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92,100 | The group G A {\displaystyle G_{\mathbb {A} }} is isomorphic to G fin × G R {\displaystyle G_{\text{fin}}\times G_{\mathbb {R} }} and is a locally compact group with the product topology, since G fin {\displaystyle G_{\text{fin}}} and G R {\displaystyle G_{\mathbb {R} }} are both locally compact. Let Z ^ = ∏ p < ∞ Z p ... | Maass cusp form | 0.78029 |
92,101 | The right side is the restricted product, concerning the compact, open subgroups K p := G Z p {\displaystyle K_{p}:=G_{\mathbb {Z} _{p}}} of G p {\displaystyle G_{p}} . Then G fin {\displaystyle G_{\text{fin}}} locally compact group, if we equip it with the restricted product topology. | Maass cusp form | 0.78029 |
92,102 | {\displaystyle G_{\mathbb {A} }^{1}.} One is again interested in a decomposition of L cusp 2 {\displaystyle L_{\text{cusp}}^{2}} into irreducible closed subspaces. We have the following theorem: The space L cusp 2 {\displaystyle L_{\text{cusp}}^{2}} decomposes in a direct sum of irreducible Hilbert-spaces with finite m... | Maass cusp form | 0.78029 |
92,103 | G = S L 2 ( R ) {\displaystyle G=\mathrm {SL} _{2}(\mathbb {R} )} is a locally compact unimodular group with the topology of R 4 . {\displaystyle \mathbb {R} ^{4}.} Let Γ {\displaystyle \Gamma } be a congruence subgroup. Since Γ {\displaystyle \Gamma } is discrete in G {\displaystyle G} , it is closed in G {\displaysty... | Maass cusp form | 0.78029 |
92,104 | The logo is a reference to the fish's defensive capabilities and to the Blowfish cryptography algorithm used in OpenSSH. OpenBSD also has a number of slogans including "Secure by default", which was used in the first OpenBSD song, "E-railed", and "Free, Functional & Secure", and OpenBSD has released at least one origin... | Comparison of BSD operating systems | 0.780289 |
92,105 | Note that there was no control group or pre-screening of the survey takers. Those who checked "Other" were asked to specify that operating system.Because survey takers were permitted to select more than one answer, the percentages shown in the graph, which are out of the number survey of participants, add up to greater... | Comparison of BSD operating systems | 0.780289 |
92,106 | OpenBSD is a security-focused BSD known for its developers' insistence on extensive, ongoing code auditing for security and correct functionality, a "secure by default" philosophy, good documentation, and adherence to strictly open source licensing. The system incorporates numerous security features that are absent or ... | Comparison of BSD operating systems | 0.780289 |
92,107 | The area and mass flow rate are held constant for Rayleigh flow. Unlike Fanno flow, the Fanning friction factor, f, remains constant. These relations are shown below with the * symbol representing the throat location where choking can occur. A = A ∗ = constant m ˙ = m ˙ ∗ = constant {\displaystyle {\begin{aligned}A&=A^... | Rayleigh flow | 0.780288 |
92,108 | Therefore, the Rayleigh flow model is critical for an initial design of the duct geometry and combustion temperature for an engine. The Rayleigh flow model is also used extensively with the Fanno flow model. These two models intersect at points on the enthalpy-entropy and Mach number-entropy diagrams, which is meaningf... | Rayleigh flow | 0.780288 |
92,109 | The library is the first place to go when looking into taking a new compound." He also recommended, and often spoke of taking, what he called "heroic doses", which he defined as five grams of dried psilocybin mushrooms, taken alone, on an empty stomach, in silent darkness, and with eyes closed. He believed that when ta... | Novelty theory | 0.780288 |
92,110 | Dudley's research has included topics in ultrafast optics, supercontinuum generation and the science of rogue waves. His research has been supported from diverse sources including the French National Research Agency and the European Research Council. In the field of optical physics, he is particularly recognized for hi... | John Dudley (physicist) | 0.780287 |
92,111 | He is also a recipient of the CNRS Silver Medal in 2013, the SPIE President's Award in 2014, the Hopkins Leadership Award of the OSA in 2015, the Institute of Physics (IOP) President's Medal in 2016, the American Physical Society Dwight Nicholson Medal for Outreach in 2017, and the SPIE Harold E. Edgerton Award for Hig... | John Dudley (physicist) | 0.780287 |
92,112 | John Michael Dudley is a physicist and currently Professor of Physics at the University Bourgogne Franche-Comté working at the joint University-CNRS research Institute FEMTO-ST in Besançon, France. Originally from New Zealand, he is known for his research in nonlinear and ultrafast optical physics, for service to inter... | John Dudley (physicist) | 0.780287 |
92,113 | Dudley was nominated to the French research body the Institut Universitaire de France in 2005 and elected a Fellow of the Optical Society of America (FOSA) in 2007. He was an IEEE LEOS Distinguished Lecturer for the period 2008-2010 and is past Chair of the Quantum Electronics and Optics Division of the European Physic... | John Dudley (physicist) | 0.780287 |
92,114 | The Federal Service for Technical and Export Control of Russia (FSTEC of Russia / FSTEK) is a military agency of the Russian Federation, under the Russian Ministry of Defence. It licenses the export of weapons and dual-use technology items, and is also responsible for Russian military information security.FSTEC of Russ... | Federal Service for Technical and Export Control | 0.780287 |
92,115 | The first prominent and explicit use of the term "urban informatics" in the sociology and media studies literature appears in the 2007 special issue "Urban Informatics: Software, Cities and the New Cartographies of Knowing Capitalism" published in the journal Information, Communication & Society, 10(6), guest edited by... | Urban informatics | 0.780287 |
92,116 | The diverse range of people, groups and organisations involved in urban informatics is reflective of the diversity of methods being used in its pursuit and practice. As a result, urban informatics borrows from a wide range of methodologies across the social sciences, humanities, arts, design, architecture, planning (in... | Urban informatics | 0.780287 |
92,117 | Urban informatics emphasises the relationship between urbanity, as expressed through the many dimensions of urban life, and technology. Later, with the increasing popularity of commercial opportunities under the label of smart city and big data, subsequent definitions became narrow and limited in defining urban informa... | Urban informatics | 0.780287 |
92,118 | The place or spatial research domains entail urban studies, architecture, urban design, urban planning, geography, and others. "Technology" can refer to various types of information and communication technology and ubiquitous computing / urban computing technology such as mobile phones, wearable devices, urban screens,... | Urban informatics | 0.780287 |
92,119 | Some researchers feel that creativity is a complex phenomenon whose study is further complicated by the plasticity of the language we use to describe it. We can describe not just the agent of creativity as "creative" but also the product and the method. Consequently, it could be claimed that it is unrealistic to speak ... | Computational models of musical creativity | 0.780285 |
92,120 | In molecular biology Type I topoisomerases are enzymes that cut one of the two strands of double-stranded DNA, relax the strand, and reanneal the strand. They are further subdivided into two structurally and mechanistically distinct topoisomerases: type IA and type IB. Type IA topoisomerases change the linking number o... | Type I topoisomerase | 0.780284 |
92,121 | The Lunar and Planetary Science Conference (LPSC), jointly sponsored by the Lunar and Planetary Institute (LPI) and NASA Johnson Space Center (JSC), brings together international specialists in petrology, geochemistry, geophysics, geology, and astronomy to present the latest results of research in planetary science. Si... | Lunar and Planetary Science Conference | 0.780282 |
92,122 | However, it does not necessarily have finitely many states. The Myhill–Nerode theorem shows that finiteness is necessary and sufficient for language regularity. Some authors refer to the ∼ L {\displaystyle \sim _{L}} relation as Nerode congruence, in honor of Anil Nerode. | Myhill–Nerode theorem | 0.780281 |
92,123 | Given a language L {\displaystyle L} , and a pair of strings x {\displaystyle x} and y {\displaystyle y} , define a distinguishing extension to be a string z {\displaystyle z} such that exactly one of the two strings x z {\displaystyle xz} and y z {\displaystyle yz} belongs to L {\displaystyle L} . Define a relation ∼ ... | Myhill–Nerode theorem | 0.780281 |
92,124 | Given the empty string, 00 {\displaystyle 00} (or 11 {\displaystyle 11} ), 01 {\displaystyle 01} , and 10 {\displaystyle 10} are distinguishing extensions resulting in the three classes (corresponding to numbers that give remainders 0, 1 and 2 when divided by 3), but after this step there is no distinguishing extension... | Myhill–Nerode theorem | 0.780281 |
92,125 | The Myhill–Nerode theorem may be used to show that a language L {\displaystyle L} is regular by proving that the number of equivalence classes of ∼ L {\displaystyle \sim _{L}} is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find... | Myhill–Nerode theorem | 0.780281 |
92,126 | The Myhill–Nerode theorem can be generalized to tree automata. | Myhill–Nerode theorem | 0.780281 |
92,127 | In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 (Nerode & Sauer 1957, p. ii). | Myhill–Nerode theorem | 0.780281 |
92,128 | Since A is an approximate symmetry, all the particles in this octet have similar mass.Every Lie group has a corresponding Lie algebra, and each group representation of the Lie group can be mapped to a corresponding Lie algebra representation on the same vector space. The Lie algebra s u {\displaystyle {\mathfrak {su}}}... | Baryon decuplet | 0.78028 |
92,129 | In physics, the eightfold way is an organizational scheme for a class of subatomic particles known as hadrons that led to the development of the quark model. Working alone, both the American physicist Murray Gell-Mann and the Israeli physicist Yuval Ne'eman proposed the idea in 1961. The name comes from Gell-Mann's (19... | Baryon decuplet | 0.78028 |
92,130 | Infineta announced its Data Mobility Switch in June 2011. The DMS was the first WAN optimization technology to work at throughput rates of 10 Gbit/s. Infineta designed the product in FPGA hardware around a multi-Gigabit switch fabric to minimize latency. The DMS used compression similar to data deduplication. | Infineta Systems | 0.780279 |
92,131 | Infineta Systems was a company that made WAN optimization products for high performance, latency-sensitive network applications. The company advertised that it allowed application data rate to exceed the nominal data rate of the link. Infineta Systems ceased operations by February 2013, a liquidator was appointed, and ... | Infineta Systems | 0.780279 |
92,132 | Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines. By 1689 he had published important... | Jacob Bernoulli | 0.780279 |
92,133 | They also studied the publications of von Tschirnhaus. It must be understood that Leibniz's publications on the calculus were very obscure to mathematicians of that time and the Bernoullis were among the first to try to understand and apply Leibniz's theories. Jacob collaborated with his brother on various applications... | Jacob Bernoulli | 0.780279 |
92,134 | He was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life. By that time, he had begun tutoring his brother Johann Bernoulli on mathematical topics. The two brothers began to study the calculus as presented by Leibniz in his 1684 paper on the differ... | Jacob Bernoulli | 0.780279 |
92,135 | During this time, he studied the new discoveries in mathematics, including Christiaan Huygens's De ratiociniis in aleae ludo, Descartes' La Géométrie and Frans van Schooten's supplements of it. He also studied Isaac Barrow and John Wallis, leading to his interest in infinitesimal geometry. Apart from these, it was betw... | Jacob Bernoulli | 0.780279 |
92,136 | Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the ... | Jacob Bernoulli | 0.780279 |
92,137 | Jacob Bernoulli (also known as James or Jacques; 6 January 1655 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous ... | Jacob Bernoulli | 0.780279 |
92,138 | It had been studied by Huygens in 1687 and Leibniz in 1689. After finding the differential equation, Bernoulli then solved it by what we now call separation of variables. Jacob Bernoulli's paper of 1690 is important for the history of calculus, since the term integral appears for the first time with its integration mea... | Jacob Bernoulli | 0.780279 |
92,139 | IsaPlanner allows the user to encode reasoning techniques, using a combinator language, for conjecturing and proving theorems. IsaPlanner works by manipulating reasoning states, records of open goals, the current proof plan and other important information, and combinators are functions mapping reasoning states to lazy ... | IsaPlanner | 0.780279 |
92,140 | To be mimetic, the interpolation must satisfy where I k {\displaystyle I_{k}} is the interpolation operator of a k {\displaystyle k} -form, i.e. ω ¯ k = I k ω k {\displaystyle {\bar {\omega }}^{k}=I_{k}\omega ^{k}} . In other words, the interpolation operators and the exterior derivatives commute. Note that different i... | Mimetic interpolation | 0.780279 |
92,141 | Mimetic interpolation respects the properties of differential forms. In particular, Stokes' theorem is satisfied with d ω k ¯ {\displaystyle {\overline {d\omega ^{k}}}} denoting the interpolation of d ω k {\displaystyle d\omega ^{k}} . Here, d {\displaystyle d} is the exterior derivative, M {\displaystyle M} is any man... | Mimetic interpolation | 0.780279 |
92,142 | Many physical fields can be represented as k {\displaystyle k} -forms. When discretizing fields in numerical modeling, each type of k {\displaystyle k} -form often acquires its own staggering in accordance with numerical stability requirements, e.g. the need to prevent the checkerboard instability. This led to the deve... | Mimetic interpolation | 0.780279 |
92,143 | "Interstellar Overdrive" was one of the first psychedelic instrumental improvisations recorded by a rock band. It was seen as Pink Floyd's first foray into space rock (along with "Astronomy Domine"), although band members would later disparage this term. It has been described as an experimental rock, psychedelic rock, ... | Interstellar Overdrive | 0.780278 |
92,144 | Sharing the same emphasis on chromaticism with "Astronomy Domine", the piece was recorded in several takes during March and April 1967. An earlier, longer recording of the song can be heard on the soundtrack to the film Tonite Let's All Make Love in London, which was recorded at Sound Technique Studios in early 1967 an... | Interstellar Overdrive | 0.780278 |
92,145 | and The Byrds' "Eight Miles High". "Interstellar Overdrive" shares an emphasis on chromaticism with "Astronomy Domine". The main theme descends chromatically from B to G, before resolving to E, all chords major. | Interstellar Overdrive | 0.780278 |
92,146 | The American Journal of Bioethics is a monthly peer-reviewed academic journal published by Taylor & Francis, covering all aspects of bioethics. It publishes target articles, open peer commentaries, editorials, book reviews, and case studies and commentaries in clinical care and research ethics. The journal also publish... | American Journal of Bioethics | 0.780277 |
92,147 | American Association of Physics Teachers (AAPT). 10 (3): 158. doi:10.1119/1.2352143. ISSN 0031-921X. | Dictionary of Scientific Biography | 0.780276 |
92,148 | Gillispie, Charles Coulston (ed.). "BOOK AND FILM REVIEWS: A Facinating Reference: Dictionary of Scientific Biography". The Physics Teacher. | Dictionary of Scientific Biography | 0.780276 |
92,149 | "Prisoner in Disguise – A Review of: Dictionary of Scientific Biography Volume XV, Supplement I". Archaeoastronomy. 8: 142. | Dictionary of Scientific Biography | 0.780276 |
92,150 | The Dictionary of Scientific Biography is a scholarly English-language reference work consisting of biographies of scientists from antiquity to modern times but excluding scientists who were alive when the Dictionary was first published. It includes scientists who worked in the areas of mathematics, physics, chemistry,... | Dictionary of Scientific Biography | 0.780276 |
92,151 | This allows for robots to deliver the perfect amount of fertilizer or for IoT devices to provide the perfect quantity of water directly to the soil. Machine learning may also provide predictions to farmers at the point of need, such as the contents of plant-available nitrogen in soil, to guide fertilization planning. A... | Smart farming | 0.780274 |
92,152 | Machine learning is commonly used in conjunction with drones, robots, and internet of things devices. It allows for the input of data from each of these sources. The computer then processes this information and sends the appropriate actions back to these devices. | Smart farming | 0.780274 |
92,153 | Aggregated images can create contour maps to track where water flows, determine variable-rate seeding, and create yield maps of areas that were more or less productive. Super resolution enhancement methods are seeing increased use in crop disease surveillance from low flying aircraft. Klapp et al. 2021 demonstrates a s... | Smart farming | 0.780274 |
92,154 | He returned to Scotland in 1984, taking up the Forbes chair of organic chemistry at the University of Edinburgh, where he remained until retirement in 2000.Outside of academia, in 1994 he founded the company Albachem, which utilised his work with peptides. He was elected Fellow of the Royal Society of Chemistry (1977),... | Robert Ramage (chemist) | 0.780273 |
92,155 | Robert ‘Bob’ Ramage FRS (4 October 1935 — 16 October 2019) was an organic chemist, born in Glasgow, who specialised in the synthesis and biosynthesis of natural products, peptides, and proteins. Following his undergraduate degree in chemistry and the University of Glasgow, he stayed on for a PhD in organic chemistry. A... | Robert Ramage (chemist) | 0.780273 |
92,156 | In the area of mathematical logic and computer science known as type theory, a kind is the type of a type constructor or, less commonly, the type of a higher-order type operator. A kind system is essentially a simply typed lambda calculus "one level up", endowed with a primitive type, denoted ∗ {\displaystyle *} and ca... | Kind (type theory) | 0.780272 |
92,157 | The term "manifold" comes from German Mannigfaltigkeit, by Bernhard Riemann. In English, "manifold" refers to spaces with a differentiable or topological structure, while "variety" refers to spaces with an algebraic structure, as in algebraic varieties. In Romance languages, manifold is translated as "variety" – such s... | History of manifolds and varieties | 0.780272 |
92,158 | The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are cal... | History of manifolds and varieties | 0.780272 |
92,159 | Eventually, in the 1920s, Lefschetz laid the basis for the study of abelian functions in terms of complex tori. He also appears to have been the first to use the name "abelian variety"; in Romance languages, "variety" was used to translate Riemann's term "Mannigfaltigkeit". It was Weil in the 1940s who gave this subjec... | History of manifolds and varieties | 0.780272 |
92,160 | Hermann Weyl gave an intrinsic definition for differentiable manifolds in 1912. During the 1930s Hassler Whitney and others clarified the foundational aspects of the subject, and thus intuitions dating back to the latter half of the 19th century became precise, and developed through differential geometry and Lie group ... | History of manifolds and varieties | 0.780272 |
92,161 | By contrast, in 1813 Antoine-Jean Lhuilier showed that the Euler characteristic of the torus is 0, since the complete graph on seven points can be embedded into the torus. The Euler characteristic of other surfaces is a useful topological invariant, which has been extended to higher dimensions using Betti numbers. In t... | History of manifolds and varieties | 0.780272 |
92,162 | Their research uncovered two types of spaces whose geometric structures differ from that of classical Euclidean space; these are called hyperbolic geometry and elliptic geometry. In the modern theory of manifolds, these notions correspond to manifolds with constant, negative and positive curvature, respectively. Carl F... | History of manifolds and varieties | 0.780272 |
92,163 | Ancestral to the modern concept of a manifold were several important results of 18th and 19th century mathematics. The oldest of these was Non-Euclidean geometry, which considers spaces where Euclid's parallel postulate fails. Saccheri first studied this geometry in 1733. Lobachevsky, Bolyai, and Riemann developed the ... | History of manifolds and varieties | 0.780272 |
92,164 | His theorema egregium gives a method for computing the curvature of a surface without considering the ambient space in which the surface lies. In modern terms, the theorem proved that the curvature of the surface is an intrinsic property. Manifold theory has come to focus exclusively on these intrinsic properties (or i... | History of manifolds and varieties | 0.780272 |
92,165 | Johann Benedict Listing, inventor of the word "topology", wrote an 1847 paper "Vorstudien zur Topologie" in which he defined a "complex". He first defined the Möbius strip in 1861 (rediscovered four years later by Möbius), as an example of a non-orientable surface. After Abel, Jacobi, and Riemann, some of the most impo... | History of manifolds and varieties | 0.780272 |
92,166 | Let K be an algebraic number field, and let OK be its ring of integers. Let b1, ..., bn be an integral basis of OK (i.e. a basis as a Z-module), and let {σ1, ..., σn} be the set of embeddings of K into the complex numbers (i.e. injective ring homomorphisms K → C). The discriminant of K is the square of the determinant ... | Brill's theorem | 0.78027 |
92,167 | Minkowski's theorem: If K is not Q, then |ΔK| > 1 (this follows directly from the Minkowski bound). Hermite–Minkowski theorem: Let N be a positive integer. There are only finitely many (up to isomorphisms) algebraic number fields K with |ΔK| < N. Again, this follows from the Minkowski bound together with Hermite's theo... | Brill's theorem | 0.78027 |
92,168 | Brill's theorem: The sign of the discriminant is (−1)r2 where r2 is the number of complex places of K. A prime p ramifies in K if and only if p divides ΔK . Stickelberger's theorem: Δ K ≡ 0 or 1 ( mod 4 ) . {\displaystyle \Delta _{K}\equiv 0{\text{ or }}1{\pmod {4}}.} | Brill's theorem | 0.78027 |
92,169 | In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field. More specifically, it is proportional to the squared volume of the fundamental domain of the ring of integers, and it regulates which ... | Brill's theorem | 0.78027 |
92,170 | Unfortunately, instead of well-being a devastating plague followed in some parts of the empire, and several important persons died. Astronomy was a respected and approved science among the Islamic clergy of the Ottoman Empire, yet the same could not be said with regard to astrology, a field which is considered to be di... | Constantinople observatory of Taqi ad-Din | 0.780268 |
92,171 | Much like a modern institution, the main building was reserved for the library and the living quarters of the staff, while the smaller building housed a collection of instruments built by Taqi ad-Din. These included a giant armillary sphere and an accurate mechanical astronomical clock for measuring the position and sp... | Constantinople observatory of Taqi ad-Din | 0.780268 |
92,172 | Taqi ad-Din wrote an important treatise on astronomical instruments entitled the Observational Instruments of the Emperor's Catalogue, which describes the astronomical instruments used in the Constantinople observatory of Taqi ad-Din. These included ancient instruments such as the armillary sphere, paralactic ruler and... | Constantinople observatory of Taqi ad-Din | 0.780268 |
92,173 | The Rare Symmetry Violating Processes (RSVP) was a physics project terminated by the National Science Foundation, in August, 2005, originally meant for construction in the same year, at Brookhaven National Laboratory on Long Island. | Rare Symmetry Violating Processes | 0.780266 |
92,174 | Healthcare, manufacturing, agriculture, wholesale trade, retail, and recreation industries all have incidence rates above 35 per 10,000 full-time workers. For example, a national survey of U.S. nurses found that 38% reported an MSD in the prior year, mainly lower back injury. The neck and back are the most common sites... | Musculoskeletal pain | 0.780264 |
92,175 | A 2015 study by Weblock analyzed more than 180,000 links from references in the full-text corpora of three major open access publishers and found a half-life of about 14 years, generally confirming a 2005 study that found that half of the URLs cited in D-Lib Magazine articles were active 10 years after publication. Oth... | Link rot | 0.780263 |
92,176 | H. C. Bolton, A select bibliography of chemistry, Washington 1893 (= Smithsonian Miscellaneous Collections, vol. XXXVI), p. 1051–1058 J. Ferguson, Bibliotheca chemica, Glasgow 1906, vol. 2, p. | Theatrum Chemicum | 0.780262 |
92,177 | Lazarus Zetzner (L. Zetzneri) published the Theatrum Chemicum in unsystematic editions, instead he reprinted issues of previous volumes that had appeared up to the date of the particular volume of Theatrum Chemicum as it was published.The material is diverse, being intended as a single body of work containing all signi... | Theatrum Chemicum | 0.780262 |
92,178 | In molecular biology, the HAND domain is a protein domain which adopts a secondary structure consisting of four alpha helices, three of which (H2, H3, H4) form an L-like configuration. Helix H2 runs antiparallel to helices H3 and H4, packing closely against helix H4, whilst helix H1 reposes in the concave surface forme... | HAND domain | 0.780262 |
92,179 | This same unbounded growth is a feature of cancerous growth.Embryonic stem cells express telomerase, which allows them to divide repeatedly and form the individual. In adults, telomerase is highly expressed only in cells that need to divide regularly, especially in male sperm cells, but also in epidermal cells, in acti... | EST1 | 0.780262 |
92,180 | The converse is often included as part of the theorem. (Note that the converse of the weaker, unsigned statement is not necessarily true.) The theorem is very similar to Ceva's theorem in that their equations differ only in sign. By re-writing each in terms of cross-ratios, the two theorems may be seen as projective du... | Menelaus's theorem | 0.780262 |
92,181 | The signed version of Menelaus's theorem states A F F B × B D D C × C E E A = − 1. {\displaystyle {\frac {AF}{FB}}\times {\frac {BD}{DC}}\times {\frac {CE}{EA}}=-1.} Equivalently, A F × B D × C E = − F B × D C × E A . | Menelaus's theorem | 0.780262 |
92,182 | Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, and AB at points D, E, and F respectively, with D, E, and F distinct from A, B, and C. A weak version of the theorem states that | A F | |... | Menelaus's theorem | 0.780262 |
92,183 | In mathematics, a paratopological group is a topological semigroup that is algebraically a group. In other words, it is a group G with a topology such that the group's product operation is a continuous function from G × G to G. This differs from the definition of a topological group in that the group inverse is not req... | Paratopological group | 0.780259 |
92,184 | The chemistry of polonium is similar to that of tellurium, although it also shows some similarities to its neighbor bismuth due to its metallic character. Polonium dissolves readily in dilute acids but is only slightly soluble in alkalis. Polonium solutions are first colored in pink by the Po2+ ions, but then rapidly b... | Polonium | 0.780257 |
92,185 | Today, polonium is usually produced in milligram quantities by the neutron irradiation of bismuth. Due to its intense radioactivity, which results in the radiolysis of chemical bonds and radioactive self-heating, its chemistry has mostly been investigated on the trace scale only. Polonium was discovered in July 1898 by... | Polonium | 0.780257 |
92,186 | Polonium dihalides are formed by direct reaction of the elements or by reduction of PoCl4 with SO2 and with PoBr4 with H2S at room temperature. Tetrahalides can be obtained by reacting polonium dioxide with HCl, HBr or HI.Other polonium compounds include the polonite, potassium polonite; various polonate solutions; and... | Polonium | 0.780257 |
92,187 | weapons utilized a pulse neutron generator for the same purpose.Much of the basic physics of polonium was classified until after the war. The fact that it was used as an initiator was classified until the 1960s.The Atomic Energy Commission and the Manhattan Project funded human experiments using polonium on five people... | Polonium | 0.780257 |
92,188 | In computing the product of the last two factors, the imaginary parts cancel, and we get ( x − 3 ) ( x 2 − 4 x + 29 ) . {\displaystyle (x-3)(x^{2}-4x+29).} The non-real factors come in pairs which when multiplied give quadratic polynomials with real coefficients. Since every polynomial with complex coefficients can be ... | Complex conjugate root theorem | 0.780257 |
92,189 | One proof of the theorem is as follows:Consider the polynomial P ( z ) = a 0 + a 1 z + a 2 z 2 + ⋯ + a n z n {\displaystyle P(z)=a_{0}+a_{1}z+a_{2}z^{2}+\cdots +a_{n}z^{n}} where all ar are real. Suppose some complex number ζ is a root of P, that is P ( ζ ) = 0 {\displaystyle P(\zeta )=0} . It needs to be shown that P ... | Complex conjugate root theorem | 0.780257 |
92,190 | It follows from the present theorem and the fundamental theorem of algebra that if the degree of a real polynomial is odd, it must have at least one real root.This can be proved as follows. Since non-real complex roots come in conjugate pairs, there are an even number of them; But a polynomial of odd degree has an odd ... | Complex conjugate root theorem | 0.780257 |
92,191 | In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.It follows from this (and the fundamental theorem of algebra) that, if the degree of a re... | Complex conjugate root theorem | 0.780257 |
92,192 | Three-dimensional (3D) topological Dirac semimetals (TDSs) are bulk analogues of graphene that also exhibit non-trivial topology in its electronic structure that shares similarities with topological insulators. Moreover, a TDS can potentially be driven into other exotic phases (such as Weyl semimetals, axion insulators... | Cadmium arsenide | 0.780255 |
92,193 | Hill's undergraduate degree is from Harvard University. He earned a PhD in mathematics from the Massachusetts Institute of Technology in 2006. His doctoral advisor was Michael J. Hopkins. His dissertation, in algebraic topology, was titled "Computational Methods for Higher Real K-Theory with Applications to Tmf." | Mike Hill (mathematician) | 0.780255 |
92,194 | Michael Anthony "Mike" Hill is an American mathematician known for his research in topology. He is a professor at the University of California, Los Angeles. Together with Michael J. Hopkins and Douglas Ravenel, he received the American Mathematical Society's Oswald Veblen Prize in Geometry in 2022 for the paper "On the... | Mike Hill (mathematician) | 0.780255 |
92,195 | In mathematics, and particularly ordinary differential equations (ODEs), a monodromy matrix is the fundamental matrix of a system of ODEs evaluated at the period of the coefficients of the system. It is used for the analysis of periodic solutions of ODEs in Floquet theory. | Monodromy operator | 0.780253 |
92,196 | Unlike behaviorism, which studies animals' reactions to non-natural stimuli in artificial, laboratory conditions, ethology sought to categorize and analyze the natural behaviors of animals in a field setting. Similarly, neuroethology asks questions about the neural bases of naturally occurring behaviors, and seeks to m... | Species-specific behavior | 0.780252 |
92,197 | The society has met every three years since its first meeting in Tokyo in 1986. Its membership draws from many research programs around the world; many of its members are students and faculty members from medical schools and neurobiology departments from various universities. Modern advances in neurophysiology techniqu... | Species-specific behavior | 0.780252 |
92,198 | Kandel, E.R. (1976) Cellular Basis of Behavior: An Introduction to Behavioral Neurobiology. W.H. | Species-specific behavior | 0.780252 |
92,199 | (2000) Behavioral Neurobiology: The Cellular Organization of Natural Behavior. Sinauer, Sunderland Mass. Simmons, P., Young, D. | Species-specific behavior | 0.780252 |
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