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82,400 | The greater the differential, the more mechanical power can be efficiently extracted out of heat energy, as per Carnot's theorem. The efficiency of the Rankine cycle is limited by the high heat of vaporization of the working fluid. Unless the pressure and temperature reach supercritical levels in the boiler, the temper... | Steam reheat | 0.799439 |
82,401 | The cousins met at the time but later followed different paths. Joan, strongly opposed to nuclear weapons, defected to Mao's China, while Taylor maintained that political policy was not within the remit of the scientist.In 1950, he published two papers estimating the yield of the explosion using the Buckingham Pi theor... | G. I. Taylor | 0.799439 |
82,402 | Lindzen's early work was concerned with ozone photochemistry, the aerodynamics of the middle atmosphere, the theory of atmospheric tides, and planetary waves. His work in these areas led him to a number of fundamental scientific discoveries, including the discovery of negative equivalent depths in classical tidal theor... | Richard Lindzen | 0.799439 |
82,403 | Mihail Roco, one of the architects of the USA's National Nanotechnology Initiative, has proposed four states of nanotechnology that seem to parallel the technical progress of the Industrial Revolution, progressing from passive nanostructures to active nanodevices to complex nanomachines and ultimately to productive nan... | Nanoscale machines | 0.799439 |
82,404 | 1977) , Pearson Higher Education, ISBN 978-0130413437. Poole, David (2010), Linear Algebra: A Modern Introduction (3rd ed. ), Cengage – Brooks/Cole, ISBN 978-0-538-73545-2 Ricardo, Henry (2010), A Modern Introduction To Linear Algebra (1st ed. | Linear Algebra | 0.799439 |
82,405 | With food shortages spreading and resources fading, some dreamed of a new industrial solution. The Hungarian Károly Ereky coined the word "biotechnology" in Hungary during 1919 to describe a technology based on converting raw materials into a more useful product. He built a slaughterhouse for a thousand pigs and also a... | History of biotechnology | 0.799438 |
82,406 | Indeed, this condition is necessary since the multiplication mapping μ: A ⊗ K A → A {\displaystyle \mu :A\otimes _{K}A\rightarrow A} arising in the definition above is a A-A-bimodule epimorphism, which is split as an A-K-bimodule map by the right inverse mapping A → A ⊗ K A {\displaystyle A\rightarrow A\otimes _{K}A} g... | Separable algebra | 0.799438 |
82,407 | The recycling process, on the other hand, as suggested by Ciez and Whitacre emits a significant amount of GHG. As shown in the battery recycling emission plot a and c, the emission of the recycling process varies with the different recycling processes, different chemistry and different form factor. Thus, the net emissi... | Traction battery | 0.799438 |
82,408 | With its focus on increasing diversity and inclusion within the computer science field, the Congressional App Challenge enrolls a large number of underrepresented minority, female, and rural students with various experience in coding. In 2018, 8% of participants were Black, 15% Hispanic, and 3% American Indian, and 36%... | Congressional App Challenge | 0.799438 |
82,409 | Cambridge Cosmology – from Cambridge University (public home page) Cosmology 101 – from the NASA WMAP group Center for Cosmological Physics. University of Chicago, Chicago. Origins, Nova Online – Provided by PBS. | Cosmological models | 0.799438 |
82,410 | In 1981, Alasdair McDowall and Jacques Dubochet, scientists at the European Molecular Biology Laboratory, reported the first successful implementation of cryo-EM. McDowall and Dubochet vitrified pure water in a thin film by spraying it onto a hydrophilic carbon film that was rapidly plunged into cryogen (liquid propane... | Electron cryo-microscopy | 0.799438 |
82,411 | Penetrance in genetics is the proportion of individuals carrying a particular variant (or allele) of a gene (the genotype) that also expresses an associated trait (the phenotype). In medical genetics, the penetrance of a disease-causing mutation is the proportion of individuals with the mutation that exhibit clinical s... | Incomplete penetrance | 0.799437 |
82,412 | There is a physical quantity closely linked to free energy (free enthalpy), with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873, Willard Gibbs created a diagram illustrating the concept of free energy corresponding to free enthalpy. On the diagram one can see the quan... | Negative entropy | 0.799437 |
82,413 | In molecular biology the Bacterial Microcompartment (BMC) domain is a protein domain found in a variety of shell proteins, including CsoS1A, CsoS1B and CsoS1C of Thiobacillus neapolitanus (Halothiobacillus neapolitanus) and their orthologs from other bacteria. These shell proteins form the polyhedral structure of the c... | BMC domain | 0.799437 |
82,414 | Like the matrix multiplication exponent, the dual matrix multiplication exponent sometimes appears in the complexity of algorithms in numerical linear algebra and optimization.The first bound on α is by Coppersmith in 1982, who showed that α > 0.17227 {\displaystyle \alpha >0.17227} . The current best peer-reviewed bou... | Fast matrix multiplication | 0.799437 |
82,415 | The experimental setup to perform Raman spectroelectrochemistry consists of a light source, a spectrometer, a potentiostat, a spectroelectrochemical cell, a three-electrode system, radiation beam conducting devices, data collection and analysis devices. Nowadays, there are commercial instruments that integrate all thes... | Raman spectroelectrochemistry | 0.799437 |
82,416 | ADNI-3 will follow current and additional patients with normal cognition, MCI, and AD for a further five years. The approach is unique to the study are: Use of web-based methods for cognitive assessment of patients in conjunction with the Brain Health Registry. Use of tau PET imaging to determine how tau tangles are re... | Alzheimer's Disease Neuroimaging Initiative | 0.799437 |
82,417 | The Breuillard–Green–Tao theorem on classification of approximate groups can be used to give a new proof of Gromov's theorem on groups of polynomial growth. The result obtained is actually a bit stronger since it establishes that there exists a "growth gap" between virtually nilpotent groups (of polynomial growth) and ... | Approximate group | 0.799437 |
82,418 | In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the failure to reject a null hypothesis that is actually false (also known as a "... | Type I error rate | 0.799436 |
82,419 | The error-correcting properties of the generators are invariant under these operations. The modified generators are as follows: g 1 = Z X Z I g 2 = Z Z I Z g 3 = Y X X Z g 4 = Z Y Y X {\displaystyle {\begin{array}{cccccc}g_{1}&=&Z&X&Z&I\\g_{2}&=&Z&Z&I&Z\\g_{3}&=&Y&X&X&Z\\g_{4}&=&Z&Y&Y&X\end{array}}} The above set of ge... | Entanglement-assisted stabilizer formalism | 0.799436 |
82,420 | The theorem can also be proven easily using Menelaus' theorem. From the transversal BOE of triangle △ACF, A B ¯ B F ¯ ⋅ F O ¯ O C ¯ ⋅ C E ¯ E A ¯ = − 1 {\displaystyle {\frac {\overline {AB}}{\overline {BF}}}\cdot {\frac {\overline {FO}}{\overline {OC}}}\cdot {\frac {\overline {CE}}{\overline {EA}}}=-1} and from the tra... | Ceva's Theorem | 0.799436 |
82,421 | XFLR5 is an analysis tool for airfoils, wings and planes operating at low Reynolds Numbers, that has implemented XFOIL's Direct and Inverse analysis capabilities. QBlade implements XFOIL via XFLR5 for use in wind turbine design. OpenVSP is a parametric aircraft geometry and aerodynamic analysis tool supported by NASA. | XFOIL | 0.799436 |
82,422 | Biofilms are being developed as consumer products that can be sprayed or wiped over porous and nonporous surfaces. The microbe resistance of a surface treated with the appropriate antimicrobial nanotechnology can last up to 90 days, or the product's usable life, if protected during the production process. On the preven... | Antimicrobial nanotechnology | 0.799436 |
82,423 | On the other hand, Scott's trick implies that the cardinal number 0 is { ∅ } {\displaystyle \{\emptyset \}} , which is also the ordinal number 1, and this may be confusing. A possible compromise (to take advantage of the alignment in finite arithmetic while avoiding reliance on the axiom of choice and confusion in infi... | Cardinal exponentiation | 0.799436 |
82,424 | In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras, for example complex number... | Cayley–Dickson construction | 0.799436 |
82,425 | Database caching is a process included in the design of computer applications which generate web pages on-demand (dynamically) by accessing backend databases. When these applications are deployed on multi-tier environments that involve browser-based clients, web application servers and backend databases, middle-tier da... | Database cache | 0.799435 |
82,426 | Participant) Pacific Northwest Neuroscience Neighborhood (B.I. Participant) University of California System Cal-BRAIN (B.I. Participant) University of Pittsburgh Brain Institute (B.I. | Brain Activity Map Project | 0.799435 |
82,427 | A neural network is described by a directed acyclic graph G(V,E), where: V is the set of nodes. Each node is a simple computation cell. E is the set of edges, Each edge has a weight. The input to the network is represented by the sources of the graph – the nodes with no incoming edges. | VC Dimension | 0.799435 |
82,428 | Construct a circle with center B and radius a (see Figure 9), which intersects the secant through A and C in C and K. The power of the point A with respect to the circle is equal to both AB2 − BC2 and AC·AK. Therefore, c 2 − a 2 = b ( b + 2 a cos ( π − γ ) ) = b ( b − 2 a cos γ ) , {\displaystyle {\begin{aligned}c^... | Laws of cosines | 0.799435 |
82,429 | In point-set topology, the closed graph theorem states the following: Non-Hausdorff spaces are rarely seen, but non-compact spaces are common. An example of non-compact Y {\displaystyle Y} is the real line, which allows the discontinuous function with closed graph f ( x ) = { 1 x if x ≠ 0 , 0 else {\displaystyle f(x)={... | Closed graph theorem | 0.799434 |
82,430 | Kraichnan received his B.S. and Ph.D. in physics from MIT, graduating in 1949. He became a member of the Institute for Advanced Study in Princeton in 1949/50, and was one of the last assistants to Albert Einstein. | Robert Kraichnan | 0.799434 |
82,431 | The NNI's budget supplement proposed by the Obama administration for Fiscal Year 2015 provides $1.5 billion in requested funding. The cumulative NNI investment since fiscal year 2001, including the 2015 request, totals almost $21 billion. Cumulative investments in nanotechnology-related environmental, health, and safet... | National Nanotechnology Initiative | 0.799434 |
82,432 | Since then, only five more of these values have been found. In the same 1955 paper, Greenwood and Gleason also computed the multicolor Ramsey number R(3,3,3): the smallest number r such that, if a complete graph on r vertices has its edges colored with three colors, then it necessarily contains a monochromatic triangle... | Andrew M. Gleason | 0.799434 |
82,433 | In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g − 1). A group for which the maximum is achieved is called a Hurwitz... | Hurwitz's automorphisms theorem | 0.799434 |
82,434 | This work has been incorporated into SpiNNaker (Spiking Neural Network Architecture) which is being used as the Neuromorphic Computing Platform for the Human Brain Project. Non-random distribution of locations: Although the storage locations are initially distributed randomly in the binary N address space, the final di... | Sparse Distributed Memory | 0.799433 |
82,435 | By combining various petrological, crystallographic, and paleontological tools, geologists are able to chronicle the geological history of the Earth as a whole. One aspect is to demonstrate the age of the Earth. Geology provides evidence for plate tectonics, the evolutionary history of life, and the Earth's past climat... | Geology | 0.799433 |
82,436 | Robin Holliday defined in 1990 epigenetics as "the study of the mechanisms of temporal and spatial control of gene activity during the development of complex organisms. "More recent usage of the word in biology follows stricter definitions. As defined by Arthur Riggs and colleagues, it is "the study of mitotically and/... | Epigenetics | 0.799433 |
82,437 | As of 2007, he joined the University of Richmond.As both a scientist and a historian, he is able to write knowledgeably about scientists such as Robert Burns Woodward, their work, and their disputes. He has published more than 55 papers on the history and sociology of chemistry. These include studies with Mark House in... | Jeffrey I. Seeman | 0.799433 |
82,438 | Because discharging ammonia-laden water into the environment, damages marine life, nitrification is often necessary to remove the ammonia. This may become a potentially sustainable source of ammonia given its abundance. Alternatively, ammonia from wastewater can be sent into an ammonia electrolyzer (ammonia electrolysi... | Ammonia production | 0.799433 |
82,439 | Osmotic shock is sometimes used to release cellular components, such as oil. Ultrasonic extraction, a branch of sonochemistry, can greatly accelerate extraction processes. | Open pond | 0.799433 |
82,440 | Currently SciEngines RIVYERA holds the record in brute-force breaking DES utilizing 128 Spartan-3 5000 FPGAs. Current systems provide a unique density of up to 256 Spartan-6 FPGAs per single system enabling scientific utilization beyond the field of cryptanalysis, like bioinformatics. 2006 original developers of the CO... | SciEngines GmbH | 0.799433 |
82,441 | In molecular biology, the hexon protein is a major coat protein found in adenoviruses. Hexon coat proteins are synthesised during late infection and form homo-trimers. The 240 copies of the hexon trimer that are produced are organised so that 12 lie on each of the 20 facets. The central 9 hexons in a facet are cemented... | Hexon protein | 0.799432 |
82,442 | Every hemicompact space is σ-compact. The converse, however, is not true; for example, the space of rationals, with the usual topology, is σ-compact but not hemicompact. The product of a finite number of σ-compact spaces is σ-compact. However the product of an infinite number of σ-compact spaces may fail to be σ-compac... | Sigma compact space | 0.79943 |
82,443 | When lactose is absent in the cell the lac repressor inhibits the production of the enzyme β-galactosidase to prevent any inefficient processes within the cell. The lac operon is used in the biotechnology industry for production of recombinant proteins for therapeutic use. The gene or genes for producing an exogenous p... | Synthetic biological circuit | 0.79943 |
82,444 | The first-derivative test depends on the "increasing–decreasing test", which is itself ultimately a consequence of the mean value theorem. It is a direct consequence of the way the derivative is defined and its connection to decrease and increase of a function locally, combined with the previous section. Suppose f is a... | First-derivative test | 0.79943 |
82,445 | Much research about triangle-free graphs has focused on graph coloring. Every bipartite graph (that is, every 2-colorable graph) is triangle-free, and Grötzsch's theorem states that every triangle-free planar graph may be 3-colored. However, nonplanar triangle-free graphs may require many more than three colors. | Triangle-free graph | 0.79943 |
82,446 | If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the sample mean (denoted x ¯ {\displaystyle {\bar {x}}} ) to distinguish it from the mean, or expected value, of the underlying distribution, the population mean (denoted μ {\displaystyle \m... | Virtual leak | 0.79943 |
82,447 | S2CID 145229344. McMullin, Ernan (September 1, 1978). "Reviewed work: The Solvay Conferences on Physics: Aspects of the Development of Physics since 1911, Jagdish Mehra". | Jagdish Mehra | 0.799429 |
82,448 | The surface emission rate (SER) is used as a measure of the rate of particles emitted from a radioactive source which is being used as a calibration standard. When the source is of plate or planar construction and the radiation of interest is emitting from one face, it is known as " 2 π {\displaystyle 2\pi } emission".... | Counts per minute | 0.799429 |
82,449 | Automath ST type theory UTT (Luo's Unified Theory of dependent Types) some forms of combinatory logic others defined in the lambda cube (also known as pure type systems) others under the name typed lambda calculus | System of types | 0.799429 |
82,450 | Mammalian alcohol dehydrogenases also have a structural zinc site. This Zn ion plays a structural role and is crucial for protein stability. The structures of the catalytic and structural zinc sites in horse liver alcohol dehydrogenase (HLADH) as revealed in crystallographic structures, which has been studied computati... | Alcohol dehydrogenase | 0.799429 |
82,451 | In medicine, common types of salines include: Ringer's lactate solution Acetated Ringer's solution Intravenous sugar solutions 5% dextrose in normal saline (D5NS) 10% dextrose in normal saline (D10NS) 5% dextrose in half-normal saline (D5HNS) 10% dextrose in half-normal saline (D10HNS)And in cell biology, in addition t... | 3% normal saline | 0.799429 |
82,452 | Pablo Jarillo-Herrero of MIT and colleagues from Harvard and the National Institute for Materials Science, Tsukuba, Japan, have reported the discovery of superconductivity in bilayer graphene with a twist angle of 1.1° between the two layers. The discovery was announced in Nature in March 2018. The findings confirmed p... | Bilayer graphene | 0.799429 |
82,453 | In quantum mechanics, Landau quantization refers to the quantization of the cyclotron orbits of charged particles in a uniform magnetic field. As a result, the charged particles can only occupy orbits with discrete, equidistant energy values, called Landau levels. These levels are degenerate, with the number of electro... | Landau level | 0.799428 |
82,454 | Introducing transgenes into organisms has been a widely used tool in plant genetics research for decades. However, researchers often find that their introduced transgenes are not expressed as strongly as expected, or sometimes even at all, a phenomenon called transgene silencing. The discovery of transgene silencing in... | RNA-directed DNA methylation | 0.799428 |
82,455 | Brane calculus deals with membranes representing the sites of activity; thus a computation happens on the membrane surface. The operations of the two basic brane calculi, pino, exo, phago (PEP) and mate, drip, bud (MBD) are directly inspired by biologic processes such as endocytosis, exocytosis and mitosis. The latter... | Mobile membranes | 0.799428 |
82,456 | He failed to recognize the complex numbers of Bombelli and needed to double-check his algebraic answers through geometrical construction. Although he was fully aware that his new algebra was sufficient to give a solution, this concession tainted his reputation. However, Viète created many innovations: the binomial form... | François Viète | 0.799428 |
82,457 | Helmut Hasse (German: ; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine geometry (Hasse principle), and to local zeta functions. | Helmut Hasse | 0.799428 |
82,458 | The International Centre for Radio Astronomy Research (ICRAR) is an international "centre of excellence" in astronomical science and technology based in Perth, Western Australia, launched in August 2009 as a joint venture between Curtin University and the University of Western Australia. The ICRAR attracts researchers ... | International Centre for Radio Astronomy Research | 0.799427 |
82,459 | The below example shows a part of such a table for a 7-segment display driver that translates the binary code for the values of a decimal digit into the signals that cause the respective segments of the display to light up. Digit Code Segments A B C D E F G 0 0000 1 1 1 1 1 1 0 -A- 1 0001 0 1 1 0 0 0 0 | | 2 0010 1 1 0... | Espresso heuristic logic minimizer | 0.799427 |
82,460 | Stapp's work has drawn criticism from scientists such as David Bourget and Danko Georgiev. Recent papers and a book by Georgiev criticize Stapp's model in two aspects: (1) The mind in Stapp's model does not have its own wavefunction or density matrix, but nevertheless can act upon the brain using projection operators. ... | Henry Stapp | 0.799427 |
82,461 | After a measurement by Alice, the state of the total system is said to have collapsed to a state P(σ). The goal of the theorem is to prove that Bob cannot in any way distinguish the pre-measurement state σ from the post-measurement state P(σ). This is accomplished mathematically by comparing the trace of σ and the trac... | No-communication theorem | 0.799427 |
82,462 | Theorem: If f is a harmonic function defined on all of R n {\displaystyle \mathbb {R} ^{n}} which is bounded above or bounded below, then f is constant. (Compare Liouville's theorem for functions of a complex variable). Edward Nelson gave a particularly short proof of this theorem for the case of bounded functions, usi... | Harmonic function | 0.799427 |
82,463 | All data used in this section were obtained from the NIST Chemistry WebBook. It is useful to note that for N2 the normal boiling point of the liquid is 77.4 K and the critical point is at 126.2 K and 34.0 bar. The figure on the right shows an overview covering a wide temperature range. | Compressibility chart | 0.799426 |
82,464 | It can be realized as a projective polyhedron (a tessellation of the real projective plane by three quadrilaterals), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing the hemisphere into three equal parts. It has three square... | Hemicube (geometry) | 0.799426 |
82,465 | Infectious diseases spread across the globe usually because of long-distance travels of carriers of the disease. These long-distance travels are made using air transportation systems and it has been shown that "network topology, traffic structure, and individual mobility patterns are all essential for accurate predicti... | Individual mobility | 0.799426 |
82,466 | When the first quantum computer is plugged in and functioning, the perspectives for the field of computational physics will look rather promising, but until that day one has to restrict oneself to the mundane tools offered by classical computers. While experimental physicists are putting a lot of effort in trying to bu... | Time-evolving block decimation | 0.799426 |
82,467 | A spatial rotation is a linear map in one-to-one correspondence with a 3 × 3 rotation matrix R that transforms a coordinate vector x into X, that is Rx = X. Therefore, another version of Euler's theorem is that for every rotation R, there is a nonzero vector n for which Rn = n; this is exactly the claim that n is an ei... | Euler's fixed point theorem | 0.799426 |
82,468 | If a matroid is regular, so is its dual matroid, and so is every one of its minors. Every direct sum of regular matroids remains regular.Every graphic matroid (and every co-graphic matroid) is regular. Conversely, every regular matroid may be constructed by combining graphic matroids, co-graphic matroids, and a certain... | Regular matroid | 0.799425 |
82,469 | Data Encryption Standard (DES) – NBS selection process, ended 1976 RIPE – division of the RACE project sponsored by the European Union, ended mid-1980s Advanced Encryption Standard (AES) – a "break-off" competition sponsored by NIST, ended in 2001 NESSIE Project – an evaluation/selection program sponsored by the Europe... | Outline of cryptography | 0.799425 |
82,470 | There is potential that holders of biotechnology patents will exploit their rights in order to make larger profits, at the potential expense of farmers, healthcare patients, and other users of patented technologies. The ethics of using patents to increase profits are also debated. A typical argument in favour of biotec... | Patenting genes | 0.799424 |
82,471 | This is usually done only when the geometry changes. Winged-edge meshes are ideally suited for dynamic geometry, such as subdivision surfaces and interactive modeling, since changes to the mesh can occur locally. Traversal across the mesh, as might be needed for collision detection, can be accomplished efficiently. See... | Polygon mesh | 0.799424 |
82,472 | In particular, if R is a superalgebra over a field K then Mr|s×p|q(R) forms a super vector space over K. Let Mp|q(R) denote the set of all square supermatices over R with dimension (p|q)×(p|q). This set forms a superring under supermatrix addition and multiplication. Furthermore, if R is a commutative superalgebra, the... | Supermatrix | 0.799424 |
82,473 | Analogously to Yau's integration of gradient estimates to find Harnack inequalities, they were able to integrate their gradient estimate to obtain control of the fundamental gap, which is the difference between the first two eigenvalues. The work of Singer–Wong–Yau–Yau initiated a series of works by various authors in ... | Shing-Tung Yau | 0.799423 |
82,474 | from Stanford University in 1960 and a Ph.D. in physics in 1971 from the University of Washington. She remained at the University of Washington following her Ph.D., initially as a research associate. She was promoted to professor of geophysics and atmospheric sciences in 1988. She retired in 2004 | Marcia Baker | 0.799423 |
82,475 | in 2006, with a thesis entitled The Chemistry of Tris(phosphino)borate Manganese and Iron Platforms.Lu conducted postdoctoral studies at the Max Planck Institute for Bioinorganic Chemistry from 2006 to 2009, under the mentorship of Prof. Karl Wieghardt. Under Wieghardt, Lu studied first-row transition metal complexes s... | Connie C. Lu | 0.799423 |
82,476 | The technique he developed for purifying the brain lipids is still referred to as "Folching" and is one of the most cited papers in the history of biochemistry. Folch solution is a solution containing chloroform and methanol, usually in a 2:1 (vol/vol) ratio. One of its uses is in separating polar from nonpolar compoun... | Jordi Folch Pi | 0.799423 |
82,477 | in 1949, a Ph.D. in 1955, and a D.Sc. in 1962, all from Prague's Czech Academy of Sciences in electrical engineering. | Petr Beckmann | 0.799423 |
82,478 | One can use Van Kampen's theorem to calculate fundamental groups for topological spaces that can be decomposed into simpler spaces. For example, consider the sphere S 2 {\displaystyle S^{2}} . Pick open sets A = S 2 ∖ { n } {\displaystyle A=S^{2}\setminus \{n\}} and B = S 2 ∖ { s } {\displaystyle B=S^{2}\setminus \{s\}... | Seifert-Van Kampen theorem | 0.799423 |
82,479 | The Hasse–Minkowski theorem implies that there is an injection W ( Q ) → W ( R ) ⊕ ∏ p W ( Q p ) . {\displaystyle W(\mathbf {Q} )\rightarrow W(\mathbf {R} )\oplus \prod _{p}W(\mathbf {Q} _{p})\ .} We make this concrete, and compute the image, by using the "second residue homomorphism" W(Qp) → W(Fp). Composed with the m... | Witt–Grothendieck ring | 0.799423 |
82,480 | In molecular biology, glycoside hydrolase family 26 is a family of glycoside hydrolases. Glycoside hydrolases EC 3.2.1. are a widespread group of enzymes that hydrolyse the glycosidic bond between two or more carbohydrates, or between a carbohydrate and a non-carbohydrate moiety. A classification system for glycoside h... | Glycoside hydrolase family 26 | 0.799423 |
82,481 | Shortly after, the coil was damaged in a control test in February 2007 and replaced in May 2007. The replacement coil was inferior, a copper wound electromagnet, that was also water cooled. Scientific results, including the observation of an inward turbulent pinch, were reported in Nature Physics. | Levitated Dipole Experiment | 0.799423 |
82,482 | : 19 The foregoing procedure is a direct application of non-relativistic quantum mechanics and can be used to quantize (complex) scalar fields, Dirac fields,: 52 vector fields (e.g. the electromagnetic field), and even strings. However, creation and annihilation operators are only well defined in the simplest theories ... | Relativistic quantum theory | 0.799423 |
82,483 | Geology Mineralogy – the study of chemistry, crystal structure, and physical (including optical) properties of minerals. Petrophysics – The study of the origin, structure, and composition of rocks. Volcanology – the study of volcanoes, volcanic features (hot springs, geysers, fumaroles), volcanic rock, and heat flow re... | Outline of geophysics | 0.799422 |
82,484 | Nanosurf invented the first scanning tunneling microscope (STM) with the compact size and stability to image individual atoms on a coffee table. In its early days, Nanosurf became known for educational AFMs, and over the course of the following decades moved more and more towards providing high-end instruments for rese... | Nanosurf | 0.799422 |
82,485 | But history decided differently: the arrival of the Nazis in 1933 - and, to a less extreme degree, the rigidification of totalitarian measures in fascist Italy - caused the emigration of a large number of Jewish and non-Jewish scientists. The majority of them fled to the US or the UK, providing an extra impulse to the ... | History of molecular biology | 0.799422 |
82,486 | Conics, also known as conic sections to emphasize their three-dimensional geometry, arise as the intersection of a plane with a cone. Degeneracy occurs when the plane contains the apex of the cone or when the cone degenerates to a cylinder and the plane is parallel to the axis of the cylinder. See Conic section#Degener... | Degenerate conic | 0.799422 |
82,487 | A factorial state of a C*-algebra A is a state such that the commutant of the corresponding GNS representation of A is a factor. | State (functional analysis) | 0.799422 |
82,488 | In 1974, the dissertation was published in German entitled Grundlagen universaler Wissensordnung. It started with conceptual clarifications, and why and how the term „universal“ was linked to knowledge, including knowledge fields, such as commodity science, artefacts, statistics, patents, standardization, communication... | Information Coding Classification | 0.799422 |
82,489 | We take E as our elliptic curve, where E is of the form y 2 = x 3 − m x {\displaystyle y^{2}=x^{3}-mx} for m ∈ Z , m ≢ 0 mod p , {\displaystyle m\in \mathbb {Z} ,m\not \equiv 0{\bmod {p}},} where p ≡ 3 mod 4 {\displaystyle p\equiv 3{\bmod {4}}} is prime, and p + 1 = 2 k n , {\displaystyle p+1=2^{k}n,} with k ∈ Z , k ≥ ... | Elliptic curve primality proving | 0.799422 |
82,490 | He developed important ideas on the quantization of magnetic flux in metals. He was awarded the Lorentz Medal in 1958, Willard Gibbs Award in 1962, and the Nobel Prize in Chemistry in 1968. He was elected a member of the American Philosophical Society in 1959 and a Foreign Member of the Royal Society (ForMemRS) in 1975... | Lars Onsager | 0.799422 |
82,491 | Reviewer Ján Plesník names the book the first ever published on the history of graph theory, and although Hazel Perfect notes that parts of it can be difficult to read, Plesník states that it can also be used as "a self-contained introduction" to the field, and Edward Maziarz suggests its use as a textbook for graph th... | Graph Theory, 1736–1936 | 0.799422 |
82,492 | Due to the Eastin–Knill theorem, a universal set like {H, S, CNOT, T } gates can't be implemented transversally. For example, the T gate can't be implemented transversely in the Steane code. This calls for ways of circumventing Eastin–Knill in order to perform fault tolerant quantum computation. In addition to investig... | Eastin-Knill theorem | 0.799421 |
82,493 | In Brazil, medical school consists of six years or twelve semesters. The final two years (or one and a half years, depending on the University in question) are the internship. During this time, students work extensive hospital hours and do basic hospital work while supervised by residents and staff. This period is usua... | Internship (medicine) | 0.799421 |
82,494 | The investigation of the biological foundations of language is associated with two historical periods, namely that of the 19th century (primarily via Darwinian evolutionary theory) and the 20th century (primarily via the integration of the mathematical linguistics (in the form of Chomskyan generative grammar) with neur... | Biolinguistics | 0.799421 |
82,495 | Polynomial rings occur and are often fundamental in many parts of mathematics such as number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings, rings of formal power series, Ore polynomials, graded rings, have bee... | Polynomial expression | 0.799421 |
82,496 | Tannaka–Krein duality concerns the interaction of a compact topological group and its category of linear representations. Tannaka's theorem describes the converse passage from the category of finite-dimensional representations of a group G back to the group G, allowing one to recover the group from its category of repr... | Category of representations | 0.79942 |
82,497 | Confusion often stems from the way that different forms of English handle agreement with collective nouns—specifically, whether or not to use the collective singular: the singular verb form with a collective noun. The plural verb forms are often used in British English with the singular forms of these countable nouns (... | Collective singular | 0.79942 |
82,498 | In short, many reasons are conceivable that by itself or in different combinations could result in developmental problems of very preterm children. Current theories on causation focus on genetic factors; more than 1,000 known genetic conditions include developmental disabilities as a symptom.Developmental disabilities ... | Developmental disability | 0.79942 |
82,499 | According to the halogen bonding concept, the trichloride anion can be described as a donor-acceptor complex consisting of a chloride anion (the halogen donor) and a dichlorine molecule (the halogen acceptor). By donation of electron density of the chloride anion into the σ-hole of the dichlorine molecule lying along t... | Triethylmethylammonium trichloride | 0.79942 |
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