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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...
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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...
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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...
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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...
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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...
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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 ...
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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 ...
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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...
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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...
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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...
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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...
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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.
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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.
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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.
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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...
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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...
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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.
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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.
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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.
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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.
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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.
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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...
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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...
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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...
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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.
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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...
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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.
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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...
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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...
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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...
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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.
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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.
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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...
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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...
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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...
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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.
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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...
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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...
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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...
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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...
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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}\...
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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 ...
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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.
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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...
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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).
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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 ...
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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...
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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...
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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...
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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.
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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...
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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}...
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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...
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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.
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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 ...
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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...
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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...
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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...
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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 ...
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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 ...
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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...
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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...
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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 ...
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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.
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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.
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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...
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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}
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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...
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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...
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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.
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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...
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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...
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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.
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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.
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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...
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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...
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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.
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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.
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