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Earth heat transport occurs by conduction, mantle convection, hydrothermal convection, and volcanic advection. Earth's internal heat flow to the surface is thought to be 80% due to mantle convection, with the remaining heat mostly originating in the Earth's crust, with about 1% due to volcanic activity, earthquakes, an...
Earth's internal heat budget
Wikipedia
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https://en.wikipedia.org/wiki/Earth%27s%20internal%20heat%20budget
Physical sciences
Geophysics
Earth science
Geoneutrino detectors can detect the decay of 238U and 232Th and thus allow estimation of their contribution to the present radiogenic heat budget, while 235U and 40K are not thus detectable. Regardless, 40K is estimated to contribute 4 TW of heating. However, due to the short half-lives the decay of 235U and 40K cont...
Earth's internal heat budget
Wikipedia
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https://en.wikipedia.org/wiki/Earth%27s%20internal%20heat%20budget
Physical sciences
Geophysics
Earth science
Controversy over the exact nature of mantle convection makes the linked evolution of Earth's heat budget and the dynamics and structure of the mantle difficult to unravel. There is evidence that the processes of plate tectonics were not active in the Earth before 3.2 billion years ago, and that early Earth's internal h...
Earth's internal heat budget
Wikipedia
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https://en.wikipedia.org/wiki/Earth%27s%20internal%20heat%20budget
Physical sciences
Geophysics
Earth science
A genetically modified tree (GMt, GM tree, genetically engineered tree, GE tree or transgenic tree) is a tree whose DNA has been modified using genetic engineering techniques. In most cases the aim is to introduce a novel trait to the plant which does not occur naturally within the species. Examples include resistance...
Genetically modified tree
Wikipedia
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https://en.wikipedia.org/wiki/Genetically%20modified%20tree
Technology
Horticulture
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Proposed uses GM trees under experimental development have been modified with traits intended to provide benefit to industry, foresters or consumers. Due to high regulatory and research costs, the majority of genetically modified trees in silviculture consist of plantation trees, such as eucalyptus, poplar, and pine. ...
Genetically modified tree
Wikipedia
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https://en.wikipedia.org/wiki/Genetically%20modified%20tree
Technology
Horticulture
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Reduced vigour Orchard trees require a rootstock with reduced vigour to allow them to remain small. Genetic modification could allow the elimination of the rootstock, by making the tree less vigorous, hence reducing its height when fully mature. Research is being done into which genes are responsible for the vigour in...
Genetically modified tree
Wikipedia
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https://en.wikipedia.org/wiki/Genetically%20modified%20tree
Technology
Horticulture
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Poplars in China In 2002 China's State Forestry Administration approved GM poplar trees for commercial use. Subsequently, 1.4 million Bt (insecticide) producing GM poplars were planted in China. They were planted both for their wood and as part of China's 'Green Wall' project, which aims to impede desertification. Rep...
Genetically modified tree
Wikipedia
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https://en.wikipedia.org/wiki/Genetically%20modified%20tree
Technology
Horticulture
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Cherax pulcher is a species of crayfish from West Papua in Indonesia. It is popular as a freshwater aquarium species across Asia, Europe, and North America. Etymology The specific name is derived from the Latin word pulcher, which means "beautiful". The name was chosen due to the species' bright coloration. Discove...
Cherax pulcher
Wikipedia
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47100486
https://en.wikipedia.org/wiki/Cherax%20pulcher
Biology and health sciences
Crayfishes and lobsters
Animals
Kepler-186f (also known by its Kepler object of interest designation KOI-571.05) is an Earth-sized exoplanet orbiting within the habitable zone of the red dwarf star Kepler-186, the outermost of five such planets discovered around the star by NASA's Kepler space telescope. It is located about from Earth in the constel...
Kepler-186f
Wikipedia
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https://en.wikipedia.org/wiki/Kepler-186f
Physical sciences
Notable exoplanets
Astronomy
A very wide range of possible masses can be calculated by combining the radius with densities derived from the possible types of matter from which planets can be made. For example, it could be a rocky terrestrial planet or a lower density ocean planet with a thick atmosphere. A massive hydrogen/helium (H/He) atmosphere...
Kepler-186f
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https://en.wikipedia.org/wiki/Kepler-186f
Physical sciences
Notable exoplanets
Astronomy
Orbit Kepler-186f orbits its star with about 5% of the Sun's luminosity with an orbital period of 129.9 days and an orbital radius of about 0.40 times that of Earth's (compared to for Mercury). The habitable zone for this system is estimated conservatively to extend over distances receiving from 88% to 25% of Earth's...
Kepler-186f
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https://en.wikipedia.org/wiki/Kepler-186f
Physical sciences
Notable exoplanets
Astronomy
Kepler-186f's axial tilt (obliquity) is likely very small, in which case it would not have tilt-induced seasons like Earth's. Its orbit is probably close to circular, so it will also lack eccentricity-induced seasonal changes like those of Mars. However, the axial tilt could be larger (about 23 degrees) if another und...
Kepler-186f
Wikipedia
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https://en.wikipedia.org/wiki/Kepler-186f
Physical sciences
Notable exoplanets
Astronomy
Future technology and observations At approximately distant, Kepler-186f is too far and its star too faint for current telescopes or the next generation of planned telescopes to determine its mass or whether it has an atmosphere. However, the discovery of Kepler-186f demonstrates conclusively that there are other Ear...
Kepler-186f
Wikipedia
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https://en.wikipedia.org/wiki/Kepler-186f
Physical sciences
Notable exoplanets
Astronomy
In popular culture Along with five other exoplanets, Kepler-186f was included in Civilization: Beyond Earths exoplanet DLC as a playable map. Dutch rock band named their 2017 album Kepler-186f after this exoplanet. Kepler-186f is the location of a future earth colony in the short story "Stars" by Drew Hayden Taylor...
Kepler-186f
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Physical sciences
Notable exoplanets
Astronomy
The subphylum Hexapoda (from Greek for 'six legs') or hexapods comprises the largest clade of arthropods and includes most of the extant arthropod species. It includes the crown group class Insecta (true insects), as well as the much smaller clade Entognatha, which includes three classes of wingless arthropods that wer...
Hexapoda
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https://en.wikipedia.org/wiki/Hexapoda
Biology and health sciences
Insects and other hexapods
null
Collembola and Diplura have segmented antenna: each segment has its own set of muscles. The antennae of insects consist of just three segments: the scape, the pedicel and the flagellum. Muscles occur only in the first two segments. The third segment, the flagellum, has no muscles and is composed of a various number of ...
Hexapoda
Wikipedia
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https://en.wikipedia.org/wiki/Hexapoda
Biology and health sciences
Insects and other hexapods
null
The non-insect hexapods have variously been considered a single evolutionary line, typically treated as Class Entognatha, or as several lines with different relationships with the Class Insecta. In particular, the Diplura may be more closely related to the Insecta than to the Collembola (springtails). A 2002 molecular...
Hexapoda
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https://en.wikipedia.org/wiki/Hexapoda
Biology and health sciences
Insects and other hexapods
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A sednoid is a trans-Neptunian object with a large semi-major axis and a high perihelion, similar to the orbit of the dwarf planet Sedna. The consensus among astronomers is that there are only three objects that are known from this population: Sedna, , and 541132 Leleākūhonua (). All three have perihelia greater than ....
Sednoid
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https://en.wikipedia.org/wiki/Sednoid
Physical sciences
Solar System
Astronomy
These objects could have had their orbits and perihelion distances "lifted" by the passage of a nearby star when the Sun was still embedded in its birth star cluster. They could have been captured from around passing stars, most likely in the Sun's birth cluster. Their orbits could have been disrupted by an as-yet-un...
Sednoid
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https://en.wikipedia.org/wiki/Sednoid
Physical sciences
Solar System
Astronomy
In late 2015, V774104 was announced at the Division for Planetary Science conference as a further candidate sednoid, but its observation arc was too short to know whether its perihelion was even outside Neptune's influence. The talk about V774104 was probably meant to refer to Leleākūhonua () even though V774104 is the...
Sednoid
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https://en.wikipedia.org/wiki/Sednoid
Physical sciences
Solar System
Astronomy
Acquiring a larger sample of such objects would therefore help in determining which scenario is most likely. "I call Sedna a fossil record of the earliest Solar System", said Brown in 2006. "Eventually, when other fossil records are found, Sedna will help tell us how the Sun formed and the number of stars that were clo...
Sednoid
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Physical sciences
Solar System
Astronomy
Macrotermes bellicosus is a species of Macrotermes. The queens are the largest amongst known termites, measuring about long when physogastric. The workers average in length and soldiers are slightly larger. means "combative" in Latin. The species is a member of a genus indigenous to Africa and South-East Asia. Beha...
Macrotermes bellicosus
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https://en.wikipedia.org/wiki/Macrotermes%20bellicosus
Biology and health sciences
Cockroaches & Termites (Blattodea)
Animals
The division of labor between minor and major workers also causes there to be a difference in the pheromone trails that each type of caste will leave. Trails that are left by minor workers, which can contain information about the presence of food based on the existence of certain pheromones, will attract both types of ...
Macrotermes bellicosus
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https://en.wikipedia.org/wiki/Macrotermes%20bellicosus
Biology and health sciences
Cockroaches & Termites (Blattodea)
Animals
Pressures from predation play a role in the foraging behavior of M. bellicosus, which will vary between the two types of environments. This was measured by observing when the termites will stop foraging in an area while varying the pressure from predators. In the savanna, there was gradual increase in the amount of unu...
Macrotermes bellicosus
Wikipedia
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https://en.wikipedia.org/wiki/Macrotermes%20bellicosus
Biology and health sciences
Cockroaches & Termites (Blattodea)
Animals
Old World quail is a collective name for several genera of mid-sized birds in the tribe Coturnicini of the pheasant family Phasianidae. Although all species commonly referred to as "Old World quail" are in the same tribe, they are paraphyletic with respect to the other members of the tribe, such as Alectoris, Tetraogal...
Old World quail
Wikipedia
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https://en.wikipedia.org/wiki/Old%20World%20quail
Biology and health sciences
Galliformes
Animals
Behaviour Old World quail are small, plump terrestrial birds. They are seed eaters, but will also take insects and similar small prey. They nest on the ground and are capable of short, rapid bursts of flight. Some species, such as the Japanese and common quail, are migratory and fly for long distances. Some quail are...
Old World quail
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https://en.wikipedia.org/wiki/Old%20World%20quail
Biology and health sciences
Galliformes
Animals
Connecticut field pumpkins are a type of pumpkin (Cucurbita pepo) first attested in the 16th century. They are one of the oldest varieties of pumpkin in existence and are known as an heirloom plant. One of the most popular Halloween pumpkins, Connecticut field pumpkins are commonly used for autumn decorations and jack-...
Connecticut field pumpkin
Wikipedia
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https://en.wikipedia.org/wiki/Connecticut%20field%20pumpkin
Biology and health sciences
Botanical fruits used as culinary vegetables
Plants
Characteristics The pumpkins have many shapes and sizes but they are commonly round. The Connecticut field pumpkin is to in size and it is round, and orange, with smooth, slightly ribbed skin. The Howden pumpkin was developed by John Howden and it is a strain selected from Connecticut field pumpkins for improved pro...
Connecticut field pumpkin
Wikipedia
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https://en.wikipedia.org/wiki/Connecticut%20field%20pumpkin
Biology and health sciences
Botanical fruits used as culinary vegetables
Plants
The variety is also used by ranchers as feed for livestock. The pulp is rich in carotenoids and the seeds are a source of fatty acid. The flowers and the pulp are both edible. Because of its many uses, the variety is a common choice for home gardeners. Economic importance In the United States, all fifty states produce...
Connecticut field pumpkin
Wikipedia
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https://en.wikipedia.org/wiki/Connecticut%20field%20pumpkin
Biology and health sciences
Botanical fruits used as culinary vegetables
Plants
North American donkeys constitute approximately 0.1% of the worldwide donkey population. Donkeys were first transported from Europe to the New World in the fifteenth century during the Second Voyage of Christopher Columbus, and subsequently spread south and west into the lands that would become México. They first reach...
North American donkeys
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https://en.wikipedia.org/wiki/North%20American%20donkeys
Biology and health sciences
Donkeys
Animals
The first presence of donkeys in what is today the U.S. is, sometimes, reported to date from 1679, when a Jesuit priest named Eusebio Kino transported several from Sonora, northern Mexico, to a new mission at San Xavier del Bac, in what is now Arizona; however, Kino did not arrive in the Americas prior to ca. 1681, lik...
North American donkeys
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https://en.wikipedia.org/wiki/North%20American%20donkeys
Biology and health sciences
Donkeys
Animals
In the twentieth century, donkeys came to be more frequently kept as farm animals, pets or as livestock guardian animals in the U.S., among other nations. In 1929, Robert Green of New York imported seven donkeys belonging to the smaller, indigenous Sardinian breed to the U.S.; the first foal was born that same year. Al...
North American donkeys
Wikipedia
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https://en.wikipedia.org/wiki/North%20American%20donkeys
Biology and health sciences
Donkeys
Animals
Windows 10 is a major release of Microsoft's Windows NT operating system. The successor to Windows 8.1, it was released to manufacturing on July 15, 2015, and later to retail on July 29, 2015. Windows 10 was made available for download via MSDN and TechNet, as a free upgrade for retail copies of Windows 8 and Windows 8...
Windows 10
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Technology
Operating Systems
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Development At the Microsoft Worldwide Partner Conference in 2011, Andrew Lees, the chief of Microsoft's mobile technologies, said that the company intended to have a single software ecosystem for PCs, smartphones, tablets, and other devices: "We won't have an ecosystem for PCs, and one for phones, and one for tablets...
Windows 10
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On September 30, 2014, Microsoft officially announced that Threshold would be unveiled during a media event as Windows 10. Myerson said that Windows 10 would be Microsoft's "most comprehensive platform ever", providing a single, unified platform for desktop and laptop computers, tablets, smartphones, and all-in-one dev...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Operating Systems
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Additional developer-oriented details surrounding the "Universal Windows Platform" concept were revealed and discussed during Microsoft's Build developers' conference. Among them were the unveiling of "Islandwood", which provides a middleware toolchain for compiling Objective-C-based software (particularly iOS) to run ...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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The general availability build of Windows10, numbered 10240, was first released to Windows Insider channels for pre-launch testing on July 15, 2015, prior to its formal release. Although a Microsoft official said there would be no specific RTM build of Windows 10, 10240 was described as an RTM build by media outlets be...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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During its first year of availability, upgrade licenses for Windows10 could be obtained at no charge for devices with a genuine license for an eligible edition of Windows7 or8.1. This offer did not apply to Enterprise editions, as customers under an active Software Assurance (SA)contract with upgrade rights are entitl...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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The Windows Insider Preview version of Windows10 automatically updated itself to the generally released version as part of the version progression and continues to be updated to new beta builds, as it had throughout the testing process. Microsoft explicitly stated that Windows Insider was not a valid upgrade path for t...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
Technology
Operating Systems
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Licensing During upgrades, Windows10 licenses are not tied directly to a product key. Instead, the license status of the system's current installation of Windows is migrated, and a "Digital license" (known as "Digital entitlement" in version 1511 or earlier) is generated during the activation process, which is bound t...
Windows 10
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The Windows Runtime app ecosystem was revised into the Universal Windows Platform (UWP). These universal apps are made to run across multiple platforms and device classes, including smartphones, tablets, Xbox One consoles, and other devices compatible with Windows 10. Windows apps share code across platforms, have resp...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Charms have been removed; their functionality in universal apps is accessed from an App commands menu on their title bar. In its place is Action Center, which displays notifications and settings toggles. It is accessed by clicking an icon in the notification area, or dragging from the right of the screen. Notifications...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Operating Systems
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In addition to biometric authentication, Windows Hello supports authentication with a PIN. By default, Windows requires a PIN to consist of four digits, but can be configured to permit more complex PINs. However, a PIN is not a simpler password. While passwords are transmitted to domain controllers, PINs are not. They ...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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The Anniversary Update added Windows Subsystem for Linux (WSL), which allows the installation of a user space environment from a supported Linux distribution that runs natively on Windows. The subsystem translates Linux system calls to those of the Windows NT kernel (only claims full system call compatibility as of WSL...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Online services and functionality Windows 10 introduces Microsoft Edge, a new default web browser. It initially featured a new standards-compliant rendering engine derived from Trident, and also includes annotation tools and integration with other Microsoft platforms present within Windows 10. Internet Explorer 11 is ...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Windows 10 also offers the Wi-Fi Sense feature originating from Windows Phone 8.1; users can optionally have their device automatically connect to suggested open hotspots, and share their home network's password with contacts (either via Skype, People, or Facebook) so they may automatically connect to the network on a ...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Windows 10 adds FLAC and HEVC codecs and support for the Matroska media container, allowing these formats to be opened in Windows Media Player and other applications. Windows Media Center is no longer bundled. Windows 10 includes DirectX 12, alongside WDDM 2.0. Unveiled March 2014 at GDC, DirectX 12 aims to provide "c...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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On May 2, 2017, Microsoft unveiled Windows 10 S (referred to in leaks as Windows 10 Cloud), a feature-limited edition of Windows 10 which was designed primarily for devices in the education market (competing, in particular, with ChromeOS netbooks), such as the Surface Laptop that Microsoft also unveiled at this time. T...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Hardware exceptions Microsoft's support lifecycle policy for the operating system notes that updates "are cumulative, with each update built upon all of the updates that preceded it", that "a device needs to install the latest update to remain supported", and that a device's ability to receive future updates will depe...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Operating Systems
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Unlike previous versions of Windows, Windows Update does not allow the selective installation of updates, and all updates (including patches, feature updates, and driver software) are downloaded and installed automatically. Users can only choose whether their system will reboot automatically to install updates when the...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Feature updates Windows 10 is often described by Microsoft as being a "service", as it receives regular "feature updates" that contain new features and other updates and fixes. In April 2017, Microsoft stated that these updates would be released twice a year every March and September in the future, which eventually co...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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Enterprise licensees may use the Windows 10 Enterprise LTSC (formerly LTSB) edition, where "LTSC" stands for "Long-Term Servicing Channel", which only receive quality of life updates (i.e. security patches), and has a full 5 or 10-year support lifecycle for each build. This edition is designed for "special-purpose devi...
Windows 10
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In February 2019, Microsoft announced changes again in delivering updates beginning with release of version 1903: a single SAC will be released, SAC-T will be retired, and users are no longer able to switch to different channels. Instead, these updates can be deferred from 30 to 90 days, or depending on how the device ...
Windows 10
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https://en.wikipedia.org/wiki/Windows%2010
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On December 7, 2016, Microsoft announced that, as part of a partnership with Qualcomm, it planned to introduce support for running Win32 software on ARM architecture with a 32-bit x86 processor emulator, in 2017. Terry Myerson stated that this move would enable the production of Qualcomm Snapdragon-based Windows device...
Windows 10
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Some pre-built devices may be described as "certified" by Microsoft. Certified tablets must include , , and keys; and keys are no longer required. As with Windows 8, all certified devices must ship with UEFI Secure Boot enabled by default. Unlike Windows 8, OEMs are no longer required to make Secure Boot settings u...
Windows 10
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Physical memory limits The maximum amount of RAM that Windows 10 can support varies depending on the product edition and the processor architecture. All 32-bit editions of Windows 10, including Home and Pro, support up to 4 GB. 64-bit editions of Windows 10 Education and Pro support up to 2 TB, 64-bit editions of Wind...
Windows 10
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Engadget was similarly positive, noting that the upgrade process was painless and that Windows10's user interface had balanced aspects of Windows8 with those of previous versions with a more mature aesthetic. Cortana's always-on voice detection was considered to be its "true strength", also citing its query capabilitie...
Windows 10
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ExtremeTech felt that Windows10 restricted the choices of users, citing its more opaque setting menus, forcing users to give up bandwidth for the peer-to-peer distribution of updates, and for taking away user control of specific functions, such as updates, explaining that "it feels, once again, as if Microsoft has take...
Windows 10
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According to StatCounter, Windows 10 overtook Windows 8.1 in December 2015. Iceland was the first country where Windows 10 was ranked first (not only on the desktop, but across all platforms), with several larger European countries following. For one week in late November 2016, Windows 10 overtook first rank from Windo...
Windows 10
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Criticism was also directed towards Microsoft's decision to no longer provide specific details on the contents of cumulative updates for Windows 10. On February 9, 2016, Microsoft retracted this decision and began to provide release notes for cumulative updates on the Windows website. Some users reported that during t...
Windows 10
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Critics have acknowledged that Microsoft's update and testing practices had been affecting the overall quality of Windows 10. In particular, it was pointed out that Microsoft's internal testing departments had been prominently affected by a major round of layoffs undertaken by the company in 2014. Microsoft relies prim...
Windows 10
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In October 2015, Windows 10 began to appear as an "Optional" update on the Windows Update interface, but pre-selected for installation on some systems. A Microsoft spokesperson said that this was a mistake, and that the download would no longer be pre-selected by default. However, on October 29, 2015, Microsoft announc...
Windows 10
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In March 2019, Microsoft announced that it would display notifications informing users on Windows 7 devices of the upcoming end of extended support for the platform, and direct users to a website urging them to upgrade to Windows 10 or purchase new hardware. This dialog will be similar to the previous Windows 10 upgrad...
Windows 10
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Rock Paper Shotgun writer Alec Meer argued that Microsoft's intent for this data collection lacked transparency, stating that "there is no world in which 45pages of policy documents and opt-out settings split across 13different settings screens and an external website constitutes 'real transparency'." Joel Hruska of Ex...
Windows 10
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The Microsoft Services agreement reads that the company's online services may automatically "download software updates or configuration changes, including those that prevent you from accessing the Services, playing counterfeit games, or using unauthorized hardware peripheral devices." Critics interpreted this statement...
Windows 10
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WISE 0855−0714 (full designation WISE J085510.83−071442.5, or W0855 for short) is a sub-brown dwarf of spectral class Y4, located from the Sun in the constellation Hydra. It is the fourth-closest star or (sub-) brown dwarf system to the Sun and was discovered by Kevin Luhman in 2013 using data from the Wide-field Infr...
WISE 0855−0714
Wikipedia
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42551986
https://en.wikipedia.org/wiki/WISE%200855%E2%88%920714
Physical sciences
Notable stars
Astronomy
Distance and proper motion Based on direct observations, WISE 0855−0714 has a large parallax of , which corresponds to a distance of around (). This makes WISE 0855−0714 the fourth-closest star or (sub-) brown dwarf system to the Sun. WISE 0855−0714 also has an exceptionally high proper motion of , the third-highest ...
WISE 0855−0714
Wikipedia
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https://en.wikipedia.org/wiki/WISE%200855%E2%88%920714
Physical sciences
Notable stars
Astronomy
Observations with NIRSpec detected methane (CH4), water vapor (H2O), ammonia (NH3) and carbon monoxide (CO) in the atmosphere, but was not able to confirm any phosphine (PH3) or carbon dioxide (CO2) in the atmosphere. Water ice clouds are also not confirmed and the spectrum is well matched with a cloudless model. Obser...
WISE 0855−0714
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Variability Variability of WISE 0855 in the infrared was measured with Spitzer IRAC. A relative small amplitude of 4–5% was measured. Water ice cloud models predicted a large amplitude. This small amplitude might suggest that the hemispheres of WISE 0855 have very small deviation in cloud coverage. The light curve is ...
WISE 0855−0714
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https://en.wikipedia.org/wiki/WISE%200855%E2%88%920714
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In probability theory, an outcome is a possible result of an experiment or trial. Each possible outcome of a particular experiment is unique, and different outcomes are mutually exclusive (only one outcome will occur on each trial of the experiment). All of the possible outcomes of an experiment form the elements of a ...
Outcome (probability)
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https://en.wikipedia.org/wiki/Outcome%20%28probability%29
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Some "mixed" distributions contain both stretches of continuous outcomes and some discrete outcomes; the discrete outcomes in such distributions can be called atoms and can have non-zero probabilities. Under the measure-theoretic definition of a probability space, the probability of an outcome need not even be defined...
Outcome (probability)
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In mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" variables take real value...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
Mathematics
Functions: General
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where and are real non-zero constants. Using the three-dimensional Cartesian coordinate system, where the xy plane is the domain and the z axis is the codomain , one can visualize the image to be a two-dimensional plane, with a slope of in the positive x direction and a slope of in the positive y direction. The fu...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
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Functions: General
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Moreover, many functions are defined in such a way that it is difficult to specify explicitly their domain. For example, given a function , it may be difficult to specify the domain of the function If is a multivariate polynomial, (which has as a domain), it is even difficult to test whether the domain of is also ....
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
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Functions: General
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Continuity and limit Until the second part of 19th century, only continuous functions were considered by mathematicians. At that time, the notion of continuity was elaborated for the functions of one or several real variables a rather long time before the formal definition of a topological space and a continuous map be...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
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Functions: General
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is symmetric in since interchanging any pair of leaves unchanged, but is not symmetric in all of , since interchanging with or or gives a different function. Function composition Suppose the functions or more compactly , are all defined on a domain . As the -tuple varies in , a subset of , the -tuple varies...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
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Functions: General
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This leads to a variety of possible stationary points: global or local maxima, global or local minima, and saddle points—the multidimensional analogue of inflection points for real functions of one real variable. The Hessian matrix is a matrix of all the second order partial derivatives, which are used to investigate t...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
Mathematics
Functions: General
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in which is an infinitesimal change in in the hypersurface , and since the dot product of and is zero, this means is perpendicular to . In arbitrary curvilinear coordinate systems in dimensions, the explicit expression for the gradient would not be so simple - there would be scale factors in terms of the metric ...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
Mathematics
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While bounded hypervolume is a useful insight, the more important idea of definite integrals is that they represent total quantities within space. This has significance in applied mathematics and physics: if is some scalar density field and are the position vector coordinates, i.e. some scalar quantity per unit n-dim...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
Mathematics
Functions: General
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Choosing a 3-dimensional (3D) Cartesian coordinate system, this function describes the surface of a 3D ellipsoid centered at the origin with constant semi-major axes , along the positive x, y and z axes respectively. In the case , we have a sphere of radius centered at the origin. Other conic section examples which c...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
Mathematics
Functions: General
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Examples in continuum mechanics include the local mass density of a mass distribution, a scalar field which depends on the spatial position coordinates (here Cartesian to exemplify), , and time : Similarly for electric charge density for electrically charged objects, and numerous other scalar potential fields. Anoth...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
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Functions: General
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The spherical harmonics occur in physics and engineering as the solution to Laplace's equation, as well as the eigenfunctions of the z-component angular momentum operator, which are complex-valued functions of real-valued spherical polar angles: In quantum mechanics, the wavefunction is necessarily complex-valued, but...
Function of several real variables
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https://en.wikipedia.org/wiki/Function%20of%20several%20real%20variables
Mathematics
Functions: General
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The Carolina Reaper chili pepper is a cultivar of the Capsicum chinense plant. Developed by American breeder Ed Currie, the pepper is red and gnarled, with a bumpy texture and small pointed tail. It was the hottest chili pepper in the world according to Guinness World Records from 2013 to 2023 before it was surpassed b...
Carolina Reaper
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https://en.wikipedia.org/wiki/Carolina%20Reaper
Biology and health sciences
Botanical fruits used as culinary vegetables
Plants
Cultivation For growing, the pepper has been described as "a good all-rounder to try at home" by James Wong, an English ethnobotanist, who stated that they require growing temperatures of at least . He suggested growing the plants in pots to restrict growth and produce fruit sooner. When fully ripe, two peppers occup...
Carolina Reaper
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https://en.wikipedia.org/wiki/Carolina%20Reaper
Biology and health sciences
Botanical fruits used as culinary vegetables
Plants
Oumuamua is the first interstellar object detected passing through the Solar System. Formally designated 1I/2017 U1, it was discovered by Robert Weryk using the Pan-STARRS telescope at Haleakalā Observatory, Hawaii, on 19 October 2017, approximately 40 days after it passed its closest point to the Sun on 9 September. W...
ʻOumuamua
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Astronomy
Oumuamua is remarkable for its extrasolar origin, high obliqueness, and observed acceleration without an apparent coma. By July 2019, most astronomers concluded that it was a natural object, but its precise characterization is contentious given the limited time window for observation. While an unconsolidated object (ru...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
The name comes (), and reflects the way the object is like a scout or messenger sent from the distant past to reach out to humanity. It roughly translates to 'first distant messenger'. The first character (not a diacritic) is a Hawaiian okina, not an apostrophe, and is pronounced as a glottal stop; the Pan-STARRS team...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
Physical sciences
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Oumuamua appears to have come from roughly the direction of Vega in the constellation Lyra. Its incoming direction of motion is 6° from the solar apex (the direction of the Sun's movement relative to local stars), the most likely direction from which objects from outside the Solar System would come. On 26 October, two ...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
On the outward leg of its journey through the Solar System, Oumuamua passed beyond the orbit of Earth on 14 October with a closest approach distance of approximately from Earth. On 16 October it moved back north of the ecliptic plane and passed beyond the orbit of Mars on 1 November. It passed beyond Jupiter's orbit i...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
Indications of origin Accounting for Vega's proper motion, it would have taken Oumuamua 600,000 years to reach the Solar System from Vega. But as a nearby star, Vega was not in the same part of the sky at that time. Astronomers calculate that 100 years ago the object was from the Sun and traveling at 26.33 km/s with ...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
It is unknown how long the object has been traveling among the stars. The Solar System is likely the first planetary system Oumuamua has closely encountered since being ejected from its birth star system, potentially several billion years ago. It has been speculated that the object may have been ejected from a stellar ...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
In May 2020, it was proposed that the object was the first observed member of a class of small H2-ice-rich bodies that form at temperatures near 3 K in the cores of giant molecular clouds. The non-gravitational acceleration and high aspect ratio shape of Oumuamua might be explainable on this basis. However, it was late...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
Appearance, shape and composition Spectra from the Hale Telescope on 25 October showed red color resembling comet nuclei or Trojans. Higher signal to noise spectra recorded by the William Herschel Telescope later that day showed that the object was featureless, and colored red like Kuiper belt objects. Spectra obtain...
ʻOumuamua
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Astronomy
The large variations on the light curves indicate that Oumuamua may be anything from a highly elongated cigar-like object, comparable to or greater than the most elongated Solar System objects, to an extremely flat object, a pancake or oblate spheroid. However, the size and shape have not been directly observed as Oumu...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
Light curve observations suggest however that the object may be composed of dense metal-rich rock that has been reddened by millions of years of exposure to cosmic rays. It is thought that its surface contains tholins, which are irradiated organic compounds that are more common in objects in the outer Solar System and ...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Astronomy
Hydrogen ice theory It has been proposed that ʻOumuamua contains a significant amount of hydrogen ice. This would point to it originating from the core of an interstellar molecular cloud, where conditions for the formation of this material might exist. The Sun's heat would cause the hydrogen to sublime, which would in ...
ʻOumuamua
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https://en.wikipedia.org/wiki/%CA%BBOumuamua
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Other notable objects
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More advanced options of using solar, laser electric, and laser sail propulsion, based on Breakthrough Starshot technology, have also been considered. The challenge is to get to the interstellar object in a reasonable amount of time (and so at a reasonable distance from Earth), and yet be able to gain useful scientific...
ʻOumuamua
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In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differ...
Ordinary differential equation
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https://en.wikipedia.org/wiki/Ordinary%20differential%20equation
Mathematics
Calculus and analysis
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Many mathematicians have studied differential equations and contributed to the field, including Newton, Leibniz, the Bernoulli family, Riccati, Clairaut, d'Alembert, and Euler. A simple example is Newton's second law of motion—the relationship between the displacement and the time of an object under the force , is ...
Ordinary differential equation
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https://en.wikipedia.org/wiki/Ordinary%20differential%20equation
Mathematics
Calculus and analysis
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For a system of the form , some sources also require that the Jacobian matrix be non-singular in order to call this an implicit ODE [system]; an implicit ODE system satisfying this Jacobian non-singularity condition can be transformed into an explicit ODE system. In the same sources, implicit ODE systems with a singul...
Ordinary differential equation
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https://en.wikipedia.org/wiki/Ordinary%20differential%20equation
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