id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
85,300 | In physics, the Pati–Salam model is a Grand Unified Theory (GUT) proposed in 1974 by Abdus Salam and Jogesh Pati. Like other GUTs, its goal is to explain the seeming arbitrariness and complexity of the Standard Model in terms of a simpler, more fundamental theory that unifies what are in the Standard Model disparate pa... | Pati–Salam model | 0.782965 |
85,301 | In a perfect lens or parabolic reflector, rays parallel to the device's axis striking the lens or reflector all pass through a single point, the focal point. In an imperfectly constructed lens or reflector, rays passing through different parts of the element do not converge to a single point but have different focal po... | Focal cloud | 0.782963 |
85,302 | In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mechanics are observable at ordinary, rather than atomic, scale. The Josephson ... | Josephson phase | 0.782963 |
85,303 | University of Rochester physics professor John Howell and graduate student Joseph Choi have announced a scalable cloaking device which uses common optical lenses to achieve visible light cloaking on the macroscopic scale, known as the "Rochester Cloak". The device consists of a series of four lenses which direct light ... | Cloaking device | 0.782962 |
85,304 | The concepts of cloaking are not limited to optics but can also be transferred to other fields of physics. For example, it was possible to cloak acoustics for certain frequencies as well as touching in mechanics. This renders an object "invisible" to sound or even hides it from touching. | Cloaking device | 0.782962 |
85,305 | In molecular biology, Smith-Magenis syndrome chromosome region, candidate 2 (non-protein coding), also known as SMCR2 is a long non-coding RNA. In humans, it is found in a region of chromosome 17 that is commonly deleted in Smith–Magenis syndrome. | SMCR2 | 0.782959 |
85,306 | In mathematics, the quantum dilogarithm is a special function defined by the formula ϕ ( x ) ≡ ( x ; q ) ∞ = ∏ n = 0 ∞ ( 1 − x q n ) , | q | < 1 {\displaystyle \phi (x)\equiv (x;q)_{\infty }=\prod _{n=0}^{\infty }(1-xq^{n}),\quad |q|<1} It is the same as the q-exponential function E q ( x ) {\displaystyle E_{q}(x)} . L... | Quantum dilogarithm | 0.782959 |
85,307 | In 2010, research operations expanded into the adjacent building, Research Advancement Centre 2 (RAC II). In 2012, IQC expanded into the Mike & Ophelia Lazaridis Quantum-Nano Centre. The 285,000-square-foot facility is shared with the Waterloo Institute for Nanotechnology, and is built to stringent standards (controls ... | Institute for Quantum Computing | 0.782958 |
85,308 | Raymond Laflamme is the founding executive director.At its establishment, the institute was composed of only a handful of researchers from the Departments of Computer Science and Physics. Ten years later, there are more than 200 researchers across six departments within the Faculties of Science, Mathematics, and Engine... | Institute for Quantum Computing | 0.782958 |
85,309 | The Institute for Quantum Computing was officially created in 2002, sparked by Research In Motion co-founder Mike Lazaridis and then-president of the University of Waterloo, David Johnston, for research into quantum information. Since inception, Lazaridis has provided more than $100 million in private funding for IQC. ... | Institute for Quantum Computing | 0.782958 |
85,310 | IQC currently has offices and laboratories in both Research Advancement Centre I and II, located in the University of Waterloo’s David Johnston Research & Technology Park. On 9 June 2008, Mike and Ophelia Lazaridis, together with Ontario Premier Dalton McGuinty, University of Waterloo President David Johnston, and othe... | Institute for Quantum Computing | 0.782958 |
85,311 | The Institute for Quantum Computing (IQC) is an affiliate scientific research institute of the University of Waterloo located in Waterloo, Ontario with a multidisciplinary approach to the field of quantum information processing. IQC was founded in 2002 primarily through a donation made by Mike Lazaridis and his wife Op... | Institute for Quantum Computing | 0.782958 |
85,312 | Research at IQC focuses on three main applications of quantum information science and technology using the physical sciences, mathematics and engineering from both theoretical and experimental perspectives.Areas of research currently studied at IQC include: quantum computing quantum communication quantum sensing quantu... | Institute for Quantum Computing | 0.782958 |
85,313 | The following outline is provided as an overview of and topical guide to energy: Energy – in physics, this is an indirectly observed quantity often understood as the ability of a physical system to do work on other physical systems. Since work is defined as a force acting through a distance (a length of space), energy ... | Outline of energy | 0.782958 |
85,314 | History of energy History of the energy industry History of coal History of coal mining Electricity § History History of electromagnetic theory History of electrical engineering History of electronic engineering History of the electric generator History of the electric motor Timeline of the electric motor History of el... | Outline of energy | 0.782958 |
85,315 | Energy industry Worldwide energy supply, outline by country/region World energy resources and consumption List of energy resources, substances like fuels, petroleum products and electricity Energy crisis, the need to conserve energy resources Energy development, development of energy resources — ongoing effort to provi... | Outline of energy | 0.782958 |
85,316 | Electronvolt (eV) – the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt (~1.60 × 10−19 J). Planck energy (EP) – natural unit of energy common in particle physics (~1.96×109 J). Barrel of oil equivalent (BOE) – energy unit equal to the energy r... | Outline of energy | 0.782958 |
85,317 | Chemical energy – energy contained in molecules Electrical energy – energy from electric fields Electro-centric energy – energy sustaining the continuous motion of free electrons. Gravitational energy – energy from gravitational fields Ionization energy – energy that binds an electron to its atom or molecule Kinetic en... | Outline of energy | 0.782958 |
85,318 | List of books about energy issues List of energy abbreviations List of energy storage projects List of large wind farms List of notable renewable energy organizations List of photovoltaics companies List of renewable energy topics by country List of solar thermal power stations Index of wave articles List of wind turbi... | Outline of energy | 0.782958 |
85,319 | Condition (i) and Borel–Cantelli give that X n = Y n {\displaystyle X_{n}=Y_{n}} for n {\displaystyle n} large, almost surely. Hence ∑ n = 1 ∞ X n {\displaystyle \textstyle \sum _{n=1}^{\infty }X_{n}} converges if and only if ∑ n = 1 ∞ Y n {\displaystyle \textstyle \sum _{n=1}^{\infty }Y_{n}} converges. Conditions (ii)... | Kolmogorov's three-series theorem | 0.782957 |
85,320 | With A = 2 {\displaystyle A=2} the summands of the first two series are identically zero and var(Yn)= n − 2 {\displaystyle n^{-2}} . The conditions of the theorem are then satisfied, so it follows that the harmonic series with random signs converges almost surely. On the other hand, the analogous series of (for example... | Kolmogorov's three-series theorem | 0.782957 |
85,321 | As an illustration of the theorem, consider the example of the harmonic series with random signs: ∑ n = 1 ∞ ± 1 n . {\displaystyle \sum _{n=1}^{\infty }\pm {\frac {1}{n}}.} Here, " ± {\displaystyle \pm } " means that each term 1 / n {\displaystyle 1/n} is taken with a random sign that is either 1 {\displaystyle 1} or −... | Kolmogorov's three-series theorem | 0.782957 |
85,322 | We see that condition (iii) implies condition (ii): Kolmogorov's two-series theorem along with condition (i) applied to the case A = 1 {\displaystyle A=1} gives the convergence of ∑ n = 1 ∞ ( Y n − E ) {\displaystyle \textstyle \sum _{n=1}^{\infty }(Y_{n}-\mathbb {E} )} . So given the convergence of ∑ n = 1 ∞ Y n {\di... | Kolmogorov's three-series theorem | 0.782957 |
85,323 | In probability theory, Kolmogorov's Three-Series Theorem, named after Andrey Kolmogorov, gives a criterion for the almost sure convergence of an infinite series of random variables in terms of the convergence of three different series involving properties of their probability distributions. Kolmogorov's three-series th... | Kolmogorov's three-series theorem | 0.782957 |
85,324 | SHYSTER is a specific example of a general category of legal expert systems, broadly defined as systems that make use of artificial intelligence (AI) techniques to solve legal problems. Legal AI systems can be divided into two categories: legal retrieval systems and legal analysis systems. SHYSTER belongs to the latter... | Shyster (expert system) | 0.782956 |
85,325 | The Publishing Requirements for Industry Standard Metadata (PRISM) for the Internet, computing, and computer science, is a specification that defines a set of XML metadata vocabularies for syndicating, aggregating, post-processing and multi-purposing content. PRISM provides a framework for the interchange and preservat... | Publishing Requirements for Industry Standard Metadata | 0.782956 |
85,326 | What locations, organizations, topics, people, and/or events it covers, the media it contains, and under what conditions it may be reproduced? When it was published? (cover date, post date, volume, number), withdrawn? Where it can be republished, and the original platform on which it appeared? How it can be reused?Comm... | Publishing Requirements for Industry Standard Metadata | 0.782956 |
85,327 | The Standard model of particle physics is the theory describing three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, while omitting gravity) in the universe, as well as classifying all known elementary particles. It was developed in stages throughout the latter half of the 20t... | ATLAS Collaboration | 0.782955 |
85,328 | Biochemistry: hypergammaglobulinaemia; raised bilirubin without liver enzymes being raised. Hematology: lymphopenia; non-regenerative—usually mild—anaemia. Serology: the cat has a high antibody titre to FCoV: this parameter should be used with caution, because of the high prevalence of FCoV in breeding and rescue catte... | Feline infectious peritonitis | 0.782954 |
85,329 | The MasSpec Pen, or the precìso MasSpec Pen System, is a mass spectrometry (MS) based cancer detection and diagnosis system that can be used for ex vivo and in vivo tissue sample analysis. The system collects biological molecules from a tissue sample surface via a solid-liquid extraction mechanism and transports the mo... | MasSpec Pen | 0.782954 |
85,330 | The MasSpec Pen, initially described in 2017, is a solvent-based ambient ionization technique but differs from its predecessors due to the handheld nature of the device, allowing analysis of samples distant from the mass spectrometer in a geometry independent manner. The MasSpec Pen used a probe that can be manipulated... | MasSpec Pen | 0.782954 |
85,331 | Livia S. Eberlin, Ph.D., an Assistant Professor of Chemistry at the University of Texas at Austin, first reported the invention of the MasSpec Pen in 2017. Within her laboratory, the device has been used to analyze human tissue biopsies, including normal and cancerous breast, lung, ovarian, and thyroid samples. The Mas... | MasSpec Pen | 0.782954 |
85,332 | Embed M in some high-dimensional Euclidean space. (Use the Whitney embedding theorem.) Take a small neighborhood of M in that Euclidean space, Nε. Extend the vector field to this neighborhood so that it still has the same zeroes and the zeroes have the same indices. | Poincaré–Hopf theorem | 0.782952 |
85,333 | In the special case of a manifold without boundary, this amounts to saying that the integral is 0. But by examining vector fields in a sufficiently small neighborhood of a source or sink, we see that sources and sinks contribute integer amounts (known as the index) to the total, and they must all sum to 0. This result ... | Poincaré–Hopf theorem | 0.782952 |
85,334 | The Euler characteristic of a closed surface is a purely topological concept, whereas the index of a vector field is purely analytic. Thus, this theorem establishes a deep link between two seemingly unrelated areas of mathematics. It is perhaps as interesting that the proof of this theorem relies heavily on integration... | Poincaré–Hopf theorem | 0.782952 |
85,335 | If M {\displaystyle M} has boundary, then we insist that v {\displaystyle v} be pointing in the outward normal direction along the boundary. Then we have the formula ∑ i index x i ( v ) = χ ( M ) {\displaystyle \sum _{i}\operatorname {index} _{x_{i}}(v)=\chi (M)\,} where the sum of the indices is over all the isolate... | Poincaré–Hopf theorem | 0.782952 |
85,336 | Theorem. Let M {\displaystyle M} be a compact differentiable manifold. Let v {\displaystyle v} be a vector field on M {\displaystyle M} with isolated zeroes. | Poincaré–Hopf theorem | 0.782952 |
85,337 | It is still possible to define the index for a vector field with nonisolated zeroes. A construction of this index and the extension of Poincaré–Hopf theorem for vector fields with nonisolated zeroes is outlined in Section 1.1.2 of (Brasselet, Seade & Suwa 2009). | Poincaré–Hopf theorem | 0.782952 |
85,338 | In mathematics, the Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used in differential topology. It is named after Henri Poincaré and Heinz Hopf. The Poincaré–Hopf theorem is often illustrated by the special case... | Poincaré–Hopf theorem | 0.782952 |
85,339 | The Sudarshan-Glauber P representation is a suggested way of writing down the phase space distribution of a quantum system in the phase space formulation of quantum mechanics. The P representation is the quasiprobability distribution in which observables are expressed in normal order. In quantum optics, this representa... | Glauber–Sudarshan P representation | 0.782951 |
85,340 | If the quantum system has a classical analog, e.g. a coherent state or thermal radiation, then P is non-negative everywhere like an ordinary probability distribution. If, however, the quantum system has no classical analog, e.g. an incoherent Fock state or entangled system, then P is negative somewhere or more singular... | Glauber–Sudarshan P representation | 0.782951 |
85,341 | In the mathematical theory of Kleinian groups, Jørgensen's inequality is an inequality involving the traces of elements of a Kleinian group, proved by Troels Jørgensen (1976).The inequality states that if A and B generate a non-elementary discrete subgroup of the SL2(C), then | Tr ( A ) 2 − 4 | + | Tr ( A B A − 1 B... | Jørgensen's inequality | 0.78295 |
85,342 | A gravity gun is a type of device in video games, particularly first-person shooters using physics engines, whereby players can directly manipulate objects in the world, often allowing them to be used as projectiles against hostile characters. The concept was popularized by the gravity gun found in Valve's Half-Life 2,... | Gravity Gun | 0.782947 |
85,343 | In Space Station 13, crew members can research and then build the One-point Bluespace-Gravitational Manipulator, which has three modes, repulse, which throws everything in an area away, attract, which does the opposite, and chaos, which does both settings, randomly. In Wild 9, the main character Wex Major can manipulat... | Gravity Gun | 0.782947 |
85,344 | In Garry's Mod, one of the items is a gravity gun directly imported from Half-Life 2. It also includes a Physics Gun, a modified gravity gun which can position items and rag doll limbs as well as freeze them for constructing scenes or objects. In Subnautica, there is a weapon called the Propulsion Cannon that the devel... | Gravity Gun | 0.782947 |
85,345 | Various other video games have included gameplay features that allow players to use the game's physics to their advantage in combat. In some cases, these are manifested as weapons or devices. For instance, Portal (also created by Valve) features the Aperture Science Handheld Portal Device which displays a limited capac... | Gravity Gun | 0.782947 |
85,346 | Valve's Half-Life 2 made significant use of physics, powered by the Source engine. The physics engine within Source is derived from Havok, which opens up a wealth of possibilities for object interaction – particularly when later in the game, Freeman receives an energy-beam weapon that lets him move huge objects. Althou... | Gravity Gun | 0.782947 |
85,347 | Although Half-Life 2 and TimeSplitters: Future Perfect were the first games released to feature a gravity gun (the former released on November 16, 2004, and the latter released on March 21, 2005), id Software had previously conceived a similar idea during the development of the earlier title Doom 3. id Software designe... | Gravity Gun | 0.782947 |
85,348 | It was not until the third installment of the TimeSplitters franchise, TimeSplitters: Future Perfect, that the Temporal Uplink was given the ability to manipulate the physics in the game. In Future Perfect, the Temporal Uplink played a much larger role than that of its previous, map and mini-game oriented functionality... | Gravity Gun | 0.782947 |
85,349 | A conventional CRT consists of an electron gun at the back of the tube that is aimed at a thin layer of phosphor at the front of the tube. Depending on the role, the beam of electrons emitted by the gun is steered around the display using magnetic (television) or electrostatic (oscilloscope) means. When the electrons s... | Storage tube | 0.782945 |
85,350 | At these meetings, the PRRS scientific awards and the Maria Skłodowska-Curie Medals are presented to the laureates. The PRRS is also active on the international stage and has been entrusted the organization of important scientific events. The Society organized two Annual Meetings (in 1981 and 2000) of the European Soci... | Polish Radiation Research Society | 0.782944 |
85,351 | The PRRS Scientific Awards for outstanding publications in the field of radiation research were established in 1970. The awards have the form of a cast bronze statuette (designed by Hanna Jelonek) and honorary diploma. They are currently awarded in five sub-disciplines: radiation chemistry and photochemistry, radiobiol... | Polish Radiation Research Society | 0.782944 |
85,352 | Intensive animal farming, industrial livestock production, and macro-farms, also known by opponents as factory farming, is a type of intensive agriculture, specifically an approach to animal husbandry designed to maximize production, while minimizing costs. To achieve this, agribusinesses keep livestock such as cattle,... | Animal feeding operations | 0.782943 |
85,353 | This journal is indexed in the following databases: Thomson Reuters BIOSIS Biological Abstracts Current Contents / Life Sciences Journal Citation Reports Science Citation Index Expanded Zoological Record PubMed/Medline (Web of Knowledge) Gale Academic OneFile Expanded Academic EBSCO host Academic Search EBSCO NAL Catal... | Journal of Mathematical Biology | 0.782942 |
85,354 | Journal of Mathematical Biology is a peer-reviewed, mathematics journal, published by Springer Verlag. Founded in 1974, the journal publishes articles on mathematical biology. In particular, papers published in this journal 'should either provide biological insight as a result of mathematical analysis or identify and o... | Journal of Mathematical Biology | 0.782942 |
85,355 | Robogals' primary activity is running engineering based workshops, either in schools or by having the schools visit the uni; the workshops are aim to inspire gender diversity in engineering by engaging girls and guys in a range engineering topics. These topics are selected by the volunteers running the sessions to refl... | Robogals | 0.782941 |
85,356 | Robogals was founded as a student club at the University of Melbourne in July 2008 by mechatronics engineering undergraduate student Marita Cheng, together with software engineering student Mark Parncutt and three other engineering and science students, Kelly Chiu, Ann Chee Lim and Vi Vu. The idea initially came from e... | Robogals | 0.782941 |
85,357 | Past events have included a robotics competition (2008), a mass robot dance that attracted significant media coverage (2009), a robot artwork exhibition, science fair (2010), the Robogals Science Challenge (2012-), and the Robogals Challenge in the UK (2015-). The organisation is predominately run by university student... | Robogals | 0.782941 |
85,358 | IDSM automatically sends signals to end-use systems to shed load depending on system conditions. This allows for very precise tuning of demand to ensure that it matches supply at all times, reduces capital expenditures for the utility. Critical system conditions could be peak times, or in areas with levels of variable ... | Energy demand management | 0.78294 |
85,359 | The under-40 rule is based on Fields's desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others." Moreover, an individual can only be awarded one Fie... | Fields Medal | 0.782939 |
85,360 | "In 1982, the congress was due to be held in Warsaw but had to be rescheduled to the next year, because of martial law introduced in Poland on 13 December 1981. The awards were announced at the ninth General Assembly of the IMU earlier in the year and awarded at the 1983 Warsaw congress.In 1990, Edward Witten became th... | Fields Medal | 0.782939 |
85,361 | In capital Greek letters the word ΑΡΧΙΜΗΔΟΥΣ, or "of Archimedes," is inscribed. On the reverse is the inscription (in Latin):CONGREGATI EX TOTO ORBE MATHEMATICI OB SCRIPTA INSIGNIA TRIBUERETranslation: "Mathematicians gathered from the entire world have awarded for outstanding writings." In the background, there is th... | Fields Medal | 0.782939 |
85,362 | Only a few physical systems are actually linear with respect to the model parameters. One such system from geophysics is that of the Earth's gravitational field. The Earth's gravitational field is determined by the density distribution of the Earth in the subsurface. Because the lithology of the Earth changes quite sig... | Doppler tomography | 0.782939 |
85,363 | In X-ray computed tomography the lines on which the parameter is integrated are straight lines: the tomographic reconstruction of the parameter distribution is based on the inversion of the Radon transform. Although from a theoretical point of view many linear inverse problems are well understood, problems involving th... | Doppler tomography | 0.782939 |
85,364 | In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane. There are one triangle, two squares, and one hexagon on each vertex. It has Schläfli symbol of rr{3,6}. John Conway calls it a rhombihexadeltille. It can be considered a cantellated by Norman Johnson's terminology or an expanded ... | Small rhombitrihexagonal tiling | 0.782938 |
85,365 | Other deltoidal tilings are possible. Point symmetry allows the plane to be filled by growing kites, with the topology as a square tiling, V4.4.4.4, and can be created by crossing string of a dream catcher. Below is an example with dihedral hexagonal symmetry. Another face transitive tiling with kite faces, also a topo... | Small rhombitrihexagonal tiling | 0.782938 |
85,366 | Cosmological observations of phenomena such as the cosmic microwave background and the cosmic abundance of elements, together with the predictions of the Standard Model of particle physics, place constraints on the physical conditions in the early universe. The success of the Standard Model at explaining these observat... | Particle cosmology | 0.782934 |
85,367 | This is roughly equal to the age of the universe at that time. For example, the pion has a mean lifetime to decay of about 26 nanoseconds. This means that particle physics processes involving pion decay can be neglected until roughly that much time has passed since the Big Bang. | Particle cosmology | 0.782934 |
85,368 | Particle physics is the study of the interactions of elementary particles at high energies, whilst physical cosmology studies the universe as a single physical entity. The interface between these two fields is sometimes referred to as particle cosmology. Particle physics must be taken into account in cosmological model... | Particle cosmology | 0.782934 |
85,369 | A neural circuit (also known as a biological neural network BNNs) is a population of neurons interconnected by synapses to carry out a specific function when activated. Multiple neural circuits interconnect with one another to form large scale brain networks.Neural circuits have inspired the design of artificial neural... | Neural circuits | 0.782933 |
85,370 | In theoretical physics, an anti-de Sitter (AdS) black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a negative cosmological constant. Such a solution asymptotically approaches anti-de Sitter space at spatial infinity, and is a generalization ... | AdS black hole | 0.782931 |
85,371 | In organic chemistry, the di-π-methane rearrangement is the photochemical rearrangement of a molecule that contains two π-systems separated by a saturated carbon atom. In the aliphatic case, this molecules is a 1,4-diene; in the aromatic case, an allyl-substituted arene. The reaction forms (respectively) an ene- or ary... | Di-π-methane rearrangement | 0.78293 |
85,372 | JADE is an acronym for Japan, Deutschland (Germany) and England, the three countries from which the participating universities originated. The JADE jet chamber is now exhibited in the physics lecture hall at the University of Heidelberg. Although the last data with JADE were taken in 1986, analysis continued, with the ... | JADE particle detector | 0.78293 |
85,373 | Bundles may also be described by their sheaves of sections. The pullback of bundles then corresponds to the inverse image of sheaves, which is a contravariant functor. A sheaf, however, is more naturally a covariant object, since it has a pushforward, called the direct image of a sheaf. The tension and interplay betwee... | Induced bundle | 0.782929 |
85,374 | Let π: E → B be a fiber bundle with abstract fiber F and let f: B′ → B be a continuous map. Define the pullback bundle by f ∗ E = { ( b ′ , e ) ∈ B ′ × E ∣ f ( b ′ ) = π ( e ) } ⊆ B ′ × E {\displaystyle f^{*}E=\{(b',e)\in B'\times E\mid f(b')=\pi (e)\}\subseteq B'\times E} and equip it with the subspace topology and th... | Induced bundle | 0.782929 |
85,375 | In mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π: E → B and a continuous map f: B′ → B one can define a "pullback" of E by f as a bundle f*E over B′. The fiber of f*E over a point b′ in B′ is just the fiber of E over f(b′). Thus f... | Induced bundle | 0.782929 |
85,376 | By restriction this representation yields an isomorphism between the subgroup of unit quaternions and their image SU(2). Topologically, the unit quaternions are the 3-sphere, so the underlying space of SU(2) is also a 3-sphere. The group SU(2) is important for describing spin in quantum mechanics; see Pauli matrices. | Vector quaternion | 0.782929 |
85,377 | In each case, the representation given is one of a family of linearly related representations. In the terminology of abstract algebra, these are injective homomorphisms from H {\displaystyle \mathbb {H} } to the matrix rings M(2,C) and M(4,R), respectively. Using 2 × 2 complex matrices, the quaternion a + bi + cj + dk ... | Vector quaternion | 0.782929 |
85,378 | Nonsingular representation (compared with Euler angles for example). Pairs of unit quaternions represent a rotation in 4D space (see Rotations in 4-dimensional Euclidean space: Algebra of 4D rotations).The set of all unit quaternions (versors) forms a 3-sphere S3 and a group (a Lie group) under multiplication, double c... | Vector quaternion | 0.782929 |
85,379 | The quaternions are "essentially" the only (non-trivial) central simple algebra (CSA) over the real numbers, in the sense that every CSA over the real numbers is Brauer equivalent to either the real numbers or the quaternions. Explicitly, the Brauer group of the real numbers consists of two classes, represented by the ... | Vector quaternion | 0.782929 |
85,380 | The total deposited charge is a direct measure of the energy of the ionizing particle (neutron or photon) entering the neutron detector. This signal integration technique is an established method for measuring ionization in the detector in nuclear physics. | Neutron detector | 0.782929 |
85,381 | Figure 1 shows the typical main components of the setup of a neutron detection unit. In principle, the diagram shows the setup as it would be in any modern particle physics lab, but the specifics describe the setup in Jefferson Lab (Newport News, Virginia). In this setup, the incoming particles, comprising neutrons and... | Neutron detector | 0.782929 |
85,382 | For example, the detected neutron rate from a plasma can give information about the ion temperature. Particle physics: Neutron detection has been proposed as a method of enhancing neutrino detectors. Materials science: Elastic and inelastic neutron scattering enables experimentalists to characterize the morphology of m... | Neutron detector | 0.782929 |
85,383 | Boiling water reactors may have dozens of neutron detectors, one per fuel assembly. Most neutron detectors used in thermal-spectrum nuclear reactors are optimized to detect thermal neutrons. Plasma physics: Neutron detection is used in fusion plasma physics experiments such as JET. | Neutron detector | 0.782929 |
85,384 | The output voltage V+ of the resistive summer can be found by applying the superposition theorem: V + = R 2 R 1 + R 2 ⋅ V i n + R 1 R 1 + R 2 ⋅ V s {\displaystyle V_{\mathrm {+} }={\frac {R_{2}}{R_{1}+R_{2}}}\cdot V_{\mathrm {in} }+{\frac {R_{1}}{R_{1}+R_{2}}}\cdot V_{\mathrm {s} }} The comparator will switch when V+=0... | Schmitt trigger | 0.782929 |
85,385 | This is Utumi's argument as it appears in (Lam 2001, p. 164-165) LemmaAssume that R satisfies the ascending chain condition on annihilators of the form { r ∈ R ∣ a r = 0 } {\displaystyle \{r\in R\mid ar=0\}} where a is in R. Then Any nil one-sided ideal is contained in the lower nil radical Nil*(R); Every nonzero nil r... | Levitzky's theorem | 0.782928 |
85,386 | In mathematics, more specifically ring theory and the theory of nil ideals, Levitzky's theorem, named after Jacob Levitzki, states that in a right Noetherian ring, every nil one-sided ideal is necessarily nilpotent. Levitzky's theorem is one of the many results suggesting the veracity of the Köthe conjecture, and indee... | Levitzky's theorem | 0.782928 |
85,387 | The Brown–McCoy radical (called the strong radical in the theory of Banach algebras) can be defined in any of the following ways: the intersection of the maximal two-sided ideals the intersection of all maximal modular ideals the upper radical of the class of all simple rings with identityThe Brown–McCoy radical is stu... | Torsion theory | 0.782927 |
85,388 | The app allows users to create and edit files online while collaborating with other users in real-time. Edits are tracked by a user with a revision history presenting changes. An editor's position is highlighted with an editor-specific color and cursor and a permissions system regulates what users can do. Updates have ... | Google Slides | 0.782926 |
85,389 | Launched in September 2016, "Explore" provides additional functionality to the Google Drive suite through machine learning. In Google Slides, Explore dynamically generates design suggestions based on the contents of each slide. The "Explore" features in the Drive suite follow the launch of a more basic research tool or... | Google Slides | 0.782926 |
85,390 | In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class groups of cyclotomic fields. A special case was first proven by Ernst Kummer (1847) while the general result is due to Ludwig Stickelberger (1890). | Stickelberger's theorem | 0.782925 |
85,391 | Stickelberger's Theorem Let F be an abelian number field. Then, the Stickelberger ideal of F annihilates the class group of F. Note that θ(F) itself need not be an annihilator, but any multiple of it in Z {\displaystyle \mathbb {Z} } is. Explicitly, the theorem is saying that if α ∈ Z {\displaystyle \mathbb {Z} } is ... | Stickelberger's theorem | 0.782925 |
85,392 | By the Kronecker–Weber theorem there is an integer m such that F is contained in Km. Fix the least such m (this is the (finite part of the) conductor of F over Q {\displaystyle \mathbb {Q} } ). There is a natural group homomorphism Gm → GF given by restriction, i.e. if σ ∈ Gm, its image in GF is its restriction to F de... | Stickelberger's theorem | 0.782925 |
85,393 | The first theorem states that the surface area A of a surface of revolution generated by rotating a plane curve C about an axis external to C and on the same plane is equal to the product of the arc length s of C and the distance d traveled by the geometric centroid of C: For example, the surface area of the torus with... | Guldinus theorem | 0.782925 |
85,394 | The theorems can be generalized for arbitrary curves and shapes, under appropriate conditions. Goodman & Goodman generalize the second theorem as follows. If the figure F moves through space so that it remains perpendicular to the curve L traced by the centroid of F, then it sweeps out a solid of volume V = Ad, where A... | Guldinus theorem | 0.782925 |
85,395 | The second theorem states that the volume V of a solid of revolution generated by rotating a plane figure F about an external axis is equal to the product of the area A of F and the distance d traveled by the geometric centroid of F. (The centroid of F is usually different from the centroid of its boundary curve C.) Th... | Guldinus theorem | 0.782925 |
85,396 | Let A {\displaystyle A} be the area of F {\displaystyle F} , W {\displaystyle W} the solid of revolution of F {\displaystyle F} , and V {\displaystyle V} the volume of W {\displaystyle W} . Suppose F {\displaystyle F} starts in the x z {\displaystyle xz} -plane and rotates around the z {\displaystyle z} -axis. The dist... | Guldinus theorem | 0.782925 |
85,397 | The controversial Toba catastrophe theory, presented in the late 1990s to early 2000s, suggested that a bottleneck of the human population occurred approximately 75,000 years ago, proposing that the human population was reduced to perhaps 10,000–30,000 individuals when the Toba supervolcano in Indonesia erupted and tri... | Population bottleneck | 0.782924 |
85,398 | A situation that temporarily prevents castling does not prevent the use of this notation. En passant target square: This is a square over which a pawn has just passed while moving two squares; it is given in algebraic notation. If there is no en passant target square, this field uses the character "-". | Forsyth–Edwards Notation | 0.782924 |
85,399 | A FEN record defines a particular game position, all in one text line and using only the ASCII character set. A text file with only FEN data records should use the filename extension .fen.A FEN record contains six fields, each separated by a space. The fields are as follows: Piece placement data: Each rank is described... | Forsyth–Edwards Notation | 0.782924 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.