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A study published in 2012 examined the phylogenetic relationships between the Eurasian and North African species in the Bufo bufo group and indicated a long evolutionary history for the group. Nine to thirteen million years ago, Bufo eichwaldi, a recently described species from south Azerbaijan and Iran, split from th...
Common toad
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https://en.wikipedia.org/wiki/Common%20toad
Biology and health sciences
Frogs and toads
Animals
Other species with which the common toad could be confused include the natterjack toad (Bufo calamita) and the European green toad (Bufo viridis). The former is usually smaller and has a yellow band running down its back while the latter has a distinctive mottled pattern. The paratoid glands of both are parallel rather...
Common toad
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Biology and health sciences
Frogs and toads
Animals
The common toad usually moves by walking rather slowly or in short shuffling jumps involving all four legs. It spends the day concealed in a lair that it has hollowed out under foliage or beneath a root or a stone where its colouring makes it inconspicuous. It emerges at dusk and may travel some distance in the dark wh...
Common toad
Wikipedia
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Frogs and toads
Animals
Predators and parasites When attacked, the common toad adopts a characteristic stance, inflating its body and standing with its hindquarters raised and its head lowered. Its chief means of defence lies in the foul tasting secretion that is produced by its paratoid glands and other glands on its skin. This contains a t...
Common toad
Wikipedia
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https://en.wikipedia.org/wiki/Common%20toad
Biology and health sciences
Frogs and toads
Animals
The males arrive first and remain in the location for several weeks while the females only stay long enough to mate and spawn. Rather than fighting for the right to mate with a female, male toads may settle disputes by means of the pitch of their voice. Croaking provides a reliable sign of body size and hence of prowes...
Common toad
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Biology and health sciences
Frogs and toads
Animals
The strings of eggs absorb water and swell in size, and small tadpoles hatch out after 10 days. At first they cling to the remains of the strings and feed on the jelly. They later attach themselves to the underside of the leaves of water weed before becoming free swimming. The tadpoles at first look similar to those of...
Common toad
Wikipedia
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Biology and health sciences
Frogs and toads
Animals
A comparison was made between the growth rate of newly metamorphosed juveniles from different altitudes and latitudes, the specimens studied being from Norway, Germany, Switzerland, the Netherlands and France. At first the growth rates for males and females was identical. By the time they became mature their growth rat...
Common toad
Wikipedia
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https://en.wikipedia.org/wiki/Common%20toad
Biology and health sciences
Frogs and toads
Animals
There are parts of its range where the common toad seems to be in decline. In Spain, increased aridity and habitat loss have led to a diminution in numbers and it is regarded as "near threatened". A population in the Sierra de Gredos mountain range is facing predation by otters and increased competition from the frog ...
Common toad
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Biology and health sciences
Frogs and toads
Animals
Bufotoxin The main substance found in the parotoid gland and skin of the common toad is called bufotoxin. It was first isolated by Heinrich Wieland and his colleagues in 1922, and they succeeded in identifying its structure about 20 years later. Meanwhile, other researchers succeeded in isolating the same compound (a...
Common toad
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Biology and health sciences
Frogs and toads
Animals
The toad has long been considered to be an animal of ill omen or a connection to a spirit world. This may have its origins in the fact that it is at home both on land and in the water. It may cause repugnance because of its drab, wart-like skin, its slow movements and the way it emerges from some dark hole. In Europe i...
Common toad
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Biology and health sciences
Frogs and toads
Animals
Mr. Toad is one of the main characters in the children's novel The Wind in the Willows, by Kenneth Grahame. This has been dramatized by several authors including A. A. Milne who called his play Toad of Toad Hall. Mr. Toad is a conceited, anthropomorphic toad and in the book he composes a ditty in his own praise which s...
Common toad
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Frogs and toads
Animals
The Centaurus A/M83 Group is a complex group of galaxies in the constellations Hydra, Centaurus, and Virgo. The group may be roughly divided into two subgroups. The Cen A Subgroup, at a distance of 11.9 Mly (3.66 Mpc), is centered on Centaurus A, a nearby radio galaxy. The M83 Subgroup, at a distance of 14.9 Mly (4.5...
Centaurus A/M83 Group
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https://en.wikipedia.org/wiki/Centaurus%20A/M83%20Group
Physical sciences
Notable galaxy clusters
Astronomy
The dwarf spheroidal galaxies of the Centaurus A group have been studied and have been found to have old, metal-poor stellar populations similar to those in the Local Group, and follow a similar metallicity–luminosity relation. One dwarf galaxy, KK98 203 (LEDA 166167), has an extended ring of Hα emission. Member list ...
Centaurus A/M83 Group
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https://en.wikipedia.org/wiki/Centaurus%20A/M83%20Group
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Notable galaxy clusters
Astronomy
LinkedIn () is a business and employment-focused social media platform that works through websites and mobile apps. It was launched on May 5, 2003 by Reid Hoffman and Eric Ly. Since December 2016, LinkedIn has been a wholly owned subsidiary of Microsoft. The platform is primarily used for professional networking and ca...
LinkedIn
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https://en.wikipedia.org/wiki/LinkedIn
Technology
Social network and blogging
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The company was founded in December 2002 by Reid Hoffman and the founding team members from PayPal and Socialnet.com (Allen Blue, Eric Ly, Jean-Luc Vaillant, Lee Hower, Konstantin Guericke, Stephen Beitzel, David Eves, Ian McNish, Yan Pujante, Chris Saccheri). In late 2003, Sequoia Capital led the Series A investment i...
LinkedIn
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https://en.wikipedia.org/wiki/LinkedIn
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LinkedIn filed for an initial public offering in January 2011. The company traded its first shares on May 19, 2011, under the NYSE symbol "LNKD", at $45 (~$ in ) per share. Shares of LinkedIn rose as much as 171% on their first day of trade on the New York Stock Exchange and closed at $94.25, more than 109% above IPO ...
LinkedIn
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In late 2016, LinkedIn announced a planned increase of 200 new positions in its Dublin office, which would bring the total employee count to 1,200. Since 2017 94% of B2B marketers use LinkedIn to distribute content. Soon after LinkedIn's acquisition by Microsoft, LinkedIn's new desktop version was introduced. The new ...
LinkedIn
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In May 2023, LinkedIn cut 716 positions from its 20,000 workforce. The move, according to a letter from the company's CEO Ryan Roslansky, was made to streamline the business's operations. Roslansky further stated that this decision would result in the creation of 250 job opportunities. Additionally, LinkedIn also annou...
LinkedIn
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In May 2017, LinkedIn sent a Cease-And-Desist letter to hiQ Labs, a Silicon Valley startup that collects data from public profiles and provides analysis of this data to its customers. The letter demanded that hiQ immediately cease "scraping" data from LinkedIn's servers, claiming violations of the CFAA (Computer Fraud ...
LinkedIn
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https://en.wikipedia.org/wiki/LinkedIn
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A member's list of connections can be used in a number of ways. For example, users can search for second-degree connections who work at a company they are interested in, and then ask a specific first-degree connection in common for an introduction. The "gated-access approach" (where contact with any professional requir...
LinkedIn
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https://en.wikipedia.org/wiki/LinkedIn
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Embedded in profile In October 2008, LinkedIn enabled an "applications platform" which allows external online services to be embedded within a member's profile page. Among the initial applications were an Amazon Reading List that allows LinkedIn members to display books they are reading, a connection to Tripit, and a ...
LinkedIn
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Groups LinkedIn also supports daily the formation of interest groups. In 2012, there were 1,248,019 such groups whose membership varies from 1 to 744,662. Groups support a limited form of discussion area, moderated by the group owners and managers. Groups may be private, accessible to members only or may be open to In...
LinkedIn
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LinkedIn is particularly well-suited for personal branding, which, according to Sandra Long, entails "actively managing one's image and unique value" to position oneself for career opportunities. LinkedIn has evolved from being a mere platform for job searchers into a social network which allows users a chance to creat...
LinkedIn
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https://en.wikipedia.org/wiki/LinkedIn
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LinkedIn also allows users to research companies, non-profit organizations, and governments they may be interested in working for. Typing the name of a company or organization in the search box causes pop-up data about the company or organization to appear. Such data may include the ratio of female to male employees, t...
LinkedIn
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Top Companies LinkedIn Top Companies is a series of lists published by LinkedIn, identifying companies in the United States, Australia, Brazil, Canada, China, France, Germany, India, Japan, Mexico, South Korea, Spain, and the United Kingdom that are attracting the most intense interest from job candidates. The 2019 li...
LinkedIn
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Publishing platform In 2015, LinkedIn added an analytics tool to its publishing platform. The tool allows authors to better track the traffic that their posts receive. In relation to this functionality, LinkedIn has gained more users over the years in the interest of clearly monitoring users' posts through post-perfor...
LinkedIn
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Endorsement feature The feature that allows LinkedIn members to "endorse" each other's skills and experience has been criticized as meaningless, since the endorsements are not necessarily accurate or given by people who have familiarity with the member's skills. In October 2016, LinkedIn acknowledged that it "really d...
LinkedIn
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In June 2012, cryptographic hashes of approximately 6.4 million LinkedIn user passwords were stolen by Yevgeniy Nikulin and other hackers who then published the stolen hashes online. This action is known as the 2012 LinkedIn hack. In response to the incident, LinkedIn asked its users to change their passwords. Security...
LinkedIn
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In 2017, Germany's Federal Office for the Protection of the Constitution (BfV) published information alleging that Chinese intelligence services had created fake social media profiles on sites such as LinkedIn, using them to gather information on German politicians and government officials. In 2022, the company ranked...
LinkedIn
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Also in 2017, sociologist Ofer Sharone conducted interviews with unemployed workers to research the effects of LinkedIn and Facebook as labor market intermediaries and found that social networking services (SNS) have had a filtration effect that has little to do with evaluations of merit, and that the SNS filtration ef...
LinkedIn
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In a September 2019 working paper, economists Laurel Wheeler, Robert Garlick, and RTI International scholars Eric Johnson, Patrick Shaw, and Marissa Gargano ran a randomized evaluation of training job seekers in South Africa to use LinkedIn as part of job readiness programs. The evaluation found that the training incre...
LinkedIn
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In October 2021, after reports of several academicians and reporters who received notifications regarding their profiles will be blocked in China, Microsoft confirmed that LinkedIn will be shutting down in China and replaced with InJobs, a China exclusive app, citing difficulties in operating environments and increasin...
LinkedIn
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In astronomy, a trojan is a small celestial body (mostly asteroids) that shares the orbit of a larger body, remaining in a stable orbit approximately 60° ahead of or behind the main body near one of its Lagrangian points and . Trojans can share the orbits of planets or of large moons. Trojans are one type of co-orbit...
Trojan (celestial body)
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https://en.wikipedia.org/wiki/Trojan%20%28celestial%20body%29
Physical sciences
Planetary science
Astronomy
The term "trojan" originally referred to the "trojan asteroids" (Jovian trojans) that orbit close to the Lagrangian points of Jupiter. These have long been named for figures from the Trojan War of Greek mythology. By convention, the asteroids orbiting near the point of Jupiter are named for the characters from the Gre...
Trojan (celestial body)
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https://en.wikipedia.org/wiki/Trojan%20%28celestial%20body%29
Physical sciences
Planetary science
Astronomy
As a rule of thumb, the system is likely to be long-lived if m1 > 100m2 > 10,000m3 (in which m1, m2, and m3 are the masses of the star, planet, and trojan). More formally, in a three-body system with circular orbits, the stability condition is 27(m1m2 + m2m3 + m3m1) < (m1 + m2 + m3)2. So the trojan being a mote of dus...
Trojan (celestial body)
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Planetary science
Astronomy
The ringtail (Bassariscus astutus) is a mammal of the raccoon family native to arid regions of North America. It is widely distributed and well-adapted to its distributed areas. It has been legally trapped for its fur. Globally, it is listed as Least Concern on the IUCN Red List but is a Conservation Strategy Species i...
Ringtail
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https://en.wikipedia.org/wiki/Ringtail
Biology and health sciences
Procyonidae
Animals
As adults, these mammals lead solitary lives, generally coming together only to mate. A typical call is a very loud, plaintive bark. They produce a variety of sounds, including clicks and chatters reminiscent of raccoons. Ringtails have been reported to exhibit fecal marking behavior as a form of intraspecific communi...
Ringtail
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https://en.wikipedia.org/wiki/Ringtail
Biology and health sciences
Procyonidae
Animals
The ringtail is found in the Southwestern United States in southern Oregon, California, eastern Kansas, Oklahoma, Arizona, New Mexico, Colorado, southern Nevada, Utah, Louisiana and Texas. In Mexico it ranges from the northern desert state of Baja California to Oaxaca. Its distribution overlaps that of B. sumichrasti ...
Ringtail
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https://en.wikipedia.org/wiki/Ringtail
Biology and health sciences
Procyonidae
Animals
Ecology Foxes, coyotes, raccoons, bobcats, hawks, and owls opportunistically prey upon ringtails of all ages, though predominantly on younger, more vulnerable specimens. Also occasional prey to coatis, lynxes, and mountain lions, the ringtail is rather adept at avoiding predators. The ringtail's success in deterring po...
Ringtail
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Biology and health sciences
Procyonidae
Animals
Procyonidae ( ) is a New World family of the order Carnivora. It includes the raccoons, ringtails, cacomistles, coatis, kinkajous, olingos, and olinguitos. Procyonids inhabit a wide range of environments and are generally omnivorous. Characteristics Procyonids are relatively small animals, with generally slender bodie...
Procyonidae
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https://en.wikipedia.org/wiki/Procyonidae
Biology and health sciences
Carnivora
null
Procyonid fossils once believed to belong to the genus Bassariscus, which includes the modern ringtail and cacomistle, have been identified from the Miocene epoch, around 20 million years (Ma) ago. It has been suggested that early procyonids were an offshoot of the canids that adapted to a more omnivorous diet. The rec...
Procyonidae
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Biology and health sciences
Carnivora
null
FAMILY PROCYONIDAE Subfamily Procyoninae (nine species in four genera) Tribe Procyonini Subtribe Procyonina Raccoons, Procyon Crab-eating raccoon, Procyon cancrivorus Cozumel raccoon, Procyon pygmaeus Common raccoon, Procyon lotor Subtribe Nasuina Nasua South American coati or ring-tailed coati, Nasua nasua ...
Procyonidae
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Biology and health sciences
Carnivora
null
Extinct taxa Below is a list of extinct taxa (many of which are fossil genera and species) compiled in alphabetical order under their respective subfamilies. Procyonidae J.E. Gray, 1825 †Broilianinae Dehm, 1950 †Broiliana Dehm, 1950 †B. dehmi Beaumont & Mein, 1973 †B. nobilis Dehm, 1950 †Stromeriella Dehm, 1950 ...
Procyonidae
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https://en.wikipedia.org/wiki/Procyonidae
Biology and health sciences
Carnivora
null
†C. clausa (Ameghino, 1904) [=Pachynasua clausa Ameghino, 1904] †C. groeberi Kraglievich & Reig, 1954 [=Amphinasua groeberi Cabrera, 1936] †C. longirostris (Rovereto, 1914) †C. lutaria (Cabrera, 1936) [=Amphinasua lutaria Cabrera, 1936] †C. meranii (Ameghino & Kraglievich 1925) [=Brachynasua meranii Ameghino & Krag...
Procyonidae
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https://en.wikipedia.org/wiki/Procyonidae
Biology and health sciences
Carnivora
null
A fathom is a unit of length in the imperial and the U.S. customary systems equal to , used especially for measuring the depth of water. The fathom is neither an international standard (SI) unit, nor an internationally accepted non-SI unit. Historically it was the maritime measure of depth in the English-speaking world...
Fathom
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https://en.wikipedia.org/wiki/Fathom
Physical sciences
English
Basics and measurement
Other definitions Other definitions of fathom include: 1.828804 m (Obsolete measurement of the fathom based on the US survey foot, only for use of historical and legacy applications) 2 yards exactly 18 hands One metre is about 0.5468 fathoms In the international yard and pound agreement of 1959 the United States,...
Fathom
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https://en.wikipedia.org/wiki/Fathom
Physical sciences
English
Basics and measurement
Some extensive flat areas of the sea bottom with constant depth are known by their fathom number, like the Broad Fourteens or the Long Forties, both in the North Sea. Line length The components of a commercial fisherman's setline were measured in fathoms. The rope called a groundline, used to form the main line of a s...
Fathom
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https://en.wikipedia.org/wiki/Fathom
Physical sciences
English
Basics and measurement
On land Until early in the 20th century, it was the unit used to measure the depth of mines (mineral extraction) in the United Kingdom. Miners also use it as a unit of area equal to 6 feet square (3.34 m2) in the plane of a vein. In Britain, it can mean the quantity of wood in a pile of any length measuring square in ...
Fathom
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https://en.wikipedia.org/wiki/Fathom
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English
Basics and measurement
The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by μ or EF for brevity. The Fermi level does not include the work required to remove the electron from wherever it came from. A precise understanding of the Fermi leve...
Fermi level
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https://en.wikipedia.org/wiki/Fermi%20level
Physical sciences
Basics_2
Physics
The Fermi level of a body expresses the work required to add an electron to it, or equally the work obtained by removing an electron. Therefore, VA − VB, the observed difference in voltage between two points, A and B, in an electronic circuit is exactly related to the corresponding chemical potential difference, μA − μ...
Fermi level
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Physics
The location of μ within a material's band structure is important in determining the electrical behaviour of the material. In an insulator, μ lies within a large band gap, far away from any states that are able to carry current. In a metal, semimetal or degenerate semiconductor, μ lies within a delocalized band. A la...
Fermi level
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Basics_2
Physics
Unlike μ, the parameter, ζ, is not a constant at equilibrium, but rather varies from location to location in a material due to variations in ϵC, which is determined by factors such as material quality and impurities/dopants. Near the surface of a semiconductor or semimetal, ζ can be strongly controlled by externally ap...
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Physics
The quasi-equilibrium approach allows one to build a simple picture of some non-equilibrium effects as the electrical conductivity of a piece of metal (as resulting from a gradient of μ) or its thermal conductivity (as resulting from a gradient in T). The quasi-μ and quasi-T can vary (or not exist at all) in any non-eq...
Fermi level
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Physics
The term Fermi level is mainly used in discussing the solid state physics of electrons in semiconductors, and a precise usage of this term is necessary to describe band diagrams in devices comprising different materials with different levels of doping. In these contexts, however, one may also see Fermi level used impre...
Fermi level
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Physics
A practical and well-justified choice of common point is a bulky, physical conductor, such as the electrical ground or earth. Such a conductor can be considered to be in a good thermodynamic equilibrium and so its μ is well defined. It provides a reservoir of charge, so that large numbers of electrons may be added or r...
Fermi level
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Physics
When the body is able to exchange electrons and energy with an electrode (reservoir), it is described by the grand canonical ensemble. The value of chemical potential can be said to be fixed by the electrode, and the number of electrons on the body may fluctuate. In this case, the chemical potential of a body is the ...
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Type 2 diabetes (T2D), formerly known as adult-onset diabetes, is a form of diabetes mellitus that is characterized by high blood sugar, insulin resistance, and relative lack of insulin. Common symptoms include increased thirst, frequent urination, fatigue and unexplained weight loss. Other symptoms include increased h...
Type 2 diabetes
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Specific diseases
Health
Rates of type 2 diabetes have increased markedly since 1960 in parallel with obesity. As of 2015, there were approximately 392 million people diagnosed with the disease compared to around 30 million in 1985. Typically, it begins in middle or older age, although rates of type 2 diabetes are increasing in young people. T...
Type 2 diabetes
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Causes The development of type 2 diabetes is caused by a combination of lifestyle and genetic factors. While some of these factors are under personal control, such as diet and obesity, other factors are not, such as increasing age, female sex, and genetics. Generous consumption of alcohol is also a risk factor. Obesity...
Type 2 diabetes
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Most cases of diabetes involve many genes, with each being a small contributor to an increased probability of becoming a type 2 diabetic. The proportion of diabetes that is inherited is estimated at 72%. More than 36 genes and 80 single nucleotide polymorphisms (SNPs) had been found that contribute to the risk of type ...
Type 2 diabetes
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Health
Type 2 diabetes is due to insufficient insulin production from beta cells in the setting of insulin resistance. Insulin resistance, which is the inability of cells to respond adequately to normal levels of insulin, occurs primarily within the muscles, liver, and fat tissue. In the liver, insulin normally suppresses glu...
Type 2 diabetes
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The World Health Organization definition of diabetes (both type 1 and type 2) is for a single raised glucose reading with symptoms, otherwise raised values on two occasions, of either: fasting plasma glucose ≥ 7.0 mmol/L (126 mg/dL) or glucose tolerance test with two hours after the oral dose a plasma glucose ≥ 11.1 ...
Type 2 diabetes
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Health
Screening Universal screening for diabetes in people without risk factors or symptoms is not recommended. The United States Preventive Services Task Force (USPSTF) recommended in 2021 screening for type 2 diabetes in adults aged 35 to 70 years old who are overweight (i.e. BMI over 25) or have obesity. For people of As...
Type 2 diabetes
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Onset of type 2 diabetes can be delayed or prevented through proper nutrition and regular exercise. Intensive lifestyle measures may reduce the risk by over half. The benefit of exercise occurs regardless of the person's initial weight or subsequent weight loss. High levels of physical activity reduce the risk of diabe...
Type 2 diabetes
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Health
Management of type 2 diabetes focuses on lifestyle interventions, lowering other cardiovascular risk factors, and maintaining blood glucose levels in the normal range. Self-monitoring of blood glucose for people with newly diagnosed type 2 diabetes may be used in combination with education, although the benefit of self...
Type 2 diabetes
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Health
Calorie restriction to promote weight loss is generally recommended. Around 80 percent of obese people with type 2 diabetes achieve complete remission with no need for medication if they sustain a weight loss of at least , but most patients are not able to achieve or sustain significant weight loss. Even modest weight ...
Type 2 diabetes
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Other classes of medications include: sulfonylureas, thiazolidinediones, dipeptidyl peptidase-4 inhibitors, SGLT2 inhibitors, and GLP-1 receptor agonists. A 2018 review found that SGLT2 inhibitors and GLP-1 agonists, but not DPP-4 inhibitors, were associated with lower mortality than placebo or no treatment. Rosiglitaz...
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Other The use of statins in diabetes to prevent cardiovascular disease should be considered after evaluating the person's total risk for cardiovascular disease. The use of aspirin (acetylsalicylic acid) to prevent cardiovascular disease in diabetes is controversial. Aspirin is recommended in people with previous card...
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Rates of diabetes in 1985 were estimated at 30 million, increasing to 135 million in 1995 and 217 million in 2005. This increase is believed to be primarily due to the global population aging, a decrease in exercise, and increasing rates of obesity. Traditionally considered a disease of adults, type 2 diabetes is incre...
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A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on metal–oxide–semiconductor (MOS) integrated circuit chips. They are widely used in audio signal processing, telecommunications, digital ima...
Digital signal processor
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The architecture of a DSP is optimized specifically for digital signal processing. Most also support some of the features of an applications processor or microcontroller, since signal processing is rarely the only task of a system. Some useful features for optimizing DSP algorithms are outlined below. Architecture So...
Digital signal processor
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Data instructions Saturation arithmetic, in which operations that produce overflows will accumulate at the maximum (or minimum) values that the register can hold rather than wrapping around (maximum+1 doesn't overflow to minimum as in many general-purpose CPUs, instead it stays at maximum). Sometimes various sticky bit...
Digital signal processor
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In 1978, American Microsystems (AMI) released the S2811. The AMI S2811 "signal processing peripheral", like many later DSPs, has a hardware multiplier that enables it to do multiply–accumulate operation in a single instruction. The S2281 was the first integrated circuit chip specifically designed as a DSP, and fabricat...
Digital signal processor
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The main improvement in the third generation was the appearance of application-specific units and instructions in the data path, or sometimes as coprocessors. These units allowed direct hardware acceleration of very specific but complex mathematical problems, like the Fourier-transform or matrix operations. Some chips,...
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XMOS produces a multi-core multi-threaded line of processor well suited to DSP operations, They come in various speeds ranging from 400 to 1600 MIPS. The processors have a multi-threaded architecture that allows up to 8 real-time threads per core, meaning that a 4 core device would support up to 32 real time threads. T...
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CSR produces the Quatro family of SoCs that contain one or more custom Imaging DSPs optimized for processing document image data for scanner and copier applications. Microchip Technology produces the PIC24 based dsPIC line of DSPs. Introduced in 2004, the dsPIC is designed for applications needing a true DSP as well a...
Digital signal processor
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Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) at the Paris conference of ...
Hilbert's problems
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1. Cantor's problem of the cardinal number of the continuum. 2. The compatibility of the arithmetical axioms. 3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes. 4. Problem of the straight line as the shortest distance between two points. 5. Lie's concept of a continuous group of transf...
Hilbert's problems
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Nature and influence of the problems Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative ans...
Hilbert's problems
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Knowability Following Gottlob Frege and Bertrand Russell, Hilbert sought to define mathematics logically using the method of formal systems, i.e., finitistic proofs from an agreed-upon set of axioms. One of the main goals of Hilbert's program was a finitistic proof of the consistency of the axioms of arithmetic: that i...
Hilbert's problems
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Follow-ups Since 1900, mathematicians and mathematical organizations have announced problem lists but, with few exceptions, these have not had nearly as much influence nor generated as much work as Hilbert's problems. One exception consists of three conjectures made by André Weil in the late 1940s (the Weil conjecture...
Hilbert's problems
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The Riemann hypothesis is noteworthy for its appearance on the list of Hilbert problems, Smale's list, the list of Millennium Prize Problems, and even the Weil conjectures, in its geometric guise. Although it has been attacked by major mathematicians of our day, many experts believe that it will still be part of unsolv...
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In mathematics, a negative number is the opposite of a positive real number. Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the ...
Negative number
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Negative numbers were used in the Nine Chapters on the Mathematical Art, which in its present form dates from the period of the Chinese Han dynasty (202 BC – AD 220), but may well contain much older material. Liu Hui (c. 3rd century) established rules for adding and subtracting negative numbers. By the 7th century, Ind...
Negative number
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Goal difference in association football and hockey; points difference in rugby football; net run rate in cricket; golf scores relative to par. Plus-minus differential in ice hockey: the difference in total goals scored for the team (+) and against the team (−) when a particular player is on the ice is the player's +/−...
Negative number
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Finance Financial statements can include negative balances, indicated either by a minus sign or by enclosing the balance in parentheses. Examples include bank account overdrafts and business losses (negative earnings). The annual percentage growth in a country's GDP might be negative, which is one indicator of being ...
Negative number
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Arithmetic involving negative numbers The minus sign "−" signifies the operator for both the binary (two-operand) operation of subtraction (as in ) and the unary (one-operand) operation of negation (as in , or twice in ). A special case of unary negation occurs when it operates on a positive number, in which case the r...
Negative number
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When multiplying numbers, the magnitude of the product is always just the product of the two magnitudes. The sign of the product is determined by the following rules: The product of one positive number and one negative number is negative. The product of two negative numbers is positive. Thus and The reason behind t...
Negative number
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In a similar manner to rational numbers, we can extend the natural numbers N to the integers Z by defining integers as an ordered pair of natural numbers (a, b). We can extend addition and multiplication to these pairs with the following rules: We define an equivalence relation ~ upon these pairs with the following ru...
Negative number
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Negative numbers appear for the first time in history in the Nine Chapters on the Mathematical Art (九章算術, Jiǔ zhāng suàn-shù), which in its present form dates from the Han period, but may well contain much older material. The mathematician Liu Hui (c. 3rd century) established rules for the addition and subtraction of n...
Negative number
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By the 12th century, al-Karaji's successors were to state the general rules of signs and use them to solve polynomial divisions. As al-Samaw'al writes: the product of a negative number—al-nāqiṣ (loss)—by a positive number—al-zāʾid (gain)—is negative, and by a negative number is positive. If we subtract a negative numbe...
Negative number
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In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as s...
Turbulence
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Smoke rising from a cigarette. For the first few centimeters, the smoke is laminar. The smoke plume becomes turbulent as its Reynolds number increases with increases in flow velocity and characteristic length scale. Flow over a golf ball. (This can be best understood by considering the golf ball to be stationary, with...
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In many geophysical flows (rivers, atmospheric boundary layer), the flow turbulence is dominated by the coherent structures and turbulent events. A turbulent event is a series of turbulent fluctuations that contain more energy than the average flow turbulence. The turbulent events are associated with coherent flow stru...
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In the medical field of cardiology, a stethoscope is used to detect heart sounds and bruits, which are due to turbulent blood flow. In normal individuals, heart sounds are a product of turbulent flow as heart valves close. However, in some conditions turbulent flow can be audible due to other reasons, some of them path...
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Rotationality Turbulent flows have non-zero vorticity and are characterized by a strong three-dimensional vortex generation mechanism known as vortex stretching. In fluid dynamics, they are essentially vortices subjected to stretching associated with a corresponding increase of the component of vorticity in the stretch...
Turbulence
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Via this energy cascade, turbulent flow can be realized as a superposition of a spectrum of flow velocity fluctuations and eddies upon a mean flow. The eddies are loosely defined as coherent patterns of flow velocity, vorticity and pressure. Turbulent flows may be viewed as made of an entire hierarchy of eddies over a ...
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where u′ is the velocity fluctuation, and is the time lag between measurements. Integral length scales Large eddies obtain energy from the mean flow and also from each other. Thus, these are the energy production eddies which contain most of the energy. They have the large flow velocity fluctuation and are low in f...
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Although it is possible to find some particular solutions of the Navier–Stokes equations governing fluid motion, all such solutions are unstable to finite perturbations at large Reynolds numbers. Sensitive dependence on the initial and boundary conditions makes fluid flow irregular both in time and in space so that a s...
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This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems, and is used to determine dynamic similitude between two different cases of fluid flow, such as between a mod...
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