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88,900 | The Centre for Gene Regulation and Expression, located within the School of Life Sciences, University of Dundee, is a research facility working in the field of gene expression and chromosome biology. Previously part of the Dundee Biocentre and receiving significant Wellcome Trust funding from 1995 onwards, it was award... | Centre for Gene Regulation and Expression | 0.781525 |
88,901 | A mixture of photo initiators and photo inhibitors is used in the setup. The absorbance spectra of two material is orthogonal this allows to control the process with the two orthogonal light sources. As the material is generated layer by layer the tray is gradually lifted and the photo inhibitors will not allow adhesio... | 3D printing speed | 0.781525 |
88,902 | Depending on the technology used, there are some challenges that could limit the speed of the 3D printing: Shape optimization. Since a product's interior can be filled using many different structures, design optimization through additive manufacturing is necessary. Finding the best way to fill in a product interior giv... | 3D printing speed | 0.781525 |
88,903 | 3D printing speed measures the amount of manufactured material over a given time period ( amount / time {\displaystyle {\text{amount}}/{\text{time}}} ), where the unit of time is measured in Seconds, and the unit of manufactured material is typically measured in units of either kg, mm or cm3, depending on the type of a... | 3D printing speed | 0.781525 |
88,904 | Increasing the speed of printing through hardware can take the following forms, many of which are used by leading 3D printing companies. Modified printheads: using different types of printheads for different printing processes. For instance, having an additional knifed feeder to prevent filament slipping. Temperature: ... | 3D printing speed | 0.781525 |
88,905 | Additive manufacturing technologies usually imply a trade off between the printing speed and quality. Improvements in speed of the entire 3D printing process can be grouped in the following two categories. | 3D printing speed | 0.781525 |
88,906 | See history of Chaotic inflation theory. It was soon understood that a homogeneous and isotropic universe could not be preserved through the violent tunneling process. This led Andrei Linde and, independently, Andreas Albrecht and Paul Steinhardt, to propose "new inflation" or "slow roll inflation" in which no tunnelli... | True vacuum | 0.781524 |
88,907 | “The greatest benefits we owe to the artist, whether painter, poet, or novelist, is the extension of our sympathies. Appeals founded on generalizations and statistics require a sympathy ready-made, a moral sentiment already in activity; but a picture of human life such as a great artist can give, surprises even the tri... | Cognitive empathy | 0.781523 |
88,908 | Studies in animal behavior and neuroscience indicate that empathy is not restricted to humans (however the interpretation of such research depends in part on how expansive a definition of empathy researchers adopt). Empathy-like behaviors have been observed in primates, both in captivity and in the wild, and in particu... | Cognitive empathy | 0.781523 |
88,909 | Mercantilism, according to Foucault, was the first rationalization of the exercise of power as a practice of government; it is the first time that a knowledge of the state can be employed as tactics for the state, namely statistics. Foucault begins to chart through this historical, political reasoning behind the doctri... | Security, Territory, Population | 0.781523 |
88,910 | All of society was enmeshed within this process including the prince (ruler) himself, thus a century later government became political and collaborative with economy (modern political science as its 'rational' spokesman) and its partnership with political economy. Foucault further notices that political economy had a n... | Security, Territory, Population | 0.781523 |
88,911 | In this essay Bacon gives a complete description on the physics of sedition, sedition and the precautions to be taken against it, and of government of the 'people'. This became a worry for Bacon and other political theorists; the first signs of sedition were circulation of libels, pamphlets and discourse against the st... | Security, Territory, Population | 0.781523 |
88,912 | This is due to the observation technique of star transits, which cross the field of view of telescope eyepieces due to Earth's rotation. The observation techniques are topics of positional astronomy and of astrogeodesy. Ideally, the Cartesian coordinate system (α, δ) refers to an inertial frame of reference. | Star position | 0.781522 |
88,913 | In quantum mechanics, the Berry phase arises in a cyclic adiabatic evolution. The quantum adiabatic theorem applies to a system whose Hamiltonian H ( R ) {\displaystyle H(\mathbf {R} )} depends on a (vector) parameter R {\displaystyle \mathbf {R} } that varies with time t {\displaystyle t} . If the n {\displaystyle n} ... | Berry curvature | 0.781521 |
88,914 | In physics, Berry connection and Berry curvature are related concepts which can be viewed, respectively, as a local gauge potential and gauge field associated with the Berry phase or geometric phase. The concept was first introduced by S. Pancharatnam as geometric phase and later elaborately explained and popularized b... | Berry curvature | 0.781521 |
88,915 | The Berry phase plays an important role in modern investigations of electronic properties in crystalline solids and in the theory of the quantum Hall effect. The periodicity of the crystalline potential allows the application of the Bloch theorem, which states that the Hamiltonian eigenstates take the form where n {\di... | Berry curvature | 0.781521 |
88,916 | The Berry curvature is an anti-symmetric second-rank tensor derived from the Berry connection via In a three-dimensional parameter space the Berry curvature can be written in the pseudovector form The tensor and pseudovector forms of the Berry curvature are related to each other through the Levi-Civita antisymmetric te... | Berry curvature | 0.781521 |
88,917 | In theoretical physics, a twisted sector is a subspace of the full Hilbert space of closed string states in a particular theory over a (good) orbifold. In the first quantized formalism of string theory (or in two-dimensional conformal field theory) the target space is an orbifold M/G if the observables of the string ar... | Twisted sector | 0.78152 |
88,918 | His first article on this topic appeared in 1894.His research in geometry led to the abstract topological definition of homotopy and homology. He also first introduced the basic concepts and invariants of combinatorial topology, such as Betti numbers and the fundamental group. Poincaré proved a formula relating the num... | Henri Poincaré | 0.781519 |
88,919 | The subject is clearly defined by Felix Klein in his "Erlangen Program" (1872): the geometry invariants of arbitrary continuous transformation, a kind of geometry. The term "topology" was introduced, as suggested by Johann Benedict Listing, instead of previously used "Analysis situs". Some important concepts were intro... | Henri Poincaré | 0.781519 |
88,920 | He noted that a Lorentz transformation is merely a rotation in four-dimensional space about the origin by introducing c t − 1 {\displaystyle ct{\sqrt {-1}}} as a fourth imaginary coordinate, and he used an early form of four-vectors. Poincaré expressed a lack of interest in a four-dimensional reformulation of his new m... | Henri Poincaré | 0.781519 |
88,921 | In 1881 Poincaré described hyperbolic geometry in terms of the hyperboloid model, formulating transformations leaving invariant the Lorentz interval x 2 + y 2 − z 2 = − 1 {\displaystyle x^{2}+y^{2}-z^{2}=-1} , which makes them mathematically equivalent to the Lorentz transformations in 2+1 dimensions. In addition, Poin... | Henri Poincaré | 0.781519 |
88,922 | He was initially appointed as the maître de conférences d'analyse (associate professor of analysis). Eventually, he held the chairs of Physical and Experimental Mechanics, Mathematical Physics and Theory of Probability, and Celestial Mechanics and Astronomy. In 1887, at the young age of 32, Poincaré was elected to the ... | Henri Poincaré | 0.781519 |
88,923 | He carried out the official investigation into the accident in a characteristically thorough and humane way. At the same time, Poincaré was preparing for his Doctorate in Science in mathematics under the supervision of Charles Hermite. His doctoral thesis was in the field of differential equations. | Henri Poincaré | 0.781519 |
88,924 | (1972), "Poincaré's Rendiconti Paper on Relativity. Part III", American Journal of Physics, 40 (9): 1282–1287, Bibcode:1972AmJPh..40.1282S, doi:10.1119/1.1986815 Scribner, C. (1964), "Henri Poincaré and the principle of relativity", American Journal of Physics, 32 (9): 672–678, Bibcode:1964AmJPh..32..672S, doi:10.1119/... | Henri Poincaré | 0.781519 |
88,925 | Part I", American Journal of Physics, 39 (7): 1287–1294, Bibcode:1971AmJPh..39.1287S, doi:10.1119/1.1976641 Schwartz, H. M. (1972), "Poincaré's Rendiconti Paper on Relativity. Part II", American Journal of Physics, 40 (6): 862–872, Bibcode:1972AmJPh..40..862S, doi:10.1119/1.1986684 Schwartz, H. M. | Henri Poincaré | 0.781519 |
88,926 | Sci., 16 (64): 273–294, doi:10.1093/bjps/XVI.64.273, S2CID 122596290 Kragh, H. (1999), Quantum Generations: A History of Physics in the Twentieth Century, Princeton University Press, ISBN 978-0-691-09552-3 Langevin, P. | Henri Poincaré | 0.781519 |
88,927 | (1970), "Poincaré's silence and Einstein's relativity", British Journal for the History of Science, 5: 73–84, doi:10.1017/S0007087400010633, S2CID 123766991 Holton, G. (1988) , "Poincaré and Relativity", Thematic Origins of Scientific Thought: Kepler to Einstein, Harvard University Press, ISBN 978-0-674-87747-4 Katzir,... | Henri Poincaré | 0.781519 |
88,928 | (1998), "The Rise of Special Relativity: Henri Poincaré's Works Before Einstein", Atti del XVIII Congresso di Storia della Fisica e dell'astronomia: 171–207 Giedymin, J. (1982), Science and Convention: Essays on Henri Poincaré's Philosophy of Science and the Conventionalist Tradition, Oxford: Pergamon Press, ISBN 978-0... | Henri Poincaré | 0.781519 |
88,929 | Cuvaj, Camillo (1969), "Henri Poincaré's Mathematical Contributions to Relativity and the Poincaré Stresses", American Journal of Physics, 36 (12): 1102–1113, Bibcode:1968AmJPh..36.1102C, doi:10.1119/1.1974373 Darrigol, O. (1995), "Henri Poincaré's criticism of Fin De Siècle electrodynamics", Studies in History and Phi... | Henri Poincaré | 0.781519 |
88,930 | Awards Oscar II, King of Sweden's mathematical competition (1887) Foreign member of the Royal Netherlands Academy of Arts and Sciences (1897) American Philosophical Society (1899) Gold Medal of the Royal Astronomical Society of London (1900) Bolyai Prize (1905) Matteucci Medal (1905) French Academy of Sciences (1906) A... | Henri Poincaré | 0.781519 |
88,931 | In 1881–1882, Poincaré created a new branch of mathematics: qualitative theory of differential equations. He showed how it is possible to derive the most important information about the behavior of a family of solutions without having to solve the equation (since this may not always be possible). He successfully used t... | Henri Poincaré | 0.781519 |
88,932 | Poincaré also developed a general theory of integral invariants and solutions of the variational equations. For the finite-difference equations, he created a new direction – the asymptotic analysis of the solutions. He applied all these achievements to study practical problems of mathematical physics and celestial mech... | Henri Poincaré | 0.781519 |
88,933 | After defending his doctoral thesis on the study of singular points of the system of differential equations, Poincaré wrote a series of memoirs under the title "On curves defined by differential equations" (1881–1882). In these articles, he built a new branch of mathematics, called "qualitative theory of differential e... | Henri Poincaré | 0.781519 |
88,934 | "The Principles of Mathematical Physics", The Monist, Vol. XV. 1910. | Henri Poincaré | 0.781519 |
88,935 | Contains the following works by Poincaré: 1894, "On the Nature of Mathematical Reasoning", 972–81. 1898, "On the Foundations of Geometry", 982–1011. 1900, "Intuition and Logic in Mathematics", 1012–20. | Henri Poincaré | 0.781519 |
88,936 | Analysis Situs (PDF), archived (PDF) from the original on 27 March 2012. The first systematic study of topology.On celestial mechanics: 1890. Poincaré, Henri (2017). | Henri Poincaré | 0.781519 |
88,937 | In James R. Newman, ed., The World of Mathematics (4 Vols). 1958. The Value of Science, New York: Dover.On algebraic topology: 1895. | Henri Poincaré | 0.781519 |
88,938 | In other words, the general solution of the three-body problem can not be expressed in terms of algebraic and transcendental functions through unambiguous coordinates and velocities of the bodies. His work in this area was the first major achievement in celestial mechanics since Isaac Newton.These monographs include an... | Henri Poincaré | 0.781519 |
88,939 | Poincaré made many contributions to different fields of pure and applied mathematics such as: celestial mechanics, fluid mechanics, optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, theory of relativity and physical cosmology. He was also a populariser of mathem... | Henri Poincaré | 0.781519 |
88,940 | Poincaré introduced group theory to physics, and was the first to study the group of Lorentz transformations. He also made major contributions to the theory of discrete groups and their representations. | Henri Poincaré | 0.781519 |
88,941 | He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrun... | Henri Poincaré | 0.781519 |
88,942 | Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "conventionalism". Poincaré believed that Newton's first law was not empirical but is a conventional framework assumption for mechanics (Gargani, 2012). | Henri Poincaré | 0.781519 |
88,943 | He strongly opposed Cantorian set theory, objecting to its use of impredicative definitions. However, Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of non-Euclidean space can be known analytically. | Henri Poincaré | 0.781519 |
88,944 | Leveugle, J. (2004), La Relativité et Einstein, Planck, Hilbert—Histoire véridique de la Théorie de la Relativitén, Pars: L'Harmattan Logunov, A.A. (2004), Henri Poincaré and relativity theory, arXiv:physics/0408077, Bibcode:2004physics...8077L, ISBN 978-5-02-033964-4 | Henri Poincaré | 0.781519 |
88,945 | Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. In 1905, Poincaré first proposed gravitational waves (ondes gravifiques) emanating from a body and propagating at the speed of light as being required by the Lorentz transformatio... | Henri Poincaré | 0.781519 |
88,946 | He is also considered to be one of the founders of the field of topology. Poincaré made clear the importance of paying attention to the invariance of laws of physics under different transformations, and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remain... | Henri Poincaré | 0.781519 |
88,947 | Jules Henri Poincaré (UK: , US: stress on last syllable; French: ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline... | Henri Poincaré | 0.781519 |
88,948 | Here is a list of theorems proved by Poincaré: | Henri Poincaré | 0.781519 |
88,949 | Einstein's first paper on relativity was published three months after Poincaré's short paper, but before Poincaré's longer version. Einstein relied on the principle of relativity to derive the Lorentz transformations and used a similar clock synchronisation procedure (Einstein synchronisation) to the one that Poincaré ... | Henri Poincaré | 0.781519 |
88,950 | Path integral may refer to: Line integral, the integral of a function along a curve Contour integral, the integral of a complex function along a curve used in complex analysis Functional integration, the integral of a functional over a space of curves Path integral formulation, Richard Feynman's formulation of quantum ... | Path integral | 0.781519 |
88,951 | The Pittsburgh Supercomputing Center (PSC) has also incorporated the CS-1 in their Neocortex supercomputer for dual HPC and AI workloads. EPCC, the supercomputing center of the University of Edinburgh, has also deployed a CS-1 system for AI-based research.In August 2021, Cerebras announced a partnership with Peptilogic... | Cerebras | 0.781518 |
88,952 | Argonne National Laboratory has been using the CS-2/CS-1 since 2020 in COVID-19 research and cancer tumor research based on the world’s largest cancer treatment database. A series of models running on the CS-1 to predict cancer drug response to tumors achieved speed-ups of many hundreds of times on the CS-1 compared to... | Cerebras | 0.781518 |
88,953 | Customers are reportedly using Cerebras technologies in the pharmaceutical, life sciences, and energy sectors.In 2020, GlaxoSmithKline (GSK) began using the Cerebras CS-1 AI system in their London AI hub, for neural network models to accelerate genetic and genomic research and reduce the time taken in drug discovery. T... | Cerebras | 0.781518 |
88,954 | Cerebras was founded in 2015 by Andrew Feldman, Gary Lauterbach, Michael James, Sean Lie and Jean-Philippe Fricker. These five founders worked together at SeaMicro, which was started in 2007 by Feldman and Lauterbach and was later sold to AMD in 2012 for $334 million.On August 19, 2019, Cerebras announced its Wafer-Sca... | Cerebras | 0.781518 |
88,955 | Cerebras Systems Inc. is an American artificial intelligence company with offices in Sunnyvale, San Diego, Toronto, Tokyo and Bangalore. Cerebras builds computer systems for complex artificial intelligence deep learning applications. | Cerebras | 0.781518 |
88,956 | Cerebras said that for the first time ever, one CS-2 system with one Cerebras wafer can train models with up to 20 billion parameters. The Cerebras CS-2 system can train multibillion-parameter natural language processing (NLP) models including GPT-3XL 1.3 billion models, GPT-J-6B, GPT-3 13B, and GPT-NeoX 20B with reduc... | Cerebras | 0.781518 |
88,957 | The WSE-2 has 850,000 cores and 2.6 trillion transistors. The WSE-2 expanded on-chip static random-access memory (SRAM) to 40 gigabytes, memory bandwidth to 20 petabytes per second and total fabric bandwidth to 220 petabits per second.In August 2021, the company announced a system which connects multiple integrated cir... | Cerebras | 0.781518 |
88,958 | Alpha-keto acids possesses extensive chemistry as acylation agents. Furthermore, alpha-keto acids such as phenylpyruvic acid are endogenous sources for carbon monoxide (as a gasotransmitter) and pharmaceutical prodrug scaffold. Important representatives: pyruvic acid, pervasive intermediate in metabolism. | Keto acid | 0.781518 |
88,959 | In organic chemistry, keto acids or ketoacids (also called oxo acids or oxoacids) are organic compounds that contain a carboxylic acid group (−COOH) and a ketone group (>C=O). In several cases, the keto group is hydrated. The alpha-keto acids are especially important in biology as they are involved in the Krebs citric ... | Keto acid | 0.781518 |
88,960 | This compound is prepared by a modified Williamson ether synthesis in the presence of a templating cation: (CH2OCH2CH2Cl)2 + (CH2OCH2CH2OH)2 + 2 KOH → (CH2CH2O)6 + 2 KCl + 2 H2O It can be also prepared by the oligomerization of ethylene oxide.It can be purified by distillation, where its tendency to supercool becomes e... | 18-Crown-6 | 0.781518 |
88,961 | The dipole moment of 18-crown-6 varies in different solvent and under different temperature. Under 25 °C, the dipole moment of 18-crown-6 is 2.76 ± 0.06 D in cyclohexane and 2.73 ± 0.02 in benzene. The synthesis of the crown ethers led to the awarding of the Nobel Prize in Chemistry to Charles J. Pedersen. | 18-Crown-6 | 0.781518 |
88,962 | The ancient Greek mathematician Pythagoras and his eponymous theorem have made numerous appearances in art and pop culture, typically as a reference to mathematical endeavors, but also as an example of abstruse higher learning in general. Pythagorean tiling has been used as proofs by the 9th-century Islamic mathematici... | Pythagoras in popular culture | 0.781517 |
88,963 | Biology, physics and gravity interact to pump organic carbon into the deep sea. The processes of fixation of inorganic carbon in organic matter during photosynthesis, its transformation by food web processes (trophodynamics), physical mixing, transport and gravitational settling are referred to collectively as the biol... | Zooplankton grazing | 0.781517 |
88,964 | Multidisciplinary observations are still needed in the deep water column to properly understand the biological pump: Physics: stratification affects particle sinking; understanding the origin of the particles and the residence time of the DIC from particle remineralization in the deep ocean requires measurement of adve... | Zooplankton grazing | 0.781517 |
88,965 | One of the objectives of the SIW geometry is to reproduce the characteristic propagation modes of rectangular waveguides inside a thin template. The width a {\displaystyle a} of the waveguide is an essential parameter of those modes. In the typical SIW geometry, a {\displaystyle a} is the distance between the two vias ... | Post-wall waveguide | 0.781514 |
88,966 | Then, given the vertical geometry of the vias, it is impossible for such modes to appear in SIWs: the electrical current cannot propagate from via to via. Only TE modes are able to propagate through SIW. Each mode appears above a precise cut-off frequency determined by the waveguide dimensions and the filling medium. F... | Post-wall waveguide | 0.781514 |
88,967 | In systems and software development, the term traceability (or requirements traceability) refers to the ability to link product requirements back to stakeholders' rationales and forward to corresponding design artifacts, code, and test cases. Traceability supports numerous software engineering activities such as change... | Traceability | 0.781514 |
88,968 | Another form of "artificial skin" has been created out of flexible semiconductor materials that can sense touch for those with prosthetic limbs. The artificial skin is anticipated to augment robotics in conducting rudimentary jobs that would be considered delicate and require sensitive "touch". Scientists found that by... | Artificial skin | 0.781513 |
88,969 | Control of the structural features of the collagen scaffold (average pore size, degradation rate and surface chemistry) was eventually found to be a critical prerequisite for its unusual biological activity. In 1981 Burke and Yannas proved that their artificial skin worked on patients with 50 to 90 percent burns, vastl... | Artificial skin | 0.781513 |
88,970 | A process for inducing regeneration in skin was invented by Dr. Ioannis V. Yannas (then an assistant professor in the Fibers and Polymers Division, Department of Mechanical Engineering, at Massachusetts Institute of Technology) and Dr. John F. Burke (then chief of staff at Shriners Burns Institute in Boston, Massachuse... | Artificial skin | 0.781513 |
88,971 | Research is continually being done on artificial skin. Newer technologies, such as an autologous spray-on skin produced by Avita Medical, are being tested in efforts to accelerate healing and minimize scarring. The Fraunhofer Institute for Interfacial Engineering and Biotechnology is working towards a fully automated p... | Artificial skin | 0.781513 |
88,972 | Under Kaplan and Winther's view, racial groupings are objective social constructions (see Mills 1998) that have conventional biological reality only insofar as the categories are chosen and constructed for pragmatic scientific reasons. In earlier work, Winther had identified "diversity partitioning" and "clustering ana... | Racial diversity | 0.781511 |
88,973 | Moreover, they argue that biology will not explain why or how people use the idea of race; only history and social relationships will. Imani Perry has argued that race "is produced by social arrangements and political decision making", and that "race is something that happens, rather than something that is. It is dynam... | Racial diversity | 0.781511 |
88,974 | Enumeration cases can have associated data (algebraic data types). Operators can be redefined for classes (operator overloading), and new operators can be defined. Strings fully support Unicode. | Swift programming language | 0.781509 |
88,975 | Many of the features introduced with Swift have well-known performance and safety trade-offs. Apple has implemented optimizations that reduce this overhead. | Swift programming language | 0.781509 |
88,976 | On 29 November 1957, shortly after the launch of Sputnik I on 4 October, two German expatriates, Dr. G. R. Miczaika (from Prussia) and Dr. Eberhart W. Wahl (from Berlin) formed Project Space Track (originally called Project Harvest Moon). : 5: 1 It was established in Building 1535 of the Geophysics Research Directorate... | Project Space Track | 0.781509 |
88,977 | Additionally, gate teleportation is a key component of magic state distillation, a technique that can be used to overcome the limitations of the Eastin-Knill theorem. Quantum gate teleportation has been demonstrated in various types of quantum computers, including linear optical, superconducting quantum computing, and ... | Quantum gate teleportation | 0.781509 |
88,978 | OV1-2 carried a six experiment package, sponsored by the Biophysics Group of the Air Force Weapons Laboratory to conduct radiation studies in orbit in support of the Manned Orbital Laboratory project. The data collected would be compared to theoretical radiation doses predicted by computer programs on the ground to ver... | OV1-2 | 0.781507 |
88,979 | Over a matrix ring Mn(R), the natural module R n is projective but is not free when n > 1. Over a semisimple ring, every module is projective, but a nonzero proper left (or right) ideal is not a free module. Thus the only semisimple rings for which all projectives are free are division rings.The difference between free... | Projective module | 0.781505 |
88,980 | This fact is easy to prove for finitely generated projective modules. In general, it is due to Kaplansky (1958); see Kaplansky's theorem on projective modules.In general though, projective modules need not be free: Over a direct product of rings R × S where R and S are nonzero rings, both R × 0 and 0 × S are non-free p... | Projective module | 0.781505 |
88,981 | Since every projective module over a principal ideal domain is free, one might ask this question: if R is a commutative ring such that every (finitely generated) projective R-module is free, then is every (finitely generated) projective R-module free? The answer is no. A counterexample occurs with R equal to the local ... | Projective module | 0.781505 |
88,982 | The Quillen–Suslin theorem, which solves Serre's problem, is another deep result: if K is a field, or more generally a principal ideal domain, and R = K is a polynomial ring over K, then every projective module over R is free. This problem was first raised by Serre with K a field (and the modules being finitely generat... | Projective module | 0.781505 |
88,983 | Let X be an affine algebraic variety embedded into the affine space k n {\displaystyle k^{n}} , with defining ideal I ⊂ k {\displaystyle I\subset k} . For any polynomial f, let in ( f ) {\displaystyle \operatorname {in} (f)} be the homogeneous component of f of the lowest degree, the initial term of f, and let in ... | Tangent cone | 0.781505 |
88,984 | In mathematics, a Garside element is an element of an algebraic structure such as a monoid that has several desirable properties. Formally, if M is a monoid, then an element Δ of M is said to be a Garside element if the set of all right divisors of Δ, { r ∈ M ∣ for some x ∈ M , Δ = x r } , {\displaystyle \{r\in M\mid {... | Garside element | 0.781504 |
88,985 | IEEE 828-2012 Standard for Configuration Management in Systems and Software Engineering, published date:2012-03-16 ISO 10007:2017 Quality management – Guidelines for configuration management NATO ACMP-2009 – Guidance on configuration management ANSI/EIA-632-1998 Processes for Engineering a System ANSI/EIA-649-1998 Nati... | Configuration Management | 0.781502 |
88,986 | Configuration management (CM) is a systems engineering process for establishing and maintaining consistency of a product's performance, functional, and physical attributes with its requirements, design, and operational information throughout its life. The CM process is widely used by military engineering organizations ... | Configuration Management | 0.781502 |
88,987 | Now widely adopted by numerous organizations and agencies, the CM discipline's concepts include systems engineering (SE), Integrated Logistics Support (ILS), Capability Maturity Model Integration (CMMI), ISO 9000, Prince2 project management method, COBIT, ITIL, product lifecycle management, and Application Lifecycle Ma... | Configuration Management | 0.781502 |
88,988 | A number of standards support or include configuration management, including: ANSI/EIA-649-1998 National Consensus Standard for Configuration Management EIA-649-A 2004 National Consensus Standard for Configuration Management SAE EIA-649-C 2019 Global Consensus Configuration Management Standard ISO 10007 Quality managem... | Configuration Management | 0.781502 |
88,989 | In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a system is two-dimensional. Therefore, a complete basis spanning the space will c... | Two state system | 0.781501 |
88,990 | Phenomena with tremendous industrial applications such as the maser and laser can be explained using the two-state formalism. The two-state formalism also forms the basis of quantum computing. Qubits, which are the building blocks of a quantum computer, are nothing but two-state systems. Any quantum computational opera... | Two state system | 0.781501 |
88,991 | Pedagogically, the two-state formalism is among the simplest of mathematical techniques used for the analysis of quantum systems. It can be used to illustrate fundamental quantum mechanical phenomena such as the interference exhibited by particles of the polarization states of the photon, but also more complex phenomen... | Two state system | 0.781501 |
88,992 | Any two-state system can also be seen as a qubit. Two-state systems are the simplest quantum systems that are of interest, since the dynamics of a one-state system is trivial (as there are no other states the system can exist in). The mathematical framework required for the analysis of two-state systems is that of line... | Two state system | 0.781501 |
88,993 | At least under the assumptions mentioned above, the probability of a given neutron star being a quark star is low, so in the Milky Way there would only be a small population of quark stars. If it is correct, however, that overdense neutron stars can turn into quark stars, that makes the possible number of quark stars h... | Quark stars | 0.7815 |
88,994 | The stability of quark matter, and hence the existence of quark stars, is for these reasons among the unsolved problems in physics. If quark stars can form, then the most likely place to find quark star matter would be inside neutron stars that exceed the internal pressure needed for quark degeneracy – the point at whi... | Quark stars | 0.7815 |
88,995 | Unlike most metal ammine complexes, metal phosphine complexes tend to be lipophilic, displaying good solubility in organic solvents. Phosphine ligands are also π-acceptors. Their π-acidity arises from overlap of P-C σ* anti-bonding orbitals with filled metal orbitals. Beryllium can coordinate with a phosphine due to it... | Organoberyllium chemistry | 0.781499 |
88,996 | Organoberyllium chemistry involves the synthesis and properties of organometallic compounds featuring the group 2 alkaline earth metal beryllium (Be). The area remains understudied, relative to the chemistry of other main-group elements, because although metallic beryllium is relatively unreactive, its dust causes bery... | Organoberyllium chemistry | 0.781499 |
88,997 | The Imaging Compton Telescope (COMPTEL) by the Max Planck Institute for Extraterrestrial Physics, the University of New Hampshire, Netherlands Institute for Space Research, and ESA's Astrophysics Division was tuned to the 0.75-30 MeV energy range and determined the angle of arrival of photons to within a degree and the... | Compton Gamma-Ray Observatory | 0.781498 |
88,998 | The CGRO was named after Arthur Compton, an American physicist and former chancellor of Washington University in St. Louis who received the Nobel prize for work involved with gamma-ray physics. CGRO was built by TRW (now Northrop Grumman Aerospace Systems) in Redondo Beach, California. | Compton Gamma-Ray Observatory | 0.781498 |
88,999 | Versions of de Finetti's theorem for finite exchangeable sequences, and for Markov exchangeable sequences have been proved by Diaconis and Freedman and by Kerns and Szekely. Two notions of partial exchangeability of arrays, known as separate and joint exchangeability lead to extensions of de Finetti's theorem for array... | De Finetti's theorem | 0.781498 |
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