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86,300 | In algebraic number theory, the different ideal (sometimes simply the different) is defined to measure the (possible) lack of duality in the ring of integers of an algebraic number field K, with respect to the field trace. It then encodes the ramification data for prime ideals of the ring of integers. It was introduced... | Different ideal | 0.798611 |
86,301 | The Schamel equation (S-equation) is a nonlinear partial differential equation of first order in time and third order in space. Similar to a Korteweg de Vries equation (KdV), it describes the development of a localized, coherent wave structure that propagates in a nonlinear dispersive medium. It was first derived in 19... | Schamel equation | 0.798611 |
86,302 | From about the 1920s onwards, it was realised that tensors play a basic role in algebraic topology (for example in the Künneth theorem). Correspondingly there are types of tensors at work in many branches of abstract algebra, particularly in homological algebra and representation theory. Multilinear algebra can be deve... | Tensor order | 0.798611 |
86,303 | Leutwyler went to the Gymnasium in Bern and studied physics, mathematics, and astronomy at the University of Bern. After the diploma in 1960 he went to the US, including Princeton. In 1962 he received his PhD under the supervision of John R. Klauder (at Bell Laboratories at the time), for his thesis entitled "Generally... | Heinrich Leutwyler | 0.798611 |
86,304 | Kečkéšová discovered that the protein LACTB can act as a tumour suppressant. She demonstrated that activation of LACTB in cancer cells can result in the death of cells; by altering the composition of lipids in cancer mitochondria.She was awarded a European Molecular Biology Organization (EMBO) Installation Grant to stu... | Zuzana Kečkéšová | 0.798611 |
86,305 | Natural language processing deals with getting computers to understand human (natural) languages at a high level. This usually means text, but also often includes speech processing and recognition. | Information engineering | 0.798611 |
86,306 | The hot plate welding process can be divided into four phases: matching, heating, change-over, and welding/forging. The matching phase serves to match the geometry of the weld surfaces to the theoretical welding plane. The weld surfaces are heated through conduction by physical contact with the hot plate. The hot plate... | Hot plate welding | 0.798611 |
86,307 | While neurons are embedded within networks, these networks are further embedded within the brain as a whole. Neural networks do not work in isolation, such as in the modularity of mind perspective. Instead, different regions interact through feedback processes and top-down interactions, constraining and specifying the ... | Neuroconstructivism | 0.79861 |
86,308 | Kenneth Ingvard Greisen (24 January 1918 in Perth Amboy, New Jersey – 17 March 2007 in Ithaca, New York) was an American physicist who worked on nuclear physics and the astrophysics of cosmic rays and gamma radiation. "He will be most remembered for his realization that the cosmic microwave background limits the high-e... | Kenneth Greisen | 0.79861 |
86,309 | Conditional on the value of the underlying physical property, any given outcome (for example, a result of + {\displaystyle +} ) must be either impossible or guaranteed. But Gleason's theorem implies that there can be no such deterministic probability measure. The mapping u → ⟨ ρ u , u ⟩ {\displaystyle u\to \langle \rho... | Gleason's theorem | 0.79861 |
86,310 | This is the assumption of σ-additivity: Any countable sequence of disjoint sets (synonymous with mutually exclusive events) E 1 , E 2 , … {\displaystyle E_{1},E_{2},\ldots } satisfies P ( ⋃ i = 1 ∞ E i ) = ∑ i = 1 ∞ P ( E i ) . {\displaystyle P\left(\bigcup _{i=1}^{\infty }E_{i}\right)=\sum _{i=1}^{\infty }P(E_{i}).} S... | Probability axiom | 0.798609 |
86,311 | His main research interest was in the field of computational chemistry. Basch was a pioneer in computational quantum chemistry, in developing methods and innovative applications of theoretical concepts and equations to solving problems in chemistry. Already in 1962, as a beginning graduate student at Columbia Universit... | Harold Basch | 0.798609 |
86,312 | During the 1960s, he associated himself with complex mathematical applications of nuclear physics. In 1960, Riazuddin used Nucleon-nucleon dispersion relation to discriminate proton-proton scattering in pseudoscalar mesons. In 1965, Riazuddin carried out the pioneering work on vector currents, in which he showed the di... | Riazuddin (physicist) | 0.798609 |
86,313 | Lunar topography, geomorphology, and geological structure Lunar Physics and internal structure Lunar Chemistry (materials and geoarchaeology) Cis-Lunar space environment Lunar-based astronomical observation Lunar based Earth observation Lunar-based biological and medical experiment Lunar Resource in-situ utilization | International Lunar Research Station | 0.798609 |
86,314 | SCWO can be classified as green chemistry or as a clean technology. The elevated pressures and temperatures required for SCWO are routinely encountered in industrial applications such as petroleum refining and chemical synthesis. A unique addition (mostly of academic interest) to the world of supercritical water (SCW) ... | Supercritical water | 0.798608 |
86,315 | The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion. This explanation of Brownian motion served as convincing evidence that atoms and molecules exist and was further verifi... | Brownian diffusion | 0.798608 |
86,316 | EIT can be viewed as the natural extension of Classical Irreversible Thermodynamics (CIT). Mainly developed by the Belgian-Dutch school headed by I. Prigogine, working on a simple hypothesis of local thermodynamic equilibrium, CIT assumes the existence of field laws of the diffusion type. Mathematically, these are para... | Extended irreversible thermodynamics | 0.798608 |
86,317 | Brown completed his senior thesis, titled "Simulating the measurement of the correlation function of the Shane–Wirtanen galaxy counts", under the supervision of Edward Groth. He did his graduate studies at the University of California, Berkeley, where he earned an M.A. degree in astronomy in 1990 and a Ph.D. degree in ... | Michael E. Brown | 0.798608 |
86,318 | He turned down offers from Oxford and Cambridge. He eventually became an Australian citizen.In 1967 he created the physics program at Macquarie University using the Feynman Lectures on Physics as primary textbooks. This program had a strong experimental emphasis and Ward himself (who originally was trained as an engine... | John Clive Ward | 0.798608 |
86,319 | In topology, the split interval, or double arrow space, is a topological space that results from splitting each point in a closed interval into two adjacent points and giving the resulting ordered set the order topology. It satisfies various interesting properties and serves as a useful counterexample in general topolo... | Split interval | 0.798607 |
86,320 | The farther two populations of a species are separated from each other, the less genetic traits they will share in common, and this may be one source of variance in culture.Another argument against the "ethnographic method" is that it is impossible to prove that there are absolutely no ecological or genetic factors in ... | Cultural transmission in animals | 0.798607 |
86,321 | Since straight lines are a concept in affine geometry, affine connections define a generalized notion of (parametrized) straight lines on any affine manifold, called affine geodesics. Abstractly, a parametric curve γ: I → M is a straight line if its tangent vector remains parallel and equipollent with itself when it is... | Affine connection | 0.798607 |
86,322 | By 1990, IBM acknowledged the software industry to be in a state of perpetual crisis. This was due to the chaos from inordinate complexity of software engineering inherited by its legacy of procedural programming practices since the 1960s. Large software projects were too difficult, fragile, expensive, and time-consumi... | Workplace OS | 0.798607 |
86,323 | Pests, species that cause diseases and their vectors, have direct importance for humans. When they are found to be cryptic species complexes, the ecology and the virulence of each of these species need to be re-evaluated to devise appropriate control strategies. Examples are cryptic species in the malaria vector genus ... | Species flock | 0.798607 |
86,324 | Cell notation or cell representation in chemistry is a shorthand method of expressing a reaction in an electrochemical cell. In cell notation, the two half-cells are described by writing the formula of each individual chemical species involved in the redox reaction across the cell, with all other common ions and inert ... | Cell notation | 0.798607 |
86,325 | In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The Riemannian Penrose inequality is an important special case. Specifically, if (M, g... | Penrose inequality | 0.798606 |
86,326 | To experiment, the team created a minigame, Zombie Basketball, in which players used a physics-manipulating gun to throw zombies through hoops. In mid-2001, to test the engine, Valve built a street war between rioting citizens and police, featuring tanks, Molotov cocktails, hand-to-hand fighting, and looting. The desig... | Half-Life 2 | 0.798606 |
86,327 | Tomás et al. proposed alternative continuous functions for the computation of F1, F2 and F3 correction parameters. These functions show maximum absolute differences with discrete functions lower than 7 points and significantly reduce subjective interpretations. Moreover, the proposed functions for SMR correction factor... | Slope Mass Rating | 0.798606 |
86,328 | In adiabatic dynamics, interatomic interactions are represented by single scalar potentials called potential energy surfaces. This is the Born–Oppenheimer approximation introduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 19... | Quantum chemical | 0.798606 |
86,329 | By this theory, the wing has a lift force smaller than that predicted by a purely two-dimensional theory using the Kutta–Joukowski theorem. This is due to the upstream effects of the trailing vortices' added downwash on the angle of attack of the wing. This reduces the wing's effective angle of attack, decreasing the a... | Kutta–Zhukovsky theorem | 0.798606 |
86,330 | Compounds with oxidation states +5 are somewhat elusive, one example is the blue anion hypomanganate 3-. Compounds with Mn in oxidation state +5 are rarely encountered and often found associated with an oxide (O2-) or nitride (N3-) ligand.Mn(IV) is somewhat enigmatic because it is common in nature but far rarer in synt... | Manganese compounds | 0.798606 |
86,331 | The Railway Technical Centre (RTC) in London Road, Derby, England, was the technical headquarters of the British Railways Board, and was built in the early 1960s. British Rail described it as the largest railway research complex in the world. The RTC centralised most of the technical services provided by the regional C... | Railway Technical Centre | 0.798605 |
86,332 | Andrew Harold Kresch (born 1972) is an American mathematician specializing in algebraic geometry and a professor at the University of Zurich. Kresch won a silver medal at the 1989 International Mathematical Olympiad. He studied at the Yale University and received his PhD from University of Chicago in 1998 under the sup... | Andrew Kresch | 0.798605 |
86,333 | A topologically distinct elongated gyrobifastigium has square and equilateral triangle faces, seen as 2 triangular prisms augmented to a central cube. This is a failed Johnson solid for not being strictly convex.This is also a space-filling polyhedron, and matches the geometry of the gyroelongated triangular prismatic ... | Elongated gyrobifastigium | 0.798605 |
86,334 | Risk associated with project outcomes is usually handled with probability theory. Although it can be factored into the discount rate (to have uncertainty increasing over time), it is usually considered separately. Particular consideration is often given to agent risk aversion: preferring a situation with less uncertain... | Benefit-cost analysis | 0.798605 |
86,335 | The Scopes Trial decision of 1925 caused the subject to become very rare in American secondary biology textbooks for a generation, but it was gradually re-introduced later and became legally protected with the 1968 Epperson v. Arkansas decision. Since then, the competing religious belief of creationism was legally disa... | Darwin Theory of Evolution | 0.798605 |
86,336 | A likelihood ratio is the ratio of any two specified likelihoods, frequently written as: The likelihood ratio is central to likelihoodist statistics: the law of likelihood states that degree to which data (considered as evidence) supports one parameter value versus another is measured by the likelihood ratio. In freque... | Profile-likelihood function | 0.798604 |
86,337 | Star-quad cable is a four-conductor cable that has a special quadrupole geometry which provides magnetic immunity when used in a balanced line. Four conductors are used to carry the two legs of the balanced line. All four conductors must be an equal distance from a common point (usually the center of a cable). The four... | Star quad cable | 0.798604 |
86,338 | The joule per mole (symbol: J·mol−1 or J/mol) is the unit of energy per amount of substance in the International System of Units (SI), such that energy is measured in joules, and the amount of substance is measured in moles. It is also an SI derived unit of molar thermodynamic energy defined as the energy equal to one ... | Joule per mole | 0.798603 |
86,339 | This group of assistants, junior colleagues and others were dedicated to carrying out Peano's logico–geometrical program of putting the foundations of geometry on firm axiomatic footing based on Peano's logical symbolism. Besides Pieri, Burali-Forti, Padoa and Fano were in this group. | Foundations of geometry | 0.798603 |
86,340 | (He later authored 19 patents on distillation.) In 1920 he became the first head of the newly formed department of chemical engineering at MIT a position he held for 13 years before returning to teaching and research. | Warren K. Lewis | 0.798602 |
86,341 | Since 2006, though, a few fossils of similar animals have been found in rocks from the Ordovician, Silurian, and Early Devonian periods, in other words up to 100 million years after the Burgess Shale. The particular way in which such animals have been fossilized may depend on types of ocean chemistry that were present ... | Signor–Lipps effect | 0.798602 |
86,342 | In solutions at neutral pH, the superoxide ion disproportionates to molecular oxygen and hydrogen peroxide. 2 O−2 + 2 H+ → O2 + H2O2In biology this type of reaction is called a dismutation reaction. It involves both oxidation and reduction of superoxide ions. | Metalloprotein | 0.798601 |
86,343 | Inversely, a topology is Alexandrov if any intersection of open sets is open. Algebraic poset. A poset is algebraic if it has a base of compact elements. | Order theory glossary | 0.798601 |
86,344 | With the TEPREL-A engine, first tested in 2017, the company included several design upgrades, such as a new combustion chamber design, an improved injector geometry and a regenerative cooling system. The later enables the engine to fire for nearly 2 minutes, which is the envisaged nominal functioning duration for the s... | TEPREL | 0.7986 |
86,345 | In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions in which the surface curves the most and the least. The theorem is named fo... | Euler's theorem (differential geometry) | 0.7986 |
86,346 | Hulme founded NPComplete Limited in 2007, and incorporated it in 2008, a few months before completing his PhD. NPComplete Limited trades as Satalia. The London-based company provides full-stack AI consultancy and products, helping organisations harness data science, machine learning and AI to solve complex problems, in... | Daniel J. Hulme | 0.798599 |
86,347 | The function of the vertex pipeline in any GPU is to take geometry data (usually supplied as vector points), work with it if needed with either fixed function processes (earlier DirectX), or a vertex shader program (later DirectX), and create all of the 3D data points in a scene to a 2D plane for display on a computer ... | Vertex pipeline | 0.798599 |
86,348 | Russell, Stuart J.; Norvig, Peter (2003). Artificial Intelligence: A Modern Approach (2nd ed.). Upper Saddle River, New Jersey: Prentice Hall. | Artificial agents | 0.798599 |
86,349 | Feline hypertrophic cardiomyopathy (HCM) is the most common heart disease in domestic cats; the disease process and genetics are believed to be similar to the disease in humans. In Maine Coon cats, HCM has been confirmed as an autosomal dominant inherited trait. Numerous cat breeds have HCM as a problem in the breed. T... | Hypertrophic obstructive cardiomyopathy | 0.798598 |
86,350 | Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomeno... | Loop gravity | 0.798598 |
86,351 | Finally, he shows that the general problem can be reduced to this special case. Gleason credits one lemma used in this last stage of the proof to his doctoral student Richard Palais. : fn 3 Robin Lyth Hudson described Gleason's theorem as "celebrated and notoriously difficult". Cooke, Keane and Moran later produced a p... | Gleason's theorem | 0.798598 |
86,352 | Second law analysis is valuable in scientific and engineering analysis in that it provides a number of benefits over energy analysis alone, including the basis for determining energy quality (exergy content), understanding fundamental physical phenomena, and improving performance evaluation and optimization. As a resul... | Kelvin–Planck statement | 0.798598 |
86,353 | After performing several iterations of random cropping, the sub images are then fed into the machine learning algorithm to help the algorithm generalize better. To tackle the problems associated with crowd counting in heavy density areas density based counting methods can be employed. | Crowd counting | 0.798598 |
86,354 | The university he founded later became a model and inspiration for modern colleges in Germany and universities in the West.The concept of academic freedom was also clearly formulated in response to the encroachments of the totalitarian state on science and academia in general for the furtherance of its own goals. For i... | Scientific freedom | 0.798598 |
86,355 | A receptor activated solely by a synthetic ligand (RASSL) or designer receptor exclusively activated by designer drugs (DREADD), is a class of artificially engineered protein receptors used in the field of chemogenetics which are selectively activated by certain ligands. They are used in biomedical research, in particu... | Receptor activated solely by a synthetic ligand | 0.798597 |
86,356 | In algebraic geometry, an Endrass surface is a nodal surface of degree 8 with 168 real nodes, found by Stephan Endrass (1997). As of 2007, it remained the record-holder for the most number of real nodes for its degree; however, the best proven upper bound, 174, does not match the lower bound given by this surface. | Endrass surface | 0.798597 |
86,357 | If the gradient of ρ {\displaystyle \rho } was known, one could use gradient ascent. Since an analytic expression for the gradient is not available, only a noisy estimate is available. Such an estimate can be constructed in many ways, giving rise to algorithms such as Williams' REINFORCE method (which is known as the l... | Reinforcement Learning | 0.798597 |
86,358 | Theories and observations of visual perception have been the main source of inspiration for computer vision (also called machine vision, or computational vision). Special hardware structures and software algorithms provide machines with the capability to interpret the images coming from a camera or a sensor. For instan... | Intromission theory | 0.798597 |
86,359 | In topology, a branch of mathematics, the suspension of a topological space X is intuitively obtained by stretching X into a cylinder and then collapsing both end faces to points. One views X as "suspended" between these end points. The suspension of X is denoted by SX or susp(X). : 76 There is a variation of the suspe... | Suspension (topology) | 0.798597 |
86,360 | "Selmer groups and the indivisibility of Heegner points", Cambridge Journal of Mathematics 2 (2014), no. 2, 191–253. (with Michael Rapoport, Ulrich Terstiege) "On the Arithmetic Fundamental Lemma in the minuscule case", Compositio Mathematica 149 (2013), no. 10, 1631–1666. (with Xinyi Yuan, Shou-Wu Zhang) "The Gross–Ko... | Wei Zhang (mathematician) | 0.798597 |
86,361 | These include especially lubricin, a protein crucial for the joint lubrication. Furthermore these cells express a number of molecules important for the mediation of the cell adhesion, such as cadherin-11, VCAM-1, various integrins and their receptors. Specific for fibroblast-like synoviocytes is also the expression of ... | Fibroblast-like synoviocyte | 0.798596 |
86,362 | The representations of GF are classified using conjugacy classes of the dual group of G. A reductive group over a finite field determines a root datum (with choice of Weyl chamber) together with an action of the Frobenius element on it. The dual group G* of a reductive algebraic group G defined over a finite field is t... | Deligne–Lusztig theory | 0.798596 |
86,363 | In mathematics, the Bloch group is a cohomology group of the Bloch–Suslin complex, named after Spencer Bloch and Andrei Suslin. It is closely related to polylogarithm, hyperbolic geometry and algebraic K-theory. | Bloch group | 0.798596 |
86,364 | The repetition code works in a classical channel, because classical bits are easy to measure and to repeat. This approach does not work for a quantum channel in which, due to the no-cloning theorem, it is not possible to repeat a single qubit three times. To overcome this, a different method has to be used, such as the... | Quantum error correction | 0.798596 |
86,365 | As originally stated, de Rham's theorem asserts that this is a perfect pairing, and that therefore each of the terms on the left-hand side are vector space duals of one another. In contemporary language, de Rham's theorem is more often phrased as the statement that singular cohomology with real coefficients is isomorph... | Harmonic form | 0.798596 |
86,366 | Gustav Niemann (Rheine, 9 February 1899 – Munich, 1 January 1982) was a mechanical engineering professor who is regarded as an expert in machine elements. | Gustav Niemann | 0.798596 |
86,367 | IEEE Spectrum – the flagship publication of the Institute of Electrical and Electronics Engineers (IEEE), explores the development, applications and implications of new technologies, and provides a forum for understanding, discussion and leadership in these areas. IEEE Transactions on Information Theory – peer-reviewed... | Outline of automation | 0.798596 |
86,368 | Like other boranes, the structure of tetraborane involves multicenter bonding, with hydrogen bridges or protonated double bonds. According to its formula, B4H10, it is classified as an arachno-cluster and has a butterfly geometry, which can be rationalized by Wade's rules. Each boron is sp3 hybridized, and “the configu... | B4H10 | 0.798595 |
86,369 | Having initially been defined at a symposium of the American Mathematical Society in the later 1950s, the term "applied probability" was popularized by Maurice Bartlett through the name of a Methuen monograph series he edited, Applied Probability and Statistics. The area did not have an established outlet until 1964, w... | Applied probability | 0.798594 |
86,370 | 2000.Acoustic identification of twelve species of echolocating bat by discriminant function analysis and artificial neural networks. The Journal of Experimental Biology. 2000 203: 2641-2656. | Greater horseshoe bat | 0.798594 |
86,371 | He attended high school at the Wilhelm von Humboldt Gymnasium, Ludwigshafen, Germany. He obtained his first degree in physics from the University of Freiburg and his master's degree in mathematics and physics from the University of Connecticut under a Fulbright scholarship. In 2001, he obtained his PhD from University ... | Jens Eisert | 0.798594 |
86,372 | Including induced drag requires information specific to the topology, In these cases it is expected that both the optimal speed-ratio and the optimal C P {\displaystyle C_{P}} would be less. The analysis focused on the aerodynamic potential, but neglected structural aspects. In reality most optimal wind-turbine design ... | Wind turbine aerodynamics | 0.798594 |
86,373 | Steven Albert Benner (born October 23, 1954) is an American chemist. He has been a professor at Harvard University, ETH Zurich, and most recently at the University of Florida, where he was the V.T. & Louise Jackson Distinguished Professor of Chemistry. In 2005, he founded The Westheimer Institute of Science and Technol... | Steven A. Benner | 0.798594 |
86,374 | Therefore, quantum mechanics is not complete. : 451 It is known, from the uncertainty principle, that position and momentum cannot be measured at the same time. But even though their values can only be determined in distinct contexts of measurement, can they both be definite at the same time? | Einstein's thought experiments | 0.798594 |
86,375 | An introduction to the Essais, which include the Dioptrique, the Météores and the Géométrie. 1637. La Géométrie (Geometry). | René Descartes | 0.798594 |
86,376 | In chemistry, a protic solvent is a solvent that has a hydrogen atom bound to an oxygen (as in a hydroxyl group −OH), a nitrogen (as in an amine group −NH2 or −NH−), or fluoride (as in hydrogen fluoride). In general terms, any solvent that contains a labile H+ is called a protic solvent. The molecules of such solvents ... | Protic solvents | 0.798594 |
86,377 | As argued by Christopher J. Date, business rules translate into data integrity constraints when one thinks in terms of the relational model of database management. Thus, a true RDBMS could be thought of in terms of a declarative business rules engine with added data management capability. However, business rules need n... | Business rules approach | 0.798593 |
86,378 | Another nerve theorem relates to the Čech nerve above: if X {\displaystyle X} is compact and all intersections of sets in C are contractible or empty, then the space | S ( π 0 ( C ) ) | {\displaystyle |S(\pi _{0}(C))|} is homotopy-equivalent to X {\displaystyle X} . | Nerve theorem | 0.798593 |
86,379 | Cyclopentyne is a cycloalkyne containing five carbon atoms in the ring. Due to the ideal bond angle of 180° at each atom of the alkyne but the structural requirement that the bonds form a ring, this chemical is a highly strained structure, and the triple bond is highly reactive. The triple bond easily undergoes both a... | Cyclopentyne | 0.798592 |
86,380 | The symposium was held in Orlando, Florida, from September 30 to October 2, 2011. It included presentations on the technology, biology, physics, philosophy, sociology, and economics of interstellar flight. More than 500 papers were submitted and more than 700 people attended. | 100 Year Starship | 0.798592 |
86,381 | The operational semantics of a specification means how to interpret it as a sequence of computational steps. We define a ground term as an algebraic expression without variables. The operational semantics of an algebraic specification refers to how ground terms can be transformed using the given equational axioms as le... | Algebraic semantics (computer science) | 0.798592 |
86,382 | In a series of publications, John Sutherland and his team at the School of Chemistry, University of Manchester, have demonstrated high yielding routes to cytidine and uridine ribonucleotides built from small 2- and 3-carbon fragments such as glycolaldehyde, glyceraldehyde or glyceraldehyde-3-phosphate, cyanamide, and c... | Peptide-RNA world | 0.798592 |
86,383 | Mid 1994, FZI Forschungszentrum Informatik in Karlsruhe – research institute for computer science in Karlsruhe) developed the first systems with master. In 1999, AS-Interface is standardized in EN 50295 and IEC 62026-2 (revised in 2012.) In 2010, AS-International introduced AS-Interface Power 24V, enabling the use of a... | AS-International | 0.798591 |
86,384 | This theorem fails in the case X {\displaystyle X} is Calabi-Yau, since ω X ≅ O X {\displaystyle \omega _{X}\cong {\mathcal {O}}_{X}} , or is the product of a variety which is Calabi-Yau. Abelian varieties are a class of examples where a reconstruction theorem could never hold. If X {\displaystyle X} is an abelian vari... | Derived noncommutative algebraic geometry | 0.798591 |
86,385 | A two-dimensional real manifold can be turned into a Riemann surface (usually in several inequivalent ways) if and only if it is orientable and metrizable. So the sphere and torus admit complex structures, but the Möbius strip, Klein bottle and real projective plane do not. Geometrical facts about Riemann surfaces are ... | Compact Riemann surface | 0.798591 |
86,386 | Let B {\displaystyle {\mathcal {B}}} be the σ-ideal of those subsets of the real line that are meager (or "of the first category") in the euclidean topology, and let L {\displaystyle {\mathcal {L}}} be the σ-ideal of those subsets of the real line that are of Lebesgue measure zero. Then the following inequalities hold:... | Cichoń's diagram | 0.798591 |
86,387 | For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of mathematics other than the use of prime numbered gear teeth to distribute wear evenly. In particular, number theorists such as British mathemati... | Prime divisor | 0.798591 |
86,388 | Proof of 1st part for symmetry: If we can prove that I ( P ) {\displaystyle \textstyle I(P)} is positive when the AVC is not symmetric, and then prove that c = max P I ( P ) {\displaystyle \textstyle c=\max _{P}I(P)} , we will be able to prove Theorem 1. Assume I ( P ) {\displaystyle \textstyle I(P)} were equal to 0 {\... | Arbitrarily varying channel | 0.798591 |
86,389 | When R is a PID, then the correct statement of the Künneth theorem is that for any topological spaces X and Y there are natural short exact sequences 0 → ⨁ i + j = k H i ( X ; R ) ⊗ R H j ( Y ; R ) → H k ( X × Y ; R ) → ⨁ i + j = k − 1 T o r 1 R ( H i ( X ; R ) , H j ( Y ; R ) ) → 0. {\displaystyle 0\to \bigoplus _{i+j... | Künneth theorem | 0.798591 |
86,390 | The web-based Snap! and older desktop-based BYOB have been both developed by Jens Mönig for Windows, OS X and Linux with design ideas and documentation provided by Brian Harvey from University of California, Berkeley and have been used to teach "The Beauty and Joy of Computing" introductory course in computer science (... | Snap! (programming language) | 0.79859 |
86,391 | 31). If R is a Prüfer domain and K is its field of fractions, then any ring S such that R ⊆ S ⊆ K is a Prüfer domain. If R is a Prüfer domain, K is its field of fractions, and L is an algebraic extension field of K, then the integral closure of R in L is a Prüfer domain (Fuchs & Salce 2001, p. | Prüfer domain | 0.79859 |
86,392 | The modus tollens rule can be stated formally as: P → Q , ¬ Q ∴ ¬ P {\displaystyle {\frac {P\to Q,\neg Q}{\therefore \neg P}}} where P → Q {\displaystyle P\to Q} stands for the statement "P implies Q". ¬ Q {\displaystyle \neg Q} stands for "it is not the case that Q" (or in brief "not Q"). Then, whenever " P → Q {\disp... | Modus tollens | 0.79859 |
86,393 | Semipermeable membrane is a type of biological or synthetic, polymeric membrane that will allow certain molecules or ions to pass through it by osmosis. The rate of passage depends on the pressure, concentration, and temperature of the molecules or solutes on either side, as well as the permeability of the membrane to ... | Cell permeability | 0.79859 |
86,394 | He then completed his dissertation, entitled The levels of modular representations, under the supervision of Richard Taylor, for which he was awarded a Ph.D. degree. He took a lectureship at Imperial College London in 1998, a readership in 2002, and was appointed to a professorship in 2004. From October to December 200... | Kevin Buzzard | 0.79859 |
86,395 | Also, Alan Edelman, professor of applied mathematics at MIT, has been selected to receive the 2019 IEEE Computer Society Sidney Fernbach Award "for outstanding breakthroughs in high-performance computing, linear algebra, and computational science and for contributions to the Julia programming language. "Both Julia 0.7 ... | Julia (programming language) | 0.79859 |
86,396 | The surface area can be calculated by integrating the length of the normal vector r u × r v {\displaystyle \mathbf {r} _{u}\times \mathbf {r} _{v}} to the surface over the appropriate region D in the parametric uv plane: Although this formula provides a closed expression for the surface area, for all but very special s... | Parametrized surface | 0.79859 |
86,397 | The 'spin' name of the spinor norm can be explained by a connection to the spin group (more accurately a pin group). This may now be explained quickly by Galois cohomology (which however postdates the introduction of the term by more direct use of Clifford algebras). The spin covering of the orthogonal group provides a... | Rotation group | 0.798589 |
86,398 | An AI accelerator is a class of specialized hardware accelerator or computer system designed to accelerate artificial intelligence and machine learning applications, including artificial neural networks and machine vision. Typical applications include algorithms for robotics, Internet of Things, and other data-intensiv... | Neural Processing Unit | 0.798589 |
86,399 | SPIRES was (in addition to the CERN Document Server (CDS), arXiv and parts of Astrophysics Data System) one of the main Particle Information Resources. A survey conducted in 2007 found that SPIRES database users wanted the portal to provide more services than the, at that time, already 30-year-old system could provide.... | INSPIRE-HEP | 0.798589 |
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