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65b13b417f0bffd8a963fd64167df88862d4a369 | near the equator the sun is almost overhead | near the equator the sun is almost overhead all year, so the orientation of slopes is unimportant. further away, the amount of sunlight varies considerably.in the alps the south-facing slopes are preferred for settlements and farming, while the north-facing slopes are used for forestry and ski resorts. in mountain regi... | wikipedia |
5c704342278addf7a3fc2a00de3fe70dbf58098d | the people of the andes maintain what john | the people of the andes maintain what john victor murra calls "vertical control", in which groups of people use kinship and other arrangements to access the resources of a range of ecological zones at different elevations, and thus to access a variety of crops and animals.this gives more security than dependence on a s... | wikipedia |
f14a9ae993a52a3e8da3c78d250577776dd94994 | maize, millet, potatoes, tomatoes and wheat have their | maize, millet, potatoes, tomatoes and wheat have their origins in mountain regions, as do tea, coffee and quinoa. a comparison of crops grown in southern switzerland, the peruvian andes and the central nepal himalaya shows strong similarities. at low elevations crops in all three regions include fruits, and at mid elev... | wikipedia |
7fb0dbcac16d07a210767cf756fec44685e8c285 | later human settlers in the mountains practiced a | later human settlers in the mountains practiced a combination of hunting and gathering, raising crops and tending livestock, with most families involved in all these activities. as specialist workers have emerged, the members of each household perform fewer activities, but there are more occupations within the communit... | wikipedia |
728e3ea4c5ae296ffa3941454ad0055c24ea6817 | paleolithic hunters and gatherers followed the mountain fauna | paleolithic hunters and gatherers followed the mountain fauna as they moved from summer to winter pastures, fished, gathered edible plants and used the abundant timber for fire and shelter.the dayaks of kalimantan still follow a traditional hunting and gathering lifestyle, although they are under growing pressure from ... | wikipedia |
35b9a7700c666805ee0de7e33d042055e967788c | 17% of the mountain population grows crops or | 17% of the mountain population grows crops or combines crop, livestock and tree farming.19% subsist from sparsely vegetated barren land, protected areas and closed forests. 44% of mountain land is used for grazing and is home to 64% of rural mountain people.at a global level, the average population density on grazing l... | wikipedia |
332900c057d1eee02d3792c241cd61f6d188333c | compared to non-mountain populations, the mountain people suffer | compared to non-mountain populations, the mountain people suffer more from malnutrition due to food shortage and deficiencies in micronutrients (vitamins and minerals), and suffer from respiratory diseases caused by the severe climate and smoke in their shelters during the cold periods.these problems are compounded by ... | wikipedia |
b22d88ef154e480c58acc6740f653d9295ca86d4 | the people of the tropical high mountains experience | the people of the tropical high mountains experience more exposure to solar irradiance than lowlanders, and must adapt to wider temperature extremes between day and night.seasonal weather imposes periods of low and high activity, and of scarce and plentiful food.unpredictable droughts, periods of intense cold, plant an... | wikipedia |
52639d41a47c98750a78a55e063c568dce2a1e6f | studies in peru of aerobic capacity, the body's | studies in peru of aerobic capacity, the body's ability to obtain oxygen, show that there is little difference between natives born at high elevations and lowlanders who move to high elevations when they were young children, although the lowlanders had more european ancestry than the high elevation natives. aerobic cap... | wikipedia |
3da8637b315b6bd55df310fe6334c29f304e39ff | many of the high-elevation people grow slowly and | many of the high-elevation people grow slowly and have small bodies.this may reduce their energy requirements without affecting their ability to handle hypoxia, cold and work demands. long term high-elevation residents have expanded lungs and hearts, higher levels of hemoglobin in their blood and shorter limbs. there i... | wikipedia |
78debc7a55bdd099f2fd767ff1370937fbef7067 | about 70% of the mountain population is rural | about 70% of the mountain population is rural and relies on farming, fishing and extraction from local forests. the permanent mountain population also includes itinerant mineral prospectors, miners, loggers, construction workers and others who move from place to place.better roads and vehicles may allow these people to... | wikipedia |
005287f2f536e61966201155d3ae180985112d19 | the food and agriculture organization estimated in their | the food and agriculture organization estimated in their 2003 report that around 720 million, or 12% of the world population, live in the mountains.of these, no more than 10% are in developed countries. about half of all mountain people are in asia, and there are large and rapidly growing populations in south and centr... | wikipedia |
85865d636ca7c46498a8f865cfa0f4cd34217db8 | while mountain areas are more isolated than lower | while mountain areas are more isolated than lower or flatter lands, when measured by the percentage of the population that lives more than 5 kilometres (3.1 mi) from a road the difference is not great as might be expected. thus in ethiopia 50% of mountain people and 40% of non-mountain people live more than 5 kilometre... | wikipedia |
7e89f11ce306a677c82e7011ef5050486fb31508 | the cultural groups that live in the mountains | the cultural groups that live in the mountains are often minorities within their countries, although they may be in the majority in their region. this is true of the tibetans, naxi, miao, yi and uyghurs in china, the kurds in the north of iraq and the east of turkey, the amhars in ethiopia and the quechua and aymara in... | wikipedia |
ca394f48e95c8ac647418aa653e57f32a81cd1e0 | the difficulty of movement between valleys in the | the difficulty of movement between valleys in the past has isolated mountain communities and contributed to high levels of cultural diversity. nearby communities may have different languages and dialects, traditions, costumes, cuisine and economic systems. this is seen in the andes and the western mountains of canada. ... | wikipedia |
ac7a646d72f9e25a13b6a933d4e1886a29049b48 | people have lived in mountain regions for thousands | people have lived in mountain regions for thousands of years.some may have sought refuge from persecution or from changing climate, while others may have migrated in search of food.the new arrivals settled and developed prosperous farming communities. streams, rivers and lakes that provide water for agriculture and dom... | wikipedia |
30ae061ebab039cd758e46e615809177ac5c67e7 | the impact of climate change on mountain environments | the impact of climate change on mountain environments is not well understood, but they seem to be more sensitive than the lowlands.the higher-level ecosystems will be forced up the mountains as temperatures rise, shrinking in size and at some point disappearing. threats include environmental stress during adaptation to... | wikipedia |
6e75d6db4075bdd04155271c60489a6f70dfaff9 | almost 28% of the world's forests grow on | almost 28% of the world's forests grow on mountains. forests are important in regulating water flows and providing fuel and construction material. before humans arrived, most mountains in tropical and temperate climates would have been forested up to the tree line.deforestation is not new, and began 3,000 years ago in ... | wikipedia |
32a05c60db190a2932d45fcfb0f8d95993c61aeb | people have both adapted to mountain conditions and | people have both adapted to mountain conditions and modified those conditions. for example, farmers in many areas use terracing to retain soil and water. contour ploughing also helps stabilize the fragile soil. often human activity has degraded the mountain environments. humans have reduced biodiversity in many of the ... | wikipedia |
344f083634900372025d252b7a950d37b3fa2f2f | temperatures tend to always be high on the | temperatures tend to always be high on the lower slopes near the equator, and there is often heavy rainfall year-round. higher up and outside the tropics, temperatures can soar in the daytime and plummet at night. usually there are strong winds, frequent freezing and thawing at the higher levels, snow, sleet and heavy ... | wikipedia |
d6e6ed314bc56054cf0238447fe15878712aa987 | mountain environments vary depending on their latitude and | mountain environments vary depending on their latitude and their proximity to the edge of a landmass.the windward side will have greater rainfall than the leeward. the mountain environment can be harsh, particularly in the alpine regions above the tree line at higher elevations and in the drier climates outside the tro... | wikipedia |
c78636b8ee632b05cfbcf6fa2ddacc768a7ed4a7 | under the world conservation monitoring centre (wcmc) classification, | under the world conservation monitoring centre (wcmc) classification, mountain regions include both hills and mountains. see " classes of mountain region " for the formal definition. 22% of the world's land, or 29,000,000 square kilometres (11,000,000 sq mi) is classified as a mountain region, of which about half is be... | wikipedia |
2559968fa3fd1e82e978a678268747fae746e682 | in parts of the developing world the mountain | in parts of the developing world the mountain communities depend on remittances from young men who have gone to work in the lowlands or overseas.although 70% of mountain people live in rural areas, the rest live in cities, including large cities such as mexico city, with a population of around 21 million.the cities att... | wikipedia |
4a36b466ccc0a2f5363852d4fb4e0fca72299aee | people have used or lived in the mountains | people have used or lived in the mountains for thousands of years, first as hunter-gatherers and later as farmers and pastoralists.the isolated communities are often culturally and linguistically diverse.today about 720 million people, or 12% of the world's population, live in mountain regions, many of them economicall... | wikipedia |
92e289d434157a17d5c2563f1c6eeb4eca39e776 | hill people, also referred to as mountain people, | hill people, also referred to as mountain people, is a general term for people who live in the hills and mountains. this includes all rugged land above 300 metres (980 ft) and all land (including plateaus) above 2,500 metres (8,200 ft) elevation.the climate is generally harsh, with steep temperature drops between day a... | wikipedia |
b95ad59e69520f0a2c4fb88e78dae7980e0ad7c7 | norman victor alexander ullman is a canadian former | norman victor alexander ullman is a canadian former ice hockey forward. he previously played for the detroit red wings and toronto maple leafs of the national hockey league (nhl) from 1955 to 1975, and with the edmonton oilers of the world hockey association from 1975 to 1977. he was inducted into the hockey hall of fa... | wikipedia |
be4493b2f8326a89b5a4fc04fff7d1d280e3427c | he was part of a six-player blockbuster transaction | he was part of a six-player blockbuster transaction in which he was traded along with paul henderson and floyd smith from the red wings to the toronto maple leafs for frank mahovlich, pete stemkowski and garry unger on march 4, 1968. the maple leafs and red wings were in fifth and sixth place respectively at the bottom... | wikipedia |
ae29d41e94c894906e02efede7105a90fd1b3ba9 | ullman led detroit in goals in 1961, 1965, | ullman led detroit in goals in 1961, 1965, and 1966 and led the league in 1964–65 with 42 goals. in that same season, he missed the overall scoring title by 4 points, second to stan mikita, and was voted a first team all-star. | wikipedia |
d765c072eb6c17369ed94080f1a2727c5fa891b5 | he was renowned as an excellent stick handler, | he was renowned as an excellent stick handler, as well as one of the paramount forecheckers in hockey history - and for his stamina and consistency which was important in centering a line with gordie howe and ted lindsay in only his second season with detroit. | wikipedia |
84796cc4cb19b233367d9c9ef00c34c724e5087d | norm ullman began his career with the edmonton | norm ullman began his career with the edmonton oil kings of the wcjhl, before moving to the edmonton flyers of the whl. he turned pro with the detroit red wings of the national hockey league in the 1955–56 nhl season. | wikipedia |
5e1502502b35514b070a1c7ebae4e73112f0e89d | norman victor alexander ullman (born december 26, 1935) | norman victor alexander ullman (born december 26, 1935) is a canadian former ice hockey forward. he previously played for the detroit red wings and toronto maple leafs of the national hockey league (nhl) from 1955 to 1975, and with the edmonton oilers of the world hockey association from 1975 to 1977. he was inducted i... | wikipedia |
ffdc5c14a2c694ec0ecac92b4ea1437a27311017 | marlène kasaj yav (born 25 january 2003) is | marlène kasaj yav (born 25 january 2003) is a dr congolese footballer who plays as an attacking midfielder for turkish women's football super league club beylerbeyi and the dr congo women's national team. | wikipedia |
3a09e95e42b43740bb7b5f5b495dd24794528a0d | wilfried benjamin balima (born 20 march 1985) commonly | wilfried benjamin balima (born 20 march 1985) commonly known as benjamin balima, is a retired burkinabé international footballer who spent the majority of career with moldovan national division club sheriff tiraspol as a right defender. | wikipedia |
cfc941af7c1c7e2100f5f512358e6bc7358031c0 | juan fernando arango sáenz is a venezuelan former | juan fernando arango sáenz is a venezuelan former professional footballer who played as an attacking midfielder. arango was considered by some in the sport as the greatest venezuelan footballer of all time. he spent the better part of his professional career in la liga with mallorca, appearing in 196 official games, an... | wikipedia |
a091f761d2680d72f26a05924882423157975508 | a left-footed playmaker, who was known for his | a left-footed playmaker, who was known for his technical skills, leadership and ability both to score and create goals, courtesy of his striking ability, crossing and passing, arango was a classic number ten, who was capable of playing both as an attacking midfielder and as a winger. nicknamed arangol, he was also a de... | wikipedia |
46085ae9e6f0a82cd6252ede6a9f2c66bd9a3c28 | in his 116th international appearance, arango levelled the | in his 116th international appearance, arango levelled the record for the most goals scored for venezuela with 22 goals, scoring in the 56th minute against bolivia in a 1–1 draw for the 2014 fifa world cup qualifiers on 7 june 2013. | wikipedia |
b8237bff03a5d79f41ead4e628d3bf6ff7b0e86c | also in that year, arango was chosen national | also in that year, arango was chosen national team captain by newly appointed coach césar farías. in the 2011 copa américa in argentina, he helped the vinotinto to a best-ever fourth-place finish in the continental competition, scoring in the third-place match, a 1–4 loss against peru for what was his 100th cap. | wikipedia |
b5132bd4a08c82c3000968fe02e9c234a3bf9a95 | at the 2004 copa américa, arango appeared in | at the 2004 copa américa, arango appeared in all three group stage matches for venezuela. in the 2007 edition, held in his country, he helped the national team finish first in the group stage, and scored in the quarterfinals against uruguay, but in a 4–1 defeat. | wikipedia |
0ddd52226d8014048c794e05376aab776f394452 | arango returned to mexico at the age of | arango returned to mexico at the age of 34, signing with club tijuana on 22 may 2014. in april of the following year, he was handed a two-match ban by the mexican football federation after footage showed him biting monterrey player jesús zavala in an action that eluded the referee. | wikipedia |
fd9115ffcf1bd4e60a0181458d3b6771bf12fe11 | arango scored his first goal of the 2013–14 | arango scored his first goal of the 2013–14 campaign on 24 august 2013, but in a 2–4 away defeat to bayer 04 leverkusen. he also found the net in his team's next league fixture, opening the scoring in a 4–1 home success over sv werder bremen. | wikipedia |
900605745ceff44c5cde1537e82bdfb4171447c6 | on 10 december 2012, gladbach manager lucien favre | on 10 december 2012, gladbach manager lucien favre hailed arango as one of the best left-footed players in the world, after the venezuelan scored a 48-yard stunner in a 2–0 defeat of 1. fsv mainz 05 the previous day. in the following year, he was ranked as the most popular footballer in the world by the international f... | wikipedia |
8e9cfc1c1d1ee6ac7c7f5c68fec1221c7dfffa75 | on 26 june 2009, as his contract was | on 26 june 2009, as his contract was due to expire at the end of 2009–10, arango was sold to borussia mönchengladbach for € 3.6 million, penning a three-year contract. in his third season in the bundesliga he netted six goals in 34 games and also provided 12 assists, as his team finished fourth and qualified for the ue... | wikipedia |
e583f3985378bf034d1c07a52a0c232114e8b1d6 | in 2006, efe chose arango as the third | in 2006, efe chose arango as the third best latin american player in the spanish league, with the first place taken by pablo aimar. the following year, he also obtained a spanish passport, in march. on 9 march 2008, he scored his first hat-trick for mallorca, in a 7–1 home thrashing of recreativo de huelva, with teamma... | wikipedia |
e676486aad8a07daac05e8b45e9223c2d781bc23 | on 20 march 2005, arango suffered a serious | on 20 march 2005, arango suffered a serious injury after a brutal collision with sevilla fc 's javi navarro. he fell unconscious, broke his cheekbone, swallowed his tongue and got serious cuts in his face; he returned to play a month later and, in the following season, was the team's top scorer with 11 league goals. | wikipedia |
810f8ce21d0e2dd1feb87be0697fd34ebedc205b | the following year, arango joined caracas fc but, | the following year, arango joined caracas fc but, after six months playing with the team he was bought by mexico's c.f. monterrey. he represented two other clubs in the latter country, c.f. pachuca and puebla fc, until 2004, when he joined la liga side rcd mallorca in spain (coached by benito floro, also his boss at mo... | wikipedia |
a2421338f3ac7775795a347800722174d873cc55 | arango's parents hailed from colombia, having immigrated to | arango's parents hailed from colombia, having immigrated to venezuela before he was born, in the city of maracay. he started playing as a professional at the age of sixteen with nueva cádiz fc, which ascended to the venezuelan primera división the following season under the name zulia fc. | wikipedia |
9335421e7b21d9aaf1c03036922826a45020ce76 | juan fernando arango sáenz (born 16 may 1980) | juan fernando arango sáenz (born 16 may 1980) is a venezuelan former professional footballer who played as an attacking midfielder. arango was considered by some in the sport as the greatest venezuelan footballer of all time. | wikipedia |
fd3371f73dee3eb8951cd5492faffd8bfc044279 | during their experiments with rat liver cells, hoagland | during their experiments with rat liver cells, hoagland and zamecnik noticed that in the presence of atp, amino acids associate with heat soluble rna, which was later named transfer rna (trna). this amino acid and trna complex was later called aminoacyl-trna. hoagland's major contribution to the laboratory was in his w... | wikipedia |
c7f097a515a521516dc041c558609f11344c71ad | by the time hoagland had joined huntington laboratories, | by the time hoagland had joined huntington laboratories, his colleagues there were well known for their work in protein synthesis. in the early 1950s, hoagland and his associates were able to show that polypeptide synthesis occurs on ribosomes. they did this by giving a rat injections of radioactive amino acids, waitin... | wikipedia |
db1f372c63b6d914e82e1a12caa8202755e6b479 | from 1953 to 1967, hoagland served as an | from 1953 to 1967, hoagland served as an associate professor of microbiology at harvard medical school. in 1967, upon leaving harvard he was appointed professor in the biochemistry department at the dartmouth medical school. in 1970, hoagland becamescientific director of the worcester foundation for experimental biolog... | wikipedia |
03ec2df942f238d4d62bf3ccf810e6a3119ecd60 | hoagland took a research position at massachusetts general | hoagland took a research position at massachusetts general hospital in the lab of paul zamecnik, where he researched and detailed the role of transfer rna in forming proteins. he was working with zamecnick and elizabeth keller when he discovered the initial steps of protein synthesis. | wikipedia |
f41de098ddd65deefae3965a5b34de53980ed341 | after graduating from harvard medical school he, his | after graduating from harvard medical school he, his daughter judith and his wife elizabeth stratton hoagland lived in the home of designer louise kenyon and her family. kenyon was part of the folly cove designers and hoagland worked with them in annisquam for several years while he commuted to boston for work. | wikipedia |
10a9d5663e0b8a8dcb0c9e0654624e53bbf208dd | mahlon bush hoagland was born in boston, massachusetts, | mahlon bush hoagland was born in boston, massachusetts, in 1921 to hudson hoagland and anna hoagland. hudson was an american physiologist who was known for co-founding the worcester foundation for experimental biology with gregory pincus. mahlon hoagland graduated from the hill school in 1940 and attended williams coll... | wikipedia |
6d5a05c0103b2a9f42e044fb7dbd54d9780cb8f3 | the 2013–14 football league two was wycombe wanderers' | the 2013–14 football league two was wycombe wanderers' 126th season in existence and their twentieth season in the football league. this page shows the statistics of the club's players in the season, and also lists all matches that the club played during the season. the season also marked the end of ivor beeks' 28-year... | wikipedia |
972eb5b927013c19bed94b83a957e8579c555af0 | wycombe ended the season in dramatic style, by | wycombe ended the season in dramatic style, by achieving league two survival on the final day of the season. on 3 may 2014, wycombe began the day three points adrift of safety in the relegation zone. however, after a 3–0 victory away at torquay, coupled with bristol rovers ' 1–0 defeat to mansfield, wycombe stayed up o... | wikipedia |
ff6cf66174e927b809a2fa56b10579a17472eb8b | the season also marked the end of ivor | the season also marked the end of ivor beeks' 28-year career as wycombe's chairman, on 21 august 2013. during the 28 years he spent as chairman, he oversaw the club's rise from the isthmian league into the football league. he continues his affiliation with the club in the role of vice-president. | wikipedia |
4f3fbf1c961f5ad62bfbb7592ed1186bbce0cf7d | the 2013–14 football league two was wycombe wanderers' | the 2013–14 football league two was wycombe wanderers' 126th season in existence and their twentieth season in the football league. this page shows the statistics of the club's players in the season, and also lists all matches that the club played during the season. | wikipedia |
9aaaff57713e4ed7da294b85b067bf6bb5b52464 | bentley builds computational software to understand the communication | bentley builds computational software to understand the communication between cells. bentley is interested in emergent behaviour of cells and how nearby cells influence them. she has shown that it is possible for cells to help their nearby cells ('adaptive') or help a pathogen ('maladapted'). she has investigated the g... | wikipedia |
62e15aa680988d2dcccaeb7ced482b0741e57e15 | in 2013, bentley was made an assistant professor | in 2013, bentley was made an assistant professor at the harvard medical school, where she worked in the center for vascular biology research, and after two years established a satellite modelling laboratory. she was appointed to the biological design centre in boston university in 2017. in 2019 bentley joined the franc... | wikipedia |
6e1d1e7afa01a102fbd37be320a943be2466bd62 | bentley studied mathematics as an undergraduate at the | bentley studied mathematics as an undergraduate at the university of sussex. she moved to university college london for doctoral research, where she studied morphological plasticity in robotic and biological systems. bentley was then appointed a postdoctoral researcher with holger gerhardt at the cancer research uk res... | wikipedia |
29c0b05e961e7a6e10654aed233976badc740615 | in number theory, a practical number or panarithmic | in number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n . for example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well... | wikipedia |
0af8d7ff6ad4675b95eb942cc87065459464adc9 | as with prime numbers in an arithmetic progression, | as with prime numbers in an arithmetic progression, given two natural numbers a {\displaystyle a} and q {\displaystyle q}, we have | { n ≤ x: n practical and n ≡ a mod q } | = c q, a x log x + o q (x (log x) 2). {\displaystyle |\{n\leq x:n{\text{ practical and }}n\equiv a{\bmod {q}}\}|={\frac {c_{q,a}x}{\log x}}+o_{q}\... | wikipedia |
33ef8239ff980fa650fe5e866bf85b3f04fb4070 | let p (x) {\displaystyle p(x)} count how many | let p (x) {\displaystyle p(x)} count how many practical numbers are at most x {\displaystyle x}. margenstern (1991) conjectured that p (x) {\displaystyle p(x)} is asymptotic to c x / log x {\displaystyle cx/\log x} for some constant c {\displaystyle c}, a formula which resembles the prime number theorem, strengthening ... | wikipedia |
4099e765abcc140d06d5a1be503979d2442b0415 | let p (x) {\displaystyle p(x)} count how many | biggl (}\sum _{p\leq \sigma (n)+1}{\frac {\log p}{p-1}}-\log n{\biggr)}\prod _{p\leq \sigma (n)+1}\left(1-{\frac {1}{p}}\right),} where γ {\displaystyle \gamma } is the euler–mascheroni constant and p {\displaystyle p} runs over primes. | wikipedia |
8cd1f4d1fb9ca200e05d79645ddb3b41a49ae40a | one reason for interest in practical numbers is | one reason for interest in practical numbers is that many of their properties are similar to properties of the prime numbers. indeed, theorems analogous to goldbach's conjecture and the twin prime conjecture are known for practical numbers: every positive even integer is the sum of two practical numbers, and there exis... | wikipedia |
4409e07169aa623bd3894998bbd0d3f9f4f578d8 | according to a september 2015 conjecture by zhi-wei | according to a september 2015 conjecture by zhi-wei sun, every positive rational number has an egyptian fraction representation in which every denominator is a practical number. the conjecture was proved by david eppstein (2021). | wikipedia |
b75cef76ea4539c8cafe4ca0ef23dd13d60fca5c | vose (1985) showed that every rational number x | vose (1985) showed that every rational number x / y {\displaystyle x/y} has an egyptian fraction representation with o (log y) {\displaystyle o({\sqrt {\log y}})} terms. the proof involves finding a sequence of practical numbers n i {\displaystyle n_{i}} with the property that every number less than n i {\displaystyle ... | wikipedia |
596a1c4306645e6fb0a182cbb32ced3f7a5628bc | fibonacci, in his 1202 book liber abaci lists | fibonacci, in his 1202 book liber abaci lists several methods for finding egyptian fraction representations of a rational number. of these, the first is to test whether the number is itself already a unit fraction, but the second is to search for a representation of the numerator as a sum of divisors of the denominator... | wikipedia |
cde4e46283dc652b7280b54b5ce3772d10175f4f | if n {\displaystyle n} is practical, then any | if n {\displaystyle n} is practical, then any rational number of the form m / n {\displaystyle m/n} with m < n {\displaystyle m<n} may be represented as a sum ∑ d i / n {\textstyle \sum d_{i}/n} where each d i {\displaystyle d_{i}} is a distinct divisor of n {\displaystyle n}. each term in this sum simplifies to a unit... | wikipedia |
62777bf63316eecce1dd6ac4101e4bdd0b0b6dd2 | the condition stated above is necessary and sufficient | the condition stated above is necessary and sufficient for a number to be practical. in one direction, this condition is necessary in order to be able to represent p i − 1 {\displaystyle p_{i}-1} as a sum of divisors of n {\displaystyle n}, because if the inequality failed to be true then even adding together all the s... | wikipedia |
ddee7221ce80bc8969c1a0b106c4754e78c8e728 | where σ (x) {\displaystyle \sigma (x)} denotes the | where σ (x) {\displaystyle \sigma (x)} denotes the sum of the divisors of x. for example, 2 × 3 × 29 × 823 = 429606 is practical, because the inequality above holds for each of its prime factors: 3 ≤ σ(2) + 1 = 4, 29 ≤ σ(2 × 3) + 1 = 40, and 823 ≤ σ(2 × 3 × 29) + 1 = 1171. | wikipedia |
ea0b4246c3b87494904b2edc929bfbaa927e00e6 | this partial characterization was extended and completed by | this partial characterization was extended and completed by stewart (1954) and sierpiński (1955) who showed that it is straightforward to determine whether a number is practical from its prime factorization.a positive integer greater than one with prime factorization n = p 1 α 1... p k α k {\displaystyle n=p_{1}^{\alph... | wikipedia |
30a42e2abaaf65534ad648f7c16ea3ff9eca0ca1 | the original characterisation by srinivasan (1948) stated that | the original characterisation by srinivasan (1948) stated that a practical number cannot be a deficient number, that is one of which the sum of all divisors (including 1 and itself) is less than twice the number unless the deficiency is one. if the ordered set of all divisors of the practical number n {\displaystyle n}... | wikipedia |
25c681e973348d2f5e05bc2441797b046a1acfb5 | the name "practical number" is due to srinivasan | the name "practical number" is due to srinivasan (1948). he noted that "the subdivisions of money, weights, and measures involve numbers like 4, 12, 16, 20 and 28 which are usually supposed to be so inconvenient as to deserve replacement by powers of 10." his partial classification of these numbers was completed by ste... | wikipedia |
d38f60b0136d401fc59d299f433cb524d8f9f5cc | practical numbers were used by fibonacci in his | practical numbers were used by fibonacci in his liber abaci (1202) in connection with the problem of representing rational numbers as egyptian fractions. fibonacci does not formally define practical numbers, but he gives a table of egyptian fraction expansions for fractions with practical denominators. | wikipedia |
432f6ded07388c993731b7ee3a52b955628a008a | in number theory, a practical number or panarithmic | in number theory, a practical number or panarithmic number is a positive integer n {\displaystyle n} such that all smaller positive integers can be represented as sums of distinct divisors of n {\displaystyle n}. for example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its ... | wikipedia |
b4b96b8f13588708ab89a2a3d0291040d3e29437 | an inexact differential or imperfect differential is a | an inexact differential or imperfect differential is a differential whose integral is path dependent. it is most often used in thermodynamics to express changes in path dependent quantities such as heat and work, but is defined more generally within mathematics as a type of differential form. in contrast, an integral o... | wikipedia |
6a037628a4e41c26ac51b0b8257d417a26738ff7 | consider the inexact differential form, δ u = | consider the inexact differential form, δ u = 2 y d x + x d y. {\displaystyle \delta u=2y\,\mathrm {d} x+x\,\mathrm {d} y.} this must be inexact by considering going to the point (1,1). if we first increase y and then increase x, then that corresponds to first integrating over y and then over x. integrating over y firs... | wikipedia |
db493cba882ced67e06ef9be312e87e6a5838db8 | it is sometimes possible to convert an inexact | it is sometimes possible to convert an inexact differential into an exact one by means of an integrating factor.the most common example of this in thermodynamics is the definition of entropy: d s = δ q rev t {\displaystyle \mathrm {d} s={\frac {\delta q_{\text{rev}}}{t}}} in this case, δq is an inexact differential, be... | wikipedia |
212ebe0686ee88e4d5e3e8b5d7562d767bab1be1 | a fire requires heat, fuel, and an oxidizing | a fire requires heat, fuel, and an oxidizing agent. the energy required to overcome the activation energy barrier for combustion is transferred as heat into the system, resulting in changes to the system's internal energy. in a process, the energy input to start a fire may comprise both work and heat, such as when one ... | wikipedia |
13e8d30536bcd1d6b9a77fb6aa72fdba6fe8b75e | internal energy u is a state function, meaning | internal energy u is a state function, meaning its change can be inferred just by comparing two different states of the system (independently of its transition path), which we can therefore indicate with u and u.since we can go from state u to state u either by providing heat q = u − u or work w = u − u, such a change ... | wikipedia |
a5ca700bd84b76cb69281239810b3e1d8a6d694f | inexact differentials show up explicitly in the first | inexact differentials show up explicitly in the first law of thermodynamics, d u = δ q − δ w {\displaystyle \mathrm {d} u=\delta q-\delta w} where u {\displaystyle u} is the energy, δ q {\displaystyle \delta q} is the differential change in heat and δ w {\displaystyle \delta w} is the differential change in work. based... | wikipedia |
89a985dc60e9483a876cb650067fff9491c4d63b | reworking the above with differentials and taking a | reworking the above with differentials and taking a b ¯ {\displaystyle {\overline {ab}}} to be along the x {\displaystyle x} -axis, the net distance differential is d f = d x {\displaystyle \mathrm {d} f=\mathrm {d} x}, an exact differential with antiderivative x {\displaystyle x}. on the other hand, the total distance... | wikipedia |
8286ccff84581d338eecd7828c80c2eeed5747f9 | when you walk from a point a {\displaystyle | when you walk from a point a {\displaystyle a} to a point b {\displaystyle b} along a line a b ¯ {\displaystyle {\overline {ab}}} (without changing directions) your net displacement and total distance covered are both equal to the length of said line a b {\displaystyle ab}. if you then return to point a {\displaystyle ... | wikipedia |
37208971004cb1fbc6e7eb01c0316079563463f5 | within statistical mechanics, inexact differentials are often denoted | within statistical mechanics, inexact differentials are often denoted with a bar through the differential operator, đ. in latex the command "\rlap{\textrm{d}}{\bar{\phantom{w}}}" is an approximation or simply "\dj" for a dyet character, which needs the t1 encoding. | wikipedia |
b23c12ffd0ebd519c8a46c99fa889e477e355206 | instead of the differential symbol d, the symbol | instead of the differential symbol d, the symbol δ is used, a convention which originated in the 19th century work of german mathematician carl gottfried neumann, indicating that q (heat) and w (work) are path-dependent, while u (internal energy) is not. | wikipedia |
e53dbeae52b19a5d45e3ac86a406cbbbe3435c41 | the fundamental theorem of calculus for line integrals | the fundamental theorem of calculus for line integrals requires path independence in order to express the values of a given vector field in terms of the partial derivatives of another function that is the multivariate analogue of the antiderivative. this is because there can be no unique representation of an antideriva... | wikipedia |
bc10ea00ae855a59267b3f56499491354d8800d3 | more generally, an inexact differential δ u {\displaystyle | more generally, an inexact differential δ u {\displaystyle \delta u} is a differential form which is not an exact differential, i.e., for all functions f {\displaystyle f}, d f ≠ δ u {\displaystyle \mathrm {d} f\neq \delta u} | wikipedia |
0ada83ea43089c2339bc8d09102dedafbc20943b | an inexact differential δ u {\displaystyle \delta u} | an inexact differential δ u {\displaystyle \delta u} is a differential for which the integral over some two paths with the same end points is different. specifically, there exist integrable paths γ 1, γ 2: → r {\displaystyle \gamma _{1},\gamma _{2}:\to \mathbb {r} } such that γ 1 (0) = γ 2 (0) {\displaystyle \gamma _{1... | wikipedia |
b4b96b8f13588708ab89a2a3d0291040d3e29437 | an inexact differential or imperfect differential is a | an inexact differential or imperfect differential is a differential whose integral is path dependent. it is most often used in thermodynamics to express changes in path dependent quantities such as heat and work, but is defined more generally within mathematics as a type of differential form. in contrast, an integral o... | wikipedia |
fea44467f1f9135b21c177eed4918180f8c1120f | blake speers is a canadian professional ice hockey | blake speers is a canadian professional ice hockey centre who is currently playing with belfast giants in the uk's elite ice hockey league (eihl). speers was most recently with västerås ik in the hockeyallsvenskan (allsv), and has formerly played in the national hockey league (nhl) with the new jersey devils and the ar... | wikipedia |
f956f4631027ad4914c5ee04404269d72ca5101d | as a free agent from the coyotes following | as a free agent from the coyotes following the 2021–22 season, speers left north america to pursue a european career in agreeing to a one-year deal with swedish second tier club, västerås ik of the hockeyallsvenskan, on august 1, 2022. | wikipedia |
23d8687b268aabfbfe89119168c0980900332023 | on december 16, 2019, speers was traded to | on december 16, 2019, speers was traded to the arizona coyotes as a part of a trade that sent taylor hall to the devils. after recording 4 goals and 9 points in 32 games with their american hockey league (ahl) affiliate, the tucson roadrunners, in addition to one assist in 10 ahl games before the trade, speers signed a... | wikipedia |
e59e168ff077f522af9e82caaf1ba6ab04b2550c | speers began his major junior career playing with | speers began his major junior career playing with the sault ste. marie greyhounds in the ontario hockey league before he was drafted in the 3rd round, 67th overall, by the new jersey devils in the 2015 nhl entry draft. on september 21, 2016, speers signed a three-year entry-level contract with the devils. on october 11... | wikipedia |
766cabbc4caeb2f48fed25d5096d5b206246d5be | in 1947 chibnall married marjorie mccallum morgan, whom | in 1947 chibnall married marjorie mccallum morgan, whom he had met after corresponding about one of his historical interests. they had a daughter and a son. marjorie died in sheffield on 23 june 2012, aged 96. | wikipedia |
ac8d8645a550eeea9117fd9a445c571d460090ff | albert chibnall married his cousin helen isabel cicely | albert chibnall married his cousin helen isabel cicely chibnall, known as cicely, in 1931. they set up home at long meadow, in chiswick mall. their first child, joan, was born in 1933. cicely died at queen charlotte's isolation hospital, hammersmith, on 19 may 1936, giving birth to their second daughter, also cicely. | wikipedia |
1f3bc45acebb2a8ce94b35b3775e2ca103ee73e9 | his notable students included fred sanger who, after | his notable students included fred sanger who, after he was awarded in phd in 1943 joined chibnall's lab. chibnall suggested sanger work on methods of identifying the terminal amino acid of insulin. chibnall then declined to have his name on sanger's paper on the grounds that sanger should get all the credit. sanger to... | wikipedia |
170d1e8deb96ca40fd20475e37c9b48b40b6206b | in 1924 he joined the laboratory of jack | in 1924 he joined the laboratory of jack drummond at university college london. in 1929 cibnall took over the chair of bichemistry at imperial college. he was appointed the second sir william dunn professor of biochemistry at cambridge university in 1943. he resigned in 1949 since he felt it was a role more suited to a... | wikipedia |
d5e9a0f0be645f026100f99cd768db86acd93b63 | after a year's work at the chelsea physic | after a year's work at the chelsea physic garden, chibnall was awarded a travelling scholarship to the usa. he secured a place with the leading expert on plant proteins, t b osborne, at the connecticut agricultural experiment station. | wikipedia |
077a5e890692d35aea6554471a76dba9907c588d | in 1919 chibnall was taken on by professor | in 1919 chibnall was taken on by professor h b baker to do research for the newly instituted phd at imperial college, but he later switched to study the nitrogenous constituents of green leaves with professor s. b. schryver, whom he succeeded in 1929. he gained his phd in 1921. | wikipedia |
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