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80,300 | He also recognized that these relations might be useful in computing observables for the case of strong interaction physics. The dispersion relations were analytic properties of the S-matrix, and they imposed more stringent conditions than those that follow from unitarity alone. This development in S-matrix theory stem... | Second Superstring Revolution | 0.785018 |
80,301 | The book is an update and rewrite of Hawking's 1988 A Brief History of Time. In this book Hawking and Mlodinow present quantum mechanics, string theory, the big bang theory, and other topics in a more accessible fashion to the general public. The book is updated with newly discovered topics, and informs of recurring su... | A Briefer History of Time (Hawking and Mlodinow book) | 0.785017 |
80,302 | For a contraction T (i.e., ( ‖ T ‖ ≤ 1 {\displaystyle \|T\|\leq 1} ), its defect operator DT is defined to be the (unique) positive square root DT = (I - T*T)½. In the special case that S is an isometry, DS* is a projector and DS=0, hence the following is an Sz. Nagy unitary dilation of S with the required polynomial f... | Sz.-Nagy's dilation theorem | 0.785017 |
80,303 | A generalisation of this theorem, by Berger, Foias and Lebow, shows that if X is a spectral set for T, and R ( X ) {\displaystyle {\mathcal {R}}(X)} is a Dirichlet algebra, then T has a minimal normal δX dilation, of the form above. A consequence of this is that any operator with a simply connected spectral set X has a... | Sz.-Nagy's dilation theorem | 0.785017 |
80,304 | The Sz.-Nagy dilation theorem (proved by Béla Szőkefalvi-Nagy) states that every contraction T {\displaystyle T} on a Hilbert space H {\displaystyle H} has a unitary dilation U {\displaystyle U} to a Hilbert space K {\displaystyle K} , containing H {\displaystyle H} , with T n = P H U n | H , n ≥ 0 , {\displaystyle T^{... | Sz.-Nagy's dilation theorem | 0.785017 |
80,305 | 2021 brought about acquisitions across a number of countries and industries: In February 2021 Tetra Tech acquired Coanda Research and Development Corporation, a Canadian engineering consulting company specializing in computational fluid dynamics, physical and predictive modeling, data analytics, process engineering, an... | Tetra Tech | 0.785015 |
80,306 | The cash infusion permitted more acquisitions of engineering firms specializing in water resources (urban drainage and flood control), civil engineering (bridges and waterway design), environmental restoration, and hazardous waste cleanup. Gross revenues totaled $96.5 million by 1994.During the early 2000s, the company... | Tetra Tech | 0.785015 |
80,307 | Two norms on a vector space are called equivalent if and only if they induce the same topology. If p {\displaystyle p} and q {\displaystyle q} are two equivalent norms on a vector space X {\displaystyle X} then the normed space ( X , p ) {\displaystyle (X,p)} is a Banach space if and only if ( X , q ) {\displaystyle (X... | Complete topological vector space | 0.785014 |
80,308 | The existence of the canonical uniformity was demonstrated above by defining it. The theorem below establishes that the canonical uniformity of any TVS ( X , τ ) {\displaystyle (X,\tau )} is the only uniformity on X {\displaystyle X} that is both (1) translation invariant, and (2) generates on X {\displaystyle X} the t... | Complete topological vector space | 0.785014 |
80,309 | Every F-space, and thus also every Fréchet space, Banach space, and Hilbert space is a complete TVS. Note that every F-space is a Baire space but there are normed spaces that are Baire but not Banach.A pseudometric d {\displaystyle d} on a vector space X {\displaystyle X} is said to be a translation invariant pseudomet... | Complete topological vector space | 0.785014 |
80,310 | {\displaystyle I\times C.} Moreover, observe that the closure of the origin in I × C {\displaystyle I\times C} is equal to I × { 0 } , {\displaystyle I\times \{0\},} and that I × { 0 } {\displaystyle I\times \{0\}} and { 0 } × C {\displaystyle \{0\}\times C} are topological complements in I × C . {\displaystyle I\times... | Complete topological vector space | 0.785014 |
80,311 | Let I = cl { 0 } {\displaystyle I=\operatorname {cl} \{0\}} denote the closure of the origin in X , {\displaystyle X,} where I {\displaystyle I} is endowed with its subspace topology induced by X {\displaystyle X} (so that I {\displaystyle I} has the indiscrete topology). Since I {\displaystyle I} has the trivial top... | Complete topological vector space | 0.785014 |
80,312 | Then I: L ( X ; Y ) → L ( C ; Y ) {\displaystyle I:L(X;Y)\to L(C;Y)} is a (surjective) vector space isomorphism. Moreover, I: L ( X ; Y ) → L ( C ; Y ) {\displaystyle I:L(X;Y)\to L(C;Y)} maps families of equicontinuous subsets onto each other. Suppose that L ( X ; Y ) {\displaystyle L(X;Y)} is endowed with a G {\displa... | Complete topological vector space | 0.785014 |
80,313 | {\displaystyle F\times F\subseteq N.} A uniform space ( X , U ) {\displaystyle (X,{\mathcal {U}})} is called a complete uniform space (respectively, a sequentially complete uniform space) if every Cauchy prefilter (respectively, every elementary Cauchy prefilter) on X {\displaystyle X} converges to at least one point o... | Complete topological vector space | 0.785014 |
80,314 | Explicitly, a subset U ⊆ X {\displaystyle U\subseteq X} is open in this topology if and only if for every u ∈ U {\displaystyle u\in U} there exists some N ∈ B ⋅ u {\displaystyle N\in {\mathcal {B}}\cdot u} such that N ⊆ U ; {\displaystyle N\subseteq U;} that is, U {\displaystyle U} is open if and only if for every u ∈ ... | Complete topological vector space | 0.785014 |
80,315 | {\displaystyle X.} The neighborhood prefilter at a point p ∈ X {\displaystyle p\in X} and, respectively, on a subset S ⊆ X {\displaystyle S\subseteq X} are the families of sets: and the filters on X {\displaystyle X} that each generates is known as the neighborhood filter of p {\displaystyle p} (respectively, of S {\di... | Complete topological vector space | 0.785014 |
80,316 | An occultation is an event that occurs when one object is hidden from the observer by another object that passes between them. The term is often used in astronomy, but can also refer to any situation in which an object in the foreground blocks from view (occults) an object in the background. In this general sense, occu... | Lunar Occultation | 0.785013 |
80,317 | Preliminary results of a 6 November 2010 occultation by the dwarf planet Eris of a magnitude 17 star in the constellation of Cetus placed an upper limit on Eris's diameter of 2320 km, making it almost the same size as Pluto. Due to their slower movement through the night sky, occultations by TNOs are far less common th... | Lunar Occultation | 0.785013 |
80,318 | In 1901, he co-developed the Runge–Kutta method, used to solve ordinary differential equations numerically. He is also remembered for the Zhukovsky–Kutta aerofoil, the Kutta–Zhukovsky theorem and the Kutta condition in aerodynamics. Kutta died in Fürstenfeldbruck, Germany in 1944. | Martin Kutta | 0.785011 |
80,319 | Hence, Archaeopteryx would have a very short and ineffective flight. In contrast to Ostrom's theory regarding flight as a hunting mechanism, physics again does not support this model. In order to effectively trap insects with the wings, Archaeopteryx would require a mechanism such as holes in the wings to reduce air re... | Origin of avian flight | 0.78501 |
80,320 | Furthermore, the mass of Archaeopteryx versus the distance needed for minimum velocity to obtain liftoff speed is proportional, therefore, as mass increases, the energy required for takeoff increases. Other research has shown that the physics involved in cursorial flight would not make this a likely answer to the origi... | Origin of avian flight | 0.78501 |
80,321 | The ubiquitous identity that relates inverses to the binary operation in any group, namely ( x y ) − 1 = y − 1 x − 1 , {\displaystyle (xy)^{-1}=y^{-1}x^{-1},} which is taken as an axiom in the more general context of a semigroup with involution, has sometimes been called an antidistributive property (of inversion as a ... | Antidistributive | 0.785007 |
80,322 | Each interpretation is responsible for different distributive laws in the Boolean algebra. Similar structures without distributive laws are near-rings and near-fields instead of rings and division rings. The operations are usually defined to be distributive on the right but not on the left. | Antidistributive | 0.785007 |
80,323 | A lattice is another kind of algebraic structure with two binary operations, ∧ and ∨ . {\displaystyle \,\land {\text{ and }}\lor .} If either of these operations distributes over the other (say ∧ {\displaystyle \,\land \,} distributes over ∨ {\displaystyle \,\lor } ), then the reverse also holds ( ∨ {\displaystyle \,\l... | Antidistributive | 0.785007 |
80,324 | See also Distributivity (order theory). A Boolean algebra can be interpreted either as a special kind of ring (a Boolean ring) or a special kind of distributive lattice (a Boolean lattice). | Antidistributive | 0.785007 |
80,325 | In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra. For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition. This basic property of ... | Antidistributive | 0.785007 |
80,326 | The Novikov conjecture is one of the most important unsolved problems in topology. It is named for Sergei Novikov who originally posed the conjecture in 1965. The Novikov conjecture concerns the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group. Accor... | Novikov conjecture | 0.785006 |
80,327 | The Copenhagen interpretation of quantum mechanics is named after work done at the institute during this time. Following his father's death in 1962, Aage Bohr succeeded him as director of the Niels Bohr Institute, a position he held until 1970. He remained active there until he retired in 1992.On January 1, 1993, the i... | Cosmic Dawn Center | 0.785005 |
80,328 | The institute was founded in 1921, as the Institute for Theoretical Physics of the University of Copenhagen, by the Danish theoretical physicist Niels Bohr, who had been on the staff of the University of Copenhagen since 1914, and who had been lobbying for its creation since his appointment as professor in 1916. On the... | Cosmic Dawn Center | 0.785005 |
80,329 | The Niels Bohr Institute (Danish: Niels Bohr Institutet) is a research institute of the University of Copenhagen. The research of the institute spans astronomy, geophysics, nanotechnology, particle physics, quantum mechanics and biophysics. | Cosmic Dawn Center | 0.785005 |
80,330 | The Cosmic Dawn Center is an Astronomy/Cosmology research center, founded as a collaboration between the University of Copenhagen and DTU Space of the Danish Technical University (DTU). The center is led by center director and NBI Professor Sune Toft and center co-director Thomas Greve, Professor at DTU and UCL. The ma... | Cosmic Dawn Center | 0.785005 |
80,331 | Research at the Niels Bohr Institute is organised in ten research sections covering a broad range of physics, i.e. astrophysics, biophysics, solid state physics, geophysics, particle physics and e-science. | Cosmic Dawn Center | 0.785005 |
80,332 | We now sketch the proof. The argument passes E to the induced map Φ E {\displaystyle \Phi _{E}} and uses Stinespring's dilation theorem. Since E is positive, so is Φ E {\displaystyle \Phi _{E}} as a map between C*-algebras, as explained above. Furthermore, because the domain of Φ E {\displaystyle \Phi _{E}} , C(X), is ... | Naimark's dilation theorem | 0.785004 |
80,333 | The theorem reads as follows: Let E be a positive L(H)-valued measure on X. There exists a Hilbert space K, a bounded operator V: K → H {\displaystyle V:K\rightarrow H} , and a self-adjoint, spectral L(K)-valued measure on X, F, such that E ( B ) = V F ( B ) V ∗ . {\displaystyle \;E(B)=VF(B)V^{*}.} | Naimark's dilation theorem | 0.785004 |
80,334 | {\displaystyle \langle \Phi _{E}(f)h,h\rangle =\int _{X}f(x)\langle E(dx)h,h\rangle \leq \|f\|_{\infty }\cdot |E|.} This shows Φ E ( f ) {\displaystyle \;\Phi _{E}(f)} is a bounded operator for all f, and Φ E {\displaystyle \Phi _{E}} itself is a bounded linear map as well. The properties of Φ E {\displaystyle \Phi _{E... | Naimark's dilation theorem | 0.785004 |
80,335 | In the physics literature, it is common to see the spelling “Neumark” instead of “Naimark.” The latter variant is according to the romanization of Russian used in translation of Soviet journals, with diacritics omitted (originally Naĭmark). The former is according to the etymology of the surname of Mark Naimark. | Naimark's dilation theorem | 0.785004 |
80,336 | In the finite-dimensional case, there is a somewhat more explicit formulation. Suppose now X = { 1 , … , n } {\displaystyle X=\{1,\dotsc ,n\}} , therefore C(X) is the finite-dimensional algebra C n {\displaystyle \mathbb {C} ^{n}} , and H has finite dimension m. A positive operator-valued measure E then assigns each i ... | Naimark's dilation theorem | 0.785004 |
80,337 | In operator theory, Naimark's dilation theorem is a result that characterizes positive operator valued measures. It can be viewed as a consequence of Stinespring's dilation theorem. | Naimark's dilation theorem | 0.785004 |
80,338 | Project Galileo is an educational astronomy project, based at Clifton College in Bristol, in the United Kingdom. | Project Galileo | 0.785003 |
80,339 | : 268 The Jesuit order played an important role in spreading the idea of mathematics as a kind of universal scientific language. As well as geometry and theoretical mathematics, Jesuit scholars worked on a number of applied projects, including calculating machines such as the one Kircher had designed and then described... | Polygraphia Nova | 0.785002 |
80,340 | Kircher reported that the origin of the work was a request from Holy Roman Emperor Ferdinand III to develop "a kind of lingua universalis" which would allow written communication between all peoples. The Emperor knew of the earlier secret communication system developed by Johannes Trithemius in his 1518 work Polygraphi... | Polygraphia Nova | 0.785002 |
80,341 | : 292 The first arca was sent to Ferdinando II de' Medici, Grand Duke of Tuscany in 1659, and Kircher then sent texts on cryptography to Emperor Leopold, Archduke Leopold Wilhelm of Austria, Bernard Ignaz von Martinitz, Augustus the Younger, Duke of Brunswick-Lüneburg, Maximilian Heinrich, Elector of Cologne and Pope A... | Polygraphia Nova | 0.785002 |
80,342 | Polygraphia nova et universalis ex combinatoria arte directa is a 1663 work by the Jesuit scholar Athanasius Kircher. It was one of Kircher's most highly regarded works: 187 and his only complete work on the subject of cryptography, although he made passing references to the topic elsewhere. : 121 The book was distribu... | Polygraphia Nova | 0.785002 |
80,343 | The main claimed application of IUT is to various conjectures in number theory, among them the abc conjecture, but also more geometric conjectures such as Szpiro's conjecture on elliptic curves and Vojta's conjecture for curves. The first step is to translate arithmetic information on these objects to the setting of Fr... | Inter-universal Teichmüller theory | 0.785002 |
80,344 | Inter-universal Teichmüller theory (abbreviated as IUT or IUTT) is the name given by mathematician Shinichi Mochizuki to a theory he developed in the 2000s, following his earlier work in arithmetic geometry. According to Mochizuki, it is "an arithmetic version of Teichmüller theory for number fields equipped with an el... | Inter-universal Teichmüller theory | 0.785002 |
80,345 | The links between theaters are not compatible with ring or scheme structures and are performed outside conventional arithmetic geometry. However, they are compatible with certain group structures, and absolute Galois groups as well as certain types of topological groups play a fundamental role in IUT. Considerations of... | Inter-universal Teichmüller theory | 0.785002 |
80,346 | On one hand, Hodge theaters generalize such classical objects in number theory as the adeles and ideles in relation to their global elements. On the other hand, they generalize certain structures appearing in the previous Hodge-Arakelov theory of Mochizuki. | Inter-universal Teichmüller theory | 0.785002 |
80,347 | IUT applies algorithmic results of mono-anabelian geometry to reconstruct relevant schemes after applying arithmetic deformations to them; a key role is played by three rigidities established in Mochizuki's etale theta theory. Roughly speaking, arithmetic deformations change the multiplication of a given ring, and the ... | Inter-universal Teichmüller theory | 0.785002 |
80,348 | Inter-universal Teichmüller theory is a continuation of Mochizuki's previous work in arithmetic geometry. This work, which has been peer-reviewed and well received by the mathematical community, includes major contributions to anabelian geometry, and the development of p-adic Teichmüller theory, Hodge–Arakelov theory a... | Inter-universal Teichmüller theory | 0.785002 |
80,349 | Starting in the 1980s, scientific advances allowed the use of DNA as a material for the identification of an individual. The first patent covering the direct use of DNA variation for forensics (US5593832A) was filed by Jeffrey Glassberg in 1983, based upon work he had done while at Rockefeller University in the United ... | Familial searching | 0.785001 |
80,350 | Evidence from an expert who has compared DNA samples must be accompanied by evidence as to the sources of the samples and the procedures for obtaining the DNA profiles. The judge must ensure that the jury must understand the significance of DNA matches and mismatches in the profiles. The judge must also ensure that the... | Familial searching | 0.785001 |
80,351 | In 2002, in the midst of a famine, Zambia refused emergency food aid that contained food from genetically modified crops, based on the precautionary principle.During a conference in the Ethiopian capital of Addis Ababa, Kingsley Amoako, Executive Secretary of the United Nations Economic Commission for Africa (UNECA), e... | GMO food labelling | 0.785 |
80,352 | Graham Brookes accused Benbrook of subjective herbicide estimates because his data, provided by the National Agricultural Statistics Service, does not distinguish between genetically modified and non-genetically modified crops. Brookes had earlier published a study that found that the use of biotech crops had reduced t... | GMO food labelling | 0.785 |
80,353 | Indeed, the science is quite clear: crop improvement by the modern molecular techniques of biotechnology is safe. Rather, these initiatives are driven by a variety of factors, ranging from the persistent perception that such foods are somehow "unnatural" and potentially dangerous to the desire to gain competitive advan... | GMO food labelling | 0.785 |
80,354 | The US has no legislation governing the relationship among mixtures of farms that grow organic, conventional, and GM crops. The country relies on a "complex but relaxed" combination of three federal agencies (FDA, EPA, and USDA/APHIS) and states' common law tort systems to manage coexistence. : 44 The Secretary of Agri... | GMO food labelling | 0.785 |
80,355 | The composition and toxicity of aerosols, including particles, depends on their source and atmospheric chemistry and varies widely. Wind-blown mineral dust tends to be made of mineral oxides and other material blown from the Earth's crust; this particulate is light-absorbing. Sea salt is considered the second-largest c... | Fine Particulate Matter | 0.784998 |
80,356 | "Aware of Raman's capacity, his physics teacher Rhishard Llewellyn Jones insisted he continue research in England. Jones arranged for Raman's physical inspection with Colonel (Sir Gerald) Giffard. Raman often had poor health and was considered as a "weakling." The inspection revealed that he would not withstand the har... | CV Raman | 0.784998 |
80,357 | He passed matriculation at age 11 and the First Examination in Arts examination (equivalent to today's intermediate examination, pre-university course) with a scholarship at age 13, securing first position in both under the Andhra Pradesh school board (now Andhra Pradesh Board of Secondary Education) examination.In 190... | CV Raman | 0.784998 |
80,358 | At my birth my father was earning the magnificent salary of ten rupees per month!" In 1892, his family moved to Visakhapatnam (then Vizagapatam or Vizag) in Andhra Pradesh as his father was appointed to the faculty of physics at Mrs A.V. Narasimha Rao College.Raman was educated at the St Aloysius' Anglo-Indian High Sch... | CV Raman | 0.784998 |
80,359 | By 1927, the phenomenon was widely accepted by scientists, including Raman. As the news of Compton's Nobel Prize in Physics was announced in December 1927, Raman ecstatically told Krishnan, saying:"Excellent news... very nice indeed. | CV Raman | 0.784998 |
80,360 | Upon his election as Fellow of the Royal Society in 1924, Mukherjee asked him of his future plans, which he replied, saying, "The Nobel Prize of course." In 1926, he established the Indian Journal of Physics and acted as the first editor. The second volume of the journal published his famous article "A new radiation", ... | CV Raman | 0.784998 |
80,361 | He reluctantly resigned as a civil servant after a decade of service, which was described as "supreme sacrifice" since his salary as a professor would be roughly half of his salary at the time. But to his advantage, the terms and conditions as a professor were explicitly indicated in the report of his joining the unive... | CV Raman | 0.784998 |
80,362 | A Professor shall vacate his office upon completion of sixtieth year of his age.Prior to 1914, Ashutosh Mukherjee had invited Jagadish Chandra Bose to take up the position, but Bose declined. As a second choice, Raman became the first Palit Professor of Physics but was delayed for taking up the position as World War I ... | CV Raman | 0.784998 |
80,363 | Raman was chosen by the University of Calcutta to become the Palit Professor of Physics, a position established after the benefactor Sir Taraknath Palit, in 1913. The university senate made the appointment on 30 January 1914, as recorded in the meeting minutes: The following appointments to the Palit Professorships wer... | CV Raman | 0.784998 |
80,364 | He nominated Raman for the Nobel Prize in Physics in 1930, presented him the Hughes Medal as President of the Royal Society in 1930, and recommended him for the position of Director at IISc in 1932.Raman had a sense of obsession with the Nobel Prize. In a speech at the University of Calcutta, he said, "I'm not flattere... | CV Raman | 0.784998 |
80,365 | Raman was the paternal uncle of Subrahmanyan Chandrasekhar, recipient of the 1983 Nobel Prize in Physics.Throughout his life, Raman developed an extensive personal collection of stones, minerals, and materials with interesting light-scattering properties, which he obtained from his world travels and as gifts. He often ... | CV Raman | 0.784998 |
80,366 | Raman presented the formal and detailed description as "A new radiation" at the meeting of the South Indian Science Association in Bangalore on 16 March. His lecture was published in the Indian Journal of Physics on 31 March. A thousand copies of the paper reprint were sent to scientists in different countries on that ... | CV Raman | 0.784998 |
80,367 | The same day, Raman made the announcement before the press. The Associated Press of India reported it the next day, on 29 February, as "New theory of radiation: Prof. Raman's Discovery." It ran the story as:Prof. C. V. Raman, F.R.S., of the Calcutta University, has made a discovery which promises to be of fundamental s... | CV Raman | 0.784998 |
80,368 | An approval for his inclusion in the 1929 Birthday Honours was delayed, and Lord Irwin, the Viceroy of India, conferred him a Knight Bachelor in a special ceremony at the Viceroy's House (now Rashtrapati Bhavan) in New Delhi. In 1930, he won the Nobel Prize in Physics "for his work on the scattering of light and for th... | CV Raman | 0.784998 |
80,369 | "Raman also studied the uniqueness of Indian drums. His analyses of the harmonic nature of the sounds of tabla and mridangam were the first scientific studies on Indian percussions. He wrote a critical research on vibrations of the pianoforte string that was known as Kaufmann's theory. During his brief visit of England... | CV Raman | 0.784998 |
80,370 | The result essentially holds even if ties are allowed in the ballots; in that case, there exists at least one "weak dictator" such that at least one of the candidates tied at the top of that voter's ballot is a winner. The Gibbard–Satterthwaite theorem is a similar theorem that deals with voting systems that elect a si... | Duggan–Schwartz theorem | 0.784997 |
80,371 | Every voter's top preference is in the set of winners. The system can be manipulated by either an optimistic voter, one who can cast a ballot that would elect some candidate to a higher rank than all of those candidates who would have been elected if that voter had voted honestly; or by a pessimistic voter, one who can... | Duggan–Schwartz theorem | 0.784997 |
80,372 | The Duggan–Schwartz theorem (named after John Duggan and Thomas Schwartz) is a result about voting systems designed to choose a nonempty set of winners from the preferences of certain individuals, where each individual ranks all candidates in order of preference. It states that for three or more candidates, at least on... | Duggan–Schwartz theorem | 0.784997 |
80,373 | In abstract algebra and functional analysis, Baer rings, Baer *-rings, Rickart rings, Rickart *-rings, and AW*-algebras are various attempts to give an algebraic analogue of von Neumann algebras, using axioms about annihilators of various sets. Any von Neumann algebra is a Baer *-ring, and much of the theory of project... | Baer *-ring | 0.784995 |
80,374 | Any semisimple ring is Baer, since all left and right ideals are summands in R, including the annihilators. Any domain is Baer, since all annihilators are { 0 } {\displaystyle \{0\}} except for the annihilator of 0, which is R, and both { 0 } {\displaystyle \{0\}} and R are summands of R. The ring of bounded linear ope... | Baer *-ring | 0.784995 |
80,375 | Local class field theory gives a description of the Galois group G of the maximal abelian extension of a local field K via the reciprocity map which acts from the multiplicative group K×=K\{0}. For a finite abelian extension L of K the reciprocity map induces an isomorphism of the quotient group K×/N(L×) of K× by the n... | Local class field theory | 0.784994 |
80,376 | For a higher-dimensional local field K {\displaystyle K} there is a higher local reciprocity map which describes abelian extensions of the field in terms of open subgroups of finite index in the Milnor K-group of the field. Namely, if K {\displaystyle K} is an n {\displaystyle n} -dimensional local field then one uses ... | Local class field theory | 0.784994 |
80,377 | In the geometry of hyperbolic 5-space, the 16-cell honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {3,3,4,3,3}, it has three 16-cell ho... | 16-cell honeycomb honeycomb | 0.784993 |
80,378 | The PA degrees are upward closed in the Turing degrees: if a is a PA degree and a ≤T b then b is a PA degree. The Turing degree 0‘, which is the degree of the halting problem, is a PA degree. There are also PA degrees that are not above 0‘. For example, the low basis theorem implies that there is a low PA degree. | PA degree | 0.784991 |
80,379 | Many of these semi-portable engines were used for large civil engineering and mining projects, driving water pumps, air compressors, drilling and piling machinery. Some specialised engines were also built with drums for winding in mine shafts, especially when exploratory shafts were being sunk. If a mine was successful... | Semi-portable engine | 0.78499 |
80,380 | Thus, in synthetic geometry, the homographies and the collineations of the projective line that are considered are those obtained by restrictions to the line of collineations and homographies of spaces of higher dimension. This means that the fundamental theorem of projective geometry (see below) remains valid in the o... | Projective transformation | 0.78499 |
80,381 | When A is a commutative ring, the homography may be written z ↦ z a + b z c + d , {\displaystyle z\mapsto {\frac {za+b}{zc+d}}\ ,} but otherwise the linear fractional transformation is seen as an equivalence: U ∼ U . {\displaystyle U\thicksim U.} The homography group of the ring of integers Z is modular group PSL(2, ... | Projective transformation | 0.78499 |
80,382 | The diet and feeding ecology of xenophyophores was long the subject of speculation; the fragile tests and deepwater habitat of the group makes in vivo observation difficult. Early propositions included suspension feeding, bacterial farming, deposit feeding, and trapping particulate matter inside the test. Studies have ... | Xenophyophorea | 0.784989 |
80,383 | Therefore, most chemistry computer software can output anaglyph images, and some chemistry textbooks include them. Today, there are more advanced solutions for 3D imaging available, like shutter glasses together with fast monitors. These solutions are already extensively used in science. Still, anaglyph images provide ... | Anaglyph 3D | 0.784987 |
80,384 | Anachrome formula lenses work well with black and white, but can provide excellent results when the glasses are used with conforming "anachrome friendly" images. The US Geological Survey has thousands of these "conforming" full-color images, which depict the geology and scenic features of the U.S. National Park system.... | Anaglyph 3D | 0.784987 |
80,385 | The Join-calculus programming language (published in 1996) implemented local and distributed concurrent computations. It incorporated asynchronous channels as well as a kind of synchronous channel that is used for procedure calls. Agha's Aπ Actor calculus (Agha and Thati 2004) is based on a typed version of the asynchr... | Actor model and process calculi | 0.784985 |
80,386 | The use of algebraic techniques was pioneered in the process calculi. Subsequently, several different process calculi intended to provide algebraic reasoning about Actor systems have been developed in (Gaspari and Zavattaro 1997), (Gaspari and Zavattaro 1999), (Agha and Thati 2004). | Actor model and process calculi | 0.784985 |
80,387 | In computer science, the Actor model and process calculi are two closely related approaches to the modelling of concurrent digital computation. See Actor model and process calculi history. There are many similarities between the two approaches, but also several differences (some philosophical, some technical): There is... | Actor model and process calculi | 0.784985 |
80,388 | The sag can be reduced by increasing the capacitance in the lower stages, and the ripple can be reduced by increasing the frequency of the input and by using a square waveform. By driving the CW from a high-frequency source, such as an inverter, or a combination of an inverter and HV transformer, the overall physical s... | Greinacher multiplier | 0.784985 |
80,389 | In mathematics, more specifically in algebraic geometry, Parshin's conjecture (also referred to as the Beilinson–Parshin conjecture) states that for any smooth projective variety X defined over a finite field, the higher algebraic K-groups vanish up to torsion: K i ( X ) ⊗ Q = 0 , i > 0. {\displaystyle K_{i}(X)\otimes ... | Parshin's conjecture | 0.784985 |
80,390 | This lets the price comparison engine collect data from almost any source without the complexities of building a crawler or the logistics of setting up data feeds at the expense of lower coverage comprehensiveness. Sites that use this method rely on visitors contributing pricing data. Unlike discussion forums, which al... | Comparison shopping agent | 0.784984 |
80,391 | More recently, Michael Palmer, a professor of chemistry at the University of Waterloo, has pointed out that DDT is still used to prevent malaria, that its declining use is primarily due to increases in manufacturing costs, and that in Africa, efforts to control malaria have been regional or local, not comprehensive. Cr... | DDT | 0.784983 |
80,392 | The geometric information of the Cantor set in the example above is contained in the ordinary fractal string L {\displaystyle {\mathcal {L}}} . From this information, we can compute the box-counting dimension of the Cantor set. This notion of fractal dimension can be generalized to that of complex dimension, which may ... | Fractal string | 0.784983 |
80,393 | These poles of (the analytic continuation of) the geometric zeta function ζ L ( s ) {\displaystyle \zeta _{\mathcal {L}}(s)} are then called complex dimensions of the fractal string L {\displaystyle {\mathcal {L}}} , and these complex dimensions appear in formulae which describe the geometry of the fractal.For fractal ... | Fractal string | 0.784983 |
80,394 | Formally, they propose to define “fractality” as the presence of at least one nonreal complex dimension with positive real part. This new definition of fractality solves some old problems in fractal geometry. For example, according to the proposed definition of fractality in the sense of Mandelbrot, Cantor's devil's st... | Fractal string | 0.784983 |
80,395 | Ordinary and generalized fractal strings may be used to study the geometry of a (one-dimensional) fractal, as well as to relate the geometry of the object to its spectrum. For example, the geometric zeta function associated to a fractal string may be used to write an explicit tube formula for the volume of a neighborho... | Fractal string | 0.784983 |
80,396 | Artificial Intelligence can be researched in theory and with practical applications. The problem with most practical application is, that the engineers don't know how to program an AI system. Instead of rejecting the challenge at all the idea is to invent an easy to solve domain which is called a toy problem. Toy probl... | Blocks world | 0.784982 |
80,397 | The blocks world is a planning domain in artificial intelligence. The algorithm is similar to a set of wooden blocks of various shapes and colors sitting on a table. The goal is to build one or more vertical stacks of blocks. Only one block may be moved at a time: it may either be placed on the table or placed atop ano... | Blocks world | 0.784982 |
80,398 | In mathematics, Pieri's formula, named after Mario Pieri, describes the product of a Schubert cycle by a special Schubert cycle in the Schubert calculus, or the product of a Schur polynomial by a complete symmetric function. In terms of Schur functions sλ indexed by partitions λ, it states that s μ h r = ∑ λ s λ {\disp... | Pieri's formula | 0.784981 |
80,399 | The consortium tries to get all those vendors to implement a set of core principles and components that are chosen by the consortium. It was originally intended that CERN host the European branch of W3C; however, CERN wished to focus on particle physics, not information technology. In April 1995, the French Institute f... | W3C Schema | 0.784981 |
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