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86,600 | In graph theory, the shuffle-exchange network is an undirected cubic multigraph, whose vertices represent binary sequences of a given length and whose edges represent two operations on these sequence, circular shifts and flipping the lowest-order bit. | Shuffle-exchange network | 0.782456 |
86,601 | In the version of this network introduced by Tomas Lang and Harold S. Stone in 1976, simplifying earlier work of Stone in 1971, the shuffle-exchange network of order d {\displaystyle d} consisted of an array of 2 d {\displaystyle 2^{d}} cells, numbered by the 2 d {\displaystyle 2^{d}} different binary numbers that can ... | Shuffle-exchange network | 0.782456 |
86,602 | Later, a group of citizen scientists with an interest in population genetics and genetic genealogy formed a working group to create an amateur tree aiming at being above all timely. The table below brings together all of these works at the point of the landmark 2002 YCC Tree. This allows a researcher reviewing older pu... | Haplogroup D-M15 | 0.782456 |
86,603 | In mathematics, De Gua's theorem is a three-dimensional analog of the Pythagorean theorem named after Jean Paul de Gua de Malves. It states that if a tetrahedron has a right-angle corner (like the corner of a cube), then the square of the area of the face opposite the right-angle corner is the sum of the squares of the... | De Gua's theorem | 0.782454 |
86,604 | The subsets I {\displaystyle I} of { 1 , 2 , 3 } {\displaystyle \{1,2,3\}} with exactly 2 elements are { 2 , 3 } {\displaystyle \{2,3\}} , { 1 , 3 } {\displaystyle \{1,3\}} and { 1 , 2 } {\displaystyle \{1,2\}} . By definition, U { 2 , 3 } {\displaystyle U_{\{2,3\}}} is the orthogonal projection of U = △ A B C {\displa... | De Gua's theorem | 0.782454 |
86,605 | Then where vol k ( U ) {\displaystyle \operatorname {vol} _{k}(U)} is the k-dimensional volume of U and the sum is over all subsets I ⊆ { 1 , … , n } {\displaystyle I\subseteq \{1,\ldots ,n\}} with exactly k elements. De Gua's theorem and its generalisation (above) to n-simplices with right-angle corners correspond t... | De Gua's theorem | 0.782454 |
86,606 | The Pythagorean theorem and de Gua's theorem are special cases (n = 2, 3) of a general theorem about n-simplices with a right-angle corner, proved by P. S. Donchian and H. S. M. Coxeter in 1935. This, in turn, is a special case of a yet more general theorem by Donald R. Conant and William A. Beyer (1974), which can be ... | De Gua's theorem | 0.782454 |
86,607 | Jean Paul de Gua de Malves (1713–85) published the theorem in 1783, but around the same time a slightly more general version was published by another French mathematician, Charles de Tinseau d'Amondans (1746–1818), as well. However the theorem had also been known much earlier to Johann Faulhaber (1580–1635) and René De... | De Gua's theorem | 0.782454 |
86,608 | {\displaystyle X.} These assignments are functorial, and we obtain a category-theoretic duality between the category of Boolean algebras (with homomorphisms as morphisms) and the category of Stone spaces (with continuous maps as morphisms). Stone's theorem gave rise to a number of similar dualities, now collectively kn... | Profinite set | 0.782452 |
86,609 | To every Boolean algebra B {\displaystyle B} we can associate a Stone space S ( B ) {\displaystyle S(B)} as follows: the elements of S ( B ) {\displaystyle S(B)} are the ultrafilters on B , {\displaystyle B,} and the topology on S ( B ) , {\displaystyle S(B),} called the Stone topology, is generated by the sets of the ... | Profinite set | 0.782452 |
86,610 | In topology and related areas of mathematics, a Stone space, also known as a profinite space or profinite set, is a compact totally disconnected Hausdorff space. Stone spaces are named after Marshall Harvey Stone who introduced and studied them in the 1930s in the course of his investigation of Boolean algebras, which ... | Profinite set | 0.782452 |
86,611 | On the other hand, Earnshaw's theorem only applies to point charges, but not to distributed charges. This led J. J. Thomson in 1904 to his plum pudding model, where the negative point charges (electrons, or "plums") are embedded into a distributed positive charge "pudding", where they could be either stationary or movi... | Earnshaw's Theorem | 0.782452 |
86,612 | For quite some time, Earnshaw's theorem posed a startling question of why matter is stable and holds together, since much evidence was found that matter was held together electromagnetically despite the proven instability of static charge configurations. Since Earnshaw's theorem only applies to stationary charges, ther... | Earnshaw's Theorem | 0.782452 |
86,613 | Earnshaw's theorem was originally formulated for electrostatics (point charges) to show that there is no stable configuration of a collection of point charges. The proofs presented here for individual dipoles should be generalizable to collections of magnetic dipoles because they are formulated in terms of energy, whic... | Earnshaw's Theorem | 0.782452 |
86,614 | Earnshaw's theorem applies to classical inverse-square law forces (electric and gravitational) and also to the magnetic forces of permanent magnets, if the magnets are hard (the magnets do not vary in strength with external fields). Earnshaw's theorem forbids magnetic levitation in many common situations. If the materi... | Earnshaw's Theorem | 0.782452 |
86,615 | Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually cited in reference to magnetic fields, but was ... | Earnshaw's Theorem | 0.782452 |
86,616 | Limiting movement in that direction allows levitation with fewer than the full 3 dimensions available for movement (note that the theorem is proven for 3 dimensions, not 1D or 2D). Diamagnetic materials are excepted because they exhibit only repulsion against the magnetic field, whereas the theorem requires materials t... | Earnshaw's Theorem | 0.782452 |
86,617 | Maglev trains are one application. Pseudo-levitation constrains the movement of the magnets usually using some form of a tether or wall. This works because the theorem shows only that there is some direction in which there will be an instability. | Earnshaw's Theorem | 0.782452 |
86,618 | Earnshaw's theorem has no exceptions for non-moving permanent ferromagnets. However, Earnshaw's theorem does not necessarily apply to moving ferromagnets, certain electromagnetic systems, pseudo-levitation and diamagnetic materials. These can thus seem to be exceptions, though in fact they exploit the constraints of th... | Earnshaw's Theorem | 0.782452 |
86,619 | As a practical consequence, this theorem also states that there is no possible static configuration of ferromagnets that can stably levitate an object against gravity, even when the magnetic forces are stronger than the gravitational forces. Earnshaw's theorem has even been proven for the general case of extended bodie... | Earnshaw's Theorem | 0.782452 |
86,620 | Intuitively, though, it is plausible that if the theorem holds for a single point charge then it would also hold for two opposite point charges connected together. In particular, it would hold in the limit where the distance between the charges is decreased to zero while maintaining the dipole moment – that is, it woul... | Earnshaw's Theorem | 0.782452 |
86,621 | This argument may not be sufficient if all the second derivatives of U are null.To be completely rigorous, strictly speaking, the existence of a stable point does not require that all neighbouring force vectors point exactly toward the stable point; the force vectors could spiral in toward the stable point, for example... | Earnshaw's Theorem | 0.782452 |
86,622 | OFF (Object File Format) is a geometry definition file format containing the description of the composing polygons of a geometric object. It can store 2D or 3D objects, and simple extensions allow it to represent higher-dimensional objects as well. Though originally developed for Geomview, a geometry visualization soft... | OFF (file format) | 0.782452 |
86,623 | The RP Photonics Encyclopedia (formerly Encyclopedia of Laser Physics and Technology) is an encyclopedia of optics and optoelectronics, laser technology, optical fibers, nonlinear optics, optical communications, imaging science, optical metrology, spectroscopy and ultrashort pulse physics. It is available online as a f... | RP Photonics Encyclopedia | 0.782446 |
86,624 | The Glasgow Mathematical Journal is a mathematics journal that publishes original research papers in any branch of pure and applied mathematics. It covers a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differe... | Glasgow Mathematical Journal | 0.782445 |
86,625 | The Acree-Rosenheim reaction is a chemical test used for detecting the presence of tryptophan in proteins. A protein mixture is mixed with formaldehyde. Concentrated sulfuric acid is added to form two layers. A purple ring appears between the two layers if the test is positive for tryptophan.The test was named after tw... | Acree–Rosenheim reaction | 0.782445 |
86,626 | Symmetry is important to chemistry because it undergirds essentially all specific interactions between molecules in nature (i.e., via the interaction of natural and human-made chiral molecules with inherently chiral biological systems). The control of the symmetry of molecules produced in modern chemical synthesis cont... | Symmetry transformation | 0.782444 |
86,627 | Symmetry (from Ancient Greek συμμετρία (summetría) 'agreement in dimensions, due proportion, arrangement') in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under s... | Symmetry transformation | 0.782444 |
86,628 | In quantum computing, the threshold theorem (or quantum fault-tolerance theorem) states that a quantum computer with a physical error rate below a certain threshold can, through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels. This shows that quantum computers ... | Quantum threshold theorem | 0.782443 |
86,629 | The problem is solved if we can show the nonexistence of an equivariant map f: X → V ∖ Z {\displaystyle f:X\to V\setminus Z} . Obstructions to the existence of such maps are often formulated algebraically from the topological data of X {\displaystyle X} and V ∖ Z {\displaystyle V\setminus Z} . An archetypal example of ... | Equivariant topology | 0.782439 |
86,630 | In the same way that one can deduce the ham sandwich theorem from the Borsuk-Ulam Theorem, one can find many applications of equivariant topology to problems of discrete geometry. This is accomplished by using the configuration-space test-map paradigm: Given a geometric problem P {\displaystyle P} , we define the confi... | Equivariant topology | 0.782439 |
86,631 | The major contribution of (Tropp 2010) is the application of Lieb's theorem where (Ahlswede & Winter 2003) had applied the Golden–Thompson inequality. Tropp's corollary is the following: If H {\displaystyle H} is a fixed self-adjoint matrix and X {\displaystyle X} is a random self-adjoint matrix, then E tr e H + X ... | Matrix Chernoff bound | 0.782439 |
86,632 | The following is immediate from the previous result: Pr { λ max ( ∑ k X k ) ≥ t } ≤ inf θ > 0 { e − θ t tr e ∑ k log M X k ( θ ) } {\displaystyle \Pr \left\{\lambda _{\max }\left(\sum _{k}\mathbf {X} _{k}\right)\geq t\right\}\leq \inf _{\theta >0}\left\{e^{-\theta t}\operatorname {tr} e^{\sum _{k}\log \mathbf {M} _... | Matrix Chernoff bound | 0.782439 |
86,633 | Ahlswede & Winter use the Golden–Thompson inequality to proceed, whereas Tropp (Tropp 2010) uses Lieb's Theorem. Suppose one wished to vary the length of the series (n) and the dimensions of the matrices (d) while keeping the right-hand side approximately constant. Then n must vary approximately as the log of d. Severa... | Matrix Chernoff bound | 0.782439 |
86,634 | It is never larger than the Ahlswede–Winter value (by the norm triangle inequality), but can be much smaller. Therefore, the theorem above gives a tighter bound than the Ahlswede–Winter result. The chief contribution of (Ahlswede & Winter 2003) was the extension of the Laplace-transform method used to prove the scalar ... | Matrix Chernoff bound | 0.782439 |
86,635 | The first bounds of this type were derived by (Ahlswede & Winter 2003). Recall the theorem above for self-adjoint matrix Gaussian and Rademacher bounds: For a finite sequence { A k } {\displaystyle \{\mathbf {A} _{k}\}} of fixed, self-adjoint matrices with dimension d {\displaystyle d} and for { ξ k } {\displaystyle \{... | Matrix Chernoff bound | 0.782439 |
86,636 | For certain applications in linear algebra, it is useful to know properties of the probability distribution of the largest eigenvalue of a finite sum of random matrices. Suppose { X k } {\displaystyle \{\mathbf {X} _{k}\}} is a finite sequence of random matrices. Analogous to the well-known Chernoff bound for sums of s... | Matrix Chernoff bound | 0.782439 |
86,637 | The classical Chernoff bounds concern the sum of independent, nonnegative, and uniformly bounded random variables. In the matrix setting, the analogous theorem concerns a sum of positive-semidefinite random matrices subjected to a uniform eigenvalue bound. | Matrix Chernoff bound | 0.782439 |
86,638 | 105. dubnium, Db, an element that is named after the city of Dubna, where the JINR is located. Originally named "hahnium" (Ha) in honor of Otto Hahn by the Berkeley group (1970) but renamed by the International Union of Pure and Applied Chemistry (1997). | Transuranium elements | 0.782438 |
86,639 | 3D printing Direct metal laser sintering Filament winding, produces composite pipes, tanks, etc. Fused deposition modeling Inkjet Printing Laminated object manufacturing Laser engineered net shaping Layered manufacturing Rapid Induction Printing Selective laser sintering Spark plasma sintering Stereolithography | Taxonomy of manufacturing processes | 0.782436 |
86,640 | Such a quantum state of motion would allow researchers to experimentally investigate decoherence, which describes the transition of objects from states that are described by quantum mechanics to states that are described by Newtonian mechanics. Optomechanical structures provide new methods to test the predictions of qu... | Cavity optomechanics | 0.782436 |
86,641 | Cavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on low-energy scales. It is a cross field of optics, quantum optics, solid-state physics and materials science. The motivation for research on cavity optomechanics comes from fundamental effects of quantum ... | Cavity optomechanics | 0.782436 |
86,642 | For example, the optomechanical coupling strength of a Fabry–Pérot cavity of length L {\displaystyle L} with a moving end-mirror can be directly determined from the geometry to be g 0 = ω cav ( 0 ) x zpf L {\displaystyle g_{0}={\frac {\omega _{\text{cav}}(0)x_{\text{zpf}}}{L}}} .This standard Hamiltonian H tot {\displa... | Cavity optomechanics | 0.782436 |
86,643 | Hybrid systems: an optomechanical system can be coupled to a system of a different nature (e.g. a cloud of ultracold atoms and a two-level system), which can lead to new effects on both the optomechanical and the additional system.Cavity optomechanics is closely related to trapped ion physics and Bose–Einstein condensa... | Cavity optomechanics | 0.782436 |
86,644 | One of the questions which are still subject to current debate is the exact mechanism of decoherence. In the Schrödinger's cat thought experiment, the cat would never be seen in a quantum state: there needs to be something like a collapse of the quantum wave functions, which brings it from a quantum state to a pure cla... | Cavity optomechanics | 0.782436 |
86,645 | The homogeneous elements of degree n are exactly the homogeneous polynomials of degree n. The tensor algebra T ∙ V {\displaystyle T^{\bullet }V} of a vector space V. The homogeneous elements of degree n are the tensors of order n, T n V {\displaystyle T^{n}V} . The exterior algebra ⋀ ∙ V {\displaystyle \textstyle \bigw... | Homogeneous ideal | 0.782435 |
86,646 | An algebra A over a ring R is a graded algebra if it is graded as a ring. In the usual case where the ring R is not graded (in particular if R is a field), it is given the trivial grading (every element of R is of degree 0). Thus, R ⊆ A 0 {\displaystyle R\subseteq A_{0}} and the graded pieces A i {\displaystyle A_{i}} ... | Homogeneous ideal | 0.782435 |
86,647 | Some graded rings (or algebras) are endowed with an anticommutative structure. This notion requires a homomorphism of the monoid of the gradation into the additive monoid of Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb {Z} } , the field with two elements. Specifically, a signed monoid consists of a pair ( Γ , ε ) {\dis... | Homogeneous ideal | 0.782435 |
86,648 | Rapid Prototyping allows designers/developers to provide an accurate idea of how the finished product will turn out before putting too much time and money into the prototype. 3D printing being used for Rapid Prototyping allows for Industrial 3D printing to take place. With this, you could have large-scale moulds to spa... | 3D fabrication | 0.782434 |
86,649 | Rapid prototyping is also commonly applied in software engineering to try out new business models and application architectures such as Aerospace, Automotive, Financial Services, Product development, and Healthcare. Aerospace design and industrial teams rely on prototyping in order to create new AM methodologies in the... | 3D fabrication | 0.782434 |
86,650 | 1 comment line: tools must account for all code and comments regardless of comment placement.Even the "logical" and "physical" SLOC values can have a large number of varying definitions. Robert E. Park (while at the Software Engineering Institute) and others developed a framework for defining SLOC values, to enable peo... | Unified Code Count (UCC) | 0.782434 |
86,651 | The International Astronomical Union (IAU) established a Working Group on Star Names (WGSN) in May 2016 to catalog and standardize proper names for stars for the international astronomical community. It operates under Division C – Education, Outreach and Heritage.The IAU states that it is keen to make a distinction bet... | IAU Working Group on Star Names | 0.782434 |
86,652 | For G = PGL(n), this amounts to the Albert–Brauer–Hasse–Noether theorem, saying that a central simple algebra over a number field is determined by its local invariants. Building on the Hasse principle, the classification of semisimple groups over number fields is well understood. For example, there are exactly three Q-... | Reductive Lie group | 0.782431 |
86,653 | In this direction, Steinberg proved Serre's "Conjecture I": for a connected linear algebraic group G over a perfect field of cohomological dimension at most 1, H1(k,G) = 1. (The case of a finite field was known earlier, as Lang's theorem.) It follows, for example, that every reductive group over a finite field is quasi... | Reductive Lie group | 0.782431 |
86,654 | Also, k-forms of a given algebraic group G (sometimes called "twists" of G) are classified by H1(k,Aut(G)). These problems motivate the systematic study of G-torsors, especially for reductive groups G. When possible, one hopes to classify G-torsors using cohomological invariants, which are invariants taking values in G... | Reductive Lie group | 0.782431 |
86,655 | A torsor for an affine group scheme G over a field k means an affine scheme X over k with an action of G such that X k ¯ {\displaystyle X_{\overline {k}}} is isomorphic to G k ¯ {\displaystyle G_{\overline {k}}} with the action of G k ¯ {\displaystyle G_{\overline {k}}} on itself by left translation. A torsor can also ... | Reductive Lie group | 0.782431 |
86,656 | A fundamental example of a reductive group is the general linear group GL n {\displaystyle {\text{GL}}_{n}} of invertible n × n matrices over a field k, for a natural number n. In particular, the multiplicative group Gm is the group GL(1), and so its group Gm(k) of k-rational points is the group k* of nonzero elements ... | Reductive Lie group | 0.782431 |
86,657 | In molecular biology, autophagy related 3 (Atg3) is the E2 enzyme for the LC3 lipidation process. It is essential for autophagy. The super protein complex, the Atg16L complex, consists of multiple Atg12-Atg5 conjugates. | ATG3 | 0.782429 |
86,658 | Some plasmids or microbial hosts include an addiction system or postsegregational killing system (PSK), such as the hok/sok (host killing/suppressor of killing) system of plasmid R1 in Escherichia coli. This variant produces both a long-lived poison and a short-lived antidote. Several types of plasmid addiction systems... | Plasmid vector | 0.782429 |
86,659 | The use of plasmids as a technique in molecular biology is supported by bioinformatics software. These programs record the DNA sequence of plasmid vectors, help to predict cut sites of restriction enzymes, and to plan manipulations. Examples of software packages that handle plasmid maps are ApE, Clone Manager, GeneCons... | Plasmid vector | 0.782429 |
86,660 | Paclitaxel total synthesis in organic chemistry is a major ongoing research effort in the total synthesis of paclitaxel (Taxol). This diterpenoid is an important drug in the treatment of cancer but, also expensive because the compound is harvested from a scarce resource, namely the Pacific yew (Taxus brevifolia). Not o... | Paclitaxel total synthesis | 0.782429 |
86,661 | The two main reasons why this type of synthesis is not feasible in the laboratory is that nature does a much better job controlling stereochemistry and a much better job activating a hydrocarbon skeleton with oxygen substituents for which cytochrome P450 is responsible in some of the oxygenations. Intermediate 5 is cal... | Paclitaxel total synthesis | 0.782429 |
86,662 | Other structures have been suggested including Lie 3-algebras and Lie superalgebras. Neither of these fit with Yang–Mills theory. In particular Lie superalgebras would introduce bosons with incorrect statistics. Supersymmetry, however, does fit with Yang–Mills. | Grand Unification Theories | 0.782427 |
86,663 | In August 2018, Toyota Tsusho began a partnership with Microsoft to create fish farming tools using the Microsoft Azure application suite for IoT technologies related to water management. Developed in part by researchers from Kindai University, the water pump mechanisms use artificial intelligence to count the number o... | Internet of Everything | 0.782427 |
86,664 | The IoT can connect various manufacturing devices equipped with sensing, identification, processing, communication, actuation, and networking capabilities. Network control and management of manufacturing equipment, asset and situation management, or manufacturing process control allow IoT to be used for industrial appl... | Internet of Everything | 0.782427 |
86,665 | The bill requires "a manufacturer of a connected device, as those terms are defined, to equip the device with a reasonable security feature or features that are appropriate to the nature and function of the device, appropriate to the information it may collect, contain, or transmit, and designed to protect the device a... | Internet of Everything | 0.782427 |
86,666 | It can also be used for scheduling repair and maintenance activities efficiently, by coordinating tasks between different service providers and users of these facilities. IoT devices can also be used to control critical infrastructure like bridges to provide access to ships. The usage of IoT devices for monitoring and ... | Internet of Everything | 0.782427 |
86,667 | Some just look at the sky using nothing more than their eyes or binoculars, but more dedicated amateurs often use portable telescopes or telescopes situated in their private or club observatories. Amateurs can also join as members of amateur astronomical societies, which can advise, educate or guide them towards ways o... | Star gazing | 0.782422 |
86,668 | Amateur astronomy is a hobby where participants enjoy observing or imaging celestial objects in the sky using the unaided eye, binoculars, or telescopes. Even though scientific research may not be their primary goal, some amateur astronomers make contributions in doing citizen science, such as by monitoring variable st... | Star gazing | 0.782422 |
86,669 | While a number of interesting celestial objects are readily identified by the naked eye, sometimes with the aid of a star chart, many others are so faint or inconspicuous that technical means are necessary to locate them. Although many methods are used in amateur astronomy, most are variations of a few specific techniq... | Star gazing | 0.782422 |
86,670 | Non-visual amateur astronomy includes the use of infrared filters on conventional telescopes, and also the use of radio telescopes. Some amateur astronomers use home-made radio telescopes, while others use radio telescopes that were originally built for astronomical research but have since been made available for use b... | Star gazing | 0.782422 |
86,671 | Astrophotography has become more popular with the introduction of far easier to use equipment including, digital cameras, DSLR cameras and relatively sophisticated purpose built high quality CCD cameras. Most amateur astronomers work at visible wavelengths, but a small minority experiment with wavelengths outside the v... | Star gazing | 0.782422 |
86,672 | Collectively, amateur astronomers observe a variety of celestial objects and phenomena. Common targets of amateur astronomers include the Sun, the Moon, planets, stars, comets, meteor showers, and a variety of deep sky objects such as star clusters, galaxies, and nebulae. Many amateurs like to specialise in observing p... | Star gazing | 0.782422 |
86,673 | Scientific research is most often not the main goal for many amateur astronomers, unlike professional astronomers. Work of scientific merit is possible, however, and many amateurs successfully contribute to the knowledge base of professional astronomers. Astronomy is sometimes promoted as one of the few remaining scien... | Star gazing | 0.782422 |
86,674 | In subterranean civil engineering, ventilation shafts, also known as airshafts or vent shafts, are vertical passages used in mines and tunnels to move fresh air underground, and to remove stale air. In architecture, an airshaft, also known as a lightwell, is typically a small, vertical space within a tall building whic... | Ventilation shaft | 0.782422 |
86,675 | Thus formed N-radicals might participate in an intramolecular 1,5-hydrogen abstraction reaction from unactivated carbons, the result being the formation of pyrrolidines.The great advantage of the Suárez modification is that the reaction can be performed under very mild neutral conditions compatible with the stability o... | Hofmann–Löffler reaction | 0.78242 |
86,676 | In order to determine the structural and geometrical factors affecting the intramolecular hydrogen atom transfer, a number of different N-chloroamines were examined in the Hofmann–Löffler–Freytag reaction. The systems were judiciously chosen in order to obtain data on the following points: relative migration tendencies... | Hofmann–Löffler reaction | 0.78242 |
86,677 | The alkyl chloride is later cyclized under the influence of alkali and the cyclic tertiary amine results. More detailed mechanistic studies were conducted by E. J. Corey et al., who examined several features of the reaction relevant to the mechanism: stereochemistry, hydrogen isotope effect, initiation, inhibition, cat... | Hofmann–Löffler reaction | 0.78242 |
86,678 | Shire was a global biotechnology company focused on serving people with rare diseases and other highly specialized conditions. The company's products were available in more than 100 countries across core therapeutic areas including Hematology, Immunology, Neuroscience, Lysosomal Storage Disorders, Gastrointestinal / In... | Shire (pharmaceutical company) | 0.78242 |
86,679 | Karl Burkart defined a green economy as based on six main sectors: Renewable energy Green buildings Sustainable transport Water management Waste management Land managementThe International Chamber of Commerce (ICC) representing global business defines green economy as "an economy in which economic growth and environmen... | Green economics | 0.782418 |
86,680 | The Kerr–Newman metric describes the geometry of spacetime for a rotating charged black hole with mass M, charge Q and angular momentum J. The formula for this metric depends upon what coordinates or coordinate conditions are selected. Two forms are given below: Boyer–Lindquist coordinates, and Kerr–Schild coordinates.... | Kerr–Schild spacetime | 0.782417 |
86,681 | In the Schrödinger picture, the wave function or field is the solution to the Schrödinger equation; one of the postulates of quantum mechanics. All relativistic wave equations can be constructed by specifying various forms of the Hamiltonian operator Ĥ describing the quantum system. Alternatively, Feynman's path integr... | Relativistic wave equation | 0.782416 |
86,682 | In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of quantum field theory (QFT), the equations determine the dynamics of qu... | Relativistic wave equation | 0.782416 |
86,683 | They were anticipated later (in a more involved way) by de Broglie (1934), and Duffin, Kemmer, and Petiau (around 1938–1939) see Duffin–Kemmer–Petiau algebra. The Dirac–Fierz–Pauli formalism was more sophisticated than Majorana's, as spinors were new mathematical tools in the early twentieth century, although Majorana'... | Relativistic wave equation | 0.782416 |
86,684 | The natural problem became clear: to generalize the Dirac equation to particles with any spin; both fermions and bosons, and in the same equations their antiparticles (possible because of the spinor formalism introduced by Dirac in his equation, and then-recent developments in spinor calculus by van der Waerden in 1929... | Relativistic wave equation | 0.782416 |
86,685 | A description of quantum mechanical systems which could account for relativistic effects was sought for by many theoretical physicists; from the late 1920s to the mid-1940s. The first basis for relativistic quantum mechanics, i.e. special relativity applied with quantum mechanics together, was found by all those who di... | Relativistic wave equation | 0.782416 |
86,686 | In mathematics, quantales are certain partially ordered algebraic structures that generalize locales (point free topologies) as well as various multiplicative lattices of ideals from ring theory and functional analysis (C*-algebras, von Neumann algebras). Quantales are sometimes referred to as complete residuated semig... | Quantale | 0.782414 |
86,687 | In general, different anaesthetics exhibit different mechanisms of action such that there are numerous molecular targets at all levels of integration within the central nervous system. However, for certain intravenous anaesthetics, such as propofol and etomidate, the main molecular target has been identified to be GABA... | Theories of general anaesthetic action | 0.782414 |
86,688 | The construction also works over finite fields, providing examples in finite projective planes. Remark: The fundamental theorem for projective planes states, that a projective mapping in a projective plane over a field (pappian plane) is uniquely determined by prescribing the images of three lines. That means that, for... | Steiner's theorem (geometry) | 0.782412 |
86,689 | The Steiner construction defines the conics in a planar linear incidence geometry (two points determine at most one line and two lines intersect in at most one point) intrinsically, that is, using only the collineation group. Specifically, E ( T , P ) {\displaystyle E(T,P)} is the conic at point P {\displaystyle P} aff... | Steiner's theorem (geometry) | 0.782412 |
86,690 | Simple example: If one shifts in the first diagram point U {\displaystyle U} and its pencil of lines onto V {\displaystyle V} and rotates the shifted pencil around V {\displaystyle V} by a fixed angle φ {\displaystyle \varphi } then the shift (translation) and the rotation generate a projective mapping π {\displaystyle... | Steiner's theorem (geometry) | 0.782412 |
86,691 | and point E = ( 1 , 1 ) {\displaystyle E=(1,1)} . The affine part of the generated curve appears to be the hyperbola y = 1 / x {\displaystyle y=1/x} .Remark: The Steiner generation of a conic section provides simple methods for the construction of ellipses, parabolas and hyperbolas which are commonly called the paralle... | Steiner's theorem (geometry) | 0.782412 |
86,692 | Sporormiella is a genus of fungi in the family Sporormiaceae. Species of the genus are obligately coprophilous, occurring on the dung of domestic livestock as well as wild herbivores. The genus is distributed across boreal and temperate regions of the world, and contains about 80 species. The spores have characteristic... | Sporormiella | 0.782408 |
86,693 | Fractal deployment framework, JBI pluggable components, and open source licensing make it modular and customizable. The originality of Petals is to implement a highly distributed topology. The first stable version of Petals ESB, called PEtALS, was released on September 21, 2006. | OW2 PEtALS | 0.782407 |
86,694 | ℓ = h . L Thus elongation, e = (H – h) / hWhen the elongation is large it is normally measured as reduction, r which is defined as the per-unit change in thickness with respect to the entry thickness H; and so if h is the exit thickness, Reduction, r = (H – h) / HNote that the thickness difference (H – h) is divided by... | Tandem rolling mill | 0.782405 |
86,695 | Reduction, r is defined as the per-unit change in thickness with respect to the entry thickness H, and so {\displaystyle \quad } r = (H – h) / H {\displaystyle \quad } where h is the exit thickness.As the material is reduced, its length becomes proportionately longer; this can be seen in the attached GIF movie. There a... | Tandem rolling mill | 0.782405 |
86,696 | Physicists from over twenty institutions in Germany, Spain, Italy, Switzerland, Croatia, Finland, Poland, India, Bulgaria and Armenia collaborate in using MAGIC; the largest groups are at Institut de Física d'Altes Energies (IFAE), Spain Universitat Autònoma de Barcelona, Spain Universidad Complutense de Madrid, Spain ... | MAGIC (telescope) | 0.782405 |
86,697 | The first telescope was built in 2004 and operated for five years in standalone mode. A second MAGIC telescope (MAGIC-II), at a distance of 85 m from the first one, started taking data in July 2009. Together they integrate the MAGIC telescope stereoscopic system.MAGIC is sensitive to cosmic gamma rays with photon energ... | MAGIC (telescope) | 0.782405 |
86,698 | The pairing is used in number theory and algebraic geometry, and has also been applied in elliptic curve cryptography and identity based encryption. | Weil pairing | 0.782402 |
86,699 | For abelian varieties over an algebraically closed field K, the Weil pairing is a nondegenerate pairing A × A ∨ ⟶ μ n {\displaystyle A\times A^{\vee }\longrightarrow \mu _{n}} for all n prime to the characteristic of K. Here A ∨ {\displaystyle A^{\vee }} denotes the dual abelian variety of A. This is the so-called We... | Weil pairing | 0.782402 |
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