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Gauss's Lemma (Polynomial)
In algebra, Gauss's lemma, named after Carl Friedrich Gauss, is a statement about polynomials over the integers, or, more generally, over a unique factorization domain (that is, a ring that has a unique factorization property similar to the fundamental theorem of arithmetic). Gauss's lemma underlies all the theory of factorization and greatest common divisors of such polynomials. Gauss's lemma asserts that the product of two primitive polynomials is primitive (a polynomial with integer coefficients is primitive if it has 1 as a greatest common divisor of its coefficients). A corollary of Gauss's lemma, sometimes also called Gauss's lemma, is that a primitive polynomial is irreducible over the integers if and only if it is irreducible over the rational numbers. More generally, a primitive polynomial has the same complete factorization over the integers and over the rational numbers. In the case of coefficients in a unique factorization domain R, "rational numbers" must be replaced by "field of fractions of R". This implies that, if R is either a field, the ring of integers, or a unique factorization domain, then every polynomial ring (in one or several indeterminates) over R is a unique factorization domain. Another consequence is that factorization and greatest common divisor computation of polynomials with integers or rational coefficients may be reduced to similar computations on integers and primitive polynomials. This is systematically used (explicitly or implicitly) in all implemented algorithms (see Polynomial greatest common divisor and Factorization of polynomials). Gauss's lemma, and all its consequences that do not involve the existence of a complete factorization remain true over any GCD domain (an integral domain over which greatest common divisors exist). In particular, a polynomial ring over a GCD domain is also a GCD domain. If one calls primitive a polynomial such that the coefficients generate the unit ideal, Gauss's lemma is true over every commutative ring. However, some care must be taken, when using this definition of primitive, as, over a unique factorization domain that is not a principal ideal domain, there are polynomials that are primitive in the above sense and not primitive in this new sense.
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  • 28 Nov 2022
Topic Review
Rudivirus
Rudivirus is a genus of viruses in the order Ligamenvirales; it is the only genus in the family Rudiviridae. These viruses are non-enveloped, stiff-rod-shaped viruses with linear dsDNA genomes, that infect hyperthermophilic archaea of the kingdom Crenarchaeota. There are currently three species in this genus including the type species Sulfolobus islandicus rod-shaped virus 2. The family name derives from the Latin rudis, thin rod, referring to the virion shape.
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  • 28 Nov 2022
Topic Review
Technology Roadmap
A technology roadmap is a flexible planning schedule to support strategic and long-range planning, by matching short-term and long-term goals with specific technology solutions. It is a plan that applies to a new product or process and may include using technology forecasting or technology scouting to identify suitable emerging technologies. It is a known technique to help manage the fuzzy front-end of innovation. It is also expected that roadmapping techniques may help companies to survive in turbulent environments and help them to plan in a more holistic way to include non-financial goals and drive towards a more sustainable development. Here roadmaps can be combined with other corporate foresight methods to facilitate systemic change. Developing a roadmap has three major uses. It helps reach a consensus about a set of needs and the technologies required to satisfy those needs, it provides a mechanism to help forecast technology developments, and it provides a framework to help plan and coordinate technology developments. It may also be used as an analysis tool to map the development and emergence from new industries.
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  • 29 Nov 2022
Topic Review
Wide Field Infrared Survey Telescope
The Wide Field Infrared Survey Telescope (WFIRST) is a NASA infrared space observatory currently under development. WFIRST was recommended in 2010 by United States National Research Council Decadal Survey committee as the top priority for the next decade of astronomy. On February 17, 2016, WFIRST was approved for development and launch. WFIRST is based on an existing 2.4 m wide field-of-view telescope and will carry two scientific instruments. The Wide-Field Instrument is a 288-megapixel multi-band near-infrared camera, providing a sharpness of images comparable to that achieved by the Hubble Space Telescope (HST) over a 0.28 square degree field of view, 100 times larger than that of the HST. The Coronagraphic Instrument is a high-contrast, small field-of-view camera and spectrometer covering visible and near-infrared wavelengths using novel starlight-suppression technology. The design of WFIRST is based on one of the proposed designs for the Joint Dark Energy Mission between NASA and DOE. WFIRST adds some extra capabilities to the original JDEM proposal, including a search for extra-solar planets using gravitational microlensing. In its present incarnation (2015), a large fraction of its primary mission will be focused on probing the expansion history of the Universe and the growth of cosmic structure with multiple methods in overlapping redshift ranges, with the goal of precisely measuring the effects of dark energy, the consistency of general relativity, and the curvature of spacetime. On February 12, 2018, development on the WFIRST mission was proposed to be terminated in the President's FY19 budget request, due to a reduction in the overall NASA astrophysics budget and higher priorities elsewhere in the agency. However, in March 2018 Congress approved funding to continue making progress on WFIRST until at least September 30, 2018, in a bill stating that Congress "rejects the cancellation of scientific priorities recommended by the National Academy of Sciences decadal survey process".[needs update] In testimony before Congress in July 2018, NASA administrator Jim Bridenstine proposed slowing down the development of WFIRST in order to accommodate a cost increase in the James Webb Space Telescope (JWST), which would result in decreased[clarification needed] funding for WFIRST in 2020/2021. In the President's FY2020 budget request, termination of WFIRST was proposed again, due to cost overruns and higher priority for JWST.. The telescope received $511 million for FY2020.
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  • 29 Nov 2022
Topic Review
Parasitic Nutrition
Parasitic nutrition is a mode of heterotrophic nutrition where a parasitic organism lives on the body surface or inside the body of another type of organism (a host) and gets nutrition directly from the body of the host. Since these parasites derive nourishment from their host, this symbiotic interaction is often harmful to the host. Parasites depend on their host for survival, since the host provides nutrition and protection. As a result of this dependence, parasites have considerable modifications to optimise parasitic nutrition and therefore their survival. Parasites are divided into two groups: endoparasites and ectoparasites. Endoparasites are parasites that live inside the body of the host, whereas ectoparasites are parasites that live on the outer surface of the host and generally attach themselves during feeding. Due to the different strategies of endoparasites and ectoparasites, they require different adaptations to derive nutrients from their host. Parasites require nutrients to carry out essential functions including reproduction and growth. Essentially, the nutrients required from the host are carbohydrates, amino acids and lipids. Carbohydrates are utilised to generate energy, whilst amino acids and fatty acids are involved in the synthesis of macromolecules and the production of eggs. Most parasites are heterotrophs, so they therefore are unable to synthesise their own 'food' i.e. organic compounds and must acquire these from their host.
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  • 29 Nov 2022
Topic Review
Qt
Qt (pronounced "cute") is cross-platform software for creating graphical user interfaces as well as cross-platform applications that run on various software and hardware platforms such as Linux, Windows, macOS, Android or embedded systems with little or no change in the underlying codebase while still being a native application with native capabilities and speed. Qt is currently being developed by The Qt Company, a publicly listed company, and the Qt Project under open-source governance, involving individual developers and organizations working to advance Qt. Qt is available under both commercial licenses and open-source GPL 2.0, GPL 3.0, and LGPL 3.0 licenses.
  • 5.3K
  • 28 Nov 2022
Topic Review
Ko Fight
A ko (Japanese: コウ, 劫, kō, from the translation of the Sanskrit term kalpa) fight is a tactical and strategic phase that can arise in the game of go.
  • 1.2K
  • 28 Nov 2022
Topic Review
Hydraulics
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counterpart of pneumatics, which concerns gases. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the applied engineering using the properties of fluids. In its fluid power applications, hydraulics is used for the generation, control, and transmission of power by the use of pressurized liquids. Hydraulic topics range through some parts of science and most of engineering modules, and cover concepts such as pipe flow, dam design, fluidics and fluid control circuitry. The principles of hydraulics are in use naturally in the human body within the vascular system and erectile tissue. Free surface hydraulics is the branch of hydraulics dealing with free surface flow, such as occurring in rivers, canals, lakes, estuaries and seas. Its sub-field open-channel flow studies the flow in open channels. The word "hydraulics" originates from the Greek word ὑδραυλικός (hydraulikos) which in turn originates from ὕδωρ (hydor, Greek for water) and αὐλός (aulos, meaning pipe).
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  • 28 Nov 2022
Topic Review
Bidirectional Text
Bidirectional text is the text containing both text directionalities, both right-to-left (RTL or dextrosinistral) and left-to-right (LTR or sinistrodextral). It generally involves text containing different types of alphabets, but may also refer to boustrophedon, which is changing text directionality in each row. Some writing systems including the Arabic and Hebrew scripts or derived systems such as the Persian, Urdu, and Yiddish scripts, are written in a form known as right-to-left (RTL), in which writing begins at the right-hand side of a page and concludes at the left-hand side. This is different from the left-to-right (LTR) direction used by the dominant Latin script. When LTR text is mixed with RTL in the same paragraph, each type of text is written in its own direction, which is known as bidirectional text. This can get rather complex when multiple levels of quotation are used. Many computer programs fail to display bidirectional text correctly. For example, the Hebrew name Sarah (שרה) is spelled: sin (ש) (which appears rightmost), then resh (ר), and finally heh (ה) (which should appear leftmost). Note: Some web browsers may display the Hebrew text in this article in the opposite direction.
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  • 28 Nov 2022
Topic Review
Outline of Green Politics
The following outline is provided as an overview and topical guide to green politics, a political ideology that aims for the creation of an ecologically sustainable society rooted in environmentalism, social liberalism, and grassroots democracy. It began taking shape in the western world in the 1970s; since then Green parties have developed and established themselves in many countries across the globe, and have achieved some electoral success.
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  • 28 Nov 2022
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