title: Neal Maupay

text: Maupay is eligible to play for the France or Argentina national teams. He won 35 caps and scored 16 goals for France at U16, U17, U19 and U21 level. He was a member of France's 2015 UEFA European U19 Championship squad and made two appearances in the tournament. Maupay had reportedly put in a personal request to Argentina boss Lionel Scaloni to consider selecting him for the national team in February 2022.


title: Neal Maupay

text: Maupay's footballing idol is Zinedine Zidane. He stated that he "can play out wide or as a number 10, but my favoured position is striker. I like to play down the middle and use my pace to get in behind defences" and "I'm used to looking after the ball and holding off defenders".


title: Neal Maupay

text: Maupay was born in Versailles and moved to the Côte d'Azur with his family at age five. He is of Argentinian descent on his mother's side and holds both French and Argentinian citizenships since 2013. He has the habit of reading in the locker room before matches.


title: Neal Maupay

text: In June 2020, Maupay was targeted with death threats after scoring a last-minute winning goal against Arsenal. A joint investigation by the Premier League and authorities in Singapore identified the culprit as 19-year-old Derek Ng, who was given a nine-month probation order. This was the first prosecution outside the UK for abusing a Premier League player.


title: Everything bagel

text: An everything bagel is a type of bagel baked with a mix of toppings. The exact ingredients vary, but recipes may include caraway seeds, garlic flakes, onion flakes, poppy seeds, sesame seeds and salt. The bagels are made with regular dough and the name is independent of additional fillings such as cream cheese.


title: Everything bagel

text: The everything bagel inspired other bread creations with similar toppings, such as everything bagel chips, everything croissants, everything rolls, everything roti, everything fusilli, and everything hot dog buns. Even mixed nuts have been flavored with the mixture. It is offered by many bakeries and fast casual restaurants. Its origins are disputed, but it was likely first created sometime between 1973 and 1980.


title: Everything bagel

text: The origin of the everything bagel is disputed. Food historian Maria Balinska, author of "The Bagel: The Surprising History of a Modest Bread", said the time saw experimentation in bagel flavors.


title: Everything bagel

text: David Gussin claims he invented it sometime around 1980: while sweeping up leftover bagel toppings from the oven, Gussin saved them in a bin and convinced the store owner to make bagels with them. He concurs that others might have previously invented the concept but insists that he coined the name "everything bagel".


title: Everything bagel

text: Others who have claimed to have invented the everything bagel include American restaurateur Joe Bastianich and sports marketer Brandon Steiner. In his blog, Seth Godin said he worked in a bagel factory that produced everything bagels two years before Gussin. Brandon Steiner, who believes his invention at a bakery in 1973 predates the others, wrote in a 2016 blog post: "One night I was screwing around with different combinations of toppings – sesame, salt, poppy, onion and garlic – making braids, onion flats, and other unorthodox concoctions. Then, after a while, I had the thought to throw all the toppings on a bagel at once. That’s how I invented the everything bagel. This was 1973; I was 14."


title: Everything bagel

text: An everything bagel typically contains from 210 to 280 calories, almost entirely carbohydrates, including 4 to 9 grams of sugar. Each contains about 2 grams of fat, mostly monounsaturated and polyunsaturated fat. Everything bagels also contain iron and calcium.


title: Everything bagel

text: An everything bagel is the MacGuffin in the 2022 movie "Everything Everywhere All at Once". In this, it is topped with literally everything in the multiverse.


title: Raleigh–Durham International Airport

text: Raleigh–Durham International Airport , locally known by its IATA code RDU, is an international airport that serves Raleigh, Durham, and the surrounding Research Triangle region of North Carolina as its main airport. It is located in unincorporated Wake County, but is surrounded by the City of Raleigh to the North and East, and the towns of Cary and Morrisville to the South. The airport covers and has three runways.


title: Raleigh–Durham International Airport

text: In August 2022, RDU had passenger service to 48 domestic destinations and 6 international destinations with nearly 400 average daily departures. The RDU Airport Authority is in charge of the airport facilities and operations and is controlled by a board of representatives from the counties of Wake and Durham and the cities of Raleigh and Durham.


title: Raleigh–Durham International Airport

text: The region's first airport opened in 1929 as Raleigh's Municipal Airport, south of town at . It was quickly outgrown, and in 1939 the North Carolina General Assembly chartered the Raleigh–Durham Aeronautical Authority to build and operate a larger airport between Raleigh and Durham. This was promoted by Eastern Air Lines, led by then chairman Eddie Rickenbacker, who wanted to make RDU a stop on the airline's New York–Miami route.


title: Raleigh–Durham International Airport

text: The new Raleigh–Durham Airport opened on May 1, 1943, with flights by Eastern Airlines. The passenger terminal was built from materials remaining after the construction of four barracks for the Army Air Forces Air Technical Service Command airfield. The three runways the airport had in 1951 are still visible on the southeast side of the airport: 4500-ft runway 5, 4500-ft runway 18 and 4490-ft runway 14.


title: Raleigh–Durham International Airport

text: After World War II, Capital Airlines joined Eastern at RDU; Piedmont Airlines arrived in 1948. The April 1957 Official Airline Guide shows 36 departures a day: twenty Eastern, eight Capital and eight Piedmont. Nonstop flights did not reach beyond Washington, Atlanta, or the Appalachians (but Eastern started a Super Constellation nonstop to Newark in 1958). The next airline (aside from United's takeover of Capital in 1961) was Delta Air Lines in 1970. In April 1969, nonstops didn't reach beyond New York or Atlanta, and Chicago was the only nonstop west of the Appalachians. RDU's first scheduled jets were Eastern 727s in 1965.


title: Raleigh–Durham International Airport

text: In the 1970s, the last decade before airline deregulation, Piedmont connected RDU to Charlotte, Greensboro, New Bern, Norfolk, Richmond, Rocky Mount, Washington, Wilmington and Winston-Salem. United flew to Asheville, Charlotte, Huntsville and Newark, while Eastern flew to Atlanta, Charlotte, Miami, New York, Philadelphia, Richmond and Washington, and Delta flew to Chicago and Greensboro.


title: Raleigh–Durham International Airport

text: After deregulation, Allegheny Airlines arrived in 1979, and by 1985 Trans World Airlines, American Airlines, Ozark, People Express, New York Air and Pan Am had all put in appearances.


title: Raleigh–Durham International Airport

text: American built a terminal at RDU between 1985 and 1987 to house a new hub, and flew to 38 cities when the hub started in June 1987. The December 1987 timetable shows AA nonstops to 36 airports and American Eagle prop nonstops to 18 more. American later flew to London and Paris. The RDU hub operated at a loss even during its heyday in the early 1990s, like the hub AA then had at Nashville. American's December 1992 timetable, around the time of the hub's peak, showed 211 daily departures to 64 destinations, almost all in the eastern United States (the westernmost destinations being American's hubs at Dallas/Fort Worth and Chicago–O'Hare). The hub faced intense competition from Delta and Eastern in Atlanta and from USAir in Charlotte, as well as the short-lived Continental hub in Greensboro that opened in 1993. American began to consider closing the hub in late 1993; operations were reduced until June 1995 when American closed the hub.


title: Raleigh–Durham International Airport

text: American retained a daily nonstop flight to London, which continued to operate until the COVID-19 pandemic and resumed in 2022. The RDU-London route was originally launched based on a purchasing commitment from GlaxoSmithKline, which has major offices at both ends of the route; however, the route is no longer dependent on GSK for revenue.


title: Raleigh–Durham International Airport

text: Midway Airlines replaced AA as the airport's hub carrier from 1995 until 2003. In 1995, Midway had flights to Boston, Hartford, Long Island, Newark, Newburgh, New York, Philadelphia and Washington in the Northeast, and to Fort Lauderdale, Jacksonville, Orlando, Tampa and West Palm Beach in Florida. American subleased its gates at RDU to Midway in order to repay $113 million in American-guaranteed bonds which had been used to construct the hub facilities. Midway suspended service for some time after the September 11, 2001 attacks, and ceased operations in 2002, filing for bankruptcy in 2003.


title: Raleigh–Durham International Airport

text: discount carriers such as Allegiant Air, Southwest Airlines and Frontier Airlines. Because of the economic downturn and high fuel prices in 2008, American ended most point to point flights it operated out of the airport. Several mainline flights were also dropped and service to other cities was reduced or downgraded. Other airlines also cut flights and destinations including United Airlines and US Airways. Also in 2008, the airport was modernized; the current rebuilt Terminal 2 opened, on the site of the old Terminal C that was built in 1987. The rebuilt was completed in 2011, and was designed by Fentress Architects.


title: Raleigh–Durham International Airport

text: By 2010, RDU's traffic began to recover. In the first few months of the year, passenger numbers stabilized at RDU, ending the decrease the airport experienced in 2008 and 2009. In the first four months of 2010, 2.7 million passengers traveled through RDU. Growth was flat compared to the same period a year before, but these signs were positive indicating that the decline was over. Airlines at RDU began to add new services to the schedule with both legacy and low-cost carriers significantly increasing service since the early 2010s.


title: Raleigh–Durham International Airport

text: Delta Air Lines maintains a focus city operation at RDU, which it decided to maintain in the wake of the COVID-19 pandemic due to the area's strong economy and lack of a dominant network carrier.


title: Raleigh–Durham International Airport

text: In November 2022, Avelo Airlines announced the opening of an operating base at Raleigh-Durham. The airline anticipates to have as many as 7 aircraft in the first 2 years and 50 crew members in the first year based at RDU.


title: Raleigh–Durham International Airport

text: The RDU Airport Authority released its Vision 2040 Master Plan in 2017 detailing the improvements which will be made by 2040. The major projects are the construction of a consolidated rental car facility, an on-site hotel, expansion of parking lots, expansion of both terminals to add gates, improvements to the taxiway layout, and the complete rebuilding of the runways. The proposal included lengthening runway 5R/23L to 9,000 feet and rebuilding runway 5L/23R to a length of 11,500 feet just northwest of its current position. The existing runway 5L/23R would become a taxiway for the new runway. Despite these plans, the FAA requested to shorten the length of runway 5L/23R to 10,000 feet because of the impact of COVID-19 on the aviation industry. The FAA ultimately approved rebuilding runway 5L/23R at 10,639 feet, allowing airlines to carry more passengers and cargo, but not allowing the desired traffic to Asia.


title: Raleigh–Durham International Airport

text: The airport contains two terminals with a total of 45 gates. The two terminals do not have an airside connection; passengers moving between the terminals may ride a shuttle bus or take the moving walkway through the covered parking decks between the terminals. All non-pre–cleared international flights are processed in Terminal 2.


title: Raleigh–Durham International Airport

text: The airport incorporates two cargo areas, North Cargo and South Cargo. The North Cargo terminal area is used by cargo airlines. The largest cargo operators are FedEx and UPS. The South Cargo terminal area is used by commercial airlines for cargo operations.


title: Yellowman

text: Winston Foster , better known by the stage name Yellowman, is a Jamaican reggae and dancehall deejay, also known as King Yellowman. He first became popular in Jamaica in the 1980s, rising to prominence with a series of singles that established his reputation.


title: Yellowman

text: Winston Foster was abandoned by his parents and grew up in the Maxfield Children's Home and the Catholic orphanage Alpha Boys School in Kingston, the latter known for its musical alumni. He was shunned due to having albinism, which was not typically socially accepted in Jamaica. In the late 1970s Yellowman first gained wide attention when he finished second to Nadine Sutherland in the 1978 Tastee Talent Contest. Like many Jamaican deejays, he honed his talents by frequently performing at outdoor sound-system dances, prominently with Aces International. He had success as a recording artist, working with producer Henry "Junjo" Lawes. In 1981, after becoming popular throughout Jamaica, Yellowman became the first dancehall artist to be signed to a major American label (Columbia Records).


title: Yellowman

text: His first album release was in 1982 entitled "Mister Yellowman" followed by "Zungguzungguguzungguzeng" in 1983 earning instant success. Yellowman's sexually explicit lyrics in popular songs such as "Mad Over Me", boasting, like other reggae singers/deejays, of his sexual prowess, earned Yellowman criticism in the mid-1980s. Yellowman appeared in "Jamaican Dancehall Volcano Hi-power 1983" which featured other major dancehall musicians such as Massive Dread, Josey Wales, Burro Banton and Eek-A-Mouse.


title: Yellowman

text: Yellowman proclaimed, "I never know why they call it slackness. I talk about sex, but it's just what happens behind closed doors. What I talk is reality."


title: Yellowman

text: He had success in 1987 with a version of "Blueberry Hill", that topped the charts for several weeks in Jamaica. Yellowman had met Fats Domino when the American performed on the island earlier in the decade, and Domino had presented him with a copy of his version.


title: Yellowman

text: By the mid-1990s, Yellowman released socially conscious material, rising to international fame along with singers such as Buju Banton. Yellowman became the island's most popular deejay. During the early 1980s, Yellowman had over 40 singles and produced up to five albums per year.


title: Yellowman

text: He re-invented himself with his 1994 album "Prayer", which stepped away from the slackness that gave him his initial fame. His latest albums are "New York" (2003), "Round 1" (2005), and "No More War" (2019). Yellowman was also a featured guest vocalist on the Run-DMC track "Roots Rap Reggae". Yellowman continues to perform internationally with his Sagittarius Band, and has toured through places such as Nigeria where he retains a following of fans, as well as Spain, Peru, Sweden, Italy, Germany, Britain, France, Kenya, the United States and Canada. He also featured on OPM's 2004 album, "Forthemasses".


title: Yellowman

text: In 2018, it was announced that he would be awarded the Order of Distinction (Officer Class) by the Jamaican government.


title: Yellowman

text: He has spoken against violence. In the "Montreal Mirror" in 2005 he said, "Now it's not your entertainment or teaching. If you notice the hip hop and dancehall artists today, all they do they sing about drugs, clothes, car, house—when they can't get it, they start get violent. I know what violence is like and what it contain and what it can do. I'm glad that the roots is coming back." The slackness style with which Yellowman is associated sometimes has homophobic lyrics. However, in the same "Montreal Mirror" article he spoke against it: "Everybody listen to me... I don't do songs against gay people, I don't do violent lyric against gay people. If you don't like a person or you don't like a thing, you don't talk about it. You don't come on stage and say kill them or burn them because everybody have a right to live."


title: Yellowman

text: In 1982, Yellowman was diagnosed with skin cancer. After several surgeries, Yellowman was able to continue his career. The cancer went into apparent remission during this time. In 1986 it was diagnosed that the cancer had spread to his jaw; Yellowman underwent very invasive jaw surgery to remove a malignant tumor. This surgery permanently disfigured Yellowman's face, as a large portion of the left side of his lower jaw had to be removed to successfully remove the tumor.


title: Yellowman

text: The instrumental for Yellowman's 1982 "Zungguzungguguzungguzeng", the "Diseases" riddim by "Junjo" Lawes, has been sampled and imitated repeatedly since its original release. The original version of this riddim was performed by Alton Ellis for a song called "Mad, Mad, Mad" produced by Coxsone Dodd in 1967. Coxsone Dodd had already released two dub cuts, "Talking Dub" and "Lusaka", plus a 1980 cut by Jennifer Lara, "Hurt So Good." This riddim came to be known as the 'Diseases' riddim after Michigan and Smiley recorded their song, "Diseases", with Henry Junjo Lawes in 1981.


title: Yellowman

text: "Zungguzungguguzungguzeng" was remade by Beenie Man and released on 3 July 2020. Yellowman said of the release, "I wish somebody else did do Zungguzungguguzungguzeng, maybe Shaggy or Sean Paul….Me nuh even hear it."


title: Yellowman

text: The vocal melody of "Zungguzungguguzungguzeng" has also been sampled heavily in various reggae and hip hop songs.


title: Farm

text: A farm (also called an agricultural holding) is an area of land that is devoted primarily to agricultural processes with the primary objective of producing food and other crops; it is the basic facility in food production. The name is used for specialized units such as arable farms, vegetable farms, fruit farms, dairy, pig and poultry farms, and land used for the production of natural fiber, biofuel and other commodities. It includes ranches, feedlots, orchards, plantations and estates, smallholdings and hobby farms, and includes the farmhouse and agricultural buildings as well as the land. In modern times the term has been extended so as to include such industrial operations as wind farms and fish farms, both of which can operate on land or sea.


title: Farm

text: There are about 570 million farms in the world, most of which are small and family-operated. Small farms with a land area of fewer than 2 hectares operate about 1% of the world's agricultural land, and family farms comprise about 75% of the world's agricultural land.


title: Farm

text: Modern farms in developed countries are highly mechanized. In the United States, livestock may be raised on range, land and finished in feedlots and the mechanization of crop production has brought about a great decrease in the number of agricultural workers needed. In Europe, traditional family farms are giving way to larger production units. In Australia, some farms are very large because the land is unable to support a high stocking density of livestock because of climatic conditions. In less developed countries, small farms are the norm, and the majority of rural residents are subsistence farmers, feeding their families and selling any surplus products in the local market. Acres can hold the crops.


title: Farm

text: The word in the sense of an agricultural land-holding derives from the verb "to farm" a revenue source, whether taxes, customs, rents of a group of manors or simply to hold an individual manor by the feudal land tenure of "fee farm". The word is from the medieval Latin noun "firma", also the source of the French word "ferme", meaning a fixed agreement, contract, from the classical Latin adjective "firmus" meaning strong, stout, firm. As in the medieval age virtually all manors were engaged in the business of agriculture, which was their principal revenue source, so to hold a manor by the tenure of "fee farm" became synonymous with the practice of agriculture itself.


title: Farm

text: Farming has been innovated at multiple different points and places in human history. The transition from hunter-gatherer to settled, agricultural societies is called the Neolithic Revolution and first began around 12,000 years ago, near the beginning of the geological epoch of the Holocene around 12,000 years ago. It was the world's first historically verifiable revolution in agriculture. Farming spread from the Middle East to Europe and by 4,000 BC people that lived in the central part of Europe were using oxen to pull plows and wagons. Subsequent step-changes in human farming practices were provoked by the British Agricultural Revolution in the 18th century, and the Green Revolution of the second half of the 20th century.


title: Farm

text: Farming originated independently in different parts of the world, as hunter gatherer societies transitioned to food production rather than food capture. It may have started about 12,000 years ago with the domestication of livestock in the Fertile Crescent in western Asia, soon to be followed by the cultivation of crops. Modern units tend to specialize in the crops or livestock best suited to the region, with their finished products being sold for the retail market or for further processing, with farm products being traded around the world.


title: Farm

text: A farm may be owned and operated by a single individual, family, community, corporation or a company, may produce one or many types of produce, and can be a holding of any size from a fraction of a hectare to several thousand hectares.


title: Farm

text: A farm may operate under a monoculture system or with a variety of cereal or arable crops, which may be separate from or combined with raising livestock. Specialist farms are often denoted as such, thus a dairy farm, fish farm, poultry farm or mink farm.


title: Farm

text: Some farms may not use the word at all, hence vineyard (grapes), orchard (nuts and other fruit), market garden or "truck farm" (vegetables and flowers). Some farms may be denoted by their topographical location, such as a hill farm, while large estates growing cash crops such as cotton or coffee may be called plantations.


title: Farm

text: Many other terms are used to describe farms to denote their methods of production, as in collective, corporate, intensive, organic or vertical.


title: Farm

text: Other farms may primarily exist for research or education, such as an ant farm, and since farming is synonymous with mass production, the word "farm" may be used to describe wind power generation or puppy farm.


title: Farm

text: Dairy farming is a class of agriculture, where female cattle, goats, or other mammals are raised for their milk, which may be either processed on-site or transported to a dairy for processing and eventual retail sale There are many breeds of cattle that can be milked some of the best producing ones include Holstein, Norwegian Red, Kostroma, Brown Swiss, and more.


title: Farm

text: In most Western countries, a centralized dairy facility processes milk and dairy products, such as cream, butter, and cheese. In the United States, these dairies are usually local companies, while in the southern hemisphere facilities may be run by very large nationwide or trans-national corporations (such as Fonterra).


title: Farm

text: Dairy farms generally sell male calves for veal meat, as dairy breeds are not normally satisfactory for commercial beef production. Many dairy farms also grow their own feed, typically including corn, alfalfa, and hay. This is fed directly to the cows, or stored as silage for use during the winter season. Additional dietary supplements are added to the feed to improve milk production.


title: Farm

text: Poultry farms are devoted to raising chickens (egg layers or broilers), turkeys, ducks, and other fowl, generally for meat or eggs.


title: Farm

text: A pig farm is one that specializes in raising pigs or hogs for bacon, ham and other pork products. They may be free range, intensive, or both.


title: Farm

text: Farm control and ownership has traditionally been a key indicator of status and power, especially in Medieval European agrarian societies. The distribution of farm ownership has historically been closely linked to form of government. Medieval feudalism was essentially a system that centralized control of farmland, control of farm labor and political power, while the early American democracy, in which land ownership was a prerequisite for voting rights, was built on relatively easy paths to individual farm ownership. However, the gradual modernization and mechanization of farming, which greatly increases both the efficiency and capital requirements of farming, has led to increasingly large farms. This has usually been accompanied by the decoupling of political power from farm ownership.


title: Farm

text: In some societies (especially socialist and communist), collective farming is the norm, with either government ownership of the land or common ownership by a local group. Especially in societies without widespread industrialized farming, tenant farming and sharecropping are common; farmers either pay landowners for the right to use farmland or give up a portion of the crops.


title: Farm

text: Enterprises where livestock are raised on rangeland are called "ranches". Where livestock are raised in confinement on feed produced elsewhere, the term "feedlot" is usually used.


title: Farm

text: In the US, in 1910 there were 6,406,000 farms and 10,174,000 family workers; In 2000 there were only 2,172,000 farms and 2,062,300 family workers. The share of U.S. farms operated by women has risen steadily over recent decades, from 5 percent in 1978 to 14 percent by 2007.In the United States, there are over three million migrant and seasonal farmworkers; 72% are foreign-born, 78% are male, they have an average age of 36 and average education of 8 years. Farmworkers make an average hourly rate of $9–10 per hour, compared to an average of over $18 per hour for nonfarm labor. Their average family income is under $20,000 and 23% live in families with incomes below the federal poverty level. One-half of all farmworker families earn less than $10,000 per year, which is significantly below the 2005 U.S. poverty level of $19,874 for a family of four.


title: Farm

text: In 2007, corn acres are expected to increase by 15% because of the high demand for ethanol, both in and outside of the U.S. Producers are expecting to plant 90.5 million acres (366,000 km) of corn, making it the largest corn crop since 1944.


title: Farm

text: In the UK, "farm" as an agricultural unit, always denotes the area of pasture and other fields together with its farmhouse, farmyard and outbuildings. Large farms, or groups of farms under the same ownership, may be called an estate. Conversely, a small farm surrounding the owner's dwelling is called a smallholding and is generally focused on self-sufficiency with only the surplus being sold.


title: Farm

text: In Europe, traditional family farms are giving way to larger production units where industrial agriculture and mechanization brings large crop yields.


title: Farm

text: The Common Agricultural Policy (CAP) is one of the most important policies of the European Union and is helping in the change of farms from traditional family farms to larger production units. The policy has the objectives of increasing agricultural production, providing certainty in food supplies, ensuring a high quality of life for farmers, stabilizing markets, and ensuring reasonable prices for consumers. It was, until recently, operated by a system of subsidies and market intervention. Until the 1990s, the policy accounted for over 60 per cent of the European Union's annual budget, and as of 2013 accounts for around 34 per cent.


title: Farm

text: According to the World Bank, "most empirical evidence indicates that land productivity on large farms in Pakistan is lower than that of small farms, holding other factors constant." Small farmers have "higher net returns per hectare" than large farms, according to farm


title: Farm

text: Nepal is an agricultural country and about 80% of the total population are engaged in farming. Rice is mainly produced in Nepal along with fruits like apples. Dairy farming and poultry farming are also growing in Nepal.


title: Farm

text: Farming is a significant economic sector in Australia. A farm is an area of land used for primary production which will include buildings.


title: Farm

text: According to the UN, "green agriculture directs a greater share of total farming input expenditures towards the purchase of locally sourced input?(e.g. labour and organic fertilisers) and a local multiplier effect is expected to kick in. Overall, green farming practices tend to require more labour inputs than conventional farming (e.g. from comparable levels to as much as 30 per cent more) (FAO 2007 and European Commission 2010), creating jobs in rural areas and a higher return on labour inputs."


title: Farm

text: Where most of the income is from some other employment, and the farm is really an expanded residence, the term "hobby farm" is common. This will allow sufficient size for recreational use but be very unlikely to produce sufficient income to be self-sustaining. Hobby farms are commonly around but may be much larger depending upon land prices (which vary regionally).


title: Farm

text: Often very small farms used for intensive primary production are referred to by the specialization they are being used for, such as a dairy rather than a dairy farm, a piggery, a market garden, etc. This also applies to feedlots, which are specifically developed to a single purpose and are often not able to be used for more general purpose (mixed) farming practices.


title: Farm

text: In remote areas farms can become quite large. As with "estates" in England, there is no defined size or method of operation at which a large farm becomes a station.


title: Farm

text: A farm in Africa includes various structures. Depending on climate-related areas primarily farming is the raising and breeding of grazing livestock, such as cattle, sheep, ostriches, horses or goats. Predominantly domestic animals are raised for their meat, milk, skin, leather or fiber (wool). You might even come across silk farms.


title: Farm

text: Furthermore, there are plenty of hunting farms, guest farms and game farms. Arable or irrigated land is often used for raising crops such as feed grains and hay for animal feeding.


title: Farm

text: On some farms (Astro Farm) star-gazing became very popular because of the excellent optical quality in the desert. The High Energy Stereoscopic System (H.E.S.S.) which investigates cosmic gamma rays is situated on "Farm Göllschau" in Namibia.


title: Farm

text: Farm equipment has evolved over the centuries from simple hand tools such as the hoe, through ox- or horse-drawn equipment such as the plough and harrow, to the modern highly technical machinery such as the tractor, baler and combine harvester replacing what was a highly labour-intensive occupation before the Industrial revolution. Today much of the farm equipment used on both small and large farms is automated (e.g. using satellite guided farming).


title: Farm

text: As new types of high-tech farm equipment have become inaccessible to farmers that historically fixed their own equipment, Wired reports there is a growing backlash, due mostly to companies using intellectual property law to prevent farmers from having the legal right to fix their equipment (or gain access to the information to allow them to do it). This has encouraged groups such as Open Source Ecology and Farm Hack to begin to make open source hardware for agricultural machinery. In addition on a smaller scale Farmbot and the RepRap open source 3D printer community has begun to make open-source farm tools available of increasing levels of sophistication.


title: Electronic circuit

text: An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. It is a type of electrical circuit and to be referred to as "electronic", rather than "electrical", generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another.


title: Electronic circuit

text: Circuits can be constructed of discrete components connected by individual pieces of wire, but today it is much more common to create interconnections by photolithographic techniques on a laminated substrate (a printed circuit board or PCB) and solder the components to these interconnections to create a finished circuit. In an integrated circuit or IC, the components and interconnections are formed on the same substrate, typically a semiconductor such as doped silicon or (less commonly) gallium arsenide.


title: Electronic circuit

text: An electronic circuit can usually be categorized as an analog circuit, a digital circuit, or a mixed-signal circuit (a combination of analog circuits and digital circuits). The most widely used semiconductor device in electronic circuits is the MOSFET (metal-oxide-semiconductor field-effect transistor).


title: Electronic circuit

text: Breadboards, perfboards, and stripboards are common for testing new designs. They allow the designer to make quick changes to the circuit during development.


title: Electronic circuit

text: Analog electronic circuits are those in which current or voltage may vary continuously with time to correspond to the information being represented.


title: Electronic circuit

text: The basic components of analog circuits are wires, resistors, capacitors, inductors, diodes, and transistors. Analog circuits are very commonly represented in schematic diagrams, in which wires are shown as lines, and each component has a unique symbol. Analog circuit analysis employs Kirchhoff's circuit laws: all the currents at a node (a place where wires meet), and the voltage around a closed loop of wires is 0. Wires are usually treated as ideal zero-voltage interconnections; any resistance or reactance is captured by explicitly adding a parasitic element, such as a discrete resistor or inductor. Active components such as transistors are often treated as controlled current or voltage sources: for example, a field-effect transistor can be modeled as a current source from the source to the drain, with the current controlled by the gate-source voltage.


title: Electronic circuit

text: When the circuit size is comparable to a wavelength of the relevant signal frequency, a more sophisticated approach must be used, the distributed-element model. Wires are treated as transmission lines, with nominally constant characteristic impedance, and the impedances at the start and end determine transmitted and reflected waves on the line. Circuits designed according to this approach are distributed-element circuits. Such considerations typically become important for circuit boards at frequencies above a GHz; integrated circuits are smaller and can be treated as lumped elements for frequencies less than 10GHz or so.


title: Electronic circuit

text: In digital electronic circuits, electric signals take on discrete values, to represent logical and numeric values. These values represent the information that is being processed. In the vast majority of cases, binary encoding is used: one voltage (typically the more positive value) represents a binary '1' and another voltage (usually a value near the ground potential, 0 V) represents a binary '0'. Digital circuits make extensive use of transistors, interconnected to create logic gates that provide the functions of Boolean logic: AND, NAND, OR, NOR, XOR and combinations thereof. Transistors interconnected so as to provide positive feedback are used as latches and flip flops, circuits that have two or more metastable states, and remain in one of these states until changed by an external input. Digital circuits therefore can provide logic and memory, enabling them to perform arbitrary computational functions. (Memory based on flip-flops is known as static random-access memory (SRAM). Memory based on the storage of charge in a capacitor, dynamic random-access memory (DRAM) is also widely used.)


title: Electronic circuit

text: The design process for digital circuits is fundamentally different from the process for analog circuits. Each logic gate regenerates the binary signal, so the designer need not account for distortion, gain control, offset voltages, and other concerns faced in an analog design. As a consequence, extremely complex digital circuits, with billions of logic elements integrated on a single silicon chip, can be fabricated at low cost. Such digital integrated circuits are ubiquitous in modern electronic devices, such as calculators, mobile phone handsets, and computers. As digital circuits become more complex, issues of time delay, logic races, power dissipation, non-ideal switching, on-chip and inter-chip loading, and leakage currents, become limitations to circuit density, speed and performance.


title: Electronic circuit

text: Digital circuitry is used to create general purpose computing chips, such as microprocessors, and custom-designed logic circuits, known as application-specific integrated circuit (ASICs). Field-programmable gate arrays (FPGAs), chips with logic circuitry whose configuration can be modified after fabrication, are also widely used in prototyping and development.


title: Electronic circuit

text: Mixed-signal or hybrid circuits contain elements of both analog and digital circuits. Examples include comparators, timers, phase-locked loops, analog-to-digital converters, and digital-to-analog converters. Most modern radio and communications circuitry uses mixed signal circuits. For example, in a receiver, analog circuitry is used to amplify and frequency-convert signals so that they reach a suitable state to be converted into digital values, after which further signal processing can be performed in the digital domain.


title: Fundamental theorem of algebra

text: The fundamental theorem of algebra, also known as d'Alembert's theorem, or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.


title: Fundamental theorem of algebra

text: Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.


title: Fundamental theorem of algebra

text: The theorem is also stated as follows: every non-zero, single-variable, degree "n" polynomial with complex coefficients has, counted with multiplicity, exactly "n" complex roots. The equivalence of the two statements can be proven through the use of successive polynomial division.


title: Fundamental theorem of algebra

text: Despite its name, there is no purely algebraic proof of the theorem, since any proof must use some form of the analytic completeness of the real numbers, which is not an algebraic concept. Additionally, it is not fundamental for modern algebra; its name was given at a time when algebra was synonymous with theory of equations.


title: Fundamental theorem of algebra

text: Peter Roth, in his book "Arithmetica Philosophica" (published in 1608, at Nürnberg, by Johann Lantzenberger), wrote that a polynomial equation of degree "n" (with real coefficients) "may" have "n" solutions. Albert Girard, in his book "L'invention nouvelle en l'Algèbre" (published in 1629), asserted that a polynomial equation of degree "n" has "n" solutions, but he did not state that they had to be real numbers. Furthermore, he added that his assertion holds "unless the equation is incomplete", by which he meant that no coefficient is equal to 0. However, when he explains in detail what he means, it is clear that he actually believes that his assertion is always true; for instance, he shows that the equation formula_1 although incomplete, has four solutions (counting multiplicities): 1 (twice), formula_2 and formula_3


title: Fundamental theorem of algebra

text: As will be mentioned again below, it follows from the fundamental theorem of algebra that every non-constant polynomial with real coefficients can be written as a product of polynomials with real coefficients whose degrees are either 1 or 2. However, in 1702 Leibniz erroneously said that no polynomial of the type (with real and distinct from 0) can be written in such a way. Later, Nikolaus Bernoulli made the same assertion concerning the polynomial , but he got a letter from Euler in 1742 in which it was shown that this polynomial is equal to


title: Fundamental theorem of algebra

text: A first attempt at proving the theorem was made by d'Alembert in 1746, but his proof was incomplete. Among other problems, it assumed implicitly a theorem (now known as Puiseux's theorem), which would not be proved until more than a century later and using the fundamental theorem of algebra. Other attempts were made by Euler (1749), de Foncenex (1759), Lagrange (1772), and Laplace (1795). These last four attempts assumed implicitly Girard's assertion; to be more precise, the existence of solutions was assumed and all that remained to be proved was that their form was "a" + "bi" for some real numbers "a" and "b". In modern terms, Euler, de Foncenex, Lagrange, and Laplace were assuming the existence of a splitting field of the polynomial "p"("z").


title: Fundamental theorem of algebra

text: At the end of the 18th century, two new proofs were published which did not assume the existence of roots, but neither of which was complete. One of them, due to James Wood and mainly algebraic, was published in 1798 and it was totally ignored. Wood's proof had an algebraic gap. The other one was published by Gauss in 1799 and it was mainly geometric, but it had a topological gap, only filled by Alexander Ostrowski in 1920, as discussed in Smale (1981).


title: Fundamental theorem of algebra

text: The first rigorous proof was published by Argand, an amateur mathematician, in 1806 (and revisited in 1813); it was also here that, for the first time, the fundamental theorem of algebra was stated for polynomials with complex coefficients, rather than just real coefficients. Gauss produced two other proofs in 1816 and another incomplete version of his original proof in 1849.


title: Fundamental theorem of algebra

text: The first textbook containing a proof of the theorem was Cauchy's "Cours d'analyse de l'École Royale Polytechnique" (1821). It contained Argand's proof, although Argand is not credited for it.


title: Fundamental theorem of algebra

text: None of the proofs mentioned so far is constructive. It was Weierstrass who raised for the first time, in the middle of the 19th century, the problem of finding a constructive proof of the fundamental theorem of algebra. He presented his solution, which amounts in modern terms to a combination of the Durand–Kerner method with the homotopy continuation principle, in 1891. Another proof of this kind was obtained by Hellmuth Kneser in 1940 and simplified by his son Martin Kneser in 1981.


title: Fundamental theorem of algebra

text: Without using countable choice, it is not possible to constructively prove the fundamental theorem of algebra for complex numbers based on the Dedekind real numbers (which are not constructively equivalent to the Cauchy real numbers without countable choice). However, Fred Richman proved a reformulated version of the theorem that does work.


title: Fundamental theorem of algebra

text: The next two statements are equivalent to the previous ones, although they do not involve any nonreal complex number. These statements can be proved from previous factorizations by remarking that, if is a non-real root of a polynomial with real coefficients, its complex conjugate formula_13 is also a root, and formula_14 is a polynomial of degree two with real coefficients. Conversely, if one has a factor of degree two, the quadratic formula gives a root.


title: Fundamental theorem of algebra

text: All proofs below involve some mathematical analysis, or at least the topological concept of continuity of real or complex functions. Some also use differentiable or even analytic functions. This requirement has led to the remark that the Fundamental Theorem of Algebra is neither fundamental, nor a theorem of algebra.


title: Fundamental theorem of algebra

text: Some proofs of the theorem only prove that any non-constant polynomial with "real" coefficients has some complex root. This lemma is enough to establish the general case because, given a non-constant polynomial "p"("z") with complex coefficients, the polynomial


title: Fundamental theorem of algebra

text: has only real coefficients and, if "z" is a zero of "q"("z"), then either "z" or its conjugate is a root of "p"("z").


title: Fundamental theorem of algebra

text: Many non-algebraic proofs of the theorem use the fact (sometimes called the "growth lemma") that a polynomial function "p"("z") of degree "n" whose dominant coefficient is 1 behaves like "z" when |"z"| is large enough. More precisely, there is some positive real number "R" such that


title: Fundamental theorem of algebra

text: Even without using complex numbers, it is possible to show that a real-valued polynomial "p"("x"): "p"(0) ≠ 0 of degree "n" > 2 can always be divided by some quadratic polynomial with real coefficients. In other words, for some real-valued "a" and "b", the coefficients of the linear remainder on dividing "p"("x") by "x" − "ax" − "b" simultaneously become zero.


title: Fundamental theorem of algebra

text: where "q"("x") is a polynomial of degree "n" − 2. The coefficients "R"("a", "b") and "S"("a", "b") are independent of "x" and completely defined by the coefficients of "p"("x"). In terms of representation, "R"("a", "b") and "S"("a", "b") are bivariate polynomials in "a" and "b". In the flavor of Gauss's first (incomplete) proof of this theorem from 1799, the key is to show that for any sufficiently large negative value of "b", all the roots of both "R"("a", "b") and "S"("a", "b") in the variable "a" are real-valued and alternating each other (interlacing property). Utilizing a Sturm-like chain that contain "R"("a", "b") and "S"("a", "b") as consecutive terms, interlacing in the variable "a" can be shown for all consecutive pairs in the chain whenever "b" has sufficiently large negative value. As "S"("a", "b" = 0) = "p"(0) has no roots, interlacing of "R"("a", "b") and "S"("a", "b") in the variable "a" fails at "b" = 0. Topological arguments can be applied on the interlacing property to show that the locus of the roots of "R"("a", "b") and "S"("a", "b") must intersect for some real-valued "a" and "b" < 0.


title: Fundamental theorem of algebra

text: Find a closed disk "D" of radius "r" centered at the origin such that |"p"("z")| > |"p"(0)| whenever |"z"| ≥ "r". The minimum of |"p"("z")| on "D", which must exist since "D" is compact, is therefore achieved at some point "z" in the interior of "D", but not at any point of its boundary. The maximum modulus principle applied to 1/"p"("z") implies that "p"("z") = 0. In other words, "z" is a zero of "p"("z").


title: Fundamental theorem of algebra

text: A variation of this proof does not require the maximum modulus principle (in fact, a similar argument also gives a proof of the maximum modulus principle for holomorphic functions). Continuing from before the principle was invoked, if "a" := "p"("z") ≠ 0, then, expanding "p"("z") in powers of "z" − "z", we can write


title: Fundamental theorem of algebra

text: Here, the "c" are simply the coefficients of the polynomial "z" → "p"("z" + "z") after expansion, and "k" is the index of the first non-zero coefficient following the constant term. For "z" sufficiently close to "z" this function has behavior asymptotically similar to the simpler polynomial formula_21. More precisely, the function


title: Fundamental theorem of algebra

text: for some positive constant "M" in some neighborhood of "z". Therefore, if we define formula_23 and let formula_24 tracing a circle of radius "r" > 0 around "z", then for any sufficiently small "r" (so that the bound "M" holds), we see that


title: Fundamental theorem of algebra

text: When "r" is sufficiently close to 0 this upper bound for |"p"("z")| is strictly smaller than |"a"|, contradicting the definition of "z". Geometrically, we have found an explicit direction θ such that if one approaches "z" from that direction one can obtain values "p"("z") smaller in absolute value than |"p"("z")|.


title: Fundamental theorem of algebra

text: Another analytic proof can be obtained along this line of thought observing that, since |"p"("z")| > |"p"(0)| outside "D", the minimum of |"p"("z")| on the whole complex plane is achieved at "z". If |"p"("z")| > 0, then 1/"p" is a bounded holomorphic function in the entire complex plane since, for each complex number "z", |1/"p"("z")| ≤ |1/"p"("z")|. Applying Liouville's theorem, which states that a bounded entire function must be constant, this would imply that 1/"p" is constant and therefore that "p" is constant. This gives a contradiction, and hence "p"("z") = 0.


title: Fundamental theorem of algebra

text: Yet another analytic proof uses the argument principle. Let "R" be a positive real number large enough so that every root of "p"("z") has absolute value smaller than "R"; such a number must exist because every non-constant polynomial function of degree "n" has at most "n" zeros. For each "r" > "R", consider the number


title: Fundamental theorem of algebra

text: where "c"("r") is the circle centered at 0 with radius "r" oriented counterclockwise; then the argument principle says that this number is the number "N" of zeros of "p"("z") in the open ball centered at 0 with radius "r", which, since "r" > "R", is the total number of zeros of "p"("z"). On the other hand, the integral of "n"/"z" along "c"("r") divided by 2π"i" is equal to "n". But the difference between the two numbers is


title: Fundamental theorem of algebra

text: The numerator of the rational expression being integrated has degree at most "n" − 1 and the degree of the denominator is "n" + 1. Therefore, the number above tends to 0 as "r" → +∞. But the number is also equal to "N" − "n" and so "N" = "n".


title: Fundamental theorem of algebra

text: Another complex-analytic proof can be given by combining linear algebra with the Cauchy theorem. To establish that every complex polynomial of degree "n" > 0 has a zero, it suffices to show that every complex square matrix of size "n" > 0 has a (complex) eigenvalue. The proof of the latter statement is by contradiction.


title: Fundamental theorem of algebra

text: Let "A" be a complex square matrix of size "n" > 0 and let "I" be the unit matrix of the same size. Assume "A" has no eigenvalues. Consider the resolvent function


title: Fundamental theorem of algebra

text: which is a meromorphic function on the complex plane with values in the vector space of matrices. The eigenvalues of "A" are precisely the poles of "R"("z"). Since, by assumption, "A" has no eigenvalues, the function "R"("z") is an entire function and Cauchy theorem implies that


title: Fundamental theorem of algebra

text: This formula is valid outside the closed disc of radius formula_31 (the operator norm of "A"). Let formula_32 Then


title: Fundamental theorem of algebra

text: (in which only the summand "k" = 0 has a nonzero integral). This is a contradiction, and so "A" has an eigenvalue.


title: Fundamental theorem of algebra

text: Suppose the minimum of |"p"("z")| on the whole complex plane is achieved at "z"; it was seen at the proof which uses Liouville's theorem that such a number must exist. We can write "p"("z") as a polynomial in "z" − "z": there is some natural number "k" and there are some complex numbers "c", "c", ..., "c" such that "c" ≠ 0 and:


title: Fundamental theorem of algebra

text: If "p"("z") is nonzero, it follows that if "a" is a "k" root of −"p"("z")/"c" and if "t" is positive and sufficiently small, then |"p"("z" + "ta")| < |"p"("z")|, which is impossible, since |"p"("z")| is the minimum of |"p"| on "D".


title: Fundamental theorem of algebra

text: For another topological proof by contradiction, suppose that the polynomial "p"("z") has no roots, and consequently is never equal to 0. Think of the polynomial as a map from the complex plane into the complex plane. It maps any circle |"z"| = "R" into a closed loop, a curve "P"("R"). We will consider what happens to the winding number of "P"("R") at the extremes when "R" is very large and when "R" = 0. When "R" is a sufficiently large number, then the leading term "z" of "p"("z") dominates all other terms combined; in other words,


title: Fundamental theorem of algebra

text: When "z" traverses the circle formula_36 once counter-clockwise formula_37 then formula_38 winds "n" times counter-clockwise formula_39 around the origin (0,0), and "P"("R") likewise. At the other extreme, with |"z"| = 0, the curve "P"(0) is merely the single point "p"(0), which must be nonzero because "p"("z") is never zero. Thus "p"(0) must be distinct from the origin (0,0), which denotes 0 in the complex plane. The winding number of "P"(0) around the origin (0,0) is thus 0. Now changing "R" continuously will deform the loop continuously. At some "R" the winding number must change. But that can only happen if the curve "P"("R") includes the origin (0,0) for some "R". But then for some "z" on that circle |"z"| = "R" we have "p"("z") = 0, contradicting our original assumption. Therefore, "p"("z") has at least one zero.


title: Fundamental theorem of algebra

text: These proofs of the Fundamental Theorem of Algebra must make use of the following two facts about real numbers that are not algebraic but require only a small amount of analysis (more precisely, the intermediate value theorem in both cases):


title: Fundamental theorem of algebra

text: The second fact, together with the quadratic formula, implies the theorem for real quadratic polynomials. In other words, algebraic proofs of the fundamental theorem actually show that if "R" is any real-closed field, then its extension "C" = "R"() is algebraically closed.


title: Fundamental theorem of algebra

text: As mentioned above, it suffices to check the statement "every non-constant polynomial "p"("z") with real coefficients has a complex root". This statement can be proved by induction on the greatest non-negative integer "k" such that 2 divides the degree "n" of "p"("z"). Let "a" be the coefficient of "z" in "p"("z") and let "F" be a splitting field of "p"("z") over "C"; in other words, the field "F" contains "C" and there are elements "z", "z", ..., "z" in "F" such that


title: Fundamental theorem of algebra

text: If "k" = 0, then "n" is odd, and therefore "p"("z") has a real root. Now, suppose that "n" = 2"m" (with "m" odd and "k" > 0) and that the theorem is already proved when the degree of the polynomial has the form 2"m"′ with "m"′ odd. For a real number "t", define:


title: Fundamental theorem of algebra

text: Then the coefficients of "q"("z") are symmetric polynomials in the "z" with real coefficients. Therefore, they can be expressed as polynomials with real coefficients in the elementary symmetric polynomials, that is, in −"a", "a", ..., (−1)"a". So "q"("z") has in fact "real" coefficients. Furthermore, the degree of "q"("z") is "n"("n" − 1)/2 = 2"m"("n" − 1), and "m"("n" − 1) is an odd number. So, using the induction hypothesis, "q" has at least one complex root; in other words, "z" + "z" + "tzz" is complex for two distinct elements "i" and "j" from {1, ..., "n"}. Since there are more real numbers than pairs ("i", "j"), one can find distinct real numbers "t" and "s" such that "z" + "z" + "tzz" and "z" + "z" + "szz" are complex (for the same "i" and "j"). So, both "z" + "z" and "zz" are complex numbers. It is easy to check that every complex number has a complex square root, thus every complex polynomial of degree 2 has a complex root by the quadratic formula. It follows that "z" and "z" are complex numbers, since they are roots of the quadratic polynomial "z" −  ("z" + "z")"z" + "zz".


title: Fundamental theorem of algebra

text: Joseph Shipman showed in 2007 that the assumption that odd degree polynomials have roots is stronger than necessary; any field in which polynomials of prime degree have roots is algebraically closed (so "odd" can be replaced by "odd prime" and this holds for fields of all characteristics). For axiomatization of algebraically closed fields, this is the best possible, as there are counterexamples if a single prime is excluded. However, these counterexamples rely on −1 having a square root. If we take a field where −1 has no square root, and every polynomial of degree "n" ∈ "I" has a root, where "I" is any fixed infinite set of odd numbers, then every polynomial "f"("x") of odd degree has a root (since has a root, where "k" is chosen so that ). Mohsen Aliabadi generalized Shipman's result in 2013, providing an independent proof that a sufficient condition for an arbitrary field (of any characteristic) to be algebraically closed is that it has a root for every polynomial of prime degree.


title: Fundamental theorem of algebra

text: Another algebraic proof of the fundamental theorem can be given using Galois theory. It suffices to show that C has no proper finite field extension. Let "K"/C be a finite extension. Since the normal closure of "K" over R still has a finite degree over C (or R), we may assume without loss of generality that "K" is a normal extension of R (hence it is a Galois extension, as every algebraic extension of a field of characteristic 0 is separable). Let "G" be the Galois group of this extension, and let "H" be a Sylow 2-subgroup of "G", so that the order of "H" is a power of 2, and the index of "H" in "G" is odd. By the fundamental theorem of Galois theory, there exists a subextension "L" of "K"/R such that Gal("K"/"L") = "H". As ["L":R] = ["G":"H"] is odd, and there are no nonlinear irreducible real polynomials of odd degree, we must have "L" = R, thus ["K":R] and ["K":C] are powers of 2. Assuming by way of contradiction that ["K":C] > 1, we conclude that the 2-group Gal("K"/C) contains a subgroup of index 2, so there exists a subextension "M" of C of degree 2. However, C has no extension of degree 2, because every quadratic complex polynomial has a complex root, as mentioned above. This shows that ["K":C] = 1, and therefore "K" = C, which completes the proof.


title: Fundamental theorem of algebra

text: There exists still another way to approach the fundamental theorem of algebra, due to J. M. Almira and A. Romero: by Riemannian geometric arguments. The main idea here is to prove that the existence of a non-constant polynomial "p"("z") without zeros implies the existence of a flat Riemannian metric over the sphere S. This leads to a contradiction since the sphere is not flat.


title: Fundamental theorem of algebra

text: A Riemannian surface ("M", "g") is said to be flat if its Gaussian curvature, which we denote by "K", is identically null. Now, the Gauss–Bonnet theorem, when applied to the sphere S, claims that


title: Fundamental theorem of algebra

text: Obviously, "p*"("z") ≠ 0 for all "z" in C. Consider the polynomial "f"("z") = "p"("z")"p*"("z"). Then "f"("z") ≠ 0 for each "z" in C. Furthermore,


title: Fundamental theorem of algebra

text: for "w" ∈ S\{0}, is a well defined Riemannian metric over the sphere S (which we identify with the extended complex plane C ∪ {∞}).


title: Fundamental theorem of algebra

text: Since the fundamental theorem of algebra can be seen as the statement that the field of complex numbers is algebraically closed, it follows that any theorem concerning algebraically closed fields applies to the field of complex numbers. Here are a few more consequences of the theorem, which are either about the field of real numbers or the relationship between the field of real numbers and the field of complex numbers:


title: Fundamental theorem of algebra

text: While the fundamental theorem of algebra states a general existence result, it is of some interest, both from the theoretical and from the practical point of view, to have information on the location of the zeros of a given polynomial. The simpler result in this direction is a bound on the modulus: all zeros ζ of a monic polynomial formula_49 satisfy an inequality |ζ| ≤ "R", where


title: Fundamental theorem of algebra

text: Notice that, as stated, this is not yet an existence result but rather an example of what is called an a priori bound: it says that "if there are solutions" then they lie inside the closed disk of center the origin and radius "R". However, once coupled with the fundamental theorem of algebra it says that the disk contains in fact at least one solution. More generally, a bound can be given directly in terms of any p-norm of the "n"-vector of coefficients formula_51 that is |ζ| ≤ "R", where "R" is precisely the "q"-norm of the 2-vector formula_52 "q" being the conjugate exponent of "p", formula_53 for any 1 ≤ "p" ≤ ∞. Thus, the modulus of any solution is also bounded by


title: Fundamental theorem of algebra

text: (where we define "a" to mean 1, which is reasonable since 1 is indeed the "n"-th coefficient of our polynomial). The case of a generic polynomial of degree "n",


title: Fundamental theorem of algebra

text: is of course reduced to the case of a monic, dividing all coefficients by "a" ≠ 0. Also, in case that 0 is not a root, i.e. "a" ≠ 0, bounds from below on the roots ζ follow immediately as bounds from above on formula_58, that is, the roots of


title: Fundamental theorem of algebra

text: Finally, the distance formula_60 from the roots ζ to any point formula_61 can be estimated from below and above, seeing formula_62 as zeros of the polynomial formula_63, whose coefficients are the Taylor expansion of "P"("z") at formula_64


title: Fundamental theorem of algebra

text: in order to prove the inequality |ζ| ≤ "R" we can assume, of course, |ζ| > 1. Writing the equation as


title: Fundamental theorem of algebra

text: In the case 1 < "p" ≤ ∞, taking into account the summation formula for a geometric progression, we have


title: PZL M28 Skytruck

text: The PZL M28 Skytruck is a Polish STOL light cargo and passenger plane, produced by PZL Mielec, as a development of licence-built Antonov An-28s. Early licence-built planes were designated PZL An-28. The maritime patrol and reconnaissance variants are named PZL M28B Bryza ("sea breeze").


title: PZL M28 Skytruck

text: The Antonov An-28 was the winner of a competition against the Beriev Be-30 for a new light passenger and utility transport for Aeroflot's short haul routes, conceived to replace the highly successful An-2 biplane. The An-28 is derived from the earlier An-14. Commonalities with the An-14 include a high wing layout, twin fins and rudders, but it differs in having a reworked and longer fuselage, with turboprop engines. The original powerplant was the TVD-850, but production versions are powered by the more powerful TVD-10B, with three-blade propellers.


title: PZL M28 Skytruck

text: The An-28 made its first flight as the An-14M in September 1969 in the USSR. A subsequent preproduction aircraft first flew in April 1975. Production of the An-28 was then transferred to Poland's PZL Mielec in 1978, although it was not until 22 July 1984 that the first Polish-built production aircraft flew. The An-28's Soviet type certificate was awarded in April 1986.


title: PZL M28 Skytruck

text: PZL Mielec has become the sole source for production An-28s. The basic variant, not differing from the Soviet one, was designated PZL An-28 and was powered with PZL-10S (licence-built TVD-10B) engines. They were built mostly for the USSR, until it broke up. The plane was next developed by the PZL Mielec into a westernised version powered by 820 kW (1100shp) Pratt & Whitney PT6A-65B turboprops with five-blade Hartzell propellers, plus some western (BendixKing) avionics (a distinguishing feature are exhaust pipes, sticking out on sides of engine nacelles). Designated the PZL M28 Skytruck, the first flight was on 24 July 1993 and it is in limited production, mostly for export (39 produced by 2006). The type received Polish certification in March 1996, and US FAR Part 23 certificate on 19 March 2004.


title: PZL M28 Skytruck

text: Apart from the Skytruck, PZL Mielec developed a family of militarized light transport and maritime reconnaissance planes for the Polish Air Force and Polish Navy in the 1990s, with original PZL-10S engines, named PZL M28B in the Air Force and Bryza in the Navy. From 2000, newly produced M28Bs started to be equipped with five-blade propellers as well.


title: PZL M28 Skytruck

text: PZL Mielec was bought by Sikorsky in 2007. Purchased primarily to produce helicopter structures, the company also produces 10 M28s per year. Sikorsky's current owner, Lockheed Martin, has marketed it to the governments of Indonesia, Jordan, Poland, Venezuela, Vietnam, the U.S. and commercial operators. Split equally between commercial and military applications, it competes with the Viking Air Twin Otter, the Let 410 and the Dornier 228.


title: PZL M28 Skytruck

text: The M28 is a twin-engined high-wing strutted monoplane with an all-metal airframe, twin vertical fins and a tricycle fixed landing gear.


title: PZL M28 Skytruck

text: Aerodynamically deployed leading edge slats when approaching stall speed enable a low stall speed and while the certification landing field is , PZL has demonstrated landing in .


title: PZL M28 Skytruck

text: Inlet air ducts inertial separators and inverted configuration of the PT6 and the high wing configuration protect the engines and propellers against foreign object damage for unprepared runways operations.


title: PZL M28 Skytruck

text: Multiple configurations are available: a 19-passenger airliner with 2-1 seating and an underbelly luggage pod; a cargo aircraft with a hand-cranked hoist option; the most common combi; a VIP transport; a medevac for six litters and seven seats; a search-and-rescue version; a 17-seat paratrooper drop version; an 18-passenger utility cabin and an aerial firefighting version is considered. A crew of two can switch between passenger and cargo configurations in 7 min. Its inward opening rear doors allow for cargo drops and utility operations as well as the passenger boarding.


title: PZL M28 Skytruck

text: 176 An-28s and M28s in all variants were built in Poland by 2006. Most numerous users are former Soviet civil aviation and the Polish Air Force and Navy (about 25 as of 2006), smaller numbers are used by the Polish civil aviation and in the United States, Nepal, Colombia, Venezuela, Vietnam and Indonesia.


title: PZL M28 Skytruck

text: On 4 November 2005, a Vietnamese Airforce M28 crashed in Gia Lam district, Hanoi. All three crewmembers were killed.


title: PZL M28 Skytruck

text: On 12 February 2009, The weekly periodical "Air Force Times" reported that the Air Force Special Operations Command (AFSOC) would receive 10 PZL M28 Skytrucks in June 2009. These aircraft carry the U.S. Air Force model design series (MDS) designation of C-145A Skytruck. In 2011 one aircraft crash landed in Afghanistan and was damaged beyond repair. 11 of AFSOC's C-145As were retired in 2015. In 2016, three were sent to Kenya, two to Costa Rica, two to Nepal, and two to Estonia.


title: An Extremely Goofy Movie

text: An Extremely Goofy Movie is a 2000 animated comedy film distributed by Walt Disney Home Video, produced by Walt Disney Television Animation, and directed by Douglas McCarthy. It is a standalone sequel to the 1995 film "A Goofy Movie" and the finale to the television series "Goof Troop", in which Max Goof goes to college and believes he will not have to deal with his father, Goofy, until he loses his job and enrolls there to receive the degree he never received years ago in order to get another one. Meanwhile, Max and his friends compete in the X Games, unaware of the reason why the school's top fraternity has a dynasty in the competition.


title: An Extremely Goofy Movie

text: The film was released on Blu-ray as a "Disney Movie Club" exclusive alongside "A Goofy Movie" on April 23, 2019 and was one of the films to be included on the streaming service Disney+ upon its launch.


title: An Extremely Goofy Movie

text: After Max Goof goes to college with his friends P.J. and Bobby Zimuruski, his father, Goofy, begins to disastrously falter during his job at the local toy factory, resulting in his dismissal following an accident he causes. At the unemployment office, Goofy is told that he needs a college degree to get another job since he dropped out after his junior year in the 1970s. Meanwhile, Max and his friends meet Bradley Uppercrust III, the leader of the Gamma Mu Mu fraternity and a veteran skateboarder. Bradley is impressed by Max's own skateboarding talent and invites him to join the Gammas and take part in the college's X Games. Max declines the offer due to the condition that he cannot bring his friends along. Following a skirmish, the two parties place a bet in which the loser becomes the other group's towel boy. To Max's horror, Goofy begins attending the same college and interrupts the group's down-time with chores. Max decides to distract his father by introducing him to the college librarian, Sylvia Marpole, with whom he has much in common. Goofy accidentally impresses Bradley with his clumsy attempt at skateboarding and is invited to join the Gammas, which he accepts upon Max's encouragement.


title: An Extremely Goofy Movie

text: During the first qualifiers for the X Games, Bradley discreetly blinds Max with a pocket mirror during his performance and installs a rocket booster on Goofy's skateboard. Goofy beats Max and his team barely makes the semi-finals. Eventually, Max lashes out at Goofy, telling him to stay out of his life and storms off in anger. A depressed Goofy fails his first midterm exam and misses a date with Sylvia. Returning home, Goofy is inadvertently inspired by his neighbor, Pete to regain his focus. Goofy goes back to college and reconciles with Sylvia, who helps him ace the rest of his exams. As Goofy decides to quit the Gammas, he overhears the group plotting to cheat for the semi-finals, but Max, still angry with his father over beating him in the qualifiers, refuses to listen.


title: An Extremely Goofy Movie

text: At the semi-finals, all teams but Max's and the Gammas' are eliminated. Just before the final triathlon, Bradley eliminates P.J. from the games, leaving Max's team short one player and spurring Max to recruit and apologize to Goofy for shunning him via the jumbotron. Throughout the race, Bradley and his team attempt to hinder Max's team, but fail. Although Goofy manages to temporarily knock out Bradley with a horseshoe in the final section of the race, his final trick results in his second-in-command, Tank, and Max getting trapped underneath the burning wreckage of a logo. As Bradley passes them by, Max and Goofy rescue Tank, who assists Max in winning the race. Afterwards, Bradley concedes his defeat as good sportsmanship and tells Max he will go through with their bet. However, Max calls off the bet, allowing a vengeful Tank to advance on Bradley for betraying him and fling him into the X Games blimp overhead. During graduation day, Max gives Goofy his grand prize trophy engraved with an affirmation of their bond as an apology gift for his outburst towards him just before Goofy drives off with Sylvia, restoring their relationship.


title: An Extremely Goofy Movie

text: Additional voices include Paddi Edwards as a receptionist and Kath Soucie, Jenna von Oÿ (who voiced Stacey in the first film) and Cree Summer as college students.


title: An Extremely Goofy Movie

text: Unlike its predecessor, this film has no musical sequences where the characters sing on-screen. However, a number of songs are used in the soundtrack and have been included in the official album release which is titled Disney's An Extremely Goofy Movie Dance Party!, released in February 2000 alongside the film itself.


title: An Extremely Goofy Movie

text: A number of McDonald's Happy Meal toys based on the film were produced and released for the month of February 2000.


title: An Extremely Goofy Movie

text: The film was released on February 29, 2000 to positive reviews from critics, who called it "likable," "fun," "funny," "ambitious and surprisingly good," and Goofy's character in the film "limber and funny as ever." Rotten Tomatoes gives the film a 63% approval rating with an average rating of 5.4/10, based on eight reviews, making it one of the few Disney sequels to be rated higher than its predecessor. The "Houston Chronicle"s Bruce Westbrook praised its "fluid" animation, "handsomely detailed" backgrounds, and the "charming" sequences with the Beret Girl. Randy Myers of the "Contra Costa Times" complimented its positive take on the father-and-son relationship trope as "refreshing" compared to other films painting it in a negative manner. Many touches were positively noted, such as the elements of 1970s' culture, the soundtrack (particularly its 1970s tracks and the newly-recorded covers), movie parodies (such as "The Gooffather", "The Goofinator" and "Pup Fiction Too"), and a line making fun of characters "always wearing gloves" in the Disney universe. Subplots such the skateboard competition and the "sweet" relationship between Goofy and Sylvia were highlighted as well.


title: An Extremely Goofy Movie

text: "An Extremely Goofy Movie"s less favorable reviews categorized the film as a weaker version of Rodney Dangerfield's "Back to School". and the "Los Angeles Times" Susan King who wrote that despite "some funny lines and scenes," it had too little emotionally due to a lack of character development for Goofy. Michael Scheinfeld of "Common Sense Media" praised the film's morals of "the importance of education, of not cheating, and staying focused on one's goals," but disliked its attempts to be hip and the "less-than-exemplary character traits" that paint an inaccurate picture of college students. Barbara Bova of "Naples Daily News" also dismissed the film for the immature behavior of the college students as well as the dysfunctional relationship between Max and Goofy and a "depressing," humorless plot where "the adults are no smarter than the kids" and "Goofy is the essential innocent who is stupid with a capital S." Scheinfeld also called the animation "less sophisticated than Disney's theatrical films, but features some amusing and stylish touches, such as a psychedelic dream sequence in the style of Yellow Submarine, and a school dance that Goofy turns into a disco inferno."


title: An Extremely Goofy Movie

text: Petrana Radulovic of "Polygon", in 2019, ranked "An Extremely Goofy Movie" the sixth best Disney sequel, labeling it as "all delightfully bonkers" and claiming its best aspects to be the Beret Girl and Bobby's poke on Disney characters wearing gloves; she also, however, criticized some of its content as "stuck in a gnarly late-’90s vortex."


title: An Extremely Goofy Movie

text: "An Extremely Goofy Movie" won the award for "Best Animated Home Video Production" and Bill Farmer was nominated for "Best Voice Acting by a Male Performer" at the 28th Annie Awards in 2000.


title: An Extremely Goofy Movie

text: Following the September 11 attacks in 2001, the scene in which Goofy rescues Max and Tank from under the burning X Games logo structure was removed from television broadcasts of the film; the scene remains in all other versions of the movie, but the broadcast version skips this scene entirely to show them skating out of the wreckage.


title: The Block (season 17)

text: The seventeenth season of Australian reality television series "The Block", titled The Block: Fans v Faves, premiered on 8 August 2021 on the Nine Network. Hosts Scott Cam and Shelley Craft, site foremen Keith Schleiger and Dan Reilly, and judges Neale Whitaker, Shaynna Blaze and Darren Palmer, all returned from the previous season.


title: The Block (season 17)

text: Applications for the seventeenth season of the series opened in August 2020 until 27 September 2020, looking for couples aged between 18 and 65 years old being sought by casting agents. Filming is expected to be a 10–12 week shoot period from late February 2021 In September 2020, the seventeenth season of The Block was officially confirmed at Nine's 2021 upfronts. In October 2020, it was reported that 5 properties on Bronte Court in Hampton, Victoria, were in the process of being purchased by Nine. In December 2020, it was confirmed that Bronte Court will be the next location for renovation, Nine Network acquired five houses in the area for $11.5 million combined.


title: The Block (season 17)

text: In July 2021, it was officially confirmed the season will be Fans vs Faves, although this is the second time the title "Fans vs Faves" will be used, this is actually the third season to have returning contestants versus new contestants (seasons 8 & 10 respectively). Season 8 was the first time the series was titled "Fans vs Faves".


title: The Block (season 17)

text: Mitch & Mark won the series with their house selling for over $4.04m. All houses sold on auction day with all teams profiting well over $295k.


title: The Block (season 17)

text: This season introduces 3 new couples (dubbed "Fans") and 2 returning couples (dubbed "Favourites"/"Faves"). The couples selected were as follows: Of the new "Fans" Josh & Luke Packham have previously participated on Love Island Australia.


title: The Block (season 17)

text: Two of the teams — House 3's Tanya and Vito and House 4's Josh and Luke — had a photo of the production schedule, which meant they knew exactly when certain rooms would be called, and the dates of challenge days. Josh and Luke said that they received the photo but wouldn't say from where, and after denials, Tanya and Vito revealed that Tanya had sent the photo to Luke. Tanya said that she received the photo from a former tradesperson on The Block. Having the production schedule was a massive advantage. When the photo was brought to Scott Cam's attention, he wiped the schedule clean and said they would pick rooms at random to complete for the rest of the season. Scott Cam punished Tanya and Vito and Josh and Luke by deducting two points per team, effectively ruling them out from winning Basement Week. There was considerable anger among fans, who thought that this punishment should have been harsher.


title: The Block (season 17)

text: In the final episode of the show, during the final interviews, Tanya was questioned about the cheating scandal once again. She again said that she hadn't taken the photograph and showed a text feed between her and a supposed ex-tradie from The Block. Her partner Vito was supporting and also denied the suspicions.


title: The Block (season 17)

text: However, House 4's Josh & Luke decided to 'get [the truth] off their chests' and did a full tell-all interview. They explained how during the filming of the promotion, they were using the toilets in the production office (which was another house being rented out by Nine Network). When Luke went to use the bathroom he noticed an open door, which was Scotty's office. The entire production schedule was written on a whiteboard at the back of the room. Luke was only able to memorise the first 3–4 weeks on the schedule but never considered taking a photo. Later in the day, Luke (and possibly Josh) was approached by Tanya, who asked if they could be on guard for her while she took a photo. They reluctantly agreed.


title: The Block (season 17)

text: The twins explained that the reason they had kept quiet was because Tanya wasn't willing to say her part in it. During Half Basement Week (the week the scandal was exposed), Josh & Luke came out but Tanya initially did not wish to. Josh and Luke initially kept her identity anonymous because of this reason. They later managed to convince Tanya to come out with her part by implementing the fake ex-tradie story which most people believed.


title: The Block (season 17)

text: Josh & Luke also explained that they didn't want to go against Tanya's will because they wouldn't have been able to get several things signed off by them, including a moved driveway and ability to use their property for access so that they could dig their pool.


title: The Block (season 17)

text: While the contestants were waiting for their reserves the day before Auctions, they were informed of the twins' story. Ronnie & Georgia and Mitch & Mark had suspected that this had been the case but had never known for sure. When Josh & Luke arrived, Luke apologised for his part in the scandal and this was generally accepted by the other contestants.


title: The Block (season 17)

text: While driving to meet the other contestants, Tanya was annoyed at the twins for not informing her that they were going to tell the truth. Her husband Vito responded by saying that he was still on her side and would support her. Tanya got very upset when confronted by other contestants about it, and using Mitch's words, "... it's too late, now she's caught."


title: The Block (season 17)

text: Because of the Schedule Scandal, the Block was thrown into disarray because all of the pre booked and planned work had to be restructured. One of these problems was Kinsman, who were booked in to do the laundries during the now Living & Dining Week. The contestants were told that they had to prep their laundries for install by Kinsman as well as doing their living/dining rooms. If they managed to complete this during the week, Kinsman would install for free as they were a sponsor. However, if a team failed to complete it they would have to pay for install during another week. All teams managed to complete it in time except for Tanya & Vito. As per the rules Tanya & Vito were required to pay for their late install, but instead they manipulated Kinsman who agreed to do it for free. However, the other contestants stepped in and caught Tanya & Vito out and made sure they paid for their laundries.


title: The Block (season 17)

text: Fans were angered by the whole scandal, particularly Tanya's failure to reveal the truth until the final episode. Most fans felt that the punishment should have been much higher, and like suggested by Ronnie, have all points and extra money taken away from the responsible teams. Some fans even felt that the auction results of the two teams should have been changed, mainly Tanya and Vito's.


title: The Block (season 17)

text: The producers and casting agents of the show were also brought under fire, fans questioning the choices of Josh & Luke and Tanya & Vito as contestants. Many fans felt that the casting agents should have spotted the bad qualities in the contestants and not cast them. They also questioned the casting of Josh & Luke, as former Love Island contestants many felt that they were cast just to cause drama and as advertising for the show.


title: The Block (season 17)

text: Fans have speculated many theories about the scandal and why Tanya would feel the need to take the photo in the first place. One of these theories is that Tanya may have felt disadvantaged as she was up against a bunch of All Stars.


title: Sitagliptin

text: Sitagliptin, sold under the brand name Januvia among others, is an anti-diabetic medication used to treat type 2 diabetes. In the United Kingdom it is listed as less preferred than metformin or a sulfonylurea. It is taken by mouth. It is also available in the fixed-dose combination medication sitagliptin/metformin (Janumet, Janumet XR).


title: Sitagliptin

text: Common side effects include headaches, swelling of the legs, and upper respiratory tract infections. Serious side effects may include angioedema, low blood sugar, kidney problems, pancreatitis, and joint pain. Whether use in pregnancy or breastfeeding is safe is unclear. It is in the dipeptidyl peptidase-4 (DPP-4) inhibitor class and works by increasing the production of insulin and decreasing the production of glucagon by the pancreas.


title: Sitagliptin

text: Sitagliptin was developed by Merck & Co. and approved for medical use in the United States in 2006. In 2020, it was the 74th most commonly prescribed medication in the United States, with more than 9million prescriptions.


title: Sitagliptin

text: Sitagliptin is used to treat type 2 diabetes. It is generally less preferred than metformin or sulfonylureas. It is taken by mouth. It is also available as the fixed-dose combinations of sitagliptin/metformin (Janumet, Janumet XR) and sitagliptin/simvastatin (Juvisync).


title: Sitagliptin

text: Sitagliptin should not be used to treat type 1 diabetes. In December 2020, the U.S. Food and Drug Administration (FDA) approved labeling changes stating that Januvia (sitagliptin), Janumet (sitagliptin and metformin hydrochloride), and Janumet XR (sitagliptin and metformin hydrochloride extended-release) are not proven to improve glycemic (blood sugar) control in children aged 10 to 17 with type 2 diabetes. The drugs are approved to improve blood sugar control in adults aged 18 and older with type 2 diabetes.


title: Sitagliptin

text: Adverse effects from sitagliptin are similar to placebo, except for rare nausea, common cold-like symptoms, and photosensitivity. It does not increase the risk of diarrhea. No significant difference exists in the occurrence of hypoglycemia between placebo and sitagliptin. In those taking sulphonylureas, the risk of low blood sugar is increased.


title: Sitagliptin

text: The existence of rare case reports of kidney failure and hypersensitivity reactions is noted in the United States prescribing information, but a causative role for sitagliptin has not been established.


title: Sitagliptin

text: Several postmarketing reports of pancreatitis (some fatal) have been made in people treated with sitagliptin and other DPP-4 inhibitors, and the U.S. package insert carries a warning to this effect, although the causal link between sitagliptin and pancreatitis has not yet been fully substantiated. One study with lab rats published in 2009 concluded that some of the possible risks of pancreatitis or pancreatic cancer may be reduced when it is used with metformin. However, while DPP-4 inhibitors showed an increase in such risk factors, as of 2009, no increase in pancreatic cancer has been reported in individuals taking DPP-4 inhibitors.


title: Sitagliptin

text: In 2015, the U.S. Food and Drug Administration (FDA) added a new warning and precaution about the risk of "severe and disabling" joint pain to the labels of all DPP-4 inhibitor medicines.


title: Sitagliptin

text: Sitagliptin works to competitively inhibit the enzyme dipeptidyl peptidase 4 (DPP-4). This enzyme breaks down the incretins GLP-1 and GIP, gastrointestinal hormones released in response to a meal. By preventing breakdown of GLP-1 and GIP, they are able to increase the secretion of insulin and suppress the release of glucagon by the alpha cells of the pancreas. This drives blood glucose levels towards normal. As the blood glucose level approaches normal, the amounts of insulin released and glucagon suppressed diminishes, thus tending to prevent an "overshoot" and subsequent low blood sugar (hypoglycemia), which is seen with some other oral hypoglycemic agents.


title: Sitagliptin

text: Sitagliptin has been shown to lower HbA1c level by about 0.7% points versus placebo. It is slightly less effective than metformin when used as a monotherapy. It does not cause weight gain and has less hypoglycemia compared to sulfonylureas. Sitagliptin is recommended as a second-line drug (in combination with other drugs) after the combination of diet/exercise and metformin fails.


title: Sitagliptin

text: Sitagliptin was approved by the U.S. Food and Drug Administration (FDA) in October 2006, and is marketed in the US as Januvia by Merck & Co. On April 2, 2007, the FDA approved an oral combination of sitagliptin/metformin sold in the US under the brand name Janumet. On October 7, 2011, the FDA approved an oral combination of sitagliptin/simvastatin marketed in the US as Juvisync.


title: M-Pesa

text: M-Pesa (M for mobile, pesa is Swahili for money) is a mobile phone-based money transfer service, payments and micro-financing service, launched in 2007 by Vodafone and Safaricom, the largest mobile network operator in Kenya. It has since expanded to Tanzania, Mozambique, DRC, Lesotho, Ghana, Egypt, Afghanistan, and South Africa. Meanwhile, services in India, Romania, and Albania have been terminated amid low market uptake. M-Pesa allows users to deposit, withdraw, transfer money, pay for goods and services (Lipa na M-Pesa), access credit and savings, all with a mobile device.


title: M-Pesa

text: The service allows users to deposit money into an account stored on their cell phones, to send balances using PIN-secured SMS text messages to other users, including sellers of goods and services, and to redeem deposits for regular money. Users are charged a small fee for sending and withdrawing money using the service.


title: M-Pesa

text: M-Pesa is a branchless banking service; M-Pesa customers can deposit and withdraw money from a network of agents that includes airtime resellers and retail outlets acting as banking agents.


title: M-Pesa

text: M-Pesa spread quickly, and by 2010 had become the most successful mobile-phone-based financial service in the developing world. By 2012, a stock of about 17 million M-Pesa accounts had been registered in Kenya. By June 2016, a total of 7 million M-Pesa accounts had been opened in Tanzania by Vodacom. The service has been lauded for giving millions of people access to the formal financial system and for reducing crime in otherwise largely cash-based societies. However, the near-monopolistic providers of the M-Pesa service are sometimes criticized for the high cost that the service imposes on its often poor users.


title: M-Pesa

text: Safaricom and Vodafone launched M-PESA, a mobile-based payment service targeting the un-banked, pre-pay mobile subscribers in Kenya on a pilot basis in October 2005. It was started as a public/private sector initiative after Vodafone was successful in winning funds from the Financial Deepening Challenge Fund competition established by the UK government's Department for International Development to encourage private sector companies to engage in innovative projects so as to deepen the provision of financial services in emerging economies.


title: M-Pesa

text: The initial obstacle in the pilot was gaining the agent's trust and encouraging them to process cash withdrawals and agent training. However, once Vodafone introduced the ability to buy airtime using M-PESA, the transaction volume increased rapidly. A 5% discount was offered on any airtime purchased through M-PESA and this served as an effective incentive. By 1 March 2006, KSh.50.7 million/= had been transferred through the system. The successful operation of the pilot was a key component in Vodafone and Safaricom's decision to take the product full scale. The learning from the pilot helped to confirm the market need for the service and although it mainly revolved around facilitating loan repayments and disbursements for Faulu customers, it also tested features such as airtime purchase and national remittance. The full commercial launch was initiated in March 2007.


title: M-Pesa

text: A snapshot of the market then depicted that only a small percentage of people in Kenya used traditional banking services. There were low levels of bank income, high bank fees incurred and charged; most of the services were out of geographical reach to the rural Kenyan. Notably, a high level of mobile penetration was evident throughout the country making the adoption of mobile payments a viable alternative to the traditional banking channels. According to a survey done by CBS in 2005, Kenya then had over 5,970,600 people employed in the informal sector. This informal sector constituted 98%.


title: M-Pesa

text: In 2002, researchers at Gamos and the Commonwealth Telecommunications Organisation, funded by the UK's Department for International Development (DFID), documented that in Uganda, Botswana and Ghana, people were spontaneously using airtime as a proxy for money transfer. Kenyans were transferring airtime to their relatives or friends who were then using it or reselling it. Gamos researchers approached MCel in Mozambique, and in 2004 MCel introduced the first authorised airtime credit swapping – a precursor step towards M-Pesa. The idea was discussed by the Commission for Africa and DFID introduced the researchers to Vodafone who had been discussing supporting microfinance and back office banking with mobile phones. S. Batchelor (Gamos) and N. Hughes (Vodafone CSR) discussed how a system of money transfer could be created in Kenya. DFID amended the terms of reference for its grant to Vodafone, and piloting began in 2005. Safaricom launched a new mobile phone-based payment and money transfer service, known as M-Pesa.


title: M-Pesa

text: The initial work of developing the product was given to a product and technology development company known as Sagentia. Development and second line support responsibilities were transferred to IBM in September 2009, where most of the original Sagentia team transferred to. Following a three-year migration project to a new technology stack, as of 26 February 2017, IBM's responsibilities have been transferred to Huawei in all markets.


title: M-Pesa

text: The initial concept of M-Pesa was to create a service which would allow microfinance borrowers to conveniently receive and repay loans using the network of Safaricom airtime resellers. This would enable microfinance institutions (MFIs) to offer more competitive loan rates to their users, as costs are lower than when dealing in cash. The users of the service would gain through being able to track their finances more easily. When the service was piloted, customers adopted the service for a variety of alternative uses and complications arose with Faulu, the partnering MFI. In discussion with other parties, M-Pesa was re-focused and launched with a different value proposition: sending remittances home across the country and making payments.


title: M-Pesa

text: M-Pesa is operated by Safaricom and Vodacom, mobile network operators (MNO) not classed as deposit-taking institutions, such as a bank. M-Pesa customers can deposit and withdraw currency from a network of agents that includes airtime resellers and retail outlets acting as banking agents. The service enables its users to:


title: M-Pesa

text: Partnerships with Kenyan banks offer expanded banking services like interest-bearing accounts, loans, and insurance.


title: M-Pesa

text: The user interface technology of M-Pesa differs between Safaricom of Kenya and Vodacom of Tanzania, although the underlying platform is the same. While Safaricom uses SIM toolkit (STK) to provide handset menus for accessing the service, Vodacom relies mostly on USSD to provide users with menus, but also supports STK.


title: M-Pesa

text: Transaction charges depend on the amount of money being transferred and whether the payee is a registered user of the service. The actual cost is a fixed amount for a given range of transaction sizes; for example Safaricom charges up to KSh.66/= () for a transaction to an unregistered user for transactions between KSh.101/= and KSh.500/= (US$–US$). For registered users the charge is KSh.27/= (US$) or 5.4% to 27% for the same amount. At the highest transfer bracket of KSh.50,001–70,000/= the fee for a transfer to a registered user is KSh.110/= (US$) or 0.16-0.22%. The maximum amount that can be transferred to a non-registered user of the system is KSh.35,000/= (US$), with a fee of KSh.275/= (US$) or 0.8%. Cash withdrawal fees are also charged. With a charge of KSh.10/= (US$), for a withdrawal of KSh.50–100/= or 10% to 20%, and up to KSh.330/= (US$) for a withdrawal of KSh.50,001–70,000/= or 0.47% to 0.66% .


title: M-Pesa

text: In an article published in 2015, Anja Bengelstorff cites the Central Bank of Kenya when she states that CHF 1 billion is moved in fiscal year 2014, with a profit of CHF 268 million, that is close to 27% of the moved money. In 2016, M-Pesa moved KSh.15 billion/= (US$) per day, with a revenue of KSh.41 billion/=. In 2017 KSh.6,869 billion/= were moved according to a figure in Safaricoms own annual report, with a revenue of 55 billion KShs. This would put Safaricom's profit ratio at around <1% of total money transferred.


title: M-Pesa

text: With the support of Financial Sector Deepening Kenya and the Bill & Melinda Gates Foundation, Tavneet Suri from the Massachusetts Institute of Technology and William Jack from Georgetown University have produced a series of papers extolling the benefits of M-Pesa. In particular, their 2016 article published in "Science" has been influential in the international development community. The much cited result of the paper was that "access to M-PESA increased per capita consumption levels and lifted 194,000 households, or 2% of Kenyan households, out of poverty." Global development institutions focusing on the development potential of financial technology frequently cite M-Pesa as a major success story in this respect, citing the poverty-reduction claim and including a reference to Suri and Jack's 2016 signature article. In a report on "Financing for Development", the United Nations write: "The digitalization of finance offers new possibilities for greater financial inclusion and alignment with the 2030 Agenda for Sustainable Development and implementation of the Social Development Goals. In Kenya, the expansion of mobile money lifted two per cent of households in the country above the poverty line."