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91,900 | The X-Files (episode:Duane Barry, relevant to the overreaching mytharc of the series. ): FBI Agent Dana Scully discovers an implant set under the skin at the back of her neck which can read her every thought and change memory through electrical signals that alter the brain chemistry. Star Trek franchise: Members of the... | Neural implants | 0.780361 |
91,901 | Postmortem enzyme analysis on liver and muscle samples revealed decreased 2,4-dienoyl-CoA reductase activity when compared to normal controls. A second case with failure to thrive, developmental delay, lactic acidosis and severe encephalopathy was reported in 2014.2,4-Dienoyl-CoA reductase deficiency was included as a ... | 2,4 Dienoyl-CoA reductase deficiency | 0.780361 |
91,902 | Myers' research concerns quantum fields and strings, and quantum gravity. His work focuses on foundational questions in quantum theory and gravity. His contributions span a broad range, from foundational quantum field theory to gravitational physics, black holes, and cosmology. Myers won the 2005 CAP-CRM Prize in Theor... | Robert Myers (physicist) | 0.78036 |
91,903 | Myers is Director of the Perimeter Institute for Theoretical Physics. where he holds the BMO Financial Group Isaac Newton Chair in Theoretical Physics. He served as Perimeter Institute's Faculty Chair from 2011 to 2018. He is also an Adjunct Professor of physics at the University of Waterloo. | Robert Myers (physicist) | 0.78036 |
91,904 | Let therefore M be a n-dimensional connected differentiable manifold, and x be any point on it. Let Diff(M) be the orientation-preserving diffeomorphism group of M (only the identity component of mappings homotopic to the identity diffeomorphism if you wish) and Diffx1(M) the stabilizer of x. Then, M is identified as a... | Representation theory of diffeomorphism groups | 0.780358 |
91,905 | Additional properties of allegories can be axiomatized. Distributive allegories have a union-like operation that is suitably well-behaved, and division allegories have a generalization of the division operation of relation algebra. Power allegories are distributive division allegories with additional powerset-like stru... | Allegory (mathematics) | 0.780358 |
91,906 | In the mathematical field of category theory, an allegory is a category that has some of the structure of the category Rel of sets and binary relations between them. Allegories can be used as an abstraction of categories of relations, and in this sense the theory of allegories is a generalization of relation algebra to... | Allegory (mathematics) | 0.780358 |
91,907 | One use of prime ideals occurs in algebraic geometry, where varieties are defined as the zero sets of ideals in polynomial rings. It turns out that the irreducible varieties correspond to prime ideals. In the modern abstract approach, one starts with an arbitrary commutative ring and turns the set of its prime ideals, ... | Prime ideals | 0.780358 |
91,908 | In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal. Primitive ideals are prime, and prime ideals are both prim... | Prime ideals | 0.780357 |
91,909 | In the case {S} = {1}, we have Krull's theorem, and this recovers the maximal ideals of R. Another prototypical m-system is the set, {x, x2, x3, x4, ...}, of all positive powers of a non-nilpotent element. The preimage of a prime ideal under a ring homomorphism is a prime ideal. The analogous fact is not always true fo... | Prime ideals | 0.780357 |
91,910 | Every nonzero ring contains at least one prime ideal (in fact it contains at least one maximal ideal), which is a direct consequence of Krull's theorem. More generally, if S is any multiplicatively closed set in R, then a lemma essentially due to Krull shows that there exists an ideal of R maximal with respect to being... | Prime ideals | 0.780357 |
91,911 | In the case {S} = {1}, we have Krull's theorem, and this recovers the maximal ideals of R. Another prototypical m-system is the set, {x, x2, x3, x4, ...}, of all positive powers of a non-nilpotent element. For a prime ideal P, the complement R∖P has another property beyond being an m-system. If xy is in R∖P, then both ... | Prime ideals | 0.780357 |
91,912 | The CRISPR/Cas system of Streptococcus pyogenes can be programmed to direct both activation and repression to natural and artificial eukaryotic promoters through the simple engineering of guide RNAs with base-pairing complementarity to target DNA sites. Cas9 can be used as a customizable RNA-guided DNA-binding platform... | DNA binding domain | 0.780357 |
91,913 | The Erwin L. Hahn Institute for Magnetic Resonance Imaging is a research institute which develops magnetic resonance imaging (MRI) for both cognitive neuroscience and medical diagnosis and treatment. | Erwin L. Hahn Institute for Magnetic Resonance Imaging | 0.780356 |
91,914 | In general relativity, Buchdahl's theorem, named after Hans Adolf Buchdahl, makes more precise the notion that there is a maximal sustainable density for ordinary gravitating matter. It gives an inequality between the mass and radius that must be satisfied for static, spherically symmetric matter configurations under c... | Buchdahl's theorem | 0.780356 |
91,915 | Given a static, spherically symmetric solution to the Einstein equations (without cosmological constant) with matter confined to areal radius R {\displaystyle R} that behaves as a perfect fluid with a density that does not increase outwards. (An areal radius R {\displaystyle R} corresponds to a sphere of surface area 4... | Buchdahl's theorem | 0.780356 |
91,916 | Extensions to Buchdahl's theorem generally either relax assumptions on the matter or on the symmetry of the problem. For instance, by introducing anisotropic matter or rotation. In addition one can also consider analogues of Buchdahl's theorem in other theories of gravity == References == | Buchdahl's theorem | 0.780356 |
91,917 | The Buchdahl theorem is useful when looking for alternatives to black holes. Such attempts are often inspired by the information paradox; a way to explain (part of) the dark matter; or to criticize that observations of black holes are based on excluding known astrophysical alternatives (such as neutron stars) rather th... | Buchdahl's theorem | 0.780356 |
91,918 | Limb development in vertebrates is an area of active research in both developmental and evolutionary biology, with much of the latter work focused on the transition from fin to limb.Limb formation begins in the morphogenetic limb field, as mesenchymal cells from the lateral plate mesoderm proliferate to the point that ... | Limb development | 0.780356 |
91,919 | Reinhardt and Rosenblum claimed that the disproof of Whitehead's theory by tidal effects was "unsubstantiated". Chiang and Hamity argued that Reinhardt and Rosenblum's approach "does not provide a unique space-time geometry for a general gravitation system", and they confirmed Will's calculations by a different method.... | Whitehead's theory of gravitation | 0.78035 |
91,920 | Clifford M. Will argued that Whitehead's theory features a prior geometry. Under Will's presentation (which was inspired by John Lighton Synge's interpretation of the theory), Whitehead's theory has the curious feature that electromagnetic waves propagate along null geodesics of the physical spacetime (as defined by th... | Whitehead's theory of gravitation | 0.78035 |
91,921 | In theoretical physics, Whitehead's theory of gravitation was introduced by the mathematician and philosopher Alfred North Whitehead in 1922. While never broadly accepted, at one time it was a scientifically plausible alternative to general relativity. However, after further experimental and theoretical consideration, ... | Whitehead's theory of gravitation | 0.78035 |
91,922 | PRT vehicles are sized for individual or small group travel, typically carrying no more than three to six passengers per vehicle. Guideways are arranged in a network topology, with all stations located on sidings, and with frequent merge/diverge points. This allows for nonstop, point-to-point travel, bypassing all inte... | Personal Rapid Transit | 0.780349 |
91,923 | condition is satisfied via an appropriate scaling of identically distributed random variables with finite variance, the weak convergence is to the normal distribution in the classical version of the central limit theorem. More generally, if the u.a.n. condition is satisfied via a scaling of identically distributed rand... | Infinitely divisible distribution | 0.780349 |
91,924 | Infinitely divisible distributions appear in a broad generalization of the central limit theorem: the limit as n → +∞ of the sum Sn = Xn1 + … + Xnn of independent uniformly asymptotically negligible (u.a.n.) random variables within a triangular array X 11 X 21 X 22 X 31 X 32 X 33 ⋮ ⋮ ⋮ ⋱ {\displaystyle {\begin{array}{c... | Infinitely divisible distribution | 0.780349 |
91,925 | A focus of SI is the exchange of IT education on university and college level and IT practice in companies. It maintains working groups, including computer science education, computer graphics and computer security. A working group, coordinated by the ETH Zurich, deals with data bases, their theory and application, inc... | Swiss Informatics Society | 0.780348 |
91,926 | The Swiss Informatics Society (Schweizer Informatik Gesellschaft), short "SI", is a Swiss organization of computer science educators, researchers, and professionals. The Swiss Informatics Society was founded in 1983. Helmar Burkhart was the president from 1990 to 1992, Bernhard M. Hämmerli has been president from 2009 ... | Swiss Informatics Society | 0.780348 |
91,927 | A related statistic is "left on base in scoring position", which includes only those LOB where the runner was occupying second or third base. Yet another related statistic is "left on base in scoring position with less than two out". The intent of these statistics is to measure the tendency of a team or player to waste... | Bases loaded | 0.780346 |
91,928 | When a given player hits a single, double, triple and home run in the same game. To accomplish this feat in order is termed a "natural cycle". Hitting for the cycle is a rare enough occurrence that Major League Baseball keeps special statistics on it. | Bases loaded | 0.780346 |
91,929 | An old-fashioned and more colorful way of saying "numbers nut", for a fan with a near-obsessive interest in the statistics or "figures" of the game. The first true "figger filbert" was probably Ernest Lanigan, who was the first historian of the Baseball Hall of Fame and prior to that was one of the first, if not the fi... | Bases loaded | 0.780346 |
91,930 | An at bat in which the batter is productive, whether that involves advancing a runner with a sacrifice bunt (or even a ground ball out), getting on base, or just making the pitcher throw a lot. Thus a quality at bat is not measured simply by the standard batting statistics such as batting average, on-base percentage, o... | Bases loaded | 0.780346 |
91,931 | In baseball statistics, earned run average is the mean of earned runs given up by a pitcher per nine innings pitched. It is determined by dividing the number of earned runs allowed by the number of innings pitched and multiplying by nine. Runs resulting from defensive errors are recorded as unearned runs and omitted fr... | Bases loaded | 0.780346 |
91,932 | Bats right; used in describing a player's statistics, for example: John Doe (TR, BR, 6', 172 lbs.) | Bases loaded | 0.780346 |
91,933 | Short for "statistics", the numbers generated by the game: runs, hits, errors, strikeouts, batting average, earned run average, fielding average, etc. Most of the numbers used by players and fans are not true mathematical statistics, but the term is in common usage. | Bases loaded | 0.780346 |
91,934 | Therefore, if the compression variant is solvable in fixed-parameter tractable time, i.e., f(k) · nc for some constant c, then the iterative compression procedure solving the entire problem runs in f(k) · nc+1 time. The same technique can be applied to finding sets of edges for graph properties closed under subgraphs (... | Iterative compression | 0.780345 |
91,935 | In computer science, iterative compression is an algorithmic technique for the design of fixed-parameter tractable algorithms, in which one element (such as a vertex of a graph) is added to the problem in each step, and a small solution for the problem prior to the addition is used to help find a small solution to the ... | Iterative compression | 0.780345 |
91,936 | From a single shot it can produce images focused at different distances, depth maps, all-in-focus images and stereo pairs. A similar optical design can be used in adaptive optics in astrophysics. Mitsubishi Electric Research Laboratories's (MERL) light field camera is based on the principle of optical heterodyning and ... | Light-field camera | 0.780344 |
91,937 | Following the publication in 1965 of two independent versions of the theorem by Felix Browder and by William Kirk, a new proof of Michael Edelstein showed that, in a uniformly convex Banach space, every iterative sequence f n x 0 {\displaystyle f^{n}x_{0}} of a non-expansive map f {\displaystyle f} has a unique asympto... | Browder fixed-point theorem | 0.780343 |
91,938 | The Browder fixed-point theorem is a refinement of the Banach fixed-point theorem for uniformly convex Banach spaces. It asserts that if K {\displaystyle K} is a nonempty convex closed bounded set in uniformly convex Banach space and f {\displaystyle f} is a mapping of K {\displaystyle K} into itself such that ‖ f ( x ... | Browder fixed-point theorem | 0.780343 |
91,939 | The existence of eigenforms is a nontrivial result, but does come directly from the fact that the Hecke algebra is commutative. | Eigenform | 0.780342 |
91,940 | In mathematics, an eigenform (meaning simultaneous Hecke eigenform with modular group SL(2,Z)) is a modular form which is an eigenvector for all Hecke operators Tm, m = 1, 2, 3, .... Eigenforms fall into the realm of number theory, but can be found in other areas of math and science such as analysis, combinatorics, and... | Eigenform | 0.780342 |
91,941 | Let us split Y {\displaystyle Y} into the direct product Y = Y 1 ⊕ Y 2 {\displaystyle Y=Y_{1}\oplus Y_{2}} , where dim Y 2 < ∞ {\displaystyle \dim Y_{2}<\infty } . Let Q {\displaystyle Q} be the projection operator onto Y 1 {\displaystyle Y_{1}} . Consider also the direct product X = X 1 ⊕ X 2 {\displaystyle X=X_{1}\... | Lyapunov-Schmidt reduction | 0.780342 |
91,942 | Let f ( x , λ ) = 0 {\displaystyle f(x,\lambda )=0\,} be the given nonlinear equation, X , Λ , {\displaystyle X,\Lambda ,} and Y {\displaystyle Y} are Banach spaces ( Λ {\displaystyle \Lambda } is the parameter space). f ( x , λ ) {\displaystyle f(x,\lambda )} is the C p {\displaystyle C^{p}} -map from a neighborhood o... | Lyapunov-Schmidt reduction | 0.780342 |
91,943 | In mathematics, the Lyapunov–Schmidt reduction or Lyapunov–Schmidt construction is used to study solutions to nonlinear equations in the case when the implicit function theorem does not work. It permits the reduction of infinite-dimensional equations in Banach spaces to finite-dimensional equations. It is named after A... | Lyapunov-Schmidt reduction | 0.780341 |
91,944 | Geometric realizations: Let T {\displaystyle T} be a simplicial set. That is, T {\displaystyle T} is a functor Δ o p → S e t {\displaystyle \Delta ^{\mathrm {op} }\to \mathbf {Set} } . The discrete topology gives a functor d: S e t → T o p {\displaystyle d:\mathbf {Set} \to \mathbf {Top} } , where T o p {\displaystyle ... | End (category theory) | 0.78034 |
91,945 | This G-code file can then be printed with 3D printing client software (which loads the G-code and uses it to instruct the 3D printer during the 3D printing process). Printer resolution describes layer thickness and X–Y resolution in dots per inch (dpi) or micrometers (μm). Typical layer thickness is around 100 μm (250 ... | Additive layer manufacturing | 0.780338 |
91,946 | 3D printing or additive manufacturing is the construction of a three-dimensional object from a CAD model or a digital 3D model. It can be done in a variety of processes in which material is deposited, joined or solidified under computer control, with the material being added together (such as plastics, liquids or powde... | Additive layer manufacturing | 0.780338 |
91,947 | In molecular biology, the Whey acidic proteins (WAP) have been identified as a major whey protein family in milk, and are important in regulating the proliferation of mammary epithelial cells. Additionally, their physiological function is thought to be similar to a protease inhibitor. It has been concluded, therefore, ... | Whey acidic protein | 0.780337 |
91,948 | Nvidia Gameworks consists of several main components: VisualFX: For rendering effects such as smoke, fire, water, depth of field, soft shadows, HBAO+, TXAA, FaceWorks and HairWorks. PhysX: For physics, destruction, particle and fluid simulations. OptiX: For baked lighting and general-purpose ray-tracing. Core SDK: For ... | Nvidia GameWorks | 0.780337 |
91,949 | Polycyclohexylenedimethylene terephthalate has good dimensional stability at excess temperatures (short-term up to 493 °F (256 °C)) making this material suitable for injection molding or 3D printing of thin-walled parts. PCT is used for electronics components like plug connectors. PCT is also processed into filaments, ... | Polycyclohexylenedimethylene terephthalate | 0.780337 |
91,950 | Notable developer platforms for virtual assistants include: Amazon Lex was opened to developers in April 2017. It involves natural language understanding technology combined with automatic speech recognition and had been introduced in November 2016. Google provides the Actions on Google and Dialogflow platforms for dev... | Intelligent personal assistant | 0.780335 |
91,951 | Mechanochemistry refers to chemical reactions triggered by mechanical forces as opposed to heat, light, or electric potential. Ball milling can crush material such as boron nitride or graphene, allowing hydrogen gas to be absorbed by the powder, storing the hydrogen. The hydrogen can be released by heating the powder. ... | Hydrogen transport | 0.780334 |
91,952 | Hydrogen can be reacted with other elements to form a variety of compounds. This allows it to be transported in either liquid (e.g., water) or solid form. One variation on this concept is to transport atomic silicon, produced using renewable energy. Mixing silicon with water separates water's oxygen from its hydrogen w... | Hydrogen transport | 0.780334 |
91,953 | A Walrasian auction, introduced by Léon Walras, is a type of simultaneous auction where each agent calculates its demand for the good at every possible price and submits this to an auctioneer. The price is then set so that the total demand across all agents equals the total amount of the good. Thus, a Walrasian auction... | Walrasian auction | 0.780334 |
91,954 | In statistics, Sheppard's corrections are approximate corrections to estimates of moments computed from binned data. The concept is named after William Fleetwood Sheppard. Let m k {\displaystyle m_{k}} be the measured kth moment, μ ^ k {\displaystyle {\hat {\mu }}_{k}} the corresponding corrected moment, and c {\displa... | Sheppard's correction | 0.780333 |
91,955 | The Next Hop Resolution Protocol (NHRP) is an extension of the ATM ARP routing mechanism that is sometimes used to improve the efficiency of routing computer network traffic over Non-Broadcast, Multiple Access (NBMA) Networks. It is defined in IETF RFC 2332, and further described in RFC 2333. It can be used by a sender... | Next Hop Resolution Protocol | 0.780332 |
91,956 | A makeshift to achieve a real-time requirement in multidimensional DSP applications is to use a lower sampling rate, which can efficiently reduce the number of samples to be processed at one time and thereby decrease the total processing time. However, this can lead to the aliasing problem due to the sampling theorem a... | Multidimensional DSP with GPU acceleration | 0.780331 |
91,957 | The key Modigliani–Miller theorem was developed in a world without taxes. However, if we move to a world where there are taxes, when the interest on debt is tax-deductible, and ignoring other frictions, the value of the company increases in proportion to the amount of debt used. The additional value equals the total di... | Modigliani-Miller theorem | 0.78033 |
91,958 | The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) is an influential element of economic theory; it forms the basis for modern thinking on capital structure. The basic theorem states that in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, th... | Modigliani-Miller theorem | 0.78033 |
91,959 | Miller and Modigliani derived and published their theorem when they were both professors at the Graduate School of Industrial Administration (GSIA) of Carnegie Mellon University. Despite limited prior experience in corporate finance, Miller and Modigliani were assigned to teach the subject to current business students.... | Modigliani-Miller theorem | 0.78033 |
91,960 | The most common statement of the Fourier inversion theorem is to state the inverse transform as an integral. For any integrable function g {\displaystyle g} and all x ∈ R n {\displaystyle x\in \mathbb {R} ^{n}} set F − 1 g ( x ) := ∫ R n e 2 π i x ⋅ ξ g ( ξ ) d ξ . {\displaystyle {\mathcal {F}}^{-1}g(x):=\int _{\mathbb... | Fourier integral theorem | 0.78033 |
91,961 | The form of the Fourier inversion theorem stated above, as is common, is that F − 1 ( F f ) ( x ) = f ( x ) . {\displaystyle {\mathcal {F}}^{-1}({\mathcal {F}}f)(x)=f(x).} In other words, F − 1 {\displaystyle {\mathcal {F}}^{-1}} is a left inverse for the Fourier transform. However it is also a right inverse for the Fo... | Fourier integral theorem | 0.78033 |
91,962 | In this case the Fourier transform cannot be defined directly as an integral since it may not be absolutely convergent, so it is instead defined by a density argument (see the Fourier transform article). For example, putting g k ( ξ ) := ∫ { y ∈ R n: | y | ≤ k } e − 2 π i y ⋅ ξ f ( y ) d y , k ∈ N , {\displaystyle g_{k... | Fourier integral theorem | 0.78033 |
91,963 | In organic chemistry, an oxime is a organic compound belonging to the imines, with the general formula RR’C=N−OH, where R is an organic side-chain and R' may be hydrogen, forming an aldoxime, or another organic group, forming a ketoxime. O-substituted oximes form a closely related family of compounds. Amidoximes are ox... | Amidoxime | 0.78033 |
91,964 | The result of this was the article in the American Economic Review and what has later been known as the M&M theorem. Miller and Modigliani published a number of follow-up papers discussing some of these issues. The theorem was first proposed by F. Modigliani and M. Miller in 1958. | Modigliani-Miller theorem | 0.78033 |
91,965 | The criteria for the certification have been developed by the Swedish Institute for Agricultural and Environmental Engineering and may pave the way for farmers to use human waste for agricultural production. The Federation of Swedish Farmers have been active in this development. Furthermore, the Swedish EPA in their la... | Ecological sanitation | 0.780329 |
91,966 | A member of the Royal Australian Chemical Institute is designated with the honorific affix "MRACI". As the professional body for chemistry in Australia, the institute has the ability to award the status of Chartered Chemist ("CChem") to suitably qualified candidates. Election to fellow of the institute ("FRACI") is dep... | Royal Australian Chemical Institute | 0.780329 |
91,967 | The Royal Australian Chemical Institute (RACI) is both the qualifying body in Australia for professional chemists and a learned society promoting the science and practice of chemistry in all its branches. The RACI hosts conferences, seminars and workshops. It is the professional body for chemistry in Australia, with th... | Royal Australian Chemical Institute | 0.780329 |
91,968 | The RACI was formed as the Australian Chemical Institute in Sydney in September 1917. The driving force was David Orme Masson, professor of chemistry at the University of Melbourne. It was incorporated under the Companies Act in New South Wales in 1923. It was given a royal charter in 1932, but it was not until a suppl... | Royal Australian Chemical Institute | 0.780329 |
91,969 | The RACI is a member of the Federation of Australian Scientific and Technological Societies (FASTS), and the Federation of Asian Chemical Societies (FACS).It has branches in all states and territories in Australia and divisions for the following areas of chemistry: Analytical and Environmental chemistry Carbon science ... | Royal Australian Chemical Institute | 0.780329 |
91,970 | The Adrien Albert award recognises the enormous contributions made by Prof. Adrien Albert to medicinal chemistry. It is the premier award of the Medicinal Chemistry and Chemical Biology Division and is given for sustained, outstanding research in the field of medicinal or agricultural chemistry or chemical biology. The... | Royal Australian Chemical Institute | 0.780329 |
91,971 | The Cornforth Medal for the most outstanding PhD thesis submitted by a member. It is named after the Australian Nobel Prize in Chemistry winner, Sir John Cornforth. The Rennie Memorial Medal for the member of less than 8 years of professional experience since completing their most recent relevant qualification who has ... | Royal Australian Chemical Institute | 0.780329 |
91,972 | Similarly, one often wants to exchange integrals and limit processes. For the Riemann integral, this can be done if uniform convergence is assumed: If ( f n ) n = 1 ∞ {\displaystyle (f_{n})_{n=1}^{\infty }} is a sequence of Riemann integrable functions defined on a compact interval I {\displaystyle I} which uniformly c... | Uniform approximation | 0.780327 |
91,973 | The Tebbe reagent converts esters and lactones to enol ethers and amides to enamines. In compounds containing both ketone and ester groups, the ketone selectively reacts in the presence of one equivalent of the Tebbe reagent. The Tebbe reagent methylidenates carbonyls without racemizing a chiral α carbon. For this reas... | Tebbe's reagent | 0.780327 |
91,974 | Tebbe's reagent contains two tetrahedral metal centers linked by a pair of bridging ligands. The titanium has two cyclopentadienyl (−, or Cp) rings and aluminium has two methyl groups. The titanium and aluminium atoms are linked together by both a methylene bridge (-CH2-) and a chloride atom in a nearly square-planar (... | Tebbe's reagent | 0.780327 |
91,975 | In finite dimensions the existence of a fixed point can often be deduced from the Brouwer fixed point theorem without any appeal to holomorphicity of the mapping. In the case of bounded symmetric domains with the Bergman metric, Neretin (1996) and Clerc (1998) showed that the same scheme of proof as that used in the Ea... | Earle–Hamilton fixed-point theorem | 0.780325 |
91,976 | In mathematics, the Earle–Hamilton fixed point theorem is a result in geometric function theory giving sufficient conditions for a holomorphic mapping of an open domain in a complex Banach space into itself to have a fixed point. The result was proved in 1968 by Clifford Earle and Richard S. Hamilton by showing that, w... | Earle–Hamilton fixed-point theorem | 0.780325 |
91,977 | The open semigroup of the complexification Gc taking the closure of D into D acts by contraction mappings, so again the Banach fixed-point theorem can be applied. Neretin extended this argument by continuity to some infinite-dimensional bounded symmetric domains, in particular the Siegel generalized disk of symmetric H... | Earle–Hamilton fixed-point theorem | 0.780325 |
91,978 | In particular d defines a metric on D. The chain rule ( g ∘ f ) ′ ( z ) = g ′ ( f ( z ) ) f ′ ( z ) {\displaystyle \displaystyle {(g\circ f)^{\prime }(z)=g^{\prime }(f(z))f^{\prime }(z)}} implies that α ( f ( z ) , f ′ ( z ) v ) ≤ α ( z , v ) {\displaystyle \displaystyle {\alpha (f(z),f^{\prime }(z)v)\leq \alpha (z,v)}... | Earle–Hamilton fixed-point theorem | 0.780325 |
91,979 | The Carathéodory metric is defined by d ( x , y ) = inf γ ( 0 ) = x , γ ( 1 ) = y ℓ ( γ ) {\displaystyle \displaystyle {d(x,y)=\inf _{\gamma (0)=x,\gamma (1)=y}\ell (\gamma )}} for x and y in D. It is a continuous function on D x D for the norm topology. If the diameter of D is less than R then, by taking suitable holo... | Earle–Hamilton fixed-point theorem | 0.780325 |
91,980 | The advantages of WBDF are utilized to resolve dislocation dynamics in Fe2MnAl single crystals where superdislocations with 4-fold dissociation were imaged. The movement of a superdislocation at the nanometer scale can be seen in the image on the right. In the paper, Liao et al. show that the superdislocations glide in... | Weak-beam dark-field microscopy | 0.78032 |
91,981 | Setting up weak-beam dark-field imaging in transmission electron microscopy involves several steps, which may vary depending on the specific TEM instrument and the sample being analyzed. This may require further optimization and adjustment to achieve the desired image quality and contrast. The general steps include: Sa... | Weak-beam dark-field microscopy | 0.78032 |
91,982 | Organoids offer researchers an exceptional model to study developmental biology. Since the identification of pluripotent stem cells, there have been great advancements in directing pluripotent stem cells fate in vitro using 2D cultures. These advancements in PSC fate direction, coupled with the advancements in 3D cultu... | Organoid | 0.780319 |
91,983 | In 2014, Qun Wang and co-workers engineered collagen-I based gels and synthetic foam biomaterials for the culture and delivery of intestinal organoids and encapsulated DNA-functionalized gold nanoparticles into intestinal organoids to form an intestinal Trojan horse for drug delivery and gene therapy. Subsequent report... | Organoid | 0.780319 |
91,984 | Attempts to create organs in vitro started with one of the first dissociation-reaggregation experiments where Henry Van Peters Wilson demonstrated that mechanically dissociated sponge cells can reaggregate and self-organize to generate a whole organism. In the subsequent decades, multiple labs were able to generate dif... | Organoid | 0.780319 |
91,985 | In the field of infection biology, different intestinal organoid-based model systems have been explored. On one hand, organoids can be infected in bulk by simply mixing them with the enteropathogen of interest. | Organoid | 0.780319 |
91,986 | Many identities interrelate the trigonometric functions. This section contains the most basic ones; for more identities, see List of trigonometric identities. These identities may be proved geometrically from the unit-circle definitions or the right-angled-triangle definitions (although, for the latter definitions, car... | Secant (trigonometry) | 0.780319 |
91,987 | This arrangement, also known as a "PDL trap" for "parallel dipole line", was the subject of the 2017 International Physics Olympiad.In the magnetic system, the camelback potential effect only occurs when the length of the diamagnetic rod is between two critical lengths. Below the minimum length, the magnet is hypothesi... | Camelback potential | 0.780318 |
91,988 | Tanium is a privately held cybersecurity and systems management company with headquarters in Kirkland, Washington, and its operations center in Emeryville, California.It was founded July 16, 2007, by father and son David Hindawi and Orion Hindawi, co-founders of information management company BigFix.Orion Hindawi was n... | Tanium | 0.780317 |
91,989 | Indirect measures assess the person and environment separately. These measures are then used to compute an index intended to represent the fit between the person and environment, such as an algebraic, absolute, or squared difference score, or are analyzed jointly to assess the effects of fit without computing a differe... | Person–environment fit | 0.780317 |
91,990 | Segal's Burnside ring conjecture, or, more briefly, the Segal conjecture, is a theorem in homotopy theory, a branch of mathematics. The theorem relates the Burnside ring of a finite group G to the stable cohomotopy of the classifying space BG. The conjecture was made in the mid 1970s by Graeme Segal and proved in 1984 ... | Segal conjecture | 0.780316 |
91,991 | Other applications of μ(n) in combinatorics are connected with the use of the Pólya enumeration theorem in combinatorial groups and combinatorial enumerations. There is a formula for calculating the Möbius function without directly knowing the factorization of its argument: μ ( n ) = ∑ gcd ( k , n ) = 1 1 ≤ k ≤ n e 2 π... | Moebius function | 0.780314 |
91,992 | The mean value (in the sense of average orders) of the Möbius function is zero. This statement is, in fact, equivalent to the prime number theorem. | Moebius function | 0.780313 |
91,993 | In number theory another arithmetic function closely related to the Möbius function is the Mertens function, defined by M ( n ) = ∑ k = 1 n μ ( k ) {\displaystyle M(n)=\sum _{k=1}^{n}\mu (k)} for every natural number n. This function is closely linked with the positions of zeroes of the Riemann zeta function. See the a... | Moebius function | 0.780313 |
91,994 | The Marcel Loncin Research Prize was established in 1994. It is awarded by the Institute of Food Technologists (IFT) in even-numbered years to fund basic chemistry, physics, and/or engineering research applied to food processing and improving food quality. It is named for Marcel Loncin (1920-1995), a Belgian-born, Fren... | Marcel Loncin Research Prize | 0.780313 |
91,995 | In the geometry of hyperbolic 3-space, the order-8 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,8}. It has eight icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing aroun... | Order-8 icosahedral honeycomb | 0.780313 |
91,996 | Thallium barium calcium copper oxide, or TBCCO (pronounced "tibco"), is a family of high-temperature superconductors having the generalized chemical formula TlmBa2Can−1CunO2n+m+2. Tl2Ba2Ca2Cu3O10 (TBCCO-2223) was discovered in Prof. Allen M. Hermann's laboratory in the physics department of the University of Arkansas i... | Thallium barium calcium copper oxide | 0.780313 |
91,997 | In the geometry of hyperbolic 3-space, the order-7 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5,7}. It has seven icosahedra, {3,5}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many icosahedra existing aroun... | Order-8 icosahedral honeycomb | 0.780313 |
91,998 | The CHondritic Uniform Reservoir or CHUR is a scientific model in astrophysics and geochemistry for the mean chemical composition of the part of the Solar Nebula from which, during the formation of the Solar System, chondrites formed. This hypothetical chemical reservoir is thought to have been similar in composition t... | Chondritic uniform reservoir | 0.780313 |
91,999 | The chiral Potts curve is an algebraic curve defined over the complex numbers that occurs in the study of the chiral Potts model of statistical mechanics. For an integer N, the parameters in the Boltzmann weights of the model are constrained to lie on the intersection of two algebraic surfaces of degree N in projective... | Chiral Potts curve | 0.780311 |
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