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95,500 | "Organic agriculture is a production system that sustains the health of soils, ecosystems and people. It relies on ecological processes, biodiversity and cycles adapted to local conditions, rather than the use of inputs with adverse effects. Organic agriculture combines tradition, innovation and science to benefit the ... | Organic agriculture | 0.778679 |
95,501 | Further work was done by Lady Eve Balfour (the Haughley Experiment) in the United Kingdom, and many others across the world. The term "eco-agriculture" was coined in 1970 by Charles Walters, founder of Acres Magazine, to describe agriculture which does not use "man-made molecules of toxic rescue chemistry", effectively... | Organic agriculture | 0.778679 |
95,502 | These new agricultural techniques, while beneficial in the short-term, had serious longer-term side-effects such as soil compaction, erosion, and declines in overall soil fertility, along with health concerns about toxic chemicals entering the food supply. : 10 In the late 1800s and early 1900s, soil biology scientists... | Organic agriculture | 0.778679 |
95,503 | Induced radioactivity, also called artificial radioactivity or man-made radioactivity, is the process of using radiation to make a previously stable material radioactive. The husband and wife team of Irène Joliot-Curie and Frédéric Joliot-Curie discovered induced radioactivity in 1934, and they shared the 1935 Nobel Pr... | Artificial radioactivity | 0.778679 |
95,504 | The Guinier regime reflecting the overall size of the object without reference to the internal or surface structure of the object and the power-law reflecting the details of the structure, in this case a linear (unbranched), mass-fractal object with mass-fractal dimension, df = 2 (connectivity dimension of 1 reflecting... | Unified scattering function | 0.778673 |
95,505 | This function has been used to describe persistence in polymer chains in good and theta solvents, branched polymers, polymers of complex topology such as star polymers, mass fractal primary particles/aggregates/agglomerates, rod diameter/length, disk thickness/width and other complex hierarchical structures. The lead c... | Unified scattering function | 0.778673 |
95,506 | When a person creates a key-pair, they keep one key private and the other, known as the public-key, is uploaded to a server where it can be accessed by anyone to send the user a private, encrypted, message. Secure Sockets Layer (SSL) uses Diffie–Hellman key exchange if the client does not have a public-private key pair... | Key distribution | 0.778672 |
95,507 | In symmetric key cryptography, both parties must possess a secret key which they must exchange prior to using any encryption. Distribution of secret keys has been problematic until recently, because it involved face-to-face meeting, use of a trusted courier, or sending the key through an existing encryption channel. Th... | Key distribution | 0.778672 |
95,508 | In molecular biology, the CBS domain is a protein domain found in a range of proteins in all species from bacteria to humans. It was first identified as a conserved sequence region in 1997 and named after cystathionine beta synthase, one of the proteins it is found in. CBS domains are also found in a wide variety of ot... | CBS domain | 0.778669 |
95,509 | Katz centrality can be used to compute centrality in directed networks such as citation networks and the World Wide Web.Katz centrality is more suitable in the analysis of directed acyclic graphs where traditionally used measures like eigenvector centrality are rendered useless.Katz centrality can also be used in estim... | Alpha centrality | 0.778668 |
95,510 | The Price equation can describe any system that changes over time, but is most often applied in evolutionary biology. The evolution of sight provides an example of simple directional selection. The evolution of sickle cell anemia shows how a heterozygote advantage can affect trait evolution. The Price equation can also... | Price's theorem | 0.778667 |
95,511 | In the theory of evolution and natural selection, the Price equation (also known as Price's equation or Price's theorem) describes how a trait or allele changes in frequency over time. The equation uses a covariance between a trait and fitness, to give a mathematical description of evolution and natural selection. It p... | Price's theorem | 0.778667 |
95,512 | The canonical symplectic form, also known as the Poincaré two-form, is given by The extension of this concept to general fibre bundles is known as the solder form. By convention, one uses the phrase "canonical form" whenever the form has a unique, canonical definition, and one uses the term "solder form", whenever an a... | Canonical symplectic form | 0.778666 |
95,513 | In mathematics, the tautological one-form is a special 1-form defined on the cotangent bundle T ∗ Q {\displaystyle T^{*}Q} of a manifold Q . {\displaystyle Q.} In physics, it is used to create a correspondence between the velocity of a point in a mechanical system and its momentum, thus providing a bridge between Lagra... | Canonical symplectic form | 0.778666 |
95,514 | In mathematics, the oriented cobordism ring is a ring where elements are oriented cobordism classes of manifolds, the multiplication is given by the Cartesian product of manifolds and the addition is given as the disjoint union of manifolds. The ring is graded by dimensions of manifolds and is denoted by Ω ∗ S O = ⊕ 0 ... | Cobordism ring | 0.778666 |
95,515 | The capital letter upsilon (Υ) can occur in different stylistic variants, with the upper strokes either straight like a Latin Y, or slightly curled. The symbol ϒ (U+03D2) is designated specifically for the curled form ( Υ {\displaystyle \Upsilon } ), used as a technical symbol, e.g. in physics. The letter phi can occur... | Greek letters | 0.778661 |
95,516 | Maleimide and its derivatives are prepared from maleic anhydride by treatment with amines followed by dehydration. A special feature of the reactivity of maleimides is their susceptibility to additions across the double bond either by Michael additions or via Diels-Alder reactions. Bismaleimides are a class of compound... | C4H3NO2 | 0.778661 |
95,517 | Presently, the main clinical fields of PET-MRI are oncology, cardiology, neurology, and neuroscience. Research studies are actively conducted at the moment to understand benefits of the new PET-MRI diagnostic method. The technology combines the exquisite structural and functional characterization of tissue provided by ... | PET-MRI | 0.778658 |
95,518 | Disadvantages of this method include difficulty with unusual anatomy, a need for a suitable library of images, and the need to account for MR coil attenuation. Synthetic, or Substitute CT (sCT) methods to generate CT like data from MRI are also of interest for radiotherapy planning, and have been primarily investigated... | PET-MRI | 0.778658 |
95,519 | Consequently, G + ( k ) + K + ( k ) f ^ + ( k , 0 ) = f ^ − ′ ( k , 0 ) / K − ( k ) − G − ( k ) . {\displaystyle G^{+}(k)+K_{+}(k){\widehat {f}}_{+}(k,0)={\widehat {f}}'_{-}(k,0)/K_{-}(k)-G^{-}(k).} Now, as the left-hand side of the above equation is analytic in the lower half-plane, whilst the right-hand side is analy... | Wiener–Hopf factorization | 0.778654 |
95,520 | In general, the governing equations and boundary conditions are transformed and these transforms are used to define a pair of complex functions (typically denoted with '+' and '−' subscripts) which are respectively analytic in the upper and lower halves of the complex plane, and have growth no faster than polynomials i... | Wiener–Hopf factorization | 0.778654 |
95,521 | The Wiener–Hopf method is a mathematical technique widely used in applied mathematics. It was initially developed by Norbert Wiener and Eberhard Hopf as a method to solve systems of integral equations, but has found wider use in solving two-dimensional partial differential equations with mixed boundary conditions on th... | Wiener–Hopf factorization | 0.778654 |
95,522 | Modern particle physics research is focused on subatomic particles, including atomic constituents, such as electrons, protons, and neutrons (protons and neutrons are composite particles called baryons, made of quarks), that are produced by radioactive and scattering processes; such particles are photons, neutrinos, and... | High Energy Physics | 0.778654 |
95,523 | Software prototyping is the activity of creating prototypes of software applications, i.e., incomplete versions of the software program being developed. It is an activity that can occur in software development and is comparable to prototyping as known from other fields, such as mechanical engineering or manufacturing. ... | Application Simulation Software | 0.778654 |
95,524 | Metop has been developed as a joint undertaking between the European Space Agency (ESA) and European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). Recognising the growing importance of Numerical Weather Prediction (NWP) in weather forecasting, Metop was designed with a suite of instruments ... | MetOp | 0.778654 |
95,525 | Selected large telescopes which are in detailed design or pre-construction phases: Large UV Optical Infrared Surveyor (LUVOIR), a proposed space telescope for launch in the mid 2030s. MUltiplexed Survey Telescope (MUST), a 6.5m spectroscopic survey telescope. Chinese Giant Solar Telescope (CGST), an infrared and optica... | Largest telescopes | 0.778651 |
95,526 | In this theory, it is the evolution of the carrier wave that is given by the Schrödinger equation. It is a deterministic theory and is entirely nonlocal. It is an example of a hidden variable theory, and all non-relativistic quantum mechanics can be accounted for in this theory. The theory was abandoned by de Broglie i... | Walking droplet | 0.77865 |
95,527 | Walking droplet systems have been found to mimic several quantum mechanical phenomena including particle diffraction, quantum tunneling, quantized orbits, the Zeeman Effect, and the quantum corral.Besides being an interesting means to visualise phenomena that are typical of the quantum-mechanical world, floating drople... | Walking droplet | 0.77865 |
95,528 | In physics, the hydrodynamic quantum analogs refer to experimentally-observed phenomena involving bouncing fluid droplets over a vibrating fluid bath that behave analogously to several quantum-mechanical systems.A droplet can be made to bounce indefinitely in a stationary position on a vibrating fluid surface. This is ... | Walking droplet | 0.77865 |
95,529 | Suppose a punctured disk D = {z: 0 < |z − c| < R} in the complex plane is given and f is a holomorphic function defined (at least) on D. The residue Res(f, c) of f at c is the coefficient a−1 of (z − c)−1 in the Laurent series expansion of f around c. Various methods exist for calculating this value, and the choice of ... | Residue (complex analysis) | 0.77865 |
95,530 | In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for any function f: C ∖ { a k } k → C {\displaystyle f\colon \mathbb {C} \setmin... | Residue (complex analysis) | 0.77865 |
95,531 | The Tantra of Kalachakra is the basis of Tibetan astronomy. It explains some phenomena in a similar manner as modern astronomy science. Hence, Sun eclipse is described as the Moon passing between the Sun and the Earth.In 1318, the 3rd Karmapa received vision of Kalachakra which he used to introduce a revised system of ... | Tibetan astronomy | 0.77865 |
95,532 | The institute began its history in 1949 when a resolution by the Politburo created the Higher School of Cryptographers, and a closed department was created under the Mechanics-Mathematics Faculty of Moscow State University by a resolution of the Council of Ministers of the USSR. Later they united to become the technica... | Institute of Cryptography, Telecommunications and Computer Science | 0.778649 |
95,533 | The Institute of Cryptography, Telecommunications and Computer Science (Russian: Институт криптографии, связи и информатики) or IKSI (ИКСИ) is a research institute within the Academy of the Federal Security Service of Russia, which trains specialists in areas such as the transfer, protection and processing of informati... | Institute of Cryptography, Telecommunications and Computer Science | 0.778649 |
95,534 | Department of Applied Mathematics Cryptography Applied Mathematics and Computer Science Automation of information and analytical processes Faculty of Special Technology Information, security telecommunications systems and electronic systems Faculty of Information Security | Institute of Cryptography, Telecommunications and Computer Science | 0.778649 |
95,535 | By 1997, 81% of the developing world's wheat area was planted to semi-dwarf wheats, giving both increased yields and better response to nitrogenous fertilizer.T. turgidum subsp. polonicum is known for its longer glumes and grains, has been bred into main wheat lines for its grain size effect, and likely has contributed... | Wheat grain | 0.778649 |
95,536 | Chinese Spring (CS42) were sequenced in Roche 454 pyrosequencer using GS FLX Titanium and GS FLX+ platforms to generate 85 Gb of sequence (220 million reads) and identified between 94,000 and 96,000 genes. The implications of the research in cereal genetics and breeding includes the examination of genome variation, ana... | Wheat grain | 0.778649 |
95,537 | In traditional agricultural systems, wheat populations often consist of landraces, informal farmer-maintained populations that often maintain high levels of morphological diversity. Although landraces of wheat are no longer extensively grown in Europe and North America, they continue to be important elsewhere. The orig... | Wheat grain | 0.778649 |
95,538 | The four iron atoms and four sulfur atoms form an alternating arrangement at the corners. The whole cluster is typically anchored by coordination of the iron atoms, usually with cysteine residues. In this way, each Fe center achieves tetrahedral coordination geometry. | Cubane-type cluster | 0.778648 |
95,539 | Other compounds having different elements in the corners, various atoms or groups bonded to the corners are all part of this class of structures. Inorganic cubane-type clusters include selenium tetrachloride, tellurium tetrachloride, and sodium silox. Cubane clusters are common throughout bioinorganic chemistry. Ferred... | Cubane-type cluster | 0.778648 |
95,540 | It was noticed by Jean-Pierre Serre in the 1960s based on the Weil conjectures that even singular (possibly reducible) and non-complete algebraic varieties should admit 'virtual Betti numbers'. More precisely, one should be able to assign to any algebraic variety X a polynomial PX(t), called its virtual Poincaré polyno... | Hodge-Riemann bilinear relations | 0.778648 |
95,541 | Margaret Burbidge was due to be given the 1972 award, but she refused it on the grounds of gender discrimination, stating: "It is high time that discrimination in favor of, as well as against, women in professional life be removed". This prompted the AAS to set up its first committee on the status of women in astronomy... | Annie Jump Cannon Award in Astronomy | 0.778643 |
95,542 | The Annie Jump Cannon Award in Astronomy is awarded annually by the American Astronomical Society (AAS) to a woman resident of North America, who is within five years of receipt of a PhD, for distinguished contributions to astronomy or for similar contributions in related sciences which have immediate application to as... | Annie Jump Cannon Award in Astronomy | 0.778643 |
95,543 | Childhood manifestation of the gene deletion is typically associated with autism, while adolescent and later expression of the gene deletion often manifests in schizophrenia or other psychotic disorders. Though the disorders are linked by genetics, there is no increased risk found for adult schizophrenia in patients wh... | Antagonistic Pleiotropy | 0.778642 |
95,544 | Most genetic traits are polygenic in nature: controlled by many genetic variants, each of small effect. These genetic variants can reside in protein coding or non-coding regions of the genome. In this context pleiotropy refers to the influence that a specific genetic variant, e.g., a single nucleotide polymorphism or S... | Antagonistic Pleiotropy | 0.778642 |
95,545 | Starting with the quasi-geostrophic equations, applying the Eady model assumptions, and linearizing yields the linearized differential equations governing the time evolution of the state of the atmosphere in the Eady model: ψ ¯ = − Λ z y {\displaystyle {\overline {\psi }}=-\Lambda zy} ∂ q ′ ∂ t + U ¯ ∂ q ′ ∂ x = 0 {\di... | Eady model | 0.778642 |
95,546 | In Australia, design work commenced on a version of MLS in 1972. Most of this work was done jointly by the Federal Department of Civil Aviation (DCA), and the Radio Physics Division of the Commonwealth Scientific and Industrial Research Organisation (CSIRO). The project was called Interscan, one of several microwave la... | Microwave Scanning Beam Landing System | 0.778641 |
95,547 | In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is larger than or equal to the size of the message being sent. In this technique, a plaintext is paired with a random secret key (also referred to as a one-time pad). Then,... | One-time tape | 0.77864 |
95,548 | Leo Marks describes inventing such a system for the British Special Operations Executive during World War II, though he suspected at the time that it was already known in the highly compartmentalized world of cryptography, as for instance at Bletchley Park.The final discovery was made by information theorist Claude Sha... | One-time tape | 0.77864 |
95,549 | Problems with data remanence can make it difficult to completely erase computer media.One-time pads solve few current practical problems in cryptography. High-quality ciphers are widely available and their security is not currently considered a major worry. Such ciphers are almost always easier to employ than one-time ... | One-time tape | 0.77864 |
95,550 | One-time pads have been used in special circumstances since the early 1900s. In 1923, they were employed for diplomatic communications by the German diplomatic establishment. The Weimar Republic Diplomatic Service began using the method in about 1920. The breaking of poor Soviet cryptography by the British, with messag... | One-time tape | 0.77864 |
95,551 | Subnormal numbers are not supported, but can be emulated with the mpfr_subnormalize function.MPFR is not able to track the accuracy of numbers in a whole program or expression; this is not its goal. Interval arithmetic packages like Arb, MPFI, or Real RAM implementations like iRRAM, which may be based on MPFR, can do t... | GNU MPFR | 0.778639 |
95,552 | Switched fabric or switching fabric is a network topology in which network nodes interconnect via one or more network switches (particularly crossbar switches). Because a switched fabric network spreads network traffic across multiple physical links, it yields higher total throughput than broadcast networks, such as th... | Switching fabric | 0.778637 |
95,553 | The distance from the incenter to the centroid is less than one third the length of the longest median of the triangle.By Euler's theorem in geometry, the squared distance from the incenter I to the circumcenter O is given by O I 2 = R ( R − 2 r ) , {\displaystyle OI^{2}=R(R-2r),} where R and r are the circumradius and... | Incenter | 0.778637 |
95,554 | In △ A C F {\displaystyle \triangle {ACF}} , A C ¯: A F ¯ = C I ¯: I F ¯ {\displaystyle {\overline {AC}}:{\overline {AF}}={\overline {CI}}:{\overline {IF}}} , by the Angle bisector theorem. In △ B C F {\displaystyle \triangle {BCF}} , B C ¯: B F ¯ = C I ¯: I F ¯ {\displaystyle {\overline {BC}}:{\overline {BF}}={\overli... | Incenter | 0.778637 |
95,555 | In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale. The incenter may be equivalently defined as the point where the internal angle bisectors of the triangle cross, as the point equidistant from the triangle's s... | Incenter | 0.778637 |
95,556 | It is a theorem in Euclidean geometry that the three interior angle bisectors of a triangle meet in a single point. In Euclid's Elements, Proposition 4 of Book IV proves that this point is also the center of the inscribed circle of the triangle. The incircle itself may be constructed by dropping a perpendicular from th... | Incenter | 0.778637 |
95,557 | Polyols may be classified according to their chemistry. Some of these chemistries are polyether, polyester, polycarbonate and also acrylic polyols. Polyether polyols may be further subdivided and classified as polyethylene oxide or polyethylene glycol (PEG), polypropylene glycol (PPG) and Polytetrahydrofuran or PTMEG. ... | Polyether polyol | 0.778636 |
95,558 | In the mathematical theory of probability, a Doob martingale (named after Joseph L. Doob, also known as a Levy martingale) is a stochastic process that approximates a given random variable and has the martingale property with respect to the given filtration. It may be thought of as the evolving sequence of best approxi... | Doob martingale | 0.778636 |
95,559 | In chemistry, photocatalysis is the acceleration of a photoreaction in the presence of a photocatalyst, the excited state of which "repeatedly interacts with the reaction partners forming reaction intermediates and regenerates itself after each cycle of such interactions." In many cases, the catalyst is a solid that up... | Photocatalysis | 0.778636 |
95,560 | Photocatalytic water splitting separates water into hydrogen and oxygen: 2 H2O → 2 H2 + O2The most prevalently investigated material, TiO2 , is inefficient. Mixtures of TiO2 and nickel oxide (NiO) are more active. NiO allows a significant explоitation of the visible spectrum. One efficient photocatalyst in the UV range... | Photocatalysis | 0.778636 |
95,561 | Of course, he did not call his solution supersymmetric, as SUSY was thirty years in the future. The SUSY solution of the hydrogen atom is only one example of the very general class of solutions which SUSY provides to shape-invariant potentials, a category which includes most potentials taught in introductory quantum me... | Supersymmetric Quantum Mechanics | 0.778636 |
95,562 | Understanding the consequences of supersymmetry (SUSY) has proven mathematically daunting, and it has likewise been difficult to develop theories that could account for symmetry breaking, i.e., the lack of observed partner particles of equal mass. To make progress on these problems, physicists developed supersymmetric ... | Supersymmetric Quantum Mechanics | 0.778636 |
95,563 | To generalize this concept, we define an anticommutator, which relates operators the same way as an ordinary commutator, but with the opposite sign: { A , B } = A B + B A . {\displaystyle \{A,B\}=AB+BA.} If operators are related by anticommutators as well as commutators, we say they are part of a Lie superalgebra. | Supersymmetric Quantum Mechanics | 0.778636 |
95,564 | In fundamental quantum mechanics, we learn that an algebra of operators is defined by commutation relations among those operators. For example, the canonical operators of position and momentum have the commutator = i {\displaystyle =i} . (Here, we use "natural units" where Planck's constant is set equal to 1.) A more ... | Supersymmetric Quantum Mechanics | 0.778636 |
95,565 | {\displaystyle H^{(1)}=H^{(2)}-\hbar \omega =H^{\rm {HO}}-{\frac {\hbar \omega }{2}}.} This is a special case of shape invariance, discussed below. Taking without proof the introductory theorem mentioned above, it is apparent that the spectrum of H ( 1 ) {\displaystyle H^{(1)}} will start with E 0 = 0 {\displaystyle E_... | Supersymmetric Quantum Mechanics | 0.778636 |
95,566 | In theoretical physics, supersymmetric quantum mechanics is an area of research where supersymmetry are applied to the simpler setting of plain quantum mechanics, rather than quantum field theory. Supersymmetric quantum mechanics has found applications outside of high-energy physics, such as providing new methods to so... | Supersymmetric Quantum Mechanics | 0.778636 |
95,567 | Each boson would have a fermionic partner of equal energy—but, in the relativistic world, energy and mass are interchangeable, so we can just as easily say that the partner particles have equal mass. SUSY concepts have provided useful extensions to the WKB approximation in the form of a modified version of the Bohr-Som... | Supersymmetric Quantum Mechanics | 0.778635 |
95,568 | (The potential energy terms which occur in the Hamiltonians are then called partner potentials.) An introductory theorem shows that for every eigenstate of one Hamiltonian, its partner Hamiltonian has a corresponding eigenstate with the same energy (except possibly for zero energy eigenstates). This fact can be exploit... | Supersymmetric Quantum Mechanics | 0.778635 |
95,569 | For example, students are typically taught to "solve" the hydrogen atom by a laborious process which begins by inserting the Coulomb potential into the Schrödinger equation. After a considerable amount of work using many differential equations, the analysis produces a recursion relation for the Laguerre polynomials. Th... | Supersymmetric Quantum Mechanics | 0.778635 |
95,570 | In 2021, supersymmetric quantum mechanics was applied to option pricing and the analysis of markets in quantum finance, and to financial networks. | Supersymmetric Quantum Mechanics | 0.778635 |
95,571 | In probability theory, a Hunt process is a strong Markov process which is quasi-left continuous with respect to the minimum completed admissible filtration { F t } t ≥ 0 {\displaystyle \{F_{t}\}_{t\geq 0}} . It is named after Gilbert Hunt. | Hunt process | 0.778634 |
95,572 | The planet is the only one known to be in the orbit of the star MOA-2009-BLG-387L, which is an M-type dwarf star that has a mass that is approximately 0.19 times that of the Sun. The star is located at an estimated 5700 parsecs (18,591 light years) from the Earth. The star is named for the Microlensing Observations in ... | MOA-2009-BLG-387Lb | 0.778631 |
95,573 | Interpretation of follow-up observations led to the planet's confirmation. The ratio between the planet's mass and its host star's mass is well-constrained, but a large interval of uncertainty exists because the host star's mass is known within a large confidence interval that spans the mass of all red dwarf stars.The ... | MOA-2009-BLG-387Lb | 0.778631 |
95,574 | MOA-2009-BLG-387 was a gravitational microlensing event detected by the Microlensing Observations in Astrophysics collaboration on July 24, 2009, which searches and documents chance and brief alignments of stars with other stars or objects; such alignments cause a gravitational lens effect, which bends light and causes... | MOA-2009-BLG-387Lb | 0.778631 |
95,575 | A number of publishing houses, initiatives, and research institutions encourage using SciCrunch‘s RRIDs: Common Citation Format Article in Nature, Cell Press, eLife, FORCE11, Frontiers Media,GigaScience,MIRIAM Registry,NIH,PLOS Biology and PLOS Genetics. | Research Resource Identifier | 0.778631 |
95,576 | By the early 1990s, many of the programs required in an operating system (such as libraries, compilers, text editors, a command-line shell, and a windowing system) were completed, although low-level elements such as device drivers, daemons, and the kernel, called GNU Hurd, were stalled and incomplete.MINIX was created ... | Linux operating system | 0.778629 |
95,577 | The term Julian date may also refer, outside of astronomy, to the day-of-year number (more properly, the ordinal date) in the Gregorian calendar, especially in computer programming, the military and the food industry, or it may refer to dates in the Julian calendar. For example, if a given "Julian date" is "October 5, ... | Reduced Julian date | 0.778627 |
95,578 | He then calculated via remainder division that he needed to add eight 532-year Paschal cycles totaling 4256 years before the cycle containing 1 BC or 0 in order for its year 457 to be indiction 3. The sum 4256 + 457 was thus JP 4713.A formula for determining the year of the Julian Period given its character involving t... | Reduced Julian date | 0.778627 |
95,579 | Each tread played a different sound when stepped on.Johns Hopkins University students turned a Hackerman Hall staircase into a piano, with a new note per step. The Hopkins Robotics Club modified the staircase so the treads played the C scale. == References == | Stair tread | 0.778627 |
95,580 | NIOSH’s responsibility under the Act is to determine the probability that an individual’s cancer was a result of their occupational radiation exposure at a DOE or AWE facility. This probability is determined by DOL and is based on the radiation dose reconstruction completed by NIOSH. The dose reconstructions are comple... | Dose reconstruction | 0.778626 |
95,581 | The next several methods involve algebraic identities such as For instance, Fibonacci represents the fraction 8/11 by splitting the numerator into a sum of two numbers, each of which divides one plus the denominator: 8/11 = 6/11 + 2/11. Fibonacci applies the algebraic identity above to each these two parts, producing t... | Egyptian fraction | 0.778625 |
95,582 | An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number a b {\displays... | Egyptian fraction | 0.778625 |
95,583 | Modern historians of mathematics have studied the Rhind papyrus and other ancient sources in an attempt to discover the methods the Egyptians used in calculating with Egyptian fractions. In particular, study in this area has concentrated on understanding the tables of expansions for numbers of the form 2 n {\displaysty... | Egyptian fraction | 0.778625 |
95,584 | The Lorentz symmetry is arranged so as to transform the indices as usual and without being deformed. An even simpler variant of this model is to let M {\displaystyle M} here be a numerical antisymmetric tensor, in which context it is usually denoted θ {\displaystyle \theta } , so the relations are = i θ μ ν {\displays... | Quantum spacetime | 0.778625 |
95,585 | In this point of view the different kinds of matter particles are manifestations of geometry in these extra noncommutative directions. Connes's first works here date from 1989 but has been developed considerably since then. Such an approach can theoretically be combined with quantum spacetime as above. | Quantum spacetime | 0.778625 |
95,586 | Although not quantum spacetime in the sense above, another use of noncommutative geometry is to tack on 'noncommutative extra dimensions' at each point of ordinary spacetime. Instead of invisible curled up extra dimensions as in string theory, Alain Connes and coworkers have argued that the coordinate algebra of this e... | Quantum spacetime | 0.778625 |
95,587 | For example, a physical parameter λ {\displaystyle \lambda } , perhaps the Planck length, might control the deviation from commutative classical spacetime, so that ordinary Lorentzian spacetime arises as λ → 0 {\displaystyle \lambda \to 0} . There might be a notion of quantum differential calculus on the quantum spacet... | Quantum spacetime | 0.778625 |
95,588 | Quantum spacetimes are often described mathematically using the noncommutative geometry of Connes, quantum geometry, or quantum groups. Any noncommutative algebra with at least four generators could be interpreted as a quantum spacetime, but the following desiderata have been suggested: Local Lorentz group and Poincaré... | Quantum spacetime | 0.778625 |
95,589 | Physical spacetime is a quantum spacetime when in quantum mechanics position and momentum variables x , p {\displaystyle x,p} are already noncommutative, obey the Heisenberg uncertainty principle, and are continuous. Because of the Heisenberg uncertainty relations, greater energy is needed to probe smaller distances. U... | Quantum spacetime | 0.778625 |
95,590 | This refers in modern usage to the angular momentum algebra = 2 i λ x 3 , = 2 i λ x 1 , = 2 i λ x 2 {\displaystyle =2i\lambda x_{3},\ =2i\lambda x_{1},\ =2i\lambda x_{2}} familiar from quantum mechanics but interpreted in this context as coordinates of a quantum space or spacetime. These relations were proposed by R... | Quantum spacetime | 0.778625 |
95,591 | The momentum space for the theory is another copy of the same algebra and there is a certain 'braided addition' of momentum on it expressed as the structure of a braided Hopf algebra or quantum group in a certain braided monoidal category). This theory by 1993 had provided the corresponding q {\displaystyle q} -deforme... | Quantum spacetime | 0.778625 |
95,592 | That is, there are indications that this model relates to quantum gravity with non-zero cosmological constant, the choice of q {\displaystyle q} depending on whether this is positive or negative. We have described the mathematically better understood but perhaps less physically justified positive case here. A full unde... | Quantum spacetime | 0.778625 |
95,593 | In particular, time t = Trace q ( α β γ δ ) = q δ + q − 1 α {\displaystyle t={\text{Trace}}_{q}{\begin{pmatrix}\alpha &\beta \\\gamma &\delta \end{pmatrix}}=q\delta +q^{-1}\alpha } is given by a natural braided trace of the matrix and commutes with the other generators (so this model has a very different flavour from t... | Quantum spacetime | 0.778625 |
95,594 | The idea of quantum spacetime was proposed in the early days of quantum theory by Heisenberg and Ivanenko as a way to eliminate infinities from quantum field theory. The germ of the idea passed from Heisenberg to Rudolf Peierls, who noted that electrons in a magnetic field can be regarded as moving in a quantum spaceti... | Quantum spacetime | 0.778625 |
95,595 | In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some vari... | Quantum spacetime | 0.778625 |
95,596 | This prediction requires the particular p 0 , p i {\displaystyle p_{0},p_{i}} to be the physical energy and spatial momentum (as opposed to some other function of them). Arguments for this identification were provided in 1999 by Giovanni Amelino-Camelia and Majid through a study of plane waves for a quantum differentia... | Quantum spacetime | 0.778625 |
95,597 | The bicrossproduct model spacetime was introduced by Shahn Majid and Henri Ruegg and has Lie algebra relations = 0 , = i λ x i {\displaystyle =0,\quad =i\lambda x_{i}} for the spatial variables x i {\displaystyle x_{i}} and the time variable t {\displaystyle t} . Here λ {\displaystyle \lambda } has dimensions of time... | Quantum spacetime | 0.778625 |
95,598 | The Cajal Blue Brain Project is coordinated by the Technical University of Madrid led by Javier de Felipe and uses the facilities of the Supercomputing and Visualization Center of Madrid and its supercomputer Magerit. The Cajal Institute also participates in this collaboration. The main lines of research currently bein... | Blue Brain | 0.778625 |
95,599 | Rhenium exists in ten known oxidation states from −3 to +7 except −2, and all but Re(−3) are represented by organorhenium compounds. Most are prepared from salts of perrhenate and related binary oxides. The halides, e.g., ReCl5 are also useful precursors as are certain oxychlorides. A noteworthy feature of organorheniu... | Organorhenium chemistry | 0.778623 |
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