accuracy and precision of an instrument, the larger the measurement uncertainty is. Precision is often determined as the standard deviation of the repeated measures of a given value, namely using the same method described above to assess measurement uncertainty. However, this method is correct only when the instrument is accurate. When it is inaccurate, the uncertainty is larger than the standard deviation of the repeated measures, and it appears evident that the uncertainty does not depend only on instrumental precision.


title: Uncertainty

text: Uncertainty in science, and science in general, may be interpreted differently in the public sphere than in the scientific community. This is due in part to the diversity of the public audience, and the tendency for scientists to misunderstand lay audiences and therefore not communicate ideas clearly and effectively. One example is explained by the information deficit model. Also, in the public realm, there are often many scientific voices giving input on a single topic. For example, depending on how an issue is reported in the public sphere, discrepancies between outcomes of multiple scientific studies due to methodological differences could be interpreted by the public as a lack of consensus in a situation where a consensus does in fact exist. This interpretation may have even been intentionally promoted, as scientific uncertainty may be managed to reach certain goals. For example, climate change deniers took the advice of Frank Luntz to frame global warming as an issue of scientific uncertainty, which was a precursor to the conflict frame used by journalists when reporting the issue.


title: Uncertainty

text: "Indeterminacy can be loosely said to apply to situations in which not all the parameters of the system and their interactions are fully known, whereas ignorance refers to situations in which it is not known what is not known." These unknowns, indeterminacy and ignorance, that exist in science are often "transformed" into uncertainty when reported to the public in order to make issues more manageable, since scientific indeterminacy and ignorance are difficult concepts for scientists to convey without losing credibility. Conversely, uncertainty is often interpreted by the public as ignorance. The transformation of indeterminacy and ignorance into uncertainty may be related to the public's misinterpretation of uncertainty as ignorance.


title: Uncertainty

text: Journalists may inflate uncertainty (making the science seem more uncertain than it really is) or downplay uncertainty (making the science seem more certain than it really is). One way that journalists inflate uncertainty is by describing new research that contradicts past research without providing context for the change. Journalists may give scientists with minority views equal weight as scientists with majority views, without adequately describing or explaining the state of scientific consensus on the issue. In the same vein, journalists may give non-scientists the same amount of attention and importance as scientists.


title: Uncertainty

text: Journalists may downplay uncertainty by eliminating "scientists' carefully chosen tentative wording, and by losing these caveats the information is skewed and presented as more certain and conclusive than it really is". Also, stories with a single source or without any context of previous research mean that the subject at hand is presented as more definitive and certain than it is in reality. There is often a "product over process" approach to science journalism that aids, too, in the downplaying of uncertainty. Finally, and most notably for this investigation, when science is framed by journalists as a triumphant quest, uncertainty is erroneously framed as "reducible and resolvable".


title: Uncertainty

text: Some media routines and organizational factors affect the overstatement of uncertainty; other media routines and organizational factors help inflate the certainty of an issue. Because the general public (in the United States) generally trusts scientists, when science stories are covered without alarm-raising cues from special interest organizations (religious groups, environmental organizations, political factions, etc.) they are often covered in a business related sense, in an economic-development frame or a social progress frame. The nature of these frames is to downplay or eliminate uncertainty, so when economic and scientific promise are focused on early in the issue cycle, as has happened with coverage of plant biotechnology and nanotechnology in the United States, the matter in question seems more definitive and certain.


title: Uncertainty

text: Sometimes, stockholders, owners, or advertising will pressure a media organization to promote the business aspects of a scientific issue, and therefore any uncertainty claims which may compromise the business interests are downplayed or eliminated.


title: Uncertainty

text: In Western philosophy the first philosopher to embrace uncertainty was Pyrrho resulting in the Hellenistic philosophies of Pyrrhonism and Academic Skepticism, the first schools of philosophical skepticism. Aporia and acatalepsy represent key concepts in ancient Greek philosophy regarding uncertainty.


title: Begging

text: Begging (also panhandling) is the practice of imploring others to grant a favor, often a gift of money, with little or no expectation of reciprocation. A person doing such is called a beggar or panhandler. Beggars may operate in public places such as transport routes, urban parks, and markets. Besides money, they may also ask for food, drinks, cigarettes or other small items.


title: Begging

text: Internet begging is the modern practice of asking people to give money to others via the Internet, rather than in person. Internet begging may encompass requests for help meeting basic needs such as medical care and shelter, as well as requests for people to pay for vacations, school trips, and other things that the beggar wants but cannot comfortably afford.


title: Begging

text: Beggars differ from religious mendicants in that some mendicants do not ask for money. Their subsistence is reciprocated by providing society with various forms of religious service, moral education, and preservation of culture.


title: Begging

text: Beggars have existed in human society since the dawn of recorded history. Street begging has happened in most societies around the world, though its prevalence and exact form vary.


title: Begging

text: Ancient Greeks distinguished between the "pénēs" (Greek: πένης, "active poor") and the "ptōchós" (Greek: πτωχός, "passive poor"). The "pénēs" was somebody with a job, only not enough to make a living, while the "ptōchós" depended on others entirely. The working poor were accorded a higher social status. The New Testament contains several references to Jesus' status as the savior of the "ptochos", usually translated as "the poor", considered the most wretched portion of society. In the Rich man and Lazarus parable, Lazarus is called 'ptochos' and presented as living in extreme poverty.


title: Begging

text: "A Caveat or Warning for Common Cursitors, vulgarly called vagabonds", was first published in 1566 by Thomas Harman. From early modern England, another example is Robert Greene in his coney-catching pamphlets, the titles of which included "The Defence of Conny-catching," in which he argued there were worse crimes to be found among "reputable" people. "The Beggar's Opera" is a ballad opera in three acts written in 1728 by John Gay. "The Life and Adventures of Bampfylde Moore Carew" was first published in 1745. There are similar writers for many European countries in the early modern period.


title: Begging

text: According to Jackson J. Spielvogel, "Poverty was a highly visible problem in the eighteenth century, both in cities and in the countryside... Beggars in Bologna were estimated at 25 percent of the population; in Mainz, figures indicate that 30 percent of the people were beggars or prostitutes... In France and Britain by the end of the century, an estimated 10 percent of the people depended on charity or begging for their food."


title: Begging

text: The British Poor Laws, dating from the Renaissance, placed various restrictions on begging. At various times, begging was restricted to the disabled. This system developed into the workhouse, a state-operated institution where those unable to obtain other employment were forced to work in often grim conditions in exchange for a small amount of food. The welfare state of the 20th century greatly reduced the number of beggars by directly providing for the basic necessities of the poor from state funds.


title: Begging

text: Begging is an age-old social phenomenon in India. In the medieval and earlier times begging was considered to be an acceptable occupation which was embraced within the traditional social structure. This system of begging and almsgiving to mendicants and the poor is still widely practiced in India, with over 500,000 beggars in 2015.


title: Begging

text: In contemporary India, beggars are often stigmatized as undeserving. People often believe that beggars are not destitute and instead call them professional beggars. There is a wide perception of begging scams. This view is refuted by grassroots research organizations such as Aashray Adhikar Abhiyan, which claim that beggars and other homeless people are overwhelmingly destitute and vulnerable. Their studies indicate that 99 percent men and 97 percent women resort to beggary due to abject poverty, distress migration from rural villages and the unavailability of employment.


title: Begging

text: After the establishment of the Ming dynasty many farmers and unemployed laborers in Beijing were forced to beg to survive. Begging was especially difficult during Ming times due to high taxes that limited the disposable income of most individuals. Beijing's harsh winters were a difficult challenge for beggars. To avoid freezing to death, some beggars paid porters one copper coin to sleep in their warehouse for the night. Others turned to burying themselves in manure and eating arsenic to avoid the pain of the cold. Thousands of beggars died of poison and exposure to the elements every year.


title: Begging

text: Begging was some people's primary occupation. A Qing dynasty source describes that "professional beggars" were not considered to be destitute, and as such were not allowed to receive government relief, such as food rations, clothing, and shelter. Beggars would often perform or train animals to perform to earn coins from passerby. Although beggars were of low status in Ming, they were considered to have higher social standing over prostitutes, entertainers, runners, and soldiers.


title: Begging

text: Some individuals capitalized on beggars and became "Beggar Chiefs". Beggar chiefs provided security in the form of food for beggars and in return received a portion of beggars daily earnings as tribute. Beggar chiefs would often lend out their surplus income back to beggars and charge interest, furthering their subjects dependence on them to the point of near slavery. Although beggar chiefs could acquire significant wealth they were still looked upon as low class citizens. The title of beggar chief was often passed through family line and could stick with an individual through occupational changes.


title: Begging

text: Many religions have prescribed begging as the only acceptable means of support for certain classes of adherents, including Hinduism, Sufism, Buddhism, Christianity, and typically to provide a way for certain adherents to focus exclusively on spiritual development without the possibility of becoming caught up in worldly affairs.


title: Begging

text: Religious ideals of ‘"Bhiksha"’ in Hinduism, ‘"Charity"’ in Christianity besides others promote almsgiving. This obligation of making gifts to God by almsgiving explains the occurrence of generous donations outside religious sites like temples and mosques to mendicants begging in the name of God.


title: Begging

text: Tzedakah plays a central role in Judaism. The Jewish practice of maaser kesafim requires a contribution of 10% of one's income as a monetary tithe, mostly to be given to the poor.


title: Begging

text: In Buddhism, monks and nuns traditionally live by begging for alms, as done by the historical Gautama Buddha himself. This is, among other reasons, so that Laity can gain religious merit by giving food, medicines, and other essential items to the monks. The monks seldom need to plead for food; in villages and towns throughout modern Myanmar, Thailand, Cambodia, Vietnam, and other Buddhist countries, householders can often be found at dawn every morning streaming down the road to the local temple to give food to the monks. In East Asia, monks and nuns were expected to farm or work for returns to feed themselves.


title: Begging

text: The biblical figure Jesus is said to have lived a simple life. He is said to have encouraged his disciples "to take nothing for their journey except a staff—no bread, no bag, no money in their belts—but to wear sandals and not put on two tunics."


title: Begging

text: Ming China was founded by former beggar Zhu Yuanzhang. Orphaned in childhood due to famine, Zhu Yuanzhang, turned to the Huangjue temple for help. When the temple ran out of resources to support its occupants he became a mendicant monk traveling China begging for food.


title: Begging

text: Begging has been restricted or prohibited at various times and for various reasons, typically revolving around a desire to preserve public order or to induce people to work rather than to beg. Various European Poor Laws prohibited or regulated begging from the Renaissance to modern times, with varying levels of effectiveness and enforcement. Similar laws were adopted by many developing countries.


title: Begging

text: "Aggressive panhandling" has been specifically prohibited by law in various jurisdictions in the United States and Canada, typically defined as persistent or intimidating begging.


title: Begging

text: Each state and territory in Australia has specific laws regarding begging and panhandling. Begging for alms is illegal in Victoria, South Australia, Northern Territory, Queensland and Tasmania.


title: Begging

text: The province of Ontario introduced its Safe Streets Act in 1999 to restrict specific kinds of begging, particularly certain narrowly defined cases of "aggressive" or abusive begging. In 2001 this law was upheld under the Canadian Charter of Rights and Freedoms. The law was further upheld by the Court of Appeal for Ontario in January 2007.


title: Begging

text: One response to the anti-panhandling laws which were passed was the creation of the Ottawa Panhandlers Union which fights for the political rights of panhandlers. The union is a shop of the Industrial Workers of the World.


title: Begging

text: British Columbia enacted its own Safe Streets Act in 2004 which resembles the Ontario law. There are also critics in that province who oppose such laws.


title: Begging

text: Those cases are violations of the Article 41 of the Public Security Administration Punishment Law of the People's Republic of China. For the first case, offenders would receive a detention between 10 days and 15 days, with an additional fine under RMB 1,000; for the second case, it is punishable by a 5-day detention or warning.


title: Begging

text: According to Article 262(2) or the Criminal Law of the People's Republic of China, organizing disabled or children under 14 to beg is illegal and will be punished by up to 7 years in prison, and fined.


title: Begging

text: Historically beggars were controlled by the "Stodderkonge" or 'beggar king' for a town or district. Today, begging in Denmark is illegal under section 197 of the penal code, which reads:


title: Begging

text: Begging is illegal under the Vagrancy Act of 1824. However it does not carry a jail sentence and is not enforced in many cities, although since the Act applies in all public places, it is enforced more frequently on public transport. Local authorities may issue public spaces protection orders for particular areas which makes begging subject to a fine.


title: Begging

text: Begging has been legal in Finland since 1987 when the poor law was invalidated. In 2003, the Public Order Act replaced local government rules and decriminalized begging.


title: Begging

text: A law against begging ended in 1994 but begging with aggressive animals or children is still outlawed.


title: Begging

text: Under article 407 of the Greek Penal Code, begging was punishable by up to 6 months in jail and up to a 3000 euro fine. However, this law was repealed in October 2018, after protests from street musicians in the city of Thessaloniki.


title: Begging

text: Hungary has a nationwide ban. This may include stricter related laws in cities such as Budapest, which also prohibits picking things from rubbish bins.


title: Begging

text: Begging is criminalized in cities such as Mumbai and Delhi as per the Bombay Prevention of Begging Act, BPBA (1959). Under this law, officials of the Social Welfare Department assisted by the police, conduct raids to pick up beggars who they then try in special courts called ‘beggar courts’. If convicted, they are sent to certified institutions called ‘beggar homes’ also known as ‘"Sewa Kutir’" for a period ranging from one to ten years for detention, training and employment. The government of Delhi, besides criminalizing alms-seeking has also criminalized almsgiving on traffic signals to reduce the ‘nuisance’ of begging and ensure the smooth flow of traffic.


title: Begging

text: Aashray Adhikar Abhiyan and People's Union of Civil Liberties, PUCL have critiqued this Act and advocated for its repeal. Section 2(1) of the BPBA broadly defines ‘beggars’ as those individuals who directly solicit alms as well as those who have no visible means of subsistence and are found wandering around as beggars. Therefore, during the implementation of this law the homeless are often mistaken as beggars. Beggar homes, which are meant to provide vocational training, have been often found to have abysmal living conditions.


title: Begging

text: In 2018, the Delhi High Court declared 25 provisions of Bombay Prevention of Begging Act (1959) as unconstitutional, following petitions filed by Harsh Mander and Karnika Sawhney. In 2021, the Supreme Court refused to ban begging and observed that begging was a socioeconomic problem.


title: Begging

text: "Passive" begging is legal in Ireland, but begging "in an aggressive, intimidating or threatening manner" is illegal, punishable by a fine. Gardaí (police) can also direct people begging in certain areas to move on, e.g. at an ATM, night safe, vending machine or shop entrance.


title: Begging

text: It is also illegal to "organise or direct someone else to beg;" under the Criminal Justice (Public Order) Act 2011, punishable by a €200,000 fine or up to 5 years in prison; this law was adopted in response to organised begging by Romani gangs.


title: Begging

text: Prior to this law, begging was outlawed by the Vagrancy (Ireland) Act 1847, adopted during the Great Famine; a 2007 High Court ruling said that it was "too vague and incompatible with constitutional provisions allowing free speech and freedom to communicate."


title: Begging

text: Buddhist monks appear in public when begging for alms. Although homelessness in Japan is common, such people rarely beg.


title: Begging

text: Most cases of begging are illegal. Especially, if it annoys someone, or bothers the traffic, or is for a personal purpose.


title: Begging

text: Begging was made illegal in the historic city center of Riga in 2012. Begging in Riga outside the historic city center requires that the beggar carries ID.


title: Begging

text: It is illegal to beg in the capital Vilnius and it is also illegal to give money to a beggar. Both can receive a fine of up to 2000 litas (€770)


title: Begging

text: Begging in Luxembourg is legal, except when it is indulged in as a group or the beggar is a part of an organised effort. According to Chachipe, a Roma rights advocacy NGO, 1639 begging cases were reported by Luxembourgian law enforcement authorities. Roma beggars were arrested, handcuffed, taken to police stations and held for hours and had their money confiscated.


title: Begging

text: Although the Begging (Prohibition) Act was introduced in 1962, this has not been enforced and the begging population in the capital, Kathmandu has since grown to over 5,000, according to police estimates. Besides the common begging tricks such as asking for money or asking for milk which will be returned to the shop for money, there is a unique scam in Nepal which involves asking a foreigner to buy a shoe box at an inflated price. This shoe box is claimed to help provide a sustainable livelihood for the beggar but in fact, will be returned to the seller for money.


title: Begging

text: Begging is banned in some counties and there were plans for a nationwide ban in 2015, however this was dropped after the Centre Party withdrew their support.


title: Begging

text: Begging is prohibited in the Philippines under the Anti-Mendicancy Law of 1978 although this is not strictly enforced.


title: Begging

text: In Poland it is illegal to beg under the Code of petty offences, if they are able to hold a job or "beg in public in a pressing or fraudulently" (Article 58). The beggar is due to a fine of €365. "Who tends to beg a minor or helpless person or dependant relative depending on him or dedicated under his custody, shall be punishable by detention, restriction of liberty or a fine" (Article 104).


title: Begging

text: In Portugal, panhandlers normally beg in front of Catholic churches, at traffic lights or on special places in Lisbon or Oporto downtowns. Begging is legal in Portugal. Many social and religious institutions support homeless people and panhandlers and the Portuguese Social Security normally gives them a survival monetary subsidy.


title: Begging

text: Under the article 278 of the Qatari penal code, the maximum sentence for begging is one year. This sentence was increased from a maximum of three months before July 2006. The alternative is housing in a specialized correctional facility. The money will be confiscated in any case. This law is enforced, with a police division dedicated solely for that purpose.


title: Begging

text: Law 61 of 1991 forbids the persistent call for the mercy of the public, by a person who is able to work.


title: Begging

text: US State Department Human Rights reports note a pattern of Roma children registered for "vagrancy and begging".


title: Begging

text: In May 2010, police in the city of Boston started cracking down on panhandling in the streets in downtown, and were conducting an educational outreach to residents advising them not to give to panhandlers. The Boston police distinguished active solicitation, or aggressive panhandling, versus passive panhandling of which an example is opening doors at a store with a cup in hand but saying nothing.


title: Begging

text: U. S. Courts have repeatedly ruled that begging is protected by the First Amendment's free speech provisions. On August 14, 2013, the U. S. Court of Appeals struck down a Grand Rapids, Michigan anti-begging law on free speech grounds. An Arcata, California law banning panhandling within twenty feet of stores was struck down on similar grounds in 2012.


title: Begging

text: A 2002 study of 54 panhandlers in Toronto reported that of a median monthly income of $638 Canadian dollars (CAD) – those interviewed spent a median of $200 on food and $192 on alcohol, tobacco and illegal drugs. The Fraser Institute criticized this study, citing problems with potential exclusion of lucrative forms of begging and the unreliability of reports from the panhandlers who were polled in the study.


title: Begging

text: In North America, panhandling money is widely reported to support substance abuse and other addictions. For example, outreach workers in downtown Winnipeg, Manitoba, Canada, surveyed that city's panhandling community and determined that approximately three-quarters use some of the donated money to buy tobacco products, while two-thirds buy solvents or alcohol.


title: Begging

text: Because of concerns that people begging on the street may use the money to support alcohol or drug abuse, some advise those wishing to give to beggars to give gift cards or vouchers for food or services, and not cash. Some shelters also offer business cards with information on the shelter's location and services, which can be given in lieu of cash.


title: Southern Min

text: Southern Min (), Minnan ( ) or Banlam (), is a group of linguistically similar and historically related Sinitic languages that form a branch of Min Chinese spoken in Fujian (especially the Minnan region), most of Taiwan (many citizens are descendants of settlers from Fujian), Eastern Guangdong, Hainan, and Southern Zhejiang. The Minnan dialects are also spoken by descendants of emigrants from these areas in diaspora, most notably the Philippines, Indonesia, Malaysia, Singapore, San Francisco, Los Angeles and New York City. It is the most populous branch of Min Chinese, spoken by an estimated 48 million people in c. 2017–2018.


title: Southern Min

text: In common parlance and in the narrower sense, Southern Min refers to the Quanzhang or Hokkien-Taiwanese variety of Southern Min originating from Southern Fujian in Mainland China. This is spoken mainly in Fujian, Taiwan, as well as certain parts of Southeast Asia. The Quanzhang variety is often called simply "Minnan Proper". It is considered the mainstream Southern Min Chinese language.


title: Southern Min

text: In the wider scope, Southern Min also includes other Min Chinese varieties that are linguistically related to Minnan proper (Quanzhang). Most variants of Southern Min have significant differences from the Quanzhang variety, some having limited mutual intelligibility with it, others almost none. Teochew, Longyan, and Zhenan may be said to have limited mutual intelligibility with Minnan Proper, sharing similar phonology and vocabulary to a small extent. On the other hand, variants such as Datian, Zhongshan, and Qiong-Lei have historical linguistic roots with Minnan Proper, but are significantly divergent from it in terms of phonology and vocabulary, and thus have almost no mutual intelligibility with the Quanzhang variety. Linguists tend to classify them as separate Min languages.


title: Southern Min

text: Southern Min is not mutually intelligible with other branches of Min Chinese nor with non-Min varieties of Chinese, such as Mandarin, and the principal varieties of Southern Min are not intelligible with each other.


title: Southern Min

text: Southern Min dialects are spoken in Fujian, three southeastern counties of Zhejiang, the Zhoushan archipelago off Ningbo in Zhejiang and the Chaoshan (Teo-swa) region in Guangdong. The variant spoken in Leizhou, Guangdong as well as Hainan is Hainanese and is not mutually intelligible with mainstream Southern Min or Teochew. Hainanese is classified in some schemes as part of Southern Min and in other schemes as separate. Puxian Min was originally based on the Quanzhou dialect, but over time became heavily influenced by Eastern Min, eventually losing intelligibility with Minnan.


title: Southern Min

text: The Southern Min dialects spoken in Taiwan, collectively known as Taiwanese, is a first language for most of the Hoklo people, the main ethnicity of Taiwan. The correspondence between language and ethnicity is not absolute, as some Hoklo have very limited proficiency in Southern Min while some non-Hoklo speak Southern Min fluently.


title: Southern Min

text: There are many Southern Min speakers among overseas Chinese in Southeast Asia. Many ethnic Chinese immigrants to the region were Hoklo from southern Fujian and brought the language to what is now Burma, Indonesia (the former Dutch East Indies) and present-day Malaysia and Singapore (formerly British Malaya and the Straits Settlements). In general, Southern Min from southern Fujian is known as Hokkien, Hokkienese, Fukien or Fookien in Southeast Asia and is mostly mutually intelligible with Hokkien spoken elsewhere. Many Southeast Asian ethnic Chinese also originated in the Chaoshan region of Guangdong and speak Teochew language, the variant of Southern Min from that region. Philippine Hokkien is reportedly the native language of up to 98.5% of the Chinese Filipino community in the Philippines, among whom it is also known as Lan-nang or Lán-lâng-oē (), literally "our people's language".


title: Southern Min

text: Southern Min speakers form the majority of Chinese in Singapore, with Hokkien being the largest group and the second largest being Teochew. Despite the similarities, the two groups are rarely seen as part of the same "Minnan" Chinese subgroups.


title: Southern Min

text: The variants of Southern Min spoken in Zhejiang province are most akin to that spoken in Quanzhou. The variants spoken in Taiwan are similar to the three Fujian variants and are collectively known as Taiwanese.


title: Southern Min

text: Those Southern Min variants that are collectively known as "Hokkien" in Southeast Asia also originate from these variants. The variants of Southern Min in the Chaoshan region of eastern Guangdong province are collectively known as Teo-Swa or Chaoshan. Chaoshan Min is of great importance in the Southeast Asian Chinese diaspora, particularly in Malaysia, Thailand, Cambodia, Vietnam, Sumatra, and West Kalimantan. The Philippines variant is mostly from the Quanzhou area as most of their forefathers are from the aforementioned area.


title: Southern Min

text: The Southern Min language variant spoken around Shanwei and Haifeng differs markedly from Teochew and may represent a later migration from Zhangzhou. Linguistically, it lies between Teochew and Amoy. In southwestern Fujian, the local variants in Longyan and Zhangping form a separate division of Minnan on their own. Among ethnic Chinese inhabitants of Penang, Malaysia and Medan, Indonesia, a distinct form based on the Zhangzhou dialect has developed. In Penang, it is called Penang Hokkien while across the Malacca Strait in Medan, an almost identical variant is known as Medan Hokkien.


title: Southern Min

text: There are two or three divisions of Southern Min, depending on the criteria for Leizhou and Hainanese inclusion :


title: Southern Min

text: More recently, Kwok (2018: 157) has classified the Southern Min dialects the Central and Southern branches grouped together, as well as a separate divergent Northern branch.


title: Southern Min

text: The group of mutually intelligible Quanzhang () dialects, spoken around the areas of Xiamen, Quanzhou and Zhangzhou in Southern Fujian, collectively called Minnan Proper () or Hokkien-Taiwanese, is the mainstream form of Southern Min. It is also the widely spoken non-official regional language in Taiwan. There are two types of standard Minnan. They are classified as Traditional Standard Minnan and Modern Standard Minnan. Traditional Standard Minnan is based on the Quanzhou dialect. It is the dialect used in Liyuan Opera () and Nanying music (). The modern standard forms of Minnan Proper are based on Amoy dialect, spoken in the city of Xiamen, and Taiwanese dialect, spoken around the city of Tainan in Taiwan. Both modern standard forms of Minnan are a combination of Quanzhou and Zhangzhou speech. Nowadays, Modern Standard Minnan is the dialect of Minnan that is popular in Minnan dialect television programming, radio programming and Minnan songs. Most Minnan language books and Minnan dictionaries are mostly based on the pronunciation of the Modern Standard Minnan. Taiwanese in northern Taiwan tends to be based on Quanzhou dialect, whereas the Taiwanese spoken in southern Taiwan tends to be based on Zhangzhou dialect. There are minor variations in pronunciation and vocabulary between Quanzhou and Zhangzhou speech. The grammar is basically the same. Additionally, in Taiwanese Minnan, extensive contact with the Japanese language has left a legacy of Japanese loanwords. This language is also spoken in Singapore, as Singaporean Hokkien, which has English and Malay loanwords.


title: Southern Min

text: Teo-Swa or Chaoshan speech () is a closely related variant of Minnan that includes the Teochew and Swatow dialects. It has limited mutual intelligibility with Quanzhang speech, though they share some cognates with each other. Chaoshan Min is significantly different from Quanzhang in both pronunciation and vocabulary. It had its origins from the Proto-Putian dialect (), a sub-dialect of Proto-Minnan, which is closely related to the Quanzhou dialect. As the Proto-Putian dialect speaking Chinese emigrants from Putian prefecture settled in the Chaoshan region, it later received influence from the Zhangzhou dialect. It follows the same grammar pattern as Minnan Proper. It is marginally understood by Minnan Proper speakers.


title: Southern Min

text: Southern Min has one of the most diverse phonologies of Chinese varieties, with more consonants than Mandarin or Cantonese. Vowels, on the other hand, are more-or-less similar to those of Mandarin. In general, Southern Min dialects have five to six tones, and tone sandhi is extensive. There are minor variations within Hokkien, and the Teochew system differs somewhat more.


title: Southern Min

text: Both Hokkien and Chaoshan (Teochew and Shantou dialects) have romanized writing systems and also respective Chinese characters. In Malaysia it is sometimes known as 唐儂字 (Tn̂g-lâng-jī), while in Mainland China it is known as 閩南文 (Bân-lâm-bûn) while the Han Characters are known as 漢字 (Hàn-jī).


title: Southern Min

text: The Min homeland of Fujian was opened to Han Chinese settlement by the defeat of the Minyue state by the armies of Emperor Wu of Han in 110 BC. The area features rugged mountainous terrain, with short rivers that flow into the South China Sea. Most subsequent migration from north to south China passed through the valleys of the Xiang and Gan rivers to the west, so that Min varieties have experienced less northern influence than other southern groups. As a result, whereas most varieties of Chinese can be treated as derived from Middle Chinese, the language described by rhyme dictionaries such as the "Qieyun" (601 AD), Min varieties contain traces of older distinctions. Linguists estimate that the oldest layers of Min dialects diverged from the rest of Chinese around the time of the Han dynasty. However, significant waves of migration from the North China Plain occurred. These include:


title: Southern Min

text: Minnan (or Hokkien) can trace its origins through the Tang Dynasty, and it also has roots from earlier periods. Minnan (Hokkien) people call themselves "Tang people", (, pronounced as "" "") which is synonymous to "Chinese people". Because of the widespread influence of the Tang culture during the great Tang dynasty, there are today still many Minnan pronunciations of words shared by the Sino-xenic pronunciations of Vietnamese, Korean and Japanese languages.


title: Partial fraction decomposition

text: In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.


title: Partial fraction decomposition

text: The importance of the partial fraction decomposition lies in the fact that it provides algorithms for various computations with rational functions, including the explicit computation of antiderivatives, Taylor series expansions, inverse Z-transforms, and inverse Laplace transforms. The concept was discovered independently in 1702 by both Johann Bernoulli and Gottfried Leibniz.


title: Partial fraction decomposition

text: In symbols, the "partial fraction decomposition" of a rational fraction of the form formula_1 where and are polynomials, is its expression as


title: Partial fraction decomposition

text: the denominator is a power of an irreducible polynomial (that is not factorable into polynomials of positive degrees), and


title: Partial fraction decomposition

text: When explicit computation is involved, a coarser decomposition is often preferred, which consists of replacing "irreducible polynomial" by "square-free polynomial" in the description of the outcome. This allows replacing polynomial factorization by the much easier-to-compute square-free factorization. This is sufficient for most applications, and avoids introducing irrational coefficients when the coefficients of the input polynomials are integers or rational numbers.


title: Partial fraction decomposition

text: be a rational fraction, where and are univariate polynomials in the indeterminate over a field. The existence of the partial fraction can be proved by applying inductively the following reduction steps.


title: Partial fraction decomposition

text: This results immediately from the Euclidean division of by , which asserts the existence of and such that formula_7 and formula_8


title: Partial fraction decomposition

text: Let formula_17 with formula_18 be the Euclidean division of by formula_19 Setting formula_20 one gets


title: Partial fraction decomposition

text: It remains to show that formula_22 By reducing the last sum of fractions to a common denominator, one gets


title: Partial fraction decomposition

text: Using the preceding decomposition inductively one gets fractions of the form formula_25 with formula_26 where is an irreducible polynomial. If , one can decompose further, by using that an irreducible polynomial is a square-free polynomial, that is, formula_27 is a greatest common divisor of the polynomial and its derivative. If formula_28 is the derivative of , Bézout's identity provides polynomials and such that formula_29 and thus formula_30 Euclidean division of formula_31 by formula_32 gives polynomials formula_33 and formula_34 such that formula_35 and formula_36 Setting formula_37 one gets


title: Partial fraction decomposition

text: Iterating this process with formula_40 in place of formula_41 leads eventually to the following theorem.


title: Partial fraction decomposition

text: The uniqueness can be proved as follows. Let . All together, and the have coefficients. The shape of the decomposition defines a linear map from coefficient vectors to polynomials of degree less than . The existence proof means that this map is surjective. As the two vector spaces have the same dimension, the map is also injective, which means uniqueness of the decomposition. By the way, this proof induces an algorithm for computing the decomposition through linear algebra.


title: Partial fraction decomposition

text: If is field of complex numbers, the fundamental theorem of algebra implies that all have degree one, and all numerators formula_42 are constants. When is the field of real numbers, some of the may be quadratic, so, in the partial fraction decomposition, quotients of linear polynomials by powers of quadratic polynomials may also occur.


title: Partial fraction decomposition

text: In the preceding theorem, one may replace "distinct irreducible polynomials" by "pairwise coprime polynomials that are coprime with their derivative". For example, the may be the factors of the square-free factorization of . When is the field of rational numbers, as it is typically the case in computer algebra, this allows to replace factorization by greatest common divisor computation for computing a partial fraction decomposition.


title: Partial fraction decomposition

text: This reduces the computation of the antiderivative of a rational function to the integration of the last sum, which is called the "logarithmic part", because its antiderivative is a linear combination of logarithms.


title: Partial fraction decomposition

text: There are various methods to compute decomposition in the Theorem. One simple way is called Hermite's method. First, "b" is immediately computed by Euclidean division of "f" by "g", reducing to the case where deg("f") < deg("g"). Next, one knows deg("c") < deg("p"), so one may write each "c" as a polynomial with unknown coefficients. Reducing the sum of fractions in the Theorem to a common denominator, and equating the coefficients of each power of "x" in the two numerators, one gets a system of linear equations which can be solved to obtain the desired (unique) values for the unknown coefficients.


title: Partial fraction decomposition

text: Given two polynomials formula_45 and formula_46, where the "α" are distinct constants and , explicit expressions for partial fractions can be obtained by supposing that


title: Partial fraction decomposition

text: and solving for the "c" constants, by substitution, by equating the coefficients of terms involving the powers of "x", or otherwise. (This is a variant of the method of undetermined coefficients. After both sides of the equation are multiplied by Q(x), one side of the equation is a specific polynomial, and the other side is a polynomial with undetermined coefficients. The equality is possible only when the coefficients of like powers of "x" are equal. This yields n equations in n unknowns, the c.)


title: Partial fraction decomposition

text: where formula_49 is the derivative of the polynomial formula_34. The coefficients of formula_51 are called the residues of "f/g".


title: Partial fraction decomposition

text: then according to the uniqueness of Laurent series, "a" is the coefficient of the term in the Laurent expansion of "g"("x") about the point "x", i.e., its residue


title: Partial fraction decomposition

text: Partial fractions are used in real-variable integral calculus to find real-valued antiderivatives of rational functions. Partial fraction decomposition of real rational functions is also used to find their Inverse Laplace transforms. For applications of partial fraction decomposition over the reals, see


title: Partial fraction decomposition

text: Let "f"("x") be any rational function over the real numbers. In other words, suppose there exist real polynomials functions "p"("x") and "q"("x") ≠ 0, such that


title: Partial fraction decomposition

text: By dividing both the numerator and the denominator by the leading coefficient of "q"("x"), we may assume without loss of generality that "q"("x") is monic. By the fundamental theorem of algebra, we can write


title: Partial fraction decomposition

text: where "a"..., "a", "b"..., "b", "c"..., "c" are real numbers with "b" − 4"c" < 0, and "j"..., "j", "k"..., "k" are positive integers. The terms ("x" − "a") are the "linear factors" of "q"("x") which correspond to real roots of "q"("x"), and the terms ("x" + "b""x" + "c") are the "irreducible quadratic factors" of "q"("x") which correspond to pairs of complex conjugate roots of "q"("x").


title: Partial fraction decomposition

text: Here, "P"("x") is a (possibly zero) polynomial, and the "A", "B", and "C" are real constants. There are a number of ways the constants can be found.


title: Partial fraction decomposition

text: The most straightforward method is to multiply through by the common denominator "q"("x"). We then obtain an equation of polynomials whose left-hand side is simply "p"("x") and whose right-hand side has coefficients which are linear expressions of the constants "A", "B", and "C". Since two polynomials are equal if and only if their corresponding coefficients are equal, we can equate the coefficients of like terms. In this way, a system of linear equations is obtained which "always" has a unique solution. This solution can be found using any of the standard methods of linear algebra. It can also be found with limits (see Example 5).


title: Partial fraction decomposition

text: Substituting "x" = −3 into this equation gives "A" = −1/4, and substituting "x" = 1 gives "B" = 1/4, so that


title: Partial fraction decomposition

text: The factor "x" − 4"x" + 8 is irreducible over the reals, as its discriminant is negative. Thus the partial fraction decomposition over the reals has the shape


title: Partial fraction decomposition

text: Taking "x" = 0, we see that 16 = 8"A", so "A" = 2. Comparing the "x" coefficients, we see that 4 = "A" + "B" = 2 + "B", so "B" = 2. Comparing linear coefficients, we see that −8 = −4"A" + "C" = −8 + "C", so "C" = 0. Altogether,


title: Partial fraction decomposition

text: The fraction can be completely decomposed using complex numbers. According to the fundamental theorem of algebra every complex polynomial of degree "n" has "n" (complex) roots (some of which can be repeated). The second fraction can be decomposed to:


title: Partial fraction decomposition

text: Equating the coefficients of and the constant (with respect to ) coefficients of both sides of this equation, one gets a system of two linear equations in and , whose solution is


title: Partial fraction decomposition

text: This example illustrates almost all the "tricks" we might need to use, short of consulting a computer algebra system.


title: Partial fraction decomposition

text: Alternatively, instead of expanding, one can obtain other linear dependences on the coefficients computing some derivatives at formula_91 in the above polynomial identity. (To this end, recall that the derivative at "x" = "a" of ("x" − "a")"p"("x") vanishes if "m" > 1 and is just "p"("a") for "m" = 1.) For instance the first derivative at "x" = 1 gives


title: Partial fraction decomposition

text: Thus, "f"("z") can be decomposed into rational functions whose denominators are "z"+1, "z"−1, "z"+i, "z"−i. Since each term is of power one, −1, 1, −"i" and "i" are simple poles.


title: Partial fraction decomposition

text: Before performing decomposition, it is obvious we must perform polynomial long division and factor the denominator. Doing this would result in:


title: Partial fraction decomposition

text: Upon substituting our values, in this case, where x=1 to solve for B and x=-2 to solve for A, we will result in:


title: Partial fraction decomposition

text: The partial fraction decomposition of a rational function can be related to Taylor's theorem as follows. Let


title: Partial fraction decomposition

text: if, and only if, each polynomial formula_122 is the Taylor polynomial of formula_123 of order formula_124 at the point formula_125:


title: Partial fraction decomposition

text: Taylor's theorem (in the real or complex case) then provides a proof of the existence and uniqueness of the partial fraction decomposition, and a characterization of the coefficients.


title: Partial fraction decomposition

text: so formula_128 is the Taylor polynomial of formula_123, because of the unicity of the polynomial expansion of order formula_124, and by assumption formula_131.


title: Partial fraction decomposition

text: Conversely, if the formula_128 are the Taylor polynomials, the above expansions at each formula_125 hold, therefore we also have


title: Partial fraction decomposition

text: The idea of partial fractions can be generalized to other integral domains, say the ring of integers where prime numbers take the role of irreducible denominators. For example:


title: Emaciation

text: Emaciation is defined as the state of extreme thinness from absence of body fat and muscle wasting usually resulting from malnutrition.


title: Emaciation

text: In humans, the physical appearance of emaciation includes thinned limbs, pronounced and protruding bones, sunken eyes, dry skin, thinning hair, a bloated stomach, and a dry or coated tongue. Emaciation is often accompanied by halitosis, hyponatremia, hypokalemia, anemia, improper function of lymph and the lymphatic system, and pleurisy and edema.


title: Emaciation

text: Emaciation can be caused by undernutrition, malaria and cholera, tuberculosis and other infectious diseases with prolonged fever, parasitic infections, many forms of cancer and their treatments, lead poisoning, and eating disorders like anorexia nervosa.


title: Emaciation

text: Emaciation is widespread in least developed countries and was a major cause of death in Nazi concentration camps during World War II.


title: Emaciation

text: A lack of resources in the habitat, disease, or neglect and cruelty from humans in captivity can result in emaciation in animals. In the rehabilitation of emaciated animals, the specific dietary needs of each animal have to be considered to avoid causing harm.


title: Samir Bannout

text: Known as "the Lion of Lebanon", Samir Bannout won the Mr. Olympia title in 1983. Bannout has appeared on the covers of many fitness and bodybuilding publications, including "Strength and Health", "MuscleMag International", "Muscle Digest", "Flex", "Muscle Training Illustrated", "Muscle and Fitness", "Muscle Up", "IronMan" and "Muscular Development" magazines.


title: Samir Bannout

text: Samir Bannout left his native Lebanon and emigrated to America where he first moved to Detroit, Michigan.


title: Samir Bannout

text: He began competing at the amateur level where he rose up the ranks and eventually achieved IFBB pro status by winning his light-heavyweight class at the 1979 IFBB World Amateur Championships. By this time Samir had already relocated to Santa Monica, California. Bannout took 4th place at the 1982 Mr. Olympia contest and returned the following year to take home the title in 1983 winning the contest to become Mr. Olympia 1983. The contest was held in Munich, Germany that year and the trophy awarded to him is called a "Sandow" for Eugen Sandow. Bannout weighed 196 lbs. for his win at the contest which made him the last Mr. Olympia to weigh under 200 lbs. His victory ended what is referred to as the "aesthetics" era for the Mr. Olympia contest which had originally started with American Frank Zane winning the title in 1977 and reverted to emphasizing increased mass and size starting with American Lee Haney winning in 1984 for the first time and following up his inaugural victory with 7 additional consecutive wins for a record grand total of 8 titles.


title: Samir Bannout

text: The extreme muscular definition that Bannout achieved in his lower back region helped to shape "Lebanon Cedar" when referring the shape made visible during a back pose on the competition stage.


title: Samir Bannout

text: After placing 6th at the 1984 Olympia, the IFBB suspended him for three years as punishment for his participation at the World Championship competition of a rival federation, the WABBA.


title: Samir Bannout

text: Samir Bannout did not get a top six placing another time at a Mr. Olympia contest despite competing at the event many more times. In 1990 he won his second IFBB pro show, the IFBB Pittsburgh Pro Invitational. His professional career lasted 17 years.


title: Samir Bannout

text: Samir Bannout has been open about his past use of anabolic steroids: "I have to be quite truthful with you, I have used anabolics, I'm not going to have to deny it, because all the other Mr Olympia contenders, I feel that they are using it, and I only use it to reverse catabolic effect." Bannout openly criticizes the IFBB during the years he competed, in that he felt that he had been "robbed" of winning in other events and that there was significant political undertones to selection of winners at the Mr. Olympia.


title: Samir Bannout

text: Today Samir Bannout lives in Los Angeles, California with his wife Randa and his three children Lea, Jesse, Sergio. He was inducted to the IFBB Hall of Fame in 2002. He was previously married to the sister of fellow IFBB professional Lee Labrada, Lourdes; they had two daughters.


title: Five solae

text: The five "solae" (from Latin, ', lit. "alone"; occasionally Anglicized to five solas"') of the Protestant Reformation are a foundational set of Christian theological principles held by theologians and clergy to be central to the doctrines of justification and salvation as taught by the Reformed and Lutheran branches of Protestantism and Pentecostalism. Each "sola" represents a key belief in these Protestant traditions in contradistinction to the theological doctrine of the Catholic Church, although they were not assembled as a theological unit until the 20th century. The Reformers are known to have only clearly stated two of the five "solae". Even today there are differences as to what constitutes the "solae" and how many there are, not to mention how to interpret them to reflect the Reformers' beliefs.


title: Five solae

text: The solae were not systematically articulated together as a set of five until the 20th century; however, "sola gratia" and "sola fide" were used in conjunction by the Reformers themselves. For example, in 1554 Melanchthon wrote, ""sola gratia justificamus et sola fide justificamur"" ("only by grace do we justify and only by faith are we justified"). All of the solae show up in various writings by the Protestant Reformers, but they are not catalogued together by any.


title: Five solae

text: In 1916, Lutheran scholar Theodore Engelder published an article titled "The Three Principles of the Reformation: "Sola Scriptura, Sola Gratia, Sola Fides"" ("only scripture, only grace, only faith"). In 1934, theologian Emil Brunner substituted "Soli Deo gloriam" for "Sola Scriptura". In 1958, historian Geoffrey Elton, summarizing the work of John Calvin, wrote that Calvin had "joined together" the "great watchwords". Elton listed "sola fide" with "sola gratia" as one term, followed by "sola scriptura" and "soli Deo gloria". Later, in commenting on Karl Barth's theological system, Brunner added "Christus solus" to the litany of solas while leaving out "sola scriptura". The first time the additional two solae are mentioned is in Johann Baptiste Metz's 1965, "The Church and the World".


title: Five solae

text: In most of the earliest articulations of the solae, three were typically specified: scripture over tradition, faith over works, and grace over merit. Each was intended to represent an important distinction compared with teachings claimed in Catholic doctrine.


title: Five solae

text: "Sola Scriptura" is upheld by Lutheran and Reformed theologies and asserts that scripture must govern over church traditions and interpretations which are themselves held to be subject to scripture. All church traditions, creeds, and teachings must be in unity with the teachings of scripture as the divinely inspired Word of God.


title: Five solae

text: The doctrine of "Sola Scriptura", in a nutshell, affirms that Scripture is our only source of normative, apostolic, infallible revelation and that “all things necessary for salvation and about faith and life are taught in the Bible with sufficient clarity so that the ordinary believer can find it there and understand it.”


title: Five solae

text: This particular sola is sometimes called the formal principle of the Reformation, since it is the source and norm of the material cause or principle, the gospel of Jesus Christ that is received "sola fide" (Latin ablative, sōlā fidē, meaning "by faith alone"), "sola gratia" (Latin ablative, sōlā grātiā, meaning "by grace alone" or by God's favor). The adjective ("sola") and the noun ("scriptura") are in the ablative case rather than in the nominative case to indicate that the Bible does not stand alone apart from God, but rather that it is the instrument of God by which he reveals himself for salvation through faith in Christ ("solus Christus" or "solo Christo").


title: Five solae

text: It should be emphasized that this doctrine in no way denies tradition, reason or experience as sources of truth. There is nothing in Sola Scriptura that eliminates other authorities, but what it does say is that there is only one authority that can absolutely bind the conscience, and that is: Holy Scripture, and that all controversies about doctrine and Theology must be resolved in the final analysis by Scripture.


title: Five solae

text: Sola fide is summarized in the Thirty-nine Articles of the Anglican church, specifically Article XI "Of the Justification of Man":


title: Five solae

text: For Luther, baptism is a work of God by which the forgiveness of sins and salvation earned by Christ's death, and confirmed by Christ's resurrection, are given to the baptized person who believes God's Word that says He is doing exactly that in baptism.


title: Five solae

text: Infant baptism is not only appropriate, but urged: "We bring the child in the conviction and hope that it believes, and we pray that God may grant it faith; but we do not baptize it upon that, but solely upon the command of God."


title: Five solae

text: The Bible talks about the idea of being justified by faith opposed to works,For we hold that one is justified by faith apart from works of the law. Romans 3:28 ESV


title: Five solae

text: For in the gospel the righteousness of God is revealed—a righteousness that is by faith from first to last,[a] just as it is written: “The righteous will live by faith.” Romans 1:17


title: Five solae

text: "Sola gratia", or "only grace", specifically excludes the merit done by a person as part of achieving salvation. "Sola gratia" is the teaching that salvation comes by divine grace or "unmerited favor" only, not as something merited by the sinner. A famous verse used to back up this doctrine isFor it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God— 9 not by works, so that no one can boast. Ephesians 2:8-9This means that salvation is an unearned gift from God for Jesus's sake. While some maintain that this doctrine is the opposite of "works' righteousness" and conflicts with some of the aspects of the Roman Catholic doctrine of merit, it might be asserted that this article, taken at face value, conflicts in no way with Roman Catholic teaching. Both Protestants and Roman Catholics hold the doctrine that grace is truly and always a gift of God. Both agree that God is the sole actor in grace – that grace is always efficacious "without" any cooperation by man. They differ on whether human action under the influence of grace can cooperate with grace to "merit" greater graces. Protestants follow the doctrine known as monergism, which asserts that God acts alone to save the sinner; the responsibility for salvation does not rest on the sinner to any degree. By contrast, the Roman Catholic view asserts that salvation does involve some form of cooperation between divine grace and human agency. This view is known as synergism.


title: Five solae

text: Protestant Arminians, such as Methodists, are synergists but may also claim the doctrine of "sola gratia", though they understand it quite differently than Lutherans and Calvinists do. Arminians believe that God saves only by grace and not at all by merit, but man, enabled by what is referred to as "prevenient grace", is enabled by the Holy Spirit to understand the Gospel and respond in faith. Arminians believe that this is compatible with salvation by grace alone, since all the actual saving is done by grace. Arminians believe that humans are only capable of receiving salvation when first enabled to do so by prevenient grace, which they believe is distributed to everyone. Arminians therefore do not reject the conception of "sola gratia" expounded by Lutheran and Reformed theologians, although their interpretation of it is quite different.


title: Five solae

text: John Owen, in "A Display of Arminianism", rejects the implied belief that the understanding of the Reformed theology has any alliance between the two doctrines and Arminianism is but another form of pelagianism, known as semipelagianism.


title: Five solae

text: While the Reformers of the 16th century wrote of all five solas in various period writings, they are not all mentioned together in one place and were not systematically brought together until the 20th century.


title: Five solae

text: "Solus Christus", or "only Christ", excludes the priestly class as necessary for sacraments. "Solus Christus" is the teaching that Christ is the only mediator between God and man, and that there is salvation through no other (hence, the phrase is sometimes rendered in the ablative case, "solo Christo", meaning that salvation is "by Christ alone").


title: Five solae

text: The Catholic Church teaches that lay people, and even unbaptized people, can validly baptize, and may do so in an emergency, and that the ministers of the sacrament of matrimony are the people getting married, not the priest, who is only a witness to the marriage, although a witness is legally required in the modern Western Catholic church. Other sacraments, according to Catholic doctrine, essentially require a bishop or at least a priest in order to be valid.


title: Five solae

text: With regard to Lutheran theology, while rejecting all other mediators between God and man, classical Lutheranism continues to honor the memory of the Virgin Mary and other exemplary saints. This principle rejects sacerdotalism, the belief that there are no sacraments in the church without the services of priests ordained by apostolic succession. Martin Luther taught the "general priesthood of the baptized", which was modified in later Lutheranism and classical Protestant theology into "the priesthood of all believers", denying the exclusive use of the title "priest" (Latin "sacerdos") to the clergy. This principle does not deny the office of the holy ministry to which is committed the public proclamation of the Gospel and the administration of the sacraments. In this way, Luther in his "Small Catechism" could speak of the role of "a confessor" to confer sacramental absolution on a penitent; the section in this catechism known as "The Office of the Keys" (not written by Luther but added with his approval) identifies the "called ministers of Christ" as being the ones who exercise the binding and loosing of absolution and excommunication through Law and Gospel ministry.


title: Five solae

text: This binding and loosing is laid out in the Lutheran formula of holy absolution: the "called and ordained servant of the Word" forgives penitents' sins (speaks Christ's words of forgiveness: "I forgive you all your sins") without any addition of penances or satisfactions and not as an interceding or mediating "priest", but "by virtue of [his] office as a called and ordained servant of the Word" and "in the stead and by the command of [his] Lord Jesus Christ". In this tradition absolution reconciles the penitent with God directly through faith in Christ's forgiveness rather than with the priest and the church as mediating entities between the penitent and God.


title: Five solae

text: "Soli Deo gloria", or "glory to God alone", stands in opposition to the veneration perceived by many to be present in the Roman Catholic Church of Mary the mother of Jesus, the saints, or angels. "Soli Deo gloria" is the teaching that all glory is to be due to God alone, since salvation is accomplished solely through His will and action – not only the gift of the all-sufficient atonement of Jesus on the cross, but also the gift of faith in that atonement, created in the heart of the believer by the Holy Spirit. Some Reformers believed that human beings – even saints canonized by the Roman Catholic Church, the popes, and the ecclesiastical hierarchy – are not worthy of the glory that was accorded them; that is, one should not exalt such humans for their good works, but rather praise and give glory to God.


title: Five solae

text: More recently, certain scholars have suggested that there should be additional solas on the list: "Sola ecclesia" ("the Church alone"), "Sola caritas" ("Charitable-love alone") and "Sola Spiritus" (In the "Spirit alone"). At the other end of the spectrum, emerging from the Imiaslavie and Primitive Catholicism streams, some Christians now affirm the “Sōlum Nōmen” position that the Holy “Name Alone” is All-sufficient, based upon the insight Jesus is “the one name that contains everything”.


title: 2022–23 EuroLeague

text: The 2022–23 Turkish Airlines EuroLeague will be the 23rd season of the modern era of the EuroLeague, and the 13th under the title sponsorship of the Turkish Airlines. Including the competition's previous incarnation as the FIBA Europe Champions Cup, this will be the 66th season of the premier basketball competition for European men's clubs. CSKA Moscow had their license for the EuroLeague rescinded for the 2022-23 season following the Russian Invasion of Ukraine.


title: 2022–23 EuroLeague

text: A total of 70 Euroleague Basketball officials are set to work on the 2022–23 season in EuroLeague and EuroCup:


title: 2022–23 EuroLeague

text: When more than two teams are tied, the ranking will be established taking into account the victories obtained in the games played only among them. Should the tie persist among some, but not all, of the teams, the ranking of the teams still tied will be determined by again taking into account the victories in the games played only among them, and repeating this same procedure until the tie is entirely resolved.


title: 2022–23 EuroLeague

text: If a tie persists, the ranking will be determined by the goal difference in favour and against in the games played only among the teams still tied.


title: Netherlands Armed Forces

text: The Netherlands Armed Forces () are the military services of the Kingdom of the Netherlands. The core of the armed forces consists of the four service branches: the Royal Netherlands Navy (), the Royal Netherlands Army (), the Royal Netherlands Air Force () and the Royal Netherlands Marechaussee (). The service branches are supplemented by various joint support organisations. In addition, local conscript forces exist on the Dutch Caribbean islands of Aruba (AruMil) and Curaçao (CurMil). These operate under the auspices of the Royal Netherlands Navy and the Netherlands Marine Corps. The armed forces are organisationally part of the Ministry of Defence.


title: Netherlands Armed Forces

text: The existence of, authority over, and tasks of the armed forces are determined in the constitution of the Netherlands. The Government, which consists of cabinet members led by the Prime Minister and the King, functions as the head of the armed forces. Although service members swear allegiance to the King of the Netherlands, the monarch does not hold the position of commander-in-chief.


title: Netherlands Armed Forces

text: The military ranks of the Netherlands armed forces are similar to those of fellow NATO member states and were established by Royal Decree. The highest-ranking officer in the Dutch military is the Chief of Defence, who is a four-star officer (NATO OF-9).


title: Netherlands Armed Forces

text: The Netherlands armed forces exist by declaration in the constitution of the Netherlands. Article 97 of this constitution determines that the armed forces exist


title: Netherlands Armed Forces

text: This means that the role and responsibility of the Dutch military in international stability and peacekeeping is constitutionally determined.


title: Netherlands Armed Forces

text: The same article of the constitution determines that supreme command of the Dutch military resides with the Government of the Netherlands. This has been the case since the constitution was changed in 1983; before then, supreme command of the armed forces of the Netherlands was held by the King of the Netherlands.


title: Netherlands Armed Forces

text: The existence of, authority over, and tasks of the armed forces are determined in the constitution of the Netherlands. The Government, which consists of cabinet members led by the Prime Minister and the King, functions as the head of the armed forces. Although service members swear allegiance to the King of the Netherlands, the monarch does not hold the position of commander-in-chief. Therefore, in practice, important decisions are made by Cabinet, while the Minister of Defence assumes political responsibility over the Ministry.


title: Netherlands Armed Forces

text: The Ministry of Defence is the government ministry which is responsible for formulating and executing defence policy. The ministry consists of the Minister, State Secretary, the Central Staff, the Netherlands Armed Forces and two independent support organisations. The Central Staff () of the Ministry comprises several directorates responsible for executing policy, advising the Minister and State Secretary, and controlling the Defence organisation. The Central Staff is led by the highest civil servant of the defence organisation, the Secretary General. Moreover, the Central Staff incorporates the Defence Staff, which is the highest military organ under command of the Chief of Defence. The Chief of Defence is the military leader of the Netherlands Armed Forces and the most senior military adviser to the Minister of Defence. The Chief of Defence has command over the Armed Forces, the Netherlands Special Operations Command (NLD SOCOM) and the Defence Cyber Command. Several special executive organisations, including the Military Intelligence and Security Service and the office of the Inspector General, are incorporated into the Central Staff as well.


title: Netherlands Armed Forces

text: The Netherlands Armed Forces are a professional military, conscription in the Netherlands having been suspended in 1996 with the exception of Aruba and Curaçao. All military branches and specialties are open to female recruits. In October 2018 the Ministry of Defence announced that the submarine service will also accept female recruits for positions as officer, NCO and sailor.


title: Netherlands Armed Forces

text: The Dutch Ministry of Defence employs over 66,000 personnel, including both civilian and military personnel. The distribution of personnel in the Defence organisation, including the Armed Forces, on 1 July 2020 was as follows:


title: Netherlands Armed Forces

text: The Dutch military is part of the NATO militaries and therefore conforms to the structure of a NATO military. It also uses conforming rank structures.


title: Netherlands Armed Forces

text: All Dutch military personnel, officers and enlisted personnel, are required to take an oath of allegiance. This oath is recorded in the law on General Military Personnel Regulations (Algemeen Militair Ambtenarenregelement) in Article 126a and states the following:


title: Netherlands Armed Forces

text: There is a wide variety of unions, including unions exclusive to officers or particular service branches. Some of the larger unions include:


title: Netherlands Armed Forces

text: The Royal Netherlands Navy () is a modern naval force which consists of 24 commissioned ships and an additional number of support ships of various types. The Navy is commanded by the Commander of the Royal Netherlands Navy (), an officer in the rank of Vice Admiral or Lieutenant General of the Marines, who reports directly to the Chief of Defence. In addition to being the commanding officer of the Royal Netherlands Navy, the holds the position of Admiral Benelux. As such, the is the commanding officer of the operational units of the Royal Netherlands Navy and the Belgian Naval Component.


title: Netherlands Armed Forces

text: The surface fleet of the Navy consist of frigates, amphibious warfare ships, patrol vessels, mine-countermeasure vessels and multiple auxiliary ships. All major surface vessels of the Royal Netherlands Navy are constructed at the Dutch shipyard Damen Schelde Naval Shipbuilding. This includes the technologically advanced air-defence frigates of the "De Zeven Provinciën"-class. Thales Nederland produces various types of high-end sensors and radars for the Dutch fleet.


title: Netherlands Armed Forces

text: The Royal Netherlands Navy Submarine Service () was established in 1906 and is responsible for the operation of all Dutch submarines. As of 2021, the operates four "Walrus"-class submarines and one submarine tender, HNLMS "Mercuur". The Dutch submarines fulfill a considerable role within NATO as their small size and expeditionary capacities allow them to operate in waters that are off-limits to larger submarines. The Ministry of Defence initiated a replacement program in November 2014, replacements are planned to enter service in the late 2020s.


title: Netherlands Armed Forces

text: The Netherlands Marine Corps is the Navy's naval infantry corps. The Corps consist of two battalion-sized Marince Combat Groups, various support units and the Netherlands Maritime Special Operations Forces. The Marines are specialised in amphibious, arctic and mountain warfare as well as special operations. The Corps operates a fleet of landing craft that can operate from one of the two Navy's amphibious transport docks.


title: Netherlands Armed Forces

text: The Royal Netherlands Army () consists of regular Army personnel and the National Reserve Corps. The Army is headed by the Commander of the Royal Netherlands Army (), its headquarters are located on the in Utrecht. The core fighting element of the Army consist of three combat brigades: 11 Airmobile Brigade, 13 Light Brigade and 43 Mechanised Brigade. The brigade-sized Operational Support Command Land fields a variety of combat support and combat service support units while the Army's special operations forces are part of the . All Army units, and their personnel, are divided into tradtitional organisation of arms, services and regiments. The Army's infantry regiments fulfil several distinct roles, these include air assault, armoured infantry, light infantry and special operations. Furthermore, the Army fields cavalry, artillery, engineering and medical regiments.


title: Netherlands Armed Forces

text: The Royal Netherlands Air Force () is the military aviation branch of the Netherlands Armed Forces and is led by the Commander of the Royal Netherlands Air Force (). The Air Force operates a diverse fleet of fixed-wing and rotary aircraft, in addition to operating and maintaining multiple airbases. Moreover, Air Force personnel contributes to the Joint Ground-based Air Defence Command by operating various air-defence systems while other units are dedicated to force protection. The Air Force operates modern fighter aircraft, such as the F-16 Fighting Falcon and F-35 Lightning II, tankers, transports, helicopters, unmanned aerial vehicles, and various types of training aircraft.


title: Netherlands Armed Forces

text: The Royal Netherlands Marechaussee () is a gendarmerie force which performs both military and civilian police duties. In addition to the military police duties, the Marechaussee has a wide variety of duties and responsibilities. This includes guarding the national borders and airports, fighting illegal immigration and transnational crime and guarding the royal palaces.


title: Netherlands Armed Forces

text: The Marechaussee was established as one of the separate Armed Forces in 1998; before then the Marechaussee was organised as one of the arms within the Army.


title: Netherlands Armed Forces

text: While the Royal Netherlands Marechaussee operates under the jurisdiction of the Ministry of Defence, the branch often performs duties delegated by the Ministry of Justice and Security and the Ministry of the Interior and Kingdom Relations. Moreover, several brigades of the Marechaussee are permanently stationed in the Dutch Caribbean.


title: Netherlands Armed Forces

text: Since the 1990s, the Dutch military has been involved in several military campaigns and peace-keeping missions, these include:


title: Netherlands Armed Forces

text: As part of Operation Enduring Freedom, the Netherlands deployed aircraft which were integrated in the European Participating Air Force (EPAF) in support of ground operations in Afghanistan. Additionally, Dutch naval frigates were tasked with policing the waters of the Middle East and Indian Ocean. Between 2001 and 2003, a reinforced army company was deployed to Afghanistan to provide support in maintaining public order and providing security in and around the capital Kabul. Furthermore, military assistance was provided to the Afghan National Army and local security forces. The troops were deployed under the command of NATO's International Security Assistance Force mission.