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<page_title> March of Progress </page_title> <path> March_of_Progress > Illustration > Sequence of species </path> <section_title> Sequence of species </section_title> <content> The 15 primate figures in Zallinger's image, from left to right, are listed below. The datings follow the original graphic and may no longer reflect current scientific opinion. Pliopithecus, 22–12 million year old "ancestor of the gibbon line" Proconsul, 21–9 million year old primate which may or may not have qualified as an ape Dryopithecus, 15–8 million year old fossil ape, the first such found (1856) and probable ancestor of modern apes Oreopithecus, 15–8 million years old Ramapithecus, 13–8 million year old ape and possible ancestor of modern orangutans (now considered a female Sivapithecus) Australopithecus, 2–3 million years old; then considered the earliest "certain hominid" Paranthropus, 1.8–0.8 million years old Advanced Australopithecus, 1.8–0.7 million year old Homo erectus, 700,000–400,000 years old, then the earliest known member of the genus Homo Early Homo sapiens, 300,000–200,000 years old; from Swanscombe, Steinheim and Montmaurin, then considered probably the earliest H. sapiens Solo Man, 100,000–50,000 years old; described as an extinct Asian "race" of H. sapiens (now considered a sub-species of H. erectus) Rhodesian Man, 50,000–30,000 years old; described as an extinct African "race" of H. sapiens (now considered either H. rhodesiensis or H. heidelbergensis and dated much earlier) Neanderthal Man, 100,000–40,000 years old Cro-Magnon Man, 40,000–5,000 years old Modern Man, 40,000 years to the present </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Singular simplicial complex </page_title> <path> Chain_homotopy_equivalence > P </path> <section_title> P </section_title> <content> properly discontinuous Not particularly a precise term. But it could mean, for example, that G is discrete and each point of the G-space has a neighborhood V such that for each g in G that is not the identity element, gV intersects V at finitely many points. pseudomanifold pseudomanifold pullback Given a map p:E→B, the pullback of p along ƒ:X→B is the space f ∗ E = { ( e , x ) ∈ E × X | p ( e ) = f ( x ) } {\displaystyle f^{*}E=\{(e,x)\in E\times X|p(e)=f(x)\}} (succinctly it is the equalizer of p and f). It is a space over X through a projection. Puppe sequence The Puppe sequence refers ro either of the sequences X → f Y → C f → Σ X → Σ Y → ⋯ , {\displaystyle X{\overset {f}{\to }}Y\to C_{f}\to \Sigma X\to \Sigma Y\to \cdots ,} ⋯ → Ω X → Ω Y → F f → X → f Y {\displaystyle \cdots \to \Omega X\to \Omega Y\to F_{f}\to X{\overset {f}{\to }}Y} where C f , F f {\displaystyle C_{f},F_{f}} are homotopy cofiber and homotopy fiber of f. pushout Given A ⊂ B {\displaystyle A\subset B} and a map f: A → X {\displaystyle f:A\to X} , the pushout of X and B along f is X ∪ f B = X ⊔ B / ( a ∼ f ( a ) ) {\displaystyle X\cup _{f}B=X\sqcup B/(a\sim f(a))} ; that is X and B are glued together along A through f. The map f is usually called the attaching map.An important example is when B = Dn, A = Sn-1; in that case, forming such a pushout is called attaching an n-cell (meaning an n-disk) to X. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Frequency doubling </page_title> <path> Frequency_doubling > Theoretical expression with Gaussian beams > No phase-matching </path> <section_title> No phase-matching </section_title> <content> A non-perfect phase-matching is a more realistic condition in practice, especially in biological samples. The paraxial approximation is however supposed still valid: k n = n k 1 {\displaystyle k_{n}=nk_{1}} , and in the harmonic expression, χ ( n ) ( z ) {\displaystyle \chi ^{(n)}(z)} is now χ ( n ) ( z ) e i Δ k z {\displaystyle \chi ^{(n)}(z)e^{i\,\Delta k\,z}} . In the special case of SHG (n = 2), in a medium of length L and a focus position z 0 {\displaystyle z_{0}} , the intensity writes: I 2 ω = 2 ω 2 π c 2 ε 0 w 0 2 n 2 ω n ω 2 I ω 2 ( χ ( 2 ) ) 2 ( ∫ z 0 z 0 + L e i Δ k z 1 + i z / z R ) 2 d z . {\displaystyle I_{2\omega }={\frac {2\omega ^{2}}{\pi c^{2}\varepsilon _{0}w_{0}^{2}n_{2\omega }n_{\omega }^{2}}}I_{\omega }^{2}(\chi ^{(2)})^{2}\left(\int _{z_{0}}^{z_{0}+L}{\frac {e^{i\,\Delta k\,z}}{1+iz/z_{R}}}\right)^{2}\,dz.} where c {\displaystyle c} is the speed of light in vacuum, ε 0 {\displaystyle \varepsilon _{0}} the vacuum permittivity, n n ω {\displaystyle n_{n\omega }} the optical index of the medium at n ω {\displaystyle n\omega } and w 0 {\displaystyle w_{0}} the waist size of excitation. Thus, the SHG intensity quickly decays in the bulk ( 0 < z 0 < L {\displaystyle 0 </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Unducted fan </page_title> <path> Unducted_fan > Definition </path> <section_title> Definition </section_title> <content> In the 1970s, Hamilton Standard described its propfan as "a small diameter, highly loaded multiple bladed variable pitch propulsor having swept blades with thin advanced airfoil sections, integrated with a nacelle contoured to retard the airflow through the blades thereby reducing compressibility losses and designed to operate with a turbine engine and using a single stage reduction gear resulting in high performance". In 1982, the weekly aviation magazine Flight International defined the propfan as a propeller with 8–10 highly swept blades that cruised at a speed of 390–480 knots (450–550 miles per hour; 720–890 kilometres per hour), although its definition evolved a few years later with the emergence of contra-rotating propfans.In 1986, British engine maker Rolls-Royce used the term open rotor as a synonym for the original meaning of a propfan. This action was to delineate the propfan engine type from a number of ducted engine proposals at the time that had propfan in their names. By the 2000s, open rotor (OR) became a preferred term for propfan technology in research and news reports, with contra-rotating open rotor (CROR) also occasionally being used to distinguish between single-rotation propfans. As of 2015, the European Aviation Safety Agency (EASA) defined an open rotor concretely (but broadly) as "a turbine engine fan stage that is not enclosed within a casing"; in contrast, it had only a working definition of an open rotor engine (the more commonly used term for propfan in the 21st century), calling it "a turbine engine featuring contra-rotating fan stages not enclosed within a casing." The engine uses a gas turbine to drive an unshrouded (open) contra-rotating propeller like a turboprop, but the design of the propeller itself is more tightly coupled to the turbine design, and the two are certified as a single unit.El-Sayed differentiates between turboprops and propfans according to 11 different criteria, including number of blades, blade shape, tip speed, bypass ratio, Mach number, and cruise altitude. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Permutation statistic </page_title> <path> Permutation_statistics > Number of permutations containing an even number of even cycles </path> <section_title> Number of permutations containing an even number of even cycles </section_title> <content> Translating to exponential generating functions (EGFs), we obtain exp ( 1 2 log 1 + z 1 − z ) cosh ( 1 2 log 1 1 − z 2 ) {\displaystyle \exp \left({\frac {1}{2}}\log {\frac {1+z}{1-z}}\right)\cosh \left({\frac {1}{2}}\log {\frac {1}{1-z^{2}}}\right)} or 1 2 exp ( 1 2 ( log 1 + z 1 − z + log 1 1 − z 2 ) ) + 1 2 exp ( 1 2 ( log 1 + z 1 − z − log 1 1 − z 2 ) ) . {\displaystyle {\frac {1}{2}}\exp \left({\frac {1}{2}}\left(\log {\frac {1+z}{1-z}}+\log {\frac {1}{1-z^{2}}}\right)\right)+{\frac {1}{2}}\exp \left({\frac {1}{2}}\left(\log {\frac {1+z}{1-z}}-\log {\frac {1}{1-z^{2}}}\right)\right).} This simplifies to 1 2 exp ( 1 2 log 1 ( 1 − z ) 2 ) + 1 2 exp ( 1 2 log ( 1 + z ) 2 ) {\displaystyle {\frac {1}{2}}\exp \left({\frac {1}{2}}\log {\frac {1}{(1-z)^{2}}}\right)+{\frac {1}{2}}\exp \left({\frac {1}{2}}\log(1+z)^{2}\right)} or 1 2 1 1 − z + 1 2 ( 1 + z ) = 1 + z + 1 2 z 2 1 − z . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Container method </page_title> <path> Container_method > Example applications > Triangle-free graphs > Informal statement </path> <section_title> Informal statement </section_title> <content> Since bipartite graphs are triangle-free, the number of triangle free graphs with n {\displaystyle n} vertices is at least 2 ⌊ n 2 / 4 ⌋ {\displaystyle 2^{\lfloor n^{2}/4\rfloor }} , obtained by enumerating all possible subgraphs of the balanced complete bipartite graph K ⌊ n / 2 ⌋ , ⌈ n / 2 ⌉ {\displaystyle K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }} . We can construct an auxiliary 3-uniform hypergraph H with vertex set V ( H ) = E ( K n ) {\displaystyle V(H)=E(K_{n})} and edge set E ( H ) = { { e 1 , e 2 , e 3 } ⊂ E ( K n ) = V ( H ) ∣ e 1 , e 2 , e 3 form a triangle } {\displaystyle E(H)=\{\{e_{1},e_{2},e_{3}\}\subset E(K_{n})=V(H)\mid e_{1},e_{2},e_{3}{\text{ form a triangle}}\}} . This hypergraph "encodes" triangles in the sense that the family of triangle-free graphs on n {\displaystyle n} vertices is exactly the collection of independent sets of this hypergraph, I ( H ) {\displaystyle {\mathcal {I}}(H)} . The above hypergraph has a nice degree distribution: each edge of K n {\displaystyle K_{n}} , and thus vertex in V ( H ) {\displaystyle V(H)} is contained in exactly n − 2 {\displaystyle n-2} triangles and each pair of elements in V ( H ) {\displaystyle V(H)} is contained in at most 1 triangle. Therefore, applying the hypergraph container lemma (iteratively), we are able to show that there is a family of n O ( n 3 / 2 ) {\displaystyle n^{O(n^{3/2})}} containers that each contain few triangles that contain every triangle-free graph/independent set of the hypergraph. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Positivism </page_title> <path> Positivism > Positivism in the social sciences > Historical positivism </path> <section_title> Historical positivism </section_title> <content> In historiography, historical or documentary positivism is the belief that historians should pursue the objective truth of the past by allowing historical sources to "speak for themselves", without additional interpretation. In the words of the French historian Fustel de Coulanges, as a positivist, "It is not I who am speaking, but history itself". The heavy emphasis placed by historical positivists on documentary sources led to the development of methods of source criticism, which seek to expunge bias and uncover original sources in their pristine state.The origin of the historical positivist school is particularly associated with the 19th-century German historian Leopold von Ranke, who argued that the historian should seek to describe historical truth "wie es eigentlich gewesen ist" ("as it actually was")—though subsequent historians of the concept, such as Georg Iggers, have argued that its development owed more to Ranke's followers than Ranke himself.Historical positivism was critiqued in the 20th century by historians and philosophers of history from various schools of thought, including Ernst Kantorowicz in Weimar Germany—who argued that "positivism ... faces the danger of becoming Romantic when it maintains that it is possible to find the Blue Flower of truth without preconceptions"—and Raymond Aron and Michel Foucault in postwar France, who both posited that interpretations are always ultimately multiple and there is no final objective truth to recover. In his posthumously published 1946 The Idea of History, the English historian R. G. Collingwood criticized historical positivism for conflating scientific facts with historical facts, which are always inferred and cannot be confirmed by repetition, and argued that its focus on the "collection of facts" had given historians "unprecedented mastery over small-scale problems", but "unprecedented weakness in dealing with large-scale problems".Historicist arguments against positivist approaches in historiography include that history differs from sciences like physics and ethology in subject matter and method; that much of what history studies is nonquantifiable, and therefore to quantify is to lose in precision; and that experimental methods and mathematical models do not generally apply to history, so that it is not possible to formulate general (quasi-absolute) laws in history. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> P-i-n diode </page_title> <path> P-i-n_junction > Applications > RF and microwave switches </path> <section_title> RF and microwave switches </section_title> <content> At 320 MHz, the capacitive reactance of 1 pF is 497 ohms: Z d i o d e = 1 2 π f C = 1 2 π ( 320 × 10 6 H z ) ( 1 × 10 − 12 F ) = 497 Ω {\displaystyle {\begin{aligned}Z_{\mathrm {diode} }&={\frac {1}{2\pi fC}}\\&={\frac {1}{2\pi (320\times 10^{6}\,\mathrm {Hz} )(1\times 10^{-12}\,\mathrm {F} )}}\\&=497\,\Omega \end{aligned}}} As a series element in a 50 ohm system, the off-state attenuation is: A = 20 log 10 ( Z l o a d Z s o u r c e + Z d i o d e + Z l o a d ) = 20 log 10 ( 50 Ω 50 Ω + 497 Ω + 50 Ω ) = 21.5 d B {\displaystyle {\begin{aligned}A&=20\log _{10}\left({\frac {Z_{\mathrm {load} }}{Z_{\mathrm {source} }+Z_{\mathrm {diode} }+Z_{\mathrm {load} }}}\right)\\&=20\log _{10}\left({\frac {50\,\Omega }{50\,\Omega +497\,\Omega +50\,\Omega }}\right)\\&={21.5}\,\mathrm {dB} \end{aligned}}} This attenuation may not be adequate. In applications where higher isolation is needed, both shunt and series elements may be used, with the shunt diodes biased in complementary fashion to the series elements. Adding shunt elements effectively reduces the source and load impedances, reducing the impedance ratio and increasing the off-state attenuation. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Eötvös rule </page_title> <path> Eötvös_rule > The Eötvös rule </path> <section_title> The Eötvös rule </section_title> <content> If V is the molar volume and Tc the critical temperature of a liquid the surface tension γ is given by γ V 2 / 3 = k ( T c − T ) {\displaystyle \gamma V^{2/3}=k(T_{c}-T)\,} where k is a constant valid for all liquids. The Eötvös constant has a value of 2.1×10−7 J/(K·mol2/3). More precise values can be gained when considering that the line normally passes the temperature axis 6 K before the critical point: γ V 2 / 3 = k ( T c − 6 K − T ) {\displaystyle \gamma V^{2/3}=k(T_{c}-6\ \mathrm {K} -T)\,} The molar volume V is given by the molar mass M and the density ρ V = M / ρ {\displaystyle V=M/\rho \,} The term γ V 2 / 3 {\displaystyle \gamma V^{2/3}} is also referred to as the "molar surface tension" γmol: γ m o l = γ V 2 / 3 {\displaystyle \gamma _{mol}=\gamma V^{2/3}\,} A useful representation that prevents the use of the unit mol−2/3 is given by the Avogadro constant NA: γ = k ′ ( M ρ N A ) − 2 / 3 ( T c − 6 K − T ) = k ′ ( N A V ) 2 / 3 ( T c − 6 K − T ) {\displaystyle \gamma =k'\left({\frac {M}{\rho N_{A}}}\right)^{-2/3}(T_{c}-6\ \mathrm {K} -T)=k'\left({\frac {N_{A}}{V}}\right)^{2/3}(T_{c}-6\ \mathrm {K} -T)} As John Lennard-Jones and Corner showed in 1940 by means of the statistical mechanics the constant k′ is nearly equal to the Boltzmann constant. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Content writing services </page_title> <path> Content_writing_services > Industry-wise content writing services </path> <section_title> Industry-wise content writing services </section_title> <content> Today content writing services are offered for various niche and industries. The popular industry-wise content writing service categories are: Content Writing Services for IT Sector — Content required by IT industry include blogs, info graphics, buyer's guides, pricing guides, White papers, software comparison content, Software product analysis, case studies, technical content, email marketing content, podcasts, research articles, surveys, eBooks, marketing content, guest blogs, product and service lists etc. Content Writing Services for Ecommerce Sector — Ecommerce content writing services provide content such as product descriptions, product reviews, blogs, website content for ecommerce platform, copywriting, social media interaction content, content for product demo, video scripts etc. Content Writing Services for Travel/Tourism Industry — Content writing services provide content to travel aggregators for their websites, travel guides, blog content, list of tourist attractions, travelogues, travel fashion articles, destination articles, memoirs, travel advice articles, tour guides. Content Writing Services for Education Sector — It offers content to educational institutes such as schools, colleges, Business schools, coaching centers, academic bodies, etc. These institutes require blogs, academic articles, educational case studies, content for flyers, brochures, and banners, etc. Content Writing Services for Digital Marketing Agencies — Content writing services for digital marketing agencies provide content such as blog posts, social media content, video scripts, SEO content, content marketing material, Client articles, resource page content, web content, guest posts, podcast content, survey questionnaire, etc. Content Writing Services for Small Businesses — Small businesses need content for their website landing page, web pages, blog page, and other web properties. Apart from these, small businesses need case studies, research articles, press release for marketing, SEO optimized content, social media post content with captions, copywriting material etc. Content Writing Services for Manufacturing Industry — Content writing services for manufacturing sector need product descriptions, analytical content, compliance related material, industry news, proposals, surveys, articles about manufacturing trends, research articles, etc. Content Writing services for Financial Sector — Finance companies hire content writing services for website content, SEO content, reviews of asset classes, articles about current financial trends, investment strategies, market reviews, stock market articles, customer help articles, self-service articles for banking customers, financial research, etc. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Scrabble letter distributions </page_title> <path> Scrabble_letter_distributions > Unofficial editions > Gwichʼin </path> <section_title> Gwichʼin </section_title> <content> Gwichʼin-language editions of Scrabble contain 200 letter tiles, in the following distribution: 4 blank tiles (scoring 0 points) 1 point: ʼ ×19, I ×17, A ×12, N ×9, T ×8, H ×7, Ą ×5, E ×2, Ę ×1, Į ×1, O ×1, Ǫ ×1, U ×1, Ų ×1 2 points: AA ×8, CH ×7, EE ×7, ĄĄ ×4, II ×4, ĘĘ ×1, ĮĮ ×1, OO ×1, ǪǪ ×1, TH ×1, UU ×1, ŲŲ ×1 3 points: AII ×4, AĮĮ ×4, D ×4, G ×4, K ×4, R ×4, Y ×4, S ×1, TTH ×1, W ×1 4 points: TS ×6, L ×2, Ł ×2, TR ×2, DH ×1, GH ×1, KH ×1, SH ×1 5 points: J ×2, TŁ ×2, V ×2, Z ×1 6 points: GW ×4, ZH ×4, DR ×1, KW ×1 7 points: DL ×2, DDH ×1, KHW ×1, SHR ×1 8 points: DZ ×1 9 points: ZHR ×1 10 points: B ×1, F ×1, M ×1Grave accents are ignored. Digraphs and trigraphs can be played with multiple tiles. GHW, ND, NH, NJ, and RH are not included, as these digraphs and trigraphs are very rare in Gwichʼin. C, P, Q, and X are also absent because these letters are not used in Gwichʼin, or, in the case of C, outside the digraph CH. Arguably B, F, and M are not used in Gwichʼin either, but they are included as these letters are used for borrowed words. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Anthropopithecus </page_title> <path> Anthropopithecus > History </path> <section_title> History </section_title> <content> The genus Anthropopithecus was first proposed in 1841 by the French zoologist and anatomist Henri-Marie Ducrotay de Blainville (1777–1850) in order to give a genus name to some chimpanzee material that he was studying at the time.After the genus Anthropopithecus was established by De Blainville in 1839, the British surgeon and naturalist John Bland-Sutton (1855–1936) proposed the species name Anthropopithecus troglodytes in 1883 to designate the common chimpanzee. However, the genus Pan had already been attributed to chimpanzees in 1816 by the German naturalist Lorenz Oken (1779–1851). Since any earlier nomenclature prevails over subsequent nomenclatures, the genus Anthropopithecus definitely lost its validity in 1895, becoming from that date a junior synonym of the genus Pan.In 1879, the French archaeologist and anthropologist Gabriel de Mortillet (1821–1898) proposed the term Anthropopithecus to designate a "missing link", a hypothetical intermediate between ape and man that lived in the Tertiary and that supposedly, following De Mortillet's theory, produced eoliths. In his work of 1883 Le Préhistorique, antiquité de l'homme (The Prehistoric: Man's Antiquity, below quoted after the 2nd edition, 1885), De Mortillet writes: Nous sommes donc forcément conduits à admettre, par une déduction logique tirée de l’observation directe des faits, que les animaux intelligents qui savaient faire du feu et tailler des pierres à l’époque tertiaire, n’étaient pas des hommes dans l’acception géologique et paléontologique du mot, mais des animaux d’un autre genre, des précurseurs de l’homme dans l’échelle des êtres, précurseurs auxquels j’ai donné le nom d’Anthropopithecus. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Lindsay Allason-Jones </page_title> <path> Lindsay_Allason-Jones > Career </path> <section_title> Career </section_title> <content> Allason-Jones completed her undergraduate degree at Newcastle University in 1974 before working for Chelmsford Excavation Committee. She then worked for Tyne and Wear Museums Service, working on, and subsequently publishing the small finds from Arbeia Roman Fort.In 1978, she began working at the Museum of Antiquities of Newcastle University and the Society of Antiquaries of Newcastle upon Tyne. She became Newcastle University Director of Museums in 1998, becoming Director the Centre for Interdisciplinary Artefact Studies when the museum was closed in 2009.Alongside her work in the museum, she was also Reader in Roman Material Culture in the Archaeology Department of Newcastle University.Between 2003 and 2006, Allason-Jones served as the President of the Royal Archaeological Institute, and again from 2021. She served as the President of the Society of Antiquaries of Newcastle upon Tyne, and still acts as the Keeper of Collections.Allason-Jones was admitted as a Fellow of the Society of Antiquaries of London in January 1988, and is a Fellow of the Society of Antiquaries of Scotland and the Royal Society of Arts. She was awarded an OBE for services to archaeology in 2014 in the New Year Honours List.Allason-Jones retired in 2011, and in 2014 an edited volume of papers was published in her honour, containing papers covering the key themes of her career.Allason-Jones has an extensive publication record on the material culture of Roman Britain and has been involved in the research of archaeological discoveries such as the Rudge Cup, the Corbridge Hoard, and Coventina's Well.She has appeared in several TV programmes on historical themes, including Time Team (1996-2000), Timewatch (2007), History Cold Case (2011) and Walking Through History (2014), as well as being the historical advisor on the 2011 film The Eagle. In July 2012, she featured as one of the guests on an episode of In Our Time on the function of Hadrian's Wall. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> List of set identities and relations </page_title> <path> List_of_set_identities_and_relations > Sequences and collections of families of sets > Sequences of sets > Partitions </path> <section_title> Partitions </section_title> <content> Suppose that S ∙ = ( S i ) i = 1 ∞ {\displaystyle S_{\bullet }=\left(S_{i}\right)_{i=1}^{\infty }} is any sequence of sets, that S ⊆ ⋃ i S i {\displaystyle S\subseteq \bigcup _{i}S_{i}} is any subset, and for every index i , {\displaystyle i,} let D i = ( S i ∩ S ) ∖ ⋃ m = 1 i ( S m ∩ S ) . {\displaystyle D_{i}=\left(S_{i}\cap S\right)\setminus \bigcup _{m=1}^{i}\left(S_{m}\cap S\right).} Then S = ⋃ i D i {\displaystyle S=\bigcup _{i}D_{i}} and D ∙ := ( D i ) i = 1 ∞ {\displaystyle D_{\bullet }:=\left(D_{i}\right)_{i=1}^{\infty }} is a sequence of pairwise disjoint sets.Suppose that S ∙ = ( S i ) i = 1 ∞ {\displaystyle S_{\bullet }=\left(S_{i}\right)_{i=1}^{\infty }} is non-decreasing, let S 0 = ∅ , {\displaystyle S_{0}=\varnothing ,} and let D i = S i ∖ S i − 1 {\displaystyle D_{i}=S_{i}\setminus S_{i-1}} for every i = 1 , 2 , … . {\displaystyle i=1,2,\ldots .} Then ⋃ i S i = ⋃ i D i {\displaystyle \bigcup _{i}S_{i}=\bigcup _{i}D_{i}} and D ∙ = ( D i ) i = 1 ∞ {\displaystyle D_{\bullet }=\left(D_{i}\right)_{i=1}^{\infty }} is a sequence of pairwise disjoint sets. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Torpedo cruiser </page_title> <path> Torpedo_cruiser > History </path> <section_title> History </section_title> <content> German shipyards also produced a number of torpedo cruisers for export to various foreign clients, with Krupp building three for the Brazilian Navy, one for the National Navy of Uruguay, and two for the Ottoman Navy Peyk-i Şevket class, which were completed in 1907.One great power battlefleet which continued to utilize the torpedo cruiser was the Imperial Russian Navy. They had employed torpedo-armed warships since the 1870s, using "torpedo cutters" successfully against the Ottomans in the 1870s, and launched the large "torpedo vessel" Vzryv in 1877, but their first ship specifically designated as a torpedo cruiser was Leytenant Ilyin of 1886, followed by one sister ship in 1889, and in the 1890s by the six ships of the Kazarskiy class and the more heavily-armed Abrek. These coexisted with conventional destroyers of the British type, and the onset of the Russo-Japanese War in 1904 prompted the construction of another twenty-four ships of the type - they were distinguished from contemporary destroyers by being slightly slower, but larger, more heavily-armed and more seaworthy. In order to accelerate production, most of them were built in collaboration with German shipyards, although the Leytenant Shestakov class were an entirely domestic design. All were similar in size and capabilities, typically with a speed of around 25 knots (46 km/h; 29 mph), three 457 mm (18.0 in) torpedo tubes, two 75 mm (3.0 in) guns, and four 57 mm (2.2 in) guns, and in a departure from the high-freeboard hullform of earlier torpedo cruisers, they were low-freeboard ships with a high forecastle: this style of hull had originated with late-nineteenth century cruisers, but was coming to be associated with destroyers (such as the British River class), and in 1907, as part of the review of naval thinking after the Battle of Tsushima, the Russians opted to reclassify all their torpedo cruisers as part of the destroyer fleet. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Armstrong Audio </page_title> <path> Armstrong_Audio > Product reviews </path> <section_title> Product reviews </section_title> <content> PCU25 Preamp/Control Unit + A20 Valve Power AmpGramophone, rev. by Philip G. Tandy, April 1962 Hi Fi News, rev. by George W. Tillett, April 1962 Amateur Tape Recording, rev. by Fred Judd, May 1962 Audio and Record Review, September 1962400 RangeHi Fi News, 426 Receiver (Amp + AM/FM tuners) rev., by George Goodall, October 1968500 Range amplifierHi Fi Sound, review of 521 Amplifier, by Fred Judd, April 1969 Audio and Record Review, review of 521 Amplifier, by Frank Roberts & Donald Aldous, 1969 Luister , review of 521 Amplifier by Jan Kool, 1969 Which, Large comparison review including the 521 Amplifier, April 1970 Hi Fi Sound, review of 526, by Fred Judd, May 1970 Hi Fi Sound, 526 included in comparison of 10 tuner-amps, by Fred Judd, October 1920600 Range amplifierAudio, 626 Receiver (Amp + AM/FM tuners) rev., by Fred Judd, May 1973 Hi Fi News, 626 Receiver (Amp + AM/FM tuners) rev., by Fred Judd, October 1973 Hi Fi Answers, 626 Receiver (Amp + AM/FM tuners) review., December 1974 Luister , 621 Amplifier rev., by Jan Kool, November 1973 Hi Fi choice, Receivers 626 Review, by Angus McKenzie, 1976 Issue 2 Hi Fi choice, Amplifiers 621 Review, by Hugh Ford, 1976 Issue 6 Hi Fi choice, Receivers 626 Review, by Angus McKenzie, 1977 Issue 7 Audio (USA), 625 Receiver (Amp + FM tuner) rev. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Arithmetic-geometric mean inequality </page_title> <path> AM-GM_Inequality > Proofs of the AM–GM inequality > Proof by Lagrangian multipliers </path> <section_title> Proof by Lagrangian multipliers </section_title> <content> , x n ) {\displaystyle F(x_{1},x_{2},...,x_{n})} subject to the constraints G ( x 1 , x 2 , … , x n ) = 1 {\displaystyle G(x_{1},x_{2},\ldots ,x_{n})=1} and ( x 1 , x 2 , … , x n ) ∈ K {\displaystyle (x_{1},x_{2},\ldots ,x_{n})\in K} is attained at some point inside K {\displaystyle K} . On the other hand, observe that if any of the x i > n {\displaystyle x_{i}>n} , then F ( x 1 , x 2 , … , x n ) > 1 {\displaystyle F(x_{1},x_{2},\ldots ,x_{n})>1} , while F ( 1 , 1 , … , 1 ) = 1 {\displaystyle F(1,1,\ldots ,1)=1} , and ( 1 , 1 , … , 1 ) ∈ K ∩ { G = 1 } {\displaystyle (1,1,\ldots ,1)\in K\cap \{G=1\}} . This means that the minimum inside K ∩ { G = 1 } {\displaystyle K\cap \{G=1\}} is in fact a global minimum, since the value of F {\displaystyle F} at any point inside K ∩ { G = 1 } {\displaystyle K\cap \{G=1\}} is certainly no smaller than the minimum, and the value of F {\displaystyle F} at any point ( y 1 , y 2 , … , y n ) {\displaystyle (y_{1},y_{2},\ldots ,y_{n})} not inside K {\displaystyle K} is strictly bigger than the value at ( 1 , 1 , … , 1 ) {\displaystyle (1,1,\ldots ,1)} , which is no smaller than the minimum. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Larson–Miller relation </page_title> <path> Larson–Miller_relation > Background and usage </path> <section_title> Background and usage </section_title> <content> F.R. Larson and J. Miller proposed that creep rate could adequately be described by the Arrhenius type equation: r = A ⋅ e − Δ H / ( R ⋅ T ) {\displaystyle r=A\cdot e^{-\Delta H/(R\cdot T)}} Where r is the creep process rate, A is a constant, R is the universal gas constant, T is the absolute temperature, and Δ H {\displaystyle \Delta H} is the activation energy for the creep process. Taking the natural log of both sides: ln ( r ) = ln ( A ) − Δ H / ( R ⋅ T ) {\displaystyle \ln(r)=\ln(A)-\Delta H/(R\cdot T)} With some rearrangement: Δ H / R = T ⋅ ( ln ( A ) − ln ( r ) ) {\displaystyle \Delta H/R=T\cdot (\ln(A)-\ln(r))} Using the fact that creep rate is inversely proportional to time, the equation can be written as: Δ l / Δ t = A ′ ⋅ e − Δ H / ( R ⋅ T ) {\displaystyle \Delta l/\Delta t=A'\cdot e^{-\Delta H/(R\cdot T)}} Taking the natural log: ln ( Δ l / Δ t ) = ln ( A ′ ) − Δ H / ( R ⋅ T ) {\displaystyle \ln(\Delta l/\Delta t)=\ln(A')-\Delta H/(R\cdot T)} After some rearrangement the relation finally becomes: Δ H / R = T ⋅ ( B + ln ( Δ t ) ) {\displaystyle \Delta H/R=T\cdot (B+\ln(\Delta t))} , where B = ln ( A ′ / Δ l ) {\displaystyle \ln(A'/\Delta l)} This equation is of the same form as the Larson–Miller relation. L M P = T ⋅ ( C + log ( t ) ) {\displaystyle LMP=T\cdot (C+\log(t))} where the quantity LMP is known as the Larson–Miller parameter. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> History of Solar System formation and evolution hypotheses </page_title> <path> History_of_Solar_System_formation_and_evolution_hypotheses > Formation hypothesis > Alternative hypotheses > Classification of the hypotheses </path> <section_title> Classification of the hypotheses </section_title> <content> Jeans, in 1931, divided the various models into two groups: those where the material for planet formation came from the Sun, and those where it did not and may be concurrent or consecutive.In 1963, William McCrea divided them into another two groups: those that relate the formation of the planets to the formation of the Sun and those where it is independent of the formation of the Sun, where the planets form after the Sun becomes a normal star.Ter Haar and Cameron distinguished between those hypotheses that consider a closed system, which is a development of the Sun and possibly a solar envelope, that starts with a protosun rather than the Sun itself, and state that Belot calls these hypotheses monistic; and those that consider an open system, which is where there is an interaction between the Sun and some foreign body that is supposed to have been the first step in the developments leading to the planetary system, and state that Belot calls these hypotheses dualistic. Hervé Reeves' classification also categorized them as co-genetic with the Sun or not, but also considered their formation from altered or unaltered stellar and interstellar material. He also recognized four groups: models based on the solar nebula, originated by Swedenborg, Kant, and Laplace in the 1700s; hypotheses proposing a cloud captured from interstellar space, major proponents being Alfvén and Gustaf Arrhenius in 1978; the binary hypotheses which propose that a sister star somehow disintegrated and a portion of its dissipating material was captured by the Sun, with the principal hypothesizer being Lyttleton in the 1940s; and the close-approach filament ideas of Jeans, Jeffreys, and Woolfson and Dormand. Iwan P. Williams and Alan William Cremin split the models between two categories: those that regard the origin and formation of the planets as being essentially related to the Sun, with the two formation processes taking place concurrently or consecutively, and those that regard the formation of the planets as being independent of the formation process of the Sun, the planets forming after the Sun becomes a normal star. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Amazon CloudFront </page_title> <path> Amazon_CloudFront > Amazon CloudFront edge locations </path> <section_title> Amazon CloudFront edge locations </section_title> <content> In October 2018, Amazon CloudFront consisted of 138 access points (127 edge locations and 11 regional edge caches) in 63 cities across 29 countries. North America Edge locations: Ashburn, VA (3); Atlanta, GA (3); Boston, MA; Chicago, IL (2); Dallas/Fort Worth, TX (5); Denver, CO (2); Hayward, CA; Jacksonville, FL; Los Angeles, CA (4); Miami, FL (3); Minneapolis, MN; Montreal, QC; New York, NY (3); Newark, NJ (3); Palo Alto, CA; Philadelphia, PA; Phoenix, AZ; San Jose, CA (2); Seattle, WA (3); South Bend, IN; St. Louis, MO; Toronto, ON Regional Edge caches: Virginia; Ohio; OregonEurope Edge locations: Amsterdam, the Netherlands (2); Berlin, Germany; Copenhagen, Denmark; Dublin, Ireland; Frankfurt, Germany (8); Helsinki, Finland; London, England (7); Madrid, Spain (2); Manchester, England; Marseille, France; Milan, Italy; Munich, Germany; Oslo, Norway; Palermo, Italy; Paris, France (4); Prague, Czech Republic; Stockholm, Sweden (3); Vienna, Austria; Warsaw, Poland; Zurich, Switzerland Regional Edge caches: Frankfurt, Germany; London, EnglandAsia Edge locations: Bangalore, India; Chennai, India (3); Bangkok, Thailand (2); Hong Kong, China (3); Kuala Lumpur, Malaysia; Mumbai, India (2); Manila, Philippines; New Delhi, India (2); Osaka, Japan; Seoul, South Korea (4); Singapore (3); Taipei, Taiwan(3); Tokyo, Japan (9) Regional Edge caches: Mumbai, India; Singapore; Seoul, South Korea; Tokyo, JapanAustralia Edge locations: Melbourne; Perth; Sydney Regional Edge caches: SydneySouth America Edge locations: São Paulo, Brazil (2); Rio de Janeiro, Brazil (2) Regional Edge caches: São Paulo, BrazilMiddle East Edge location: Dubai, United Arab Emirates; Fujairah, United Arab Emirates; Tel Aviv, IsraelAfrica Edge locations: Nairobi, Kenya; Johannesburg, South Africa; Cape Town, South Africa </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Van Vleck paramagnetism </page_title> <path> Van_Vleck_paramagnetism > Derivation > First order perturbation theory </path> <section_title> First order perturbation theory </section_title> <content> First order perturbation theory on the second term of the Hamiltonian (proportional to H {\displaystyle H} ) for electrons bound to an atom, gives a positive correction to energy given by Δ E ( 1 ) = μ 0 μ B ℏ ⟨ g | ( L + g S ) ⋅ H | g ⟩ = g J μ 0 μ B ℏ ⟨ g | J ⋅ H | g ⟩ {\displaystyle \Delta E^{(1)}=\mu _{0}{\frac {\mu _{\rm {B}}}{\hbar }}\langle \mathrm {g} |(\mathbf {L} +g\mathbf {S} )\cdot \mathbf {H} |\mathrm {g} \rangle =g_{J}\mu _{0}{\frac {\mu _{\rm {B}}}{\hbar }}\langle \mathrm {g} |\mathbf {J} \cdot \mathbf {H} |\mathrm {g} \rangle } where | g ⟩ {\displaystyle |\mathrm {g} \rangle } is the ground state, g J {\displaystyle g_{J}} is the Landé g-factor of the ground state and J = L + S {\displaystyle \mathbf {J} =\mathbf {L} +\mathbf {S} } is the total angular momentum operator (see Wigner–Eckart theorem). This correction leads to what is known as Langevin paramagnetism (the quantum theory is sometimes called Brillouin paramagnetism), that leads to a positive magnetic susceptibility. For sufficiently large temperatures , this contribution is described by Curie's law: χ C u r i e ≈ C 1 T {\displaystyle \chi _{\rm {Curie}}\approx {\frac {C_{1}}{T}}} ,a susceptibility that is inversely proportional to the temperature T {\displaystyle T} , where C 0 ≈ C 1 {\displaystyle C_{0}\approx C_{1}} is the material dependent Curie constant. If the ground state has no total angular momentum there is no Curie contribution and other terms dominate. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Dittert conjecture </page_title> <path> Dittert_conjecture </path> <section_title> Summary </section_title> <content> The Dittert conjecture, or Dittert–Hajek conjecture, is a mathematical hypothesis (in combinatorics) concerning the maximum achieved by a particular function ϕ {\displaystyle \phi } of matrices with real, nonnegative entries satisfying a summation condition. The conjecture is due to Eric Dittert and (independently) Bruce Hajek.Let A = {\displaystyle A=} be a square matrix of order n {\displaystyle n} with nonnegative entries and with ∑ i = 1 n ( ∑ j = 1 n a i j ) = n {\displaystyle \sum _{i=1}^{n}\left(\sum _{j=1}^{n}a_{ij}\right)=n} . Its permanent is defined as per ( A ) = ∑ σ ∈ S n ∏ i = 1 n a i , σ ( i ) {\displaystyle \operatorname {per} (A)=\sum _{\sigma \in S_{n}}\prod _{i=1}^{n}a_{i,\sigma (i)}} , where the sum extends over all elements σ {\displaystyle \sigma } of the symmetric group. The Dittert conjecture asserts that the function ϕ ( A ) {\displaystyle \operatorname {\phi } (A)} defined by ∏ i = 1 n ( ∑ j = 1 n a i j ) + ∏ j = 1 n ( ∑ i = 1 n a i j ) − per ( A ) {\displaystyle \prod _{i=1}^{n}\left(\sum _{j=1}^{n}a_{ij}\right)+\prod _{j=1}^{n}\left(\sum _{i=1}^{n}a_{ij}\right)-\operatorname {per} (A)} is (uniquely) maximized when A = ( 1 / n ) J n {\displaystyle A=(1/n)J_{n}} , where J n {\displaystyle J_{n}} is defined to be the square matrix of order n {\displaystyle n} with all entries equal to 1. == References == </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Georgi–Glashow model </page_title> <path> Georgi–Glashow_model > Minimal supersymmetric SU(5) > Vacua > The Φ sector </path> <section_title> The Φ sector </section_title> <content> W = T r {\displaystyle \ W=Tr\left\ } The F zeros corresponds to finding the stationary points of W subject to the traceless constraint T r = 0 . {\displaystyle \ Tr=0~.} So, 2 a Φ + 3 b Φ 2 = λ 1 , {\displaystyle \ 2a\Phi +3b\Phi ^{2}=\lambda \mathbf {1} \ ,} where λ is a Lagrange multiplier. Up to an SU(5) (unitary) transformation, Φ = { diag ( 0 , 0 , 0 , 0 , 0 ) diag ( 2 a 9 b , 2 a 9 b , 2 a 9 b , 2 a 9 b , − 8 a 9 b ) diag ( 4 a 3 b , 4 a 3 b , 4 a 3 b , − 2 a b , − 2 a b ) {\displaystyle \Phi ={\begin{cases}\operatorname {diag} (0,0,0,0,0)\\\operatorname {diag} ({\frac {2a}{9b}},{\frac {2a}{9b}},{\frac {2a}{9b}},{\frac {2a}{9b}},-{\frac {8a}{9b}})\\\operatorname {diag} ({\frac {4a}{3b}},{\frac {4a}{3b}},{\frac {4a}{3b}},-{\frac {2a}{b}},-{\frac {2a}{b}})\end{cases}}} The three cases are called case I, II, and III and they break the gauge symmetry into S U ( 5 ) , / Z 4 {\displaystyle \ SU(5),\ \left/\mathbb {Z} _{4}\ } and / Z 6 {\displaystyle \ \left/\mathbb {Z} _{6}} respectively (the stabilizer of the VEV). </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Micromagnetics </page_title> <path> Micromagnetics > Dynamic micromagnetics > Effective field </path> <section_title> Effective field </section_title> <content> The effective field is the local field felt by the magnetization. It can be described informally as the derivative of the magnetic energy density with respect to the orientation of the magnetization, as in: H e f f = − 1 μ 0 M s d 2 E d m d V {\displaystyle \mathbf {H} _{\mathrm {eff} }=-{\frac {1}{\mu _{0}M_{s}}}{\frac {\mathrm {d} ^{2}E}{\mathrm {d} \mathbf {m} \mathrm {d} V}}} where dE/dV is the energy density. In variational terms, a change dm of the magnetization and the associated change dE of the magnetic energy are related by: d E = − μ 0 M s ∫ V ( d m ) ⋅ H eff d V {\displaystyle \mathrm {d} E=-\mu _{0}M_{s}\int _{V}(\mathrm {d} \mathbf {m} )\cdot \mathbf {H} _{\text{eff}}\,\mathrm {d} V} Since m is a unit vector, dm is always perpendicular to m. Then the above definition leaves unspecified the component of Heff that is parallel to m. This is usually not a problem, as this component has no effect on the magnetization dynamics. From the expression of the different contributions to the magnetic energy, the effective field can be found to be: H e f f = 2 A μ 0 M s ∇ 2 m − 1 μ 0 M s ∂ F anis ∂ m + H a + H d {\displaystyle \mathbf {H} _{\mathrm {eff} }={\frac {2A}{\mu _{0}M_{s}}}\nabla ^{2}\mathbf {m} -{\frac {1}{\mu _{0}M_{s}}}{\frac {\partial F_{\text{anis}}}{\partial \mathbf {m} }}+\mathbf {H} _{\text{a}}+\mathbf {H} _{\text{d}}} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Lambert's problem </page_title> <path> Lambert's_problem > Initial geometrical analysis </path> <section_title> Initial geometrical analysis </section_title> <content> The three points F 1 {\displaystyle F_{1}} , the centre of attraction, P 1 {\displaystyle P_{1}} , the point corresponding to vector r ¯ 1 {\displaystyle {\bar {r}}_{1}} , P 2 {\displaystyle P_{2}} , the point corresponding to vector r ¯ 2 {\displaystyle {\bar {r}}_{2}} ,form a triangle in the plane defined by the vectors r ¯ 1 {\displaystyle {\bar {r}}_{1}} and r ¯ 2 {\displaystyle {\bar {r}}_{2}} as illustrated in figure 1. The distance between the points P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} is 2 d {\displaystyle 2d} , the distance between the points P 1 {\displaystyle P_{1}} and F 1 {\displaystyle F_{1}} is r 1 = r m − A {\displaystyle r_{1}=r_{m}-A} and the distance between the points P 2 {\displaystyle P_{2}} and F 1 {\displaystyle F_{1}} is r 2 = r m + A {\displaystyle r_{2}=r_{m}+A} . The value A {\displaystyle A} is positive or negative depending on which of the points P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} that is furthest away from the point F 1 {\displaystyle F_{1}} . The geometrical problem to solve is to find all ellipses that go through the points P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} and have a focus at the point F 1 {\displaystyle F_{1}} The points F 1 {\displaystyle F_{1}} , P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} define a hyperbola going through the point F 1 {\displaystyle F_{1}} with foci at the points P 1 {\displaystyle P_{1}} and P 2 {\displaystyle P_{2}} . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Bifilar sundial </page_title> <path> Bifilar_sundial > Horizontal bifilar dial > The proof </path> <section_title> The proof </section_title> <content> The Y-axis is the north–south line passing through the origin. The positive Y direction is northward. One can show that if the position of the sun is known and determined by the spherical coordinates t ⊙ {\displaystyle t_{\odot }} et δ {\displaystyle \delta \,} (pronounced t-dot and delta, respectively the known as the hour angle et declination), the co-ordinates x I {\displaystyle x_{I}\,} and y I {\displaystyle y_{I}\,} of point I {\displaystyle I\,} , the intersection on the two shadows on the dial-plate Π {\displaystyle \Pi \,} have values of: x I = h 1 sin t ⊙ sin φ tan δ + cos φ cos t ⊙ y I = h 2 − cos φ tan δ + sin φ cos t ⊙ sin φ tan δ + cos φ cos t ⊙ {\displaystyle {\begin{matrix}x_{I}&=&h_{1}{\frac {\sin t_{\odot }}{\sin \varphi \ \operatorname {tan} \delta \ +\ \cos \varphi \cos t_{\odot }}}\\\ &\ &\ \\y_{I}&=&h_{2}{\frac {-\cos \varphi \ \operatorname {tan} \delta \ +\ \sin \varphi \cos t_{\odot }}{\sin \varphi \ \operatorname {tan} \delta \ +\ \cos \varphi \cos t_{\odot }}}\end{matrix}}} Eliminating the variable δ {\displaystyle \delta \,} in the two preceding equations, one obtains a new equation defined for x I {\displaystyle x_{I}\,} and y I {\displaystyle y_{I}\,} which gives, as a function of the latitude φ {\displaystyle \varphi } and the solar hour angle solaire t ⊙ {\displaystyle t_{\odot }} , the equation of the trace of the sun associated with the local apparent time. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> First-fit-decreasing bin packing </page_title> <path> First-fit-decreasing_bin_packing > Monotonicity properties > Examples </path> <section_title> Examples </section_title> <content> For example, suppose the input is: 44, 24, 24, 22, 21, 17, 8, 8, 6, 6. With capacity 60, FFD packs 3 bins: 44, 8, 8; 24, 24, 6, 6; 22, 21, 17.But with capacity 61, FFD packs 4 bins: 44, 17; 24, 24, 8; 22, 21, 8, 6; 6.This is because, with capacity 61, the 17 fits into the first bin, and thus blocks the way to the following 8, 8. As another example,: Ex.5.1 suppose the inputs are: 51, 28, 28, 28, 27, 25, 12, 12, 10, 10, 10, 10, 10, 10, 10, 10. With capacity 75, FFD packs 4 bins: 51, 12, 12 28, 28, 10 28, 27, 10, 10 25, 10, 10, 10, 10, 10But with capacity 76, it needs 5 bins: 51, 25 28, 28, 12 28, 27, 12 10, 10, 10, 10, 10, 10, 10 10Consider the above example with capacity 60. If the 17 becomes 16, then the resulting packing is: 44, 16; 24, 24, 8; 22, 21, 8, 6; 6. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Chernoff bound </page_title> <path> Chernoff_bound > Sums of independent Bernoulli random variables > Additive form (absolute error) </path> <section_title> Additive form (absolute error) </section_title> <content> random variables, taking values in {0, 1}. Let p = E and ε > 0. Pr ( 1 n ∑ X i ≥ p + ε ) ≤ ( ( p p + ε ) p + ε ( 1 − p 1 − p − ε ) 1 − p − ε ) n = e − D ( p + ε ∥ p ) n Pr ( 1 n ∑ X i ≤ p − ε ) ≤ ( ( p p − ε ) p − ε ( 1 − p 1 − p + ε ) 1 − p + ε ) n = e − D ( p − ε ∥ p ) n {\displaystyle {\begin{aligned}\Pr \left({\frac {1}{n}}\sum X_{i}\geq p+\varepsilon \right)\leq \left(\left({\frac {p}{p+\varepsilon }}\right)^{p+\varepsilon }{\left({\frac {1-p}{1-p-\varepsilon }}\right)}^{1-p-\varepsilon }\right)^{n}&=e^{-D(p+\varepsilon \parallel p)n}\\\Pr \left({\frac {1}{n}}\sum X_{i}\leq p-\varepsilon \right)\leq \left(\left({\frac {p}{p-\varepsilon }}\right)^{p-\varepsilon }{\left({\frac {1-p}{1-p+\varepsilon }}\right)}^{1-p+\varepsilon }\right)^{n}&=e^{-D(p-\varepsilon \parallel p)n}\end{aligned}}} where D ( x ∥ y ) = x ln x y + ( 1 − x ) ln ( 1 − x 1 − y ) {\displaystyle D(x\parallel y)=x\ln {\frac {x}{y}}+(1-x)\ln \left({\frac {1-x}{1-y}}\right)} is the Kullback–Leibler divergence between Bernoulli distributed random variables with parameters x and y respectively. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Telescopium−Grus Cloud </page_title> <path> Telescopium−Grus_Cloud > Observational history </path> <section_title> Observational history </section_title> <content> Even before the Telescopium−Grus Cloud was identified, major concentrations in the filament were identified: group G27 which would later be known as the Grus Group, group G39 which would later be known as the NGC 134 Group, group G45 (Pavo-Indus) which would later be known as the NGC 7079, NGC 7144, NGC 7196 and NGC 7213 groups, and group G52 which would later be known as the Telescopium Cluster. These concentrations were first identified by astronomer Gérard de Vaucouleurs in 1975.In 1987, astronomer Brent Tully with colleague Richard Fisher first identified and described the Telescopium−Grus Cloud in his book The Nearby Galaxies Atlas and its companion book The Nearby Galaxies Catalog. Later in 1992, Fouque et al. grouped the Telescopium−Grus Cloud, also known as cloud 61 in the book The Nearby Galaxies Atlas along with the Pavo-Indus Spur (cloud 62), the Pisces Austrinus Spur (cloud 63), the Pegaus Cloud and Pegaus Spur (clouds 64 and 65) with the Pavo-Indus Suercluster which at the time was known as the Indus Supercluster. However in a paper published in 1993 titled, Dynamics of the Pavo-Indus and Grus clouds of galaxies., Fouque et al. instead classified the Telescopium−Grus Cloud as a connection between the Pavo–Indus Supercluster and the Local Supercluster.In 2001, Pebeles et.al identified another galaxy filament that originates at the Virgo Cluster, passes through a knot of galaxies containing the Sombrero Galaxy, then passes at its closest point to the Milky Way at the Centaurus/M83 group, and then passes from the perspective from the Milky Way though the galactic plane near the Circinus galaxy to meet up with the Telescopium−Grus Cloud. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Pupillary light reflex </page_title> <path> Pupillary_light_reflex > Mathematical model </path> <section_title> Mathematical model </section_title> <content> Pupillary light reflex is modeled as a physiologically-based non-linear delay differential equation that describes the changes in the pupil diameter as a function of the environment lighting: M ( D ) = tanh − 1 ( D − 4.9 3 ) d M d D d D d t + 2.3026 tanh − 1 ( D − 4.9 3 ) = 5.2 − 0.45 ln ( Φ 4.8118 × 10 − 10 ) {\displaystyle {\begin{aligned}M(D){}&=\tanh ^{-1}\left({\frac {D-4.9}{3}}\right)\\{\frac {\mathrm {d} M}{\mathrm {d} D}}{\frac {\mathrm {d} D}{\mathrm {d} t}}+2.3026\tanh ^{-1}\left({\frac {D-4.9}{3}}\right)&=5.2-0.45\ln \left({\frac {\Phi }{4.8118\times 10^{-10}}}\right)\end{aligned}}} where D {\displaystyle D} is the pupil diameter measured in millimeters and Φ ( t − τ ) {\displaystyle \Phi (t-\tau )} is the luminous intensity reaching the retina in a time t {\displaystyle t} , which can be described as Φ = I A {\displaystyle \Phi =IA}: luminance reaching the eye in lumens/mm2 times the pupil area in mm2. τ {\displaystyle \tau } is the pupillary latency, a time delay between the instant in which the light pulse reaches the retina and the beginning of iridal reaction due nerve transmission, neuro-muscular excitation and activation delays. d M {\displaystyle \mathrm {d} M} , d D {\displaystyle \mathrm {d} D} and d t {\displaystyle \mathrm {d} t} are the derivatives for the M {\displaystyle M} function, pupil diameter D {\displaystyle D} and time t {\displaystyle t} . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Diffusive–thermal instability </page_title> <path> Diffusive–thermal_instability > Dispersion relation for premixed flames </path> <section_title> Dispersion relation for premixed flames </section_title> <content> To neglect the influences by hydrodynamic instabilities such as Darrieus–Landau instability, Rayleigh–Taylor instability etc., the analysis usually neglects effects due to the thermal expansion of the gas mixture by assuming a constant density model. Such an approximation is referred to as diffusive-thermal approximation or thermo-diffusive approximation which was first introudced by Grigory Barenblatt, Yakov Zeldovich and A. G. Istratov in 1962. With a one-step chemistry model and assuming the perturbations to a steady planar flame in the form e i k ⋅ x ⊥ + ω t {\displaystyle e^{i\mathbf {k} \cdot \mathbf {x} _{\bot }+\omega t}} , where x ⊥ {\displaystyle \mathbf {x} _{\bot }} is the transverse coordinate system perpendicular to flame, t {\displaystyle t} is the time, k {\displaystyle \mathbf {k} } is the perturbation wavevector and ω {\displaystyle \omega } is the temporal growth rate of the disturbance, the dispersion relation ω ( k ) {\displaystyle \omega (k)} for one-reactant flames is given implicitly by 2 Γ 2 ( Γ − 1 ) + l ( Γ − 1 − 2 ω ) = 0 {\displaystyle 2\Gamma ^{2}(\Gamma -1)+l(\Gamma -1-2\omega )=0} where Γ = 1 + 4 ω + 4 k 2 {\displaystyle \Gamma ={\sqrt {1+4\omega +4k^{2}}}} , l ≡ ( L e − 1 ) / β {\displaystyle l\equiv (Le-1)/\beta } , L e {\displaystyle Le} is the Lewis number of the fuel and β {\displaystyle \beta } is the Zeldovich number. This relation provides in general three roots for ω {\displaystyle \omega } in which the one with maximum ℜ { ω } {\displaystyle \Re \{\omega \}} would determine the stability character. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Reciprocal Gamma function </page_title> <path> Reciprocal_Gamma_function > Taylor series </path> <section_title> Taylor series </section_title> <content> Taylor series expansion around 0 gives: 1 Γ ( z ) = z + γ z 2 + ( γ 2 2 − π 2 12 ) z 3 + ( γ 3 6 − γ π 2 12 + ζ ( 3 ) 3 ) z 4 + ⋯ {\displaystyle {\frac {1}{\ \Gamma (z)\ }}=z+\gamma \ z^{2}+\left({\frac {\gamma ^{2}}{2}}-{\frac {\pi ^{2}}{12}}\right)\ z^{3}+\left({\frac {\gamma ^{3}}{6}}-{\frac {\gamma \pi ^{2}}{12}}+{\frac {\zeta (3)}{3}}\ \right)z^{4}+\cdots \ } where γ is the Euler–Mascheroni constant. For n > 2, the coefficient an for the zn term can be computed recursively as a n = a 2 a n − 1 + ∑ j = 2 n − 1 ( − 1 ) j + 1 ζ ( j ) a n − j n − 1 = γ a n − 1 − ζ ( 2 ) a n − 2 + ζ ( 3 ) a n − 3 − ⋯ n − 1 {\displaystyle a_{n}={\frac {\ {a_{2}\ a_{n-1}+\sum _{j=2}^{n-1}(-1)^{j+1}\ \zeta (j)\ a_{n-j}}\ }{n-1}}={\frac {\ \gamma \ a_{n-1}-\zeta (2)\ a_{n-2}+\zeta (3)\ a_{n-3}-\cdots \ }{n-1}}} where ζ is the Riemann zeta function. An integral representation for these coefficients was recently found by Fekih-Ahmed (2014): a n = ( − 1 ) n π n ! ∫ 0 ∞ e − t I m d t . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Large eddy simulation </page_title> <path> Large_eddy_simulation > Modeling unresolved scales > Sub-grid scale models > Functional (eddy–viscosity) models > The Dynamic Model (Germano et al. and beyond) </path> <section_title> The Dynamic Model (Germano et al. and beyond) </section_title> <content> The procedure for determining C {\displaystyle C} remains identical to the "unconstrained" version except that the tensors α i j = − 2 Δ ^ K S ¯ ^ i j {\displaystyle \alpha _{ij}=-2{\hat {\Delta }}{\sqrt {K}}{\hat {\bar {S}}}_{ij}} , β i j = − 2 Δ ^ k S ¯ i j {\displaystyle \beta _{ij}=-2{\hat {\Delta }}{\sqrt {k}}{\bar {S}}_{ij}} where the sub-test scale kinetic energy K is related to the subgrid scale kinetic energy k by K = k + L i i / 2 {\displaystyle K=k+L_{ii}/2} (follows by taking the trace of the Germano identity). To determine k we now use a transport equation ∂ k ∂ t + u j ∂ k ∂ x j = − τ i j S ¯ i j − C ∗ Δ k 3 / 2 + ∂ ∂ x j ( D Δ k ∂ k ∂ x j ) + ν ∂ 2 k ∂ x j ∂ x j {\displaystyle {\frac {\partial k}{\partial t}}+u_{j}{\frac {\partial k}{\partial x_{j}}}=-\tau _{ij}{\bar {S}}_{ij}-{\frac {C_{*}}{\Delta }}k^{3/2}+{\frac {\partial }{\partial x_{j}}}\left(D\Delta {\sqrt {k}}{\frac {\partial k}{\partial x_{j}}}\right)+\nu {\frac {\partial ^{2}k}{\partial x_{j}\partial x_{j}}}} where ν {\displaystyle \nu } is the kinematic viscosity and C ∗ , D {\displaystyle C_{*},D} are positive coefficients representing kinetic energy dissipation and diffusion respectively. These can be determined following the dynamic procedure with constrained minimization as in DLM(+). </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Life Cycle Climate Performance </page_title> <path> Life_Cycle_Climate_Performance </path> <section_title> Summary </section_title> <content> Life Cycle Climate Performance (LCCP) is an evolving method to evaluate the carbon footprint and global warming impact of heating, ventilation, air conditioning (AC), refrigeration systems, and potentially other applications such as thermal insulating foam. It is calculated as the sum of direct, indirect, and embodied greenhouse gas (GHG) emissions generated over the lifetime of the system “from cradle to grave,” i.e. from manufacture to disposal. Direct emissions include all climate forcing effects from the release of refrigerants into the atmosphere, including annual leakage and losses during service and disposal of the unit. Indirect emissions include the climate forcing effects of GHG emissions from the electricity powering the equipment. The embodied emissions include the climate forcing effects of the manufacturing processes, transport, and installation for the refrigerant, materials, and equipment, and for recycle or other disposal of the product at end of its useful life.LCCP is more inclusive than previous metrics such as Total Equivalent Warming Impact (TEWI), which considers direct and indirect GHG emissions but overlooks embodied emissions, and Life Cycle Warming Impact (LCWI), which considers direct, indirect and refrigerant manufacturing emissions but overlooks appliance manufacturing, materials, transport installation and recycle. Enhanced and Localized Life Cycle Climate Performance (EL-LCCP) is the latest and most comprehensive carbon metric and takes into account: 1) real-world operating conditions, including the actual hour-by-hour carbon intensity of electricity generation, transmission, and distribution, which is degraded by high ambient temperature; 2) specific conditions of AC condensers located within urban heat islands and in locations with poor air circulation (mounted to close to buildings, clustered and stacked), as well of refrigerators and refrigerated display cases located against walls, inside cabinets, and other locations that compromise energy efficiency; 3) local climate conditions, such as higher ambient temperature at the location of the equipment than at the weather monitoring stations, which typically are located away from human influence.TEWI was developed by experts at Oak Ridge National Laboratory under contract from Allied Signal (now Honeywell) and was a step forward as a complement and enhancement of previous metrics like coefficient of performance (COP) and Seasonal Energy Efficiency Ratio (SEER), which consider energy use but not global warming potential (GWP) and emissions of refrigerants. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Robert Michels </page_title> <path> Robert_Michels > Writings </path> <section_title> Writings </section_title> <content> Kritik der Moralstatistik (Morality in Numerics? Criticism of Morale Statistics) (1928) Patriotismus, Prolegomena zu seiner soziologischen Analyse (Patriotism, Prolegomena to his sociological analysis) (1929) Einfluss der faschistischen Arbeitsverfassung auf die Weltwirtschaft (Influence of the Fascist Arbeitsverfassung on the World Economy) (1929) Italien von heute. Politische und wirtschaftliche Kulturgeschichte von 1860 bis 1930 (Italy Today - Political and Economical Cultural History from 1860 to 1930) (1930) Introduzione alla storia delle dottrine economiche e politiche (Introduction to the history of economic and political doctrines) (1932) Boicottaggio, saggio su un aspetto delle crisi (Boycotts, an essay on an aspect of crises) (1934) Boycottage international (International boycotts) (1936) Verelendungstheorie. Studien und Untersuchungen zur internationalen Dogmengeschichte der Volkswirtschaft, with a foreword by Heinz Maus (Pauperization Theory - Studies and Research into International Dogmas History of National Economy) (1970) Elite e/o democrazia (Elites and/or democracy) (G. Volpe, 1972) Antologia di scritti sociologici (Anthology of publications on sociology); edited by Giordano Sivini (1980) Works on paper, 1918-1930 (Barbara Mathes Gallery, 1984) Critique du socialisme: contribution aux débats du début du XXè siècle (Critique of Socialism: contributions to the debates at the start of the 20th century); articles selected and presented by Pierre Cours-Salies and Jean-Marie Vincent (Editions Kimé, 1992, ISBN 2-908212-43-9) </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Girish Sant </page_title> <path> Girish_Sant > Membership in policy related committees </path> <section_title> Membership in policy related committees </section_title> <content> Member, BASIC Expert Group (2011–12) Convener Transport Working Group, of The Expert Group appointed by The Planning Commission (India) in 2010, to work out the 'Low Carbon Strategy for Inclusive Growth’ Member, World Bank Expert Committee to review West Bengal Power Sector Reforms (2008) Member, 'Working Group on Power' for formulation of XIth five-year plan for the National Planning Commission (India) (2006–07) Member, Expert Group, convened by Secretary of Power (Government of India) to seek "radical" policy suggestions (2006) Member Expert Group on "Financing access to basic utilities for all" formed by the Friedrich Ebert Foundation in co-operation with the Financing for Development Office, June 2006. Member, Expert Committee appointed by The Supreme Court of India for evaluating 'Waste to Energy projects from Municipal Solid Waste', appointed through Ministry of Non-Conventional Energy Sources (2005–06) Member, Central Advisory Committee of Central Electricity Regulatory Commission (India), since 1998 till 2010 Member, State Advisory Committee of Maharashtra Electricity Regulatory Commission, since 1999 till 2010 Member, 'Consultative Group on Power & Energy' of Planning Commission (India) for review of energy sector performance in the Xth plan Member, Advisory Committee, ADB Policy Research Network to strengthen policy reforms – Infrastructure Development for Poverty Reduction: Priorities, Constraints and Strategies (2004–05) Member, Western Regional Energy Committee Confederation of Indian Industries (CII) (2003 and 2004) Member Advisory Committee, Distribution Reforms Upgrade Management (DRUM) program of Government of India and USAID (2003) Member, Study Group on Benefits of Sardar Sarovar Dam Project, Government of Maharashtra (2001) Member, Task Force to review Narmada Dams, Government of M.P. (1998) Member, International team of civil society to review status of rehabilitation of project affected persons at by Coal mines and Thermal plants at Singrauli (UP) (1995) </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Soyuz 7K-L1 </page_title> <path> Soyuz_7K-L1 > Test missions </path> <section_title> Test missions </section_title> <content> Cosmos 146 (Soyuz 7K-L1 s/n 1) Launched on 10 March 1967 Prototype Soyuz 7K-L1P launched by Proton into a planned highly elliptical Earth orbit.Cosmos 154 (Soyuz 7K-L1 s/n 3) Launched on 8 April 1967 Prototype Soyuz 7K-L1P launched by Proton and failed into a planned translunar trajectory.Zond 1967A (Soyuz 7K-L1 s/n 4) Launched on 27 September 1967 First stage - 1 x RD-253 failed, resulting in at T+67 seconds in deviation from the flight path.Zond 1967B (Soyuz 7K-L1 s/n 5) Launched on 22 November 1967 Second stage - 1 x RD-210 failure, shutoff of stage 4 seconds after ignition. Launcher crashed downrange.Zond 4 (Soyuz 7K-L1 s/n 6) Launched on 2 March 1968 Study of remote regions of circumterrestrial space, development of new on-board systems and units of space stations. Returned to Earth on 7 March 1968 - Self-destruct system automatically blew up the capsule at 10 to 15 km altitude, 180–200 km off the African coast at Guinea.Zond 1968A (Soyuz 7K-L1 s/n 7) Launched on 23 April 1968 Second stage failed 260 seconds after launch. Attempted Lunar flyby.Zond 1968B (Zond 7K-L1 s/n 8) Launched on 21 July 1968 Blok D stage exploded on the pad, killing three people.Zond 5 (Soyuz 7K-L1 s/n 5) Launched on 15 September 1968 Circumlunar on 18 September 1968. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Nephroid caustic </page_title> <path> Nephroid_caustic > Metric properties </path> <section_title> Metric properties </section_title> <content> {\displaystyle {\dot {y}}=12a\sin ^{2}\varphi \cos \varphi \quad ,\quad \quad \quad \quad {\ddot {y}}=12a\sin \varphi (3\cos ^{2}\varphi -1)\ .} Proof for the arc length L = 2 ∫ 0 π x ˙ 2 + y ˙ 2 d φ = ⋯ = 12 a ∫ 0 π sin φ d φ = 24 a {\displaystyle L=2\int _{0}^{\pi }{\sqrt {{\dot {x}}^{2}+{\dot {y}}^{2}}}\;d\varphi =\cdots =12a\int _{0}^{\pi }\sin \varphi \;d\varphi =24a} .Proof for the area A = 2 ⋅ 1 2 | ∫ 0 π d φ | = ⋯ = 24 a 2 ∫ 0 π sin 2 φ d φ = 12 π a 2 {\displaystyle A=2\cdot {\tfrac {1}{2}}|\int _{0}^{\pi }\;d\varphi |=\cdots =24a^{2}\int _{0}^{\pi }\sin ^{2}\varphi \;d\varphi =12\pi a^{2}} .Proof for the radius of curvature ρ = | ( x ˙ 2 + y ˙ 2 ) 3 2 x ˙ y ¨ − y ˙ x ¨ | = ⋯ = | 3 a sin φ | . {\displaystyle \rho =\left|{\frac {\left({{\dot {x}}^{2}+{\dot {y}}^{2}}\right)^{\frac {3}{2}}}{{\dot {x}}{\ddot {y}}-{\dot {y}}{\ddot {x}}}}\right|=\cdots =|3a\sin \varphi |.} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> List of carnivorous plants </page_title> <path> List_of_carnivorous_plants > Extant species > Nepenthes </path> <section_title> Nepenthes </section_title> <content> : Nepenthes boschiana var.sumatrana) Nepenthes suratensis M.Catal., 2010 Nepenthes surigaoensis Elmer, 1915 Nepenthes talaandig Gronem., Coritico, Wistuba, Micheler, Marwinski, Gieray & V.B.Amoroso, 2014 Nepenthes talangensis Nerz & Wistuba, 1994 Nepenthes tboli Jebb & Cheek, 2014 Nepenthes tenax C.Clarke & R.Kruger, 2006 Nepenthes tentaculata Hook.f., 1873 Nepenthes tenuis Nerz & Wistuba, 1994 Nepenthes thai Cheek, 2009 Nepenthes thorelii Lecomte, 1909 Nepenthes tobaica Danser, 1928 Nepenthes tomoriana Danser, 1928 Nepenthes treubiana Warb., 1851 Nepenthes truncata Macfarl., 1911 Nepenthes ultra Jebb & Cheek, 2013 Nepenthes undulatifolia Nerz, Wistuba, U.Zimm., Chi C.Lee, Pirade & Pitopang, 2011 Nepenthes veitchii Hook.f., 1859 Nepenthes ventricosa Blanco, 1837 Nepenthes vieillardii Hook.f., 1873Nepenthes villosa Hook.f., 1852 Nepenthes viridis Micheler, Gronem., Wistuba, Marwinski, W.Suarez & V.B.Amoroso, 2013 Nepenthes vogelii Schuit. & de Vogel, 2002 Nepenthes weda Cheek, 2015 Nepenthes zygon Jebb & Cheek, 2014 Nepenthes sp. Anipahan Nepenthes sp. Misool </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Seifert matrix </page_title> <path> Seifert_surface > Existence and Seifert matrix </path> <section_title> Existence and Seifert matrix </section_title> <content> The homology group H 1 ( S ) {\displaystyle H_{1}(S)} is free abelian on 2g generators, where g = 1 2 ( 2 + d − f − m ) {\displaystyle g={\frac {1}{2}}(2+d-f-m)} is the genus of S {\displaystyle S} . The intersection form Q on H 1 ( S ) {\displaystyle H_{1}(S)} is skew-symmetric, and there is a basis of 2g cycles a 1 , a 2 , … , a 2 g {\displaystyle a_{1},a_{2},\ldots ,a_{2g}} with Q = ( Q ( a i , a j ) ) {\displaystyle Q=(Q(a_{i},a_{j}))} equal to a direct sum of the g copies of the matrix ( 0 − 1 1 0 ) {\displaystyle {\begin{pmatrix}0&-1\\1&0\end{pmatrix}}} The 2g × 2g integer Seifert matrix V = ( v ( i , j ) ) {\displaystyle V=(v(i,j))} has v ( i , j ) {\displaystyle v(i,j)} the linking number in Euclidean 3-space (or in the 3-sphere) of ai and the "pushoff" of aj in the positive direction of S {\displaystyle S} . More precisely, recalling that Seifert surfaces are bicollared, meaning that we can extend the embedding of S {\displaystyle S} to an embedding of S × {\displaystyle S\times } , given some representative loop x {\displaystyle x} which is homology generator in the interior of S {\displaystyle S} , the positive pushout is x × { 1 } {\displaystyle x\times \{1\}} and the negative pushout is x × { − 1 } {\displaystyle x\times \{-1\}} .With this, we have V − V ∗ = Q , {\displaystyle V-V^{*}=Q,} where V∗ = (v(j, i)) the transpose matrix. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Human Systems Integration </page_title> <path> Human_Systems_Integration > Domains > Human Factors Engineering </path> <section_title> Human Factors Engineering </section_title> <content> Human Factors Engineering (HFE) is an engineering discipline that ensures human capabilities and limitations in areas such as perception, cognition, sensory and physical attributes are incorporated into requirements and design. Effective HFE ensures that systems design capitalizes on, and does not exceed, the abilities of the human user population. HFE can reduce the scope of manpower and training requirements, and ensure the system can be operated maintained and supported by users, in a habitable, safe and survivable manner. HFE is concerned with designing human-systems interfaces such as: Functional interfaces: functions, tasks, and allocation of functions to human or automation Informational interfaces: information and characteristics of information that support understanding and awareness of the environment and system Environmental interfaces: natural and artificial environments, environmental controls, and facility design Cooperational interfaces: provisions for team performance, cooperation and collaboration Organizational interfaces: job design, management structure, policies and regulations that impact behavior Cognitive interfaces: decision rules, decision support systems, provisioning for situational awareness and mental models. Physical interfaces: hardware and software elements such as controls, displays, workstations, worksites, accesses, labels and markings, structures, steps and ladders, handholds, maintenance provisions, and more.Technical standards and requirements: ASTM F1166-07 Standard Practice for Human Engineering Design for Marine Systems, Equipment and Facilities HFES-200 Human Factors Engineering of Software User Interfaces MIL-STD 46855 Human Engineering Requirements for Military Systems, Equipment and Facilities MIL-STD 1472 DoD Design Criteria Standard for Human Engineering FAA Human Factors Design Standards (HFDS) HF-STD-001B HFE Data Information Descriptions: Human Engineering Program Plan (HEPP) DI-HFAC- 81742 Human Engineering Systems Analysis Report (HESAR) DI-HFAC-80745 Human Engineering Design Approach Document (HEDAD-M) DI-HFAC-80747 Human Engineering Design Approach Document (HEDAD-O) DI-HFAC-80746 Human Engineering Test Plan (HETP) DI-HFAC-80743 Human Engineering Test Reports (HETR) DI-HFAC-80744 </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Gauge theory (mathematics) </page_title> <path> Gauge_theory_(mathematics) > Fundamental objects of interest > Connections on principal bundles </path> <section_title> Connections on principal bundles </section_title> <content> This gives the local connection one-form A α = s α ∗ ν ∈ Ω 1 ( U α , ad ( P ) ) {\displaystyle A_{\alpha }=s_{\alpha }^{*}\nu \in \Omega ^{1}(U_{\alpha },\operatorname {ad} (P))} which takes values in the adjoint bundle of P {\displaystyle P} . Cartan's structure equation says that the curvature may be expressed in terms of the local one-form A α {\displaystyle A_{\alpha }} by the expression F = d A α + 1 2 {\displaystyle F=dA_{\alpha }+{\frac {1}{2}}} where we use the Lie bracket on the Lie algebra bundle ad ( P ) {\displaystyle \operatorname {ad} (P)} which is identified with U α × g {\displaystyle U_{\alpha }\times {\mathfrak {g}}} on the local trivialisation U α {\displaystyle U_{\alpha }} . Under a local gauge transformation g: U α → G {\displaystyle g:U_{\alpha }\to G} so that A ~ α = ( g ∘ s ) ∗ ν {\displaystyle {\tilde {A}}_{\alpha }=(g\circ s)^{*}\nu } , the local connection one-form transforms by the expression A ~ α = ad ( g ) ∘ A α + ( g − 1 ) ∗ θ {\displaystyle {\tilde {A}}_{\alpha }=\operatorname {ad} (g)\circ A_{\alpha }+(g^{-1})^{*}\theta } where θ {\displaystyle \theta } denotes the Maurer–Cartan form of the Lie group G {\displaystyle G} . In the case where G {\displaystyle G} is a matrix Lie group, one has the simpler expression A ~ α = g A α g − 1 − ( d g ) g − 1 . {\displaystyle {\tilde {A}}_{\alpha }=gA_{\alpha }g^{-1}-(dg)g^{-1}.} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Bessel polynomials </page_title> <path> Bessel_polynomials > Zeros </path> <section_title> Zeros </section_title> <content> If one denotes the zeros of y n ( x ; α , β ) {\displaystyle y_{n}(x;\alpha ,\beta )} as α k ( n ) ( α , β ) {\displaystyle \alpha _{k}^{(n)}(\alpha ,\beta )} , and that of the θ n ( x ; α , β ) {\displaystyle \theta _{n}(x;\alpha ,\beta )} by β k ( n ) ( α , β ) {\displaystyle \beta _{k}^{(n)}(\alpha ,\beta )} , then the following estimates exist:: 82 2 n ( n + α − 1 ) ≤ α k ( n ) ( α , 2 ) ≤ 2 n + α − 1 , {\displaystyle {\frac {2}{n(n+\alpha -1)}}\leq \alpha _{k}^{(n)}(\alpha ,2)\leq {\frac {2}{n+\alpha -1}},} and n + α − 1 2 ≤ β k ( n ) ( α , 2 ) ≤ n ( n + α − 1 ) 2 , {\displaystyle {\frac {n+\alpha -1}{2}}\leq \beta _{k}^{(n)}(\alpha ,2)\leq {\frac {n(n+\alpha -1)}{2}},} for all α ≥ 2 {\displaystyle \alpha \geq 2} . Moreover, all these zeros have negative real part. Sharper results can be said if one resorts to more powerful theorems regarding the estimates of zeros of polynomials (more concretely, the Parabola Theorem of Saff and Varga, or differential equations techniques). : 88 One result is the following: 2 2 n + α − 2 3 ≤ α k ( n ) ( α , 2 ) ≤ 2 n + α − 1 . {\displaystyle {\frac {2}{2n+\alpha -{\frac {2}{3}}}}\leq \alpha _{k}^{(n)}(\alpha ,2)\leq {\frac {2}{n+\alpha -1}}.} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Tree automaton </page_title> <path> Nondeterministic_tree_automaton > Examples > Top-down automaton accepting multiples of 3 in binary notation </path> <section_title> Top-down automaton accepting multiples of 3 in binary notation </section_title> <content> Using the same colorization as above, this example shows how tree automata generalize ordinary string automata. The finite deterministic string automaton shown in the picture accepts all strings of binary digits that denote a multiple of 3. Using the notions from Deterministic finite automaton#Formal definition, it is defined by: the set Q of states being { S0, S1, S2 }, the input alphabet being { 0, 1 }, the initial state being S0, the set of final states being { S0 }, and the transitions being as shown in column (B) of the table.In the tree automaton setting, the input alphabet is changed such that the symbols 0 and 1 are both unary, and a nullary symbol, say nil is used for tree leaves. For example, the binary string "110" in the string automaton setting corresponds to the term "1(1(0(nil)))" in the tree automaton setting; this way, strings can be generalized to trees, or terms. The top-down finite tree automaton accepting the set of all terms corresponding to multiples of 3 in binary string notation is then defined by: the set Q of states being still { S0, S1, S2 }, the ranked input alphabet being { 0, 1, nil }, with Arity(0)=Arity(1)=1 and Arity(nil)=0, as explained, the set of initial states being { S0 }, and the transitions being as shown in column (C) of the table.For example, the tree "1(1(0(nil)))" is accepted by the following tree automaton run: In contrast, the term "1(0(nil))" leads to following non-accepting automaton run: Since there are no other initial states than S0 to start an automaton run with, the term "1(0(nil))" is not accepted by the tree automaton. For comparison purposes, the table gives in column (A) and (D) a (right) regular (string) grammar, and a regular tree grammar, respectively, each accepting the same language as its automaton counterpart. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Pharmacodynamics of testosterone </page_title> <path> Pharmacodynamics_of_testosterone > Pharmacology > Pharmacodynamics > Effects in the body and brain </path> <section_title> Effects in the body and brain </section_title> <content> The ARs are expressed widely throughout the body, including in the penis, testicles, epididymides, prostate gland, seminal vesicles, fat, skin, bone, bone marrow, muscle, larynx, heart, liver, kidneys, pituitary gland, hypothalamus, and elsewhere throughout the brain. Through activation of the ARs (as well as the mARs), testosterone has many effects, including the following: Promotes growth, function, and maintenance of the prostate gland, seminal vesicles, and penis during puberty and thereafter Promotes growth and maintenance of muscles, particularly of the upper body Causes subcutaneous fat to be deposited in a masculine pattern and decreases overall body fat Suppresses breast development induced by estrogens, but can also still produce gynecomastia via excessive conversion into estradiol if levels are too high Maintains skin health, integrity, appearance, and hydration and slows the rate of aging of the skin, but can also cause oily skin, acne, and seborrhea Promotes the growth of facial and body hair, but can also cause scalp hair loss and hirsutism Contributes to bone growth and causes broadening of the shoulders at puberty Modulates liver protein synthesis, such as the production of sex hormone-binding globulin and many other proteins Increases production of erythropoietin in the kidneys and thereby stimulates red blood cell production in bone marrow and elevates hematocrit Exerts negative feedback on the hypothalamic–pituitary–gonadal axis by suppressing the secretion of the gonadotropins follicle-stimulating hormone (FSH) and luteinizing hormone (LH) from the pituitary gland, thereby inhibiting gonadal sex hormone production as well as spermatogenesis and fertility Regulates the vasomotor system and body temperature via the hypothalamus, thereby preventing hot flashes Modulates brain function, with effects on mood, emotionality, aggression, and sexuality, as well as cognition and memory Increases sex drive and erectile capacity and causes spontaneous erections and nocturnal emissions Increases the risk of benign prostatic hyperplasia and prostate cancer and accelerates the progression of prostate cancer Decreases breast proliferation and the risk of breast cancer </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Inbreeding Coefficient </page_title> <path> Inbreeding_Coefficient > Coefficient of relationship </path> <section_title> Coefficient of relationship </section_title> <content> The coefficient of relationship r B C {\displaystyle r_{BC}} is now obtained by summing over all path coefficients: r B C = ∑ p A B ⋅ p A C {\displaystyle r_{BC}=\sum {p_{AB}\cdot p_{AC}}} By assuming that the pedigree can be traced back to a sufficiently remote population of perfectly random-bred stock (fA = 0 for all A in the sum) the definition of r may be simplified to r B C = ∑ p 2 − L ( p ) {\displaystyle r_{BC}=\sum _{p}{2^{-L(p)}}} where p enumerates all paths connecting B and C with unique common ancestors (i.e. all paths terminate at a common ancestor and may not pass through a common ancestor to a common ancestor's ancestor), and L(p) is the length of the path p. To give an (artificial) example: Assuming that two individuals share the same 32 ancestors of n = 5 generations ago, but do not have any common ancestors at four or fewer generations ago, their coefficient of relationship would be r = 2 n ⋅ 2 − 2 n = 2 − n {\textstyle r=2^{n}\cdot 2^{-2n}=2^{-n}} , which for n = 5, is, 2 − 5 = 1 32 {\textstyle 2^{-5}={\frac {1}{32}}} , or approximately 0.0313 or 3%.Individuals for which the same situation applies for their 1024 ancestors of ten generations ago would have a coefficient of r = 2−10 = 0.1%. If follows that the value of r can be given to an accuracy of a few percent if the family tree of both individuals is known for a depth of five generations, and to an accuracy of a tenth of a percent if the known depth is at least ten generations. The contribution to r from common ancestors of 20 generations ago (corresponding to roughly 500 years in human genealogy, or the contribution from common descent from a medieval population) falls below one part-per-million. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> False friend </page_title> <path> False_friend > Causes > Shared etymology </path> <section_title> Shared etymology </section_title> <content> If language A borrowed a word from language B, or both borrowed the word from a third language or inherited it from a common ancestor, and later the word shifted in meaning or acquired additional meanings in at least one of these languages, a native speaker of one language will face a false friend when learning the other. Sometimes, presumably both senses were present in the common ancestor language, but the cognate words got different restricted senses in Language A and Language B.Actual, which in English is usually a synonym of real, has a different meaning in other European languages, in which it means 'current' or 'up-to-date', and has the logical derivative as a verb, meaning 'to make current' or 'to update'. Actualise (or 'actualize') in English means 'to make a reality of'.The word friend itself has cognates in the other Germanic languages; but the Scandinavian ones (like Swedish frände, Danish frænde) predominantly mean 'relative'. The original Proto-Germanic word meant simply 'someone whom one cares for' and could therefore refer to both a friend and a relative, but lost various degrees of the 'friend' sense in Scandinavian languages, while it mostly lost the sense of 'relative' in English (the plural friends is still, rarely, used for "kinsfolk", as in the Scottish proverb Friends agree best at a distance, quoted in 1721). The Estonian and Finnish languages are closely related, which gives rise to false friends such as swapped forms for south and south-west: Or Estonian vaimu 'spirit; ghost' and Finnish vaimo 'wife'; or Estonian huvitav 'interesting' and Finnish huvittava 'amusing'.A high level of lexical similarity exists between German and Dutch, but shifts in meaning of words with a shared etymology have in some instances resulted in 'bi-directional false friends': The Italian word confetti "sugared almonds" has acquired a new meaning in English, French and Dutch; in Italian, the corresponding word is coriandoli.English and Spanish, both of which have borrowed from Ancient Greek and Latin, have multiple false friends, such as: English and Japanese also have diverse false friends, many of them being wasei-eigo and gairaigo words. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Eicosanoid metabolism </page_title> <path> Eicosanoid_metabolism > Biosynthesis > Peroxidation and reactive oxygen species </path> <section_title> Peroxidation and reactive oxygen species </section_title> <content> The two COX enzymes likewise initiate the metabolism of: a) eicosapentaenoic acid, which has 5 double bonds compared to the 4 double bonds of arachidonic acid, to prostanoid, prostacyclin, and thromboxane products that have three double bonds, e.g. PGE3, PGI3, and TXA3 and b) Dihomo-γ-linolenic acid, which has three double bonds, to prostanoid, prostacyclin, and thromboxane products that have only one double bond, e.g. PGE1, PGI1, and TXA1. Lipoxygenases (LOXs): 5-Lipoxygenase (5-LOX or ALOX5) initiates the metabolism of arachidonic acid to 5-hydroperoxyeicosatetraenoic acid (5-HpETE) which then may be rapidly reduced to 5-hydroxyeicosatetraenoic acid (5-HETE) or further metabolized to the leukotrienes (e.g. LTB4 and LTC4); 5-HETE may be oxidized to 5-oxo-eicosatetraenoic acid (5-oxo-ETE). In similar fashions, 15-lipoxygenase (15-lipoxygenase 1, 15-LOX, 15-LOX1, or ALOX15) initiates the metabolism of arachidonic acid to 15-HpETE, 15-HETE, eoxins, 8,15-dihydroxyeicosatetraenoic acid (i.e. 8,15-DiHETE), and 15-oxo-ETE and 12-lipoxygenase (12-LOX or ALOX12) initiates the metabolism of arachidonic acid to 12-HpETE, 12-HETE, hepoxilins, and 12-oxo-ETE. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Berkson's fallacy </page_title> <path> Berkson's_fallacy > Statement > Explanation </path> <section_title> Explanation </section_title> <content> By comparing the conditional probability of A {\displaystyle A} to the unconditional probability of A {\displaystyle A}: P ( A | A ∪ B ) = 50 / 75 = 2 / 3 > P ( A ) = 50 / 100 = 1 / 2 {\displaystyle P(A|A\cup B)=50/75=2/3>P(A)=50/100=1/2} We see that the probability of A {\displaystyle A} is higher ( 2 / 3 {\displaystyle 2/3} ) in the subset of outcomes where ( A {\displaystyle A} or B {\displaystyle B} ) occurs, than in the overall population ( 1 / 2 {\displaystyle 1/2} ). On the other hand, the probability of A {\displaystyle A} given both B {\displaystyle B} and ( A {\displaystyle A} or B {\displaystyle B} ) is simply the unconditional probability of A {\displaystyle A} , P ( A ) {\displaystyle P(A)} , since A {\displaystyle A} is independent of B {\displaystyle B} . In the numerical example, we have conditioned on being in the top row: Here the probability of A {\displaystyle A} is 25 / 50 = 1 / 2 {\displaystyle 25/50=1/2} . Berkson's paradox arises because the conditional probability of A {\displaystyle A} given B {\displaystyle B} within the three-cell subset equals the conditional probability in the overall population, but the unconditional probability within the subset is inflated relative to the unconditional probability in the overall population, hence, within the subset, the presence of B {\displaystyle B} decreases the conditional probability of A {\displaystyle A} (back to its overall unconditional probability): P ( A | B , A ∪ B ) = P ( A | B ) = P ( A ) {\displaystyle P(A|B,A\cup B)=P(A|B)=P(A)} P ( A | A ∪ B ) > P ( A ) {\displaystyle P(A|A\cup B)>P(A)} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Euler polynomials </page_title> <path> Bernoulli_polynomial > Differences and derivatives > Symmetries </path> <section_title> Symmetries </section_title> <content> B n ( 1 − x ) = ( − 1 ) n B n ( x ) , n ≥ 0 , {\displaystyle B_{n}(1-x)=(-1)^{n}B_{n}(x),\quad n\geq 0,} E n ( 1 − x ) = ( − 1 ) n E n ( x ) {\displaystyle E_{n}(1-x)=(-1)^{n}E_{n}(x)} ( − 1 ) n B n ( − x ) = B n ( x ) + n x n − 1 {\displaystyle (-1)^{n}B_{n}(-x)=B_{n}(x)+nx^{n-1}} ( − 1 ) n E n ( − x ) = − E n ( x ) + 2 x n {\displaystyle (-1)^{n}E_{n}(-x)=-E_{n}(x)+2x^{n}} B n ( 1 2 ) = ( 1 2 n − 1 − 1 ) B n , n ≥ 0 from the multiplication theorems below. {\displaystyle B_{n}\left({\frac {1}{2}}\right)=\left({\frac {1}{2^{n-1}}}-1\right)B_{n},\quad n\geq 0{\text{ from the multiplication theorems below.}}} Zhi-Wei Sun and Hao Pan established the following surprising symmetry relation: If r + s + t = n and x + y + z = 1, then r n + s n + t n = 0 , {\displaystyle r_{n}+s_{n}+t_{n}=0,} where n = ∑ k = 0 n ( − 1 ) k ( s k ) ( t n − k ) B n − k ( x ) B k ( y ) . {\displaystyle _{n}=\sum _{k=0}^{n}(-1)^{k}{s \choose k}{t \choose {n-k}}B_{n-k}(x)B_{k}(y).} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Warming stripes </page_title> <path> Warming_stripes > Background, publication and content > Data sources and data visualization </path> <section_title> Data sources and data visualization </section_title> <content> Warming stripe graphics are defined with various parameters, including: source of dataset (meteorological organization) measurement location (global, country, state, etc.) time period (year range, for horizontal "axis") temperature range (range of anomaly (deviation) about a reference or baseline temperature) colour scale (assignment of colours to represent respective ranges of temperature anomaly), and colour choice (shades of blue and red), as well as temperature boundaries (temperature above which a stripe is red and below which is blue, determined by an average annual temperature over a "reference period" or "baseline" of usually 30 years).Hawkins' original graphics use the eight most saturated blues and reds from the ColorBrewer 9-class single hue palettes, which optimize colour palettes for maps and are noted for their colourblind-friendliness. Hawkins said the specific colour choice was an aesthetic decision ("I think they look just right"), also selecting baseline periods to ensure equally dark shades of blue and red for aesthetic balance.A Republik analysis said that "this graphic explains everything in the blink of an eye", attributing its effect mainly to the chosen colors, which "have a magical effect on our brain, (letting) us recognize connections before we have even actively thought about them". The analysis concluded that colors other than blue and red "don't convey the same urgency as (Hawkins') original graphic, in which the colors were used in the classic way: blue=cold, red=warm. "ShowYourStripes.info cites dataset sources Berkeley Earth, NOAA, UK Met Office, MeteoSwiss, DWD (Germany), specifically explaining that the data for most countries comes from the Berkeley Earth temperature dataset, except that for the US, UK, Switzerland & Germany the data comes from respective national meteorological agencies.For each country-level #ShowYourStripes graphic (Hawkins, June 2019), the average temperature in the 1971–2000 reference period is set as the boundary between blue (cooler) and red (warmer) colours, the colour scale varying +/- 2.6 standard deviations of the annual average temperatures between 1901 and 2000. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Supercompact cardinal </page_title> <path> Supercompact_cardinal > Formal definition </path> <section_title> Formal definition </section_title> <content> Then κ {\displaystyle \kappa } is supercompact means that it is λ {\displaystyle \lambda } -supercompact for all ordinals λ {\displaystyle \lambda } . Alternatively, an uncountable cardinal κ {\displaystyle \kappa } is supercompact if for every A {\displaystyle A} such that | A | ≥ κ {\displaystyle \vert A\vert \geq \kappa } there exists a normal measure over < κ {\displaystyle ^{<\kappa }} , in the following sense. < κ {\displaystyle ^{<\kappa }} is defined as follows: < κ := { x ⊆ A ∣ | x | < κ } {\displaystyle ^{<\kappa }:=\{x\subseteq A\mid \vert x\vert <\kappa \}} .An ultrafilter U {\displaystyle U} over < κ {\displaystyle ^{<\kappa }} is fine if it is κ {\displaystyle \kappa } -complete and { x ∈ < κ ∣ a ∈ x } ∈ U {\displaystyle \{x\in ^{<\kappa }\mid a\in x\}\in U} , for every a ∈ A {\displaystyle a\in A} . A normal measure over < κ {\displaystyle ^{<\kappa }} is a fine ultrafilter U {\displaystyle U} over < κ {\displaystyle ^{<\kappa }} with the additional property that every function f: < κ → A {\displaystyle f:^{<\kappa }\to A} such that { x ∈ < κ | f ( x ) ∈ x } ∈ U {\displaystyle \{x\in ^{<\kappa }|f(x)\in x\}\in U} is constant on a set in U {\displaystyle U} . Here "constant on a set in U {\displaystyle U} " means that there is a ∈ A {\displaystyle a\in A} such that { x ∈ < κ | f ( x ) = a } ∈ U {\displaystyle \{x\in ^{<\kappa }|f(x)=a\}\in U} . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Witt vectors </page_title> <path> Witt_vectors > Motivation > Detailed motivational sketch > Representing elements in Zp as elements in the ring of Witt vectors W(Fp) </path> <section_title> Representing elements in Zp as elements in the ring of Witt vectors W(Fp) </section_title> <content> The process is then repeated, subtracting ω ( x 1 ′ ) p {\displaystyle \omega (x'_{1})p} and proceed likewise. This yields a sequence of congruences x ≡ ω ( x 0 ) mod p x ≡ ω ( x 0 ) + ω ( x 1 ′ ) p mod p 2 ⋯ {\displaystyle {\begin{aligned}x&\equiv \omega (x_{0})&&{\bmod {p}}\\x&\equiv \omega (x_{0})+\omega (x'_{1})p&&{\bmod {p}}^{2}\\&\cdots \end{aligned}}} So that x ≡ ∑ j = 0 i ω ( x ¯ j ) p j mod p i + 1 {\displaystyle x\equiv \sum _{j=0}^{i}\omega ({\bar {x}}_{j})p^{j}{\bmod {p}}^{i+1}} and i ′ > i {\displaystyle i'>i} implies: ∑ j = 0 i ′ ω ( x ¯ j ) p j ≡ ∑ j = 0 i ω ( x ¯ j ) p j mod p i + 1 {\displaystyle \sum _{j=0}^{i'}\omega ({\bar {x}}_{j})p^{j}\equiv \sum _{j=0}^{i}\omega ({\bar {x}}_{j})p^{j}{\bmod {p}}^{i+1}} for x ¯ i := m ( x − ∑ j = 0 i − 1 ω ( x ¯ j ) p j p i ) . {\displaystyle {\bar {x}}_{i}:=m\left({\frac {x-\sum _{j=0}^{i-1}\omega ({\bar {x}}_{j})p^{j}}{p^{i}}}\right).} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> FD&C Red 40 </page_title> <path> FD&C_Red_40 > Studies on safety </path> <section_title> Studies on safety </section_title> <content> Allura Red has been heavily studied by food safety groups in North America and Europe, and remains in wide use. The UK's Food Standards Agency commissioned a study of six food dyes (tartrazine, Allura red, Ponceau 4R, Quinoline Yellow, sunset yellow, carmoisine (dubbed the "Southampton 6")), and sodium benzoate (a preservative) on children in the general population, who consumed them in beverages. The study found "a possible link between the consumption of these artificial colours and a sodium benzoate preservative and increased hyperactivity" in the children; the advisory committee to the FSA that evaluated the study also determined that because of study limitations, the results could not be extrapolated to the general population, and further testing was recommended.The European Food Safety Authority, with a stronger emphasis on the precautionary principle, required labelling and temporarily reduced the acceptable daily intake (ADI) for the food colorings; the UK FSA called for voluntary withdrawal of the colorings by food manufacturers. However, in 2009, the EFSA re-evaluated the data at hand and determined that "the available scientific evidence does not substantiate a link between the color additives and behavioral effects", and in 2014, after further review of the data, the European Food Safety Authority (EFSA) restored the prior ADI levels. In 2015, the EFSA found that the exposure estimates did not exceed the ADI of 7 mg/kg per day in any population.The US FDA did not make changes following the publication of the Southampton study, but following a citizen petition filed by the Center for Science in the Public Interest in 2008, requesting the FDA ban several food additives, the FDA commenced a review of the available evidence, but found no evidence to justify changes.Allura Red AC was at one time banned in Denmark, Belgium, France, and Switzerland, and was also banned in Sweden until the country joined the European Union in 1994. In Norway and Iceland, it was banned between 1978 and 2001, a period in which azo dyes were only legally used in alcoholic beverages and some fish products. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> DPANN </page_title> <path> DPANN > Classification > Taxonomy </path> <section_title> Taxonomy </section_title> <content> Probst et al. 2014 Phylum "Iainarchaeota" (DUSEL-3) Class "Iainarchaeia" Rinke et al. 2020 Order "Forterreales" Probst & Banfield 2017 Order "Iainarchaeales" Rinke et al. 2020 Phylum "Micrarchaeota" Baker & Dick 2013 Class "Micrarchaeia" Vazquez-Campos et al. 2021 Order "Anstonellales" Vazquez-Campos et al. 2021 (LFWA-IIIc) Order "Burarchaeales" Vazquez-Campos et al. 2021 (LFWA-IIIb) Order "Fermentimicrarchaeales" Kadnikov et al. 2020 Order "Gugararchaeales" Vazquez-Campos et al. 2021 (LFWA-IIIa) Order "Micrarchaeales" Vazquez-Campos et al. 2021 Order "Norongarragalinales" Vazquez-Campos et al. 2021 (LFWA-II) Phylum "Nanoarchaeota" Huber et al. 2002 Class "Nanoarchaeia" Vazquez-Campos et al. 2021 Order "Jingweiarchaeales" Rao et al. 2023 Order "Nanoarchaeales" Huber et al. 2011 Order "Pacearchaeales" (DHVE-5, DUSEL-1) Order "Parvarchaeales" Rinke et al. 2020 (ARMAN 4 & 5) Order "Tiddalikarchaeales" Vazquez-Campos et al. 2021 (LFW-252_1) Order "Woesearchaeales" (DHVE-6) Phylum ? "Mamarchaeota" Order ? "Wiannamattarchaeales" </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Stable count distribution </page_title> <path> Stable_count_distribution > Alternative derivation – lambda decomposition </path> <section_title> Alternative derivation – lambda decomposition </section_title> <content> Another approach to derive the stable count distribution is to use the Laplace transform of the one-sided stable distribution, (Section 2.4 of ) ∫ 0 ∞ e − z x L α ( x ) d x = e − z α , {\displaystyle \int _{0}^{\infty }e^{-zx}L_{\alpha }(x)\,dx=e^{-z^{\alpha }},} where 0 < α < 1 {\displaystyle 0<\alpha <1} .Let x = 1 / ν {\displaystyle x=1/\nu } , and one can decompose the integral on the left hand side as a product distribution of a standard Laplace distribution and a standard stable count distribution, 1 2 1 Γ ( 1 α + 1 ) e − | z | α = ∫ 0 ∞ 1 ν ( 1 2 e − | z | / ν ) ( 1 Γ ( 1 α + 1 ) 1 ν L α ( 1 ν ) ) d ν , {\displaystyle {\frac {1}{2}}{\frac {1}{\Gamma ({\frac {1}{\alpha }}+1)}}e^{-|z|^{\alpha }}=\int _{0}^{\infty }{\frac {1}{\nu }}\left({\frac {1}{2}}e^{-|z|/\nu }\right)\left({\frac {1}{\Gamma ({\frac {1}{\alpha }}+1)}}{\frac {1}{\nu }}L_{\alpha }\left({\frac {1}{\nu }}\right)\right)\,d\nu ,} where z ∈ R {\displaystyle z\in {\mathsf {R}}} . This is called the "lambda decomposition" (See Section 4 of ) since the LHS was named as "symmetric lambda distribution" in Lihn's former works. However, it has several more popular names such as "exponential power distribution", or the "generalized error/normal distribution", often referred to when α > 1 {\displaystyle \alpha >1} . It is also the Weibull survival function in Reliability engineering. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Driver Monitoring System </page_title> <path> Driver_Monitoring_System > Vehicles </path> <section_title> Vehicles </section_title> <content> Lexus models that have adopted the Driver Monitoring System to date, listed by model year:: 2006-2011 Lexus GS 450h (not available as configured in the US market) 2010-2017 Lexus LS 460 2008-2017 Lexus LS 600h 2010 Lexus HS 250h 2010-2019 Lexus GX 460Toyota models that have adopted the Driver Monitoring System: 2008 Toyota Crown Hybrid (includes drowsiness detection)General Motors first demonstrated their Super Cruise hands free driving using Seeing Machines Driver Monitoring System in the Cadillac CT6, soon to be rolled out across 22 models. 2017 Cadillac CT6 2021 Cadillac EscaladeBMW models have adopted driver monitoring system in 2019 in the optional "BMW Live Cockpit Professional" available in: BMW 1 Series (F40) BMW 2 Series (F44) BMW 3 Series (G20) BMW 5 Series (G30) BMW 6 Series (G32) BMW 7 Series (G11) BMW 8 Series (G15) BMW X3 (G01) BMW X4 (G02) BMW X5 (G05) BMW X6 (G06) BMW X7 (G07) BMW Z4 (G29) BMW iX3The infrared cameras are in the top middle part of the instrument cluster, part of iDrive BMW Live Cockpit and driven by BMW Operating System 7.0. Ford use the Seeing Machines DMS with infrared LEDs in a module located on the steering column behind the steering wheel as part of their active drive assist hands free driving "BlueCruise" in the 2021 Ford Mustang Mach-E and the 2021 F-150. Ford Mustang Mach-E Ford F-SeriesMercedes-Benz have integrated the camera from their Seeing Machines driver monitoring system with the 3D instrument display, head-up display, lighting and car controls in the 2021 Mercedes-Benz S-Class (W223) model. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Kaniadakis Exponential distribution </page_title> <path> Kaniadakis_Exponential_distribution > Type II > Properties > Skewness </path> <section_title> Skewness </section_title> <content> The skewness of the κ-exponential distribution of type II may be computed thought: Thus, the skewness of the κ-exponential distribution of type II distribution is given by: Skew = − 2 ( 15 κ 6 + 6 κ 4 + 2 κ 2 + 1 ) β 3 σ κ 3 ( κ 2 − 1 ) 3 ( 36 κ 4 − 13 κ 2 + 1 ) for 0 ≤ κ < 1 / 3 {\displaystyle \operatorname {Skew} =-{\frac {2(15\kappa ^{6}+6\kappa ^{4}+2\kappa ^{2}+1)}{\beta ^{3}\sigma _{\kappa }^{3}(\kappa ^{2}-1)^{3}(36\kappa ^{4}-13\kappa ^{2}+1)}}\quad {\text{for}}\quad 0\leq \kappa <1/3} or Skew = 2 ( 15 κ 6 + 6 κ 4 + 2 κ 2 + 1 ) ( 1 − 9 κ 2 ) ( 2 κ 4 + 1 ) 1 − 4 κ 2 1 + 2 κ 4 for 0 ≤ κ < 1 / 3 {\displaystyle \operatorname {Skew} ={\frac {2(15\kappa ^{6}+6\kappa ^{4}+2\kappa ^{2}+1)}{(1-9\kappa ^{2})(2\kappa ^{4}+1)}}{\sqrt {\frac {1-4\kappa ^{2}}{1+2\kappa ^{4}}}}\quad {\text{for}}\quad 0\leq \kappa <1/3} The skewness of the ordinary exponential distribution is recovered in the limit κ → 0 {\displaystyle \kappa \rightarrow 0} . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Systemic vascular resistance </page_title> <path> Peripheral_resistance > Calculation > Pulmonary calculations </path> <section_title> Pulmonary calculations </section_title> <content> The pulmonary vascular resistance can be calculated in units of dyn·s·cm−5 as 80 ⋅ ( m e a n p u l m o n a r y a r t e r i a l p r e s s u r e − m e a n p u l m o n a r y a r t e r y w e d g e p r e s s u r e ) c a r d i a c o u t p u t {\displaystyle {\frac {80\cdot (mean\ pulmonary\ arterial\ pressure-mean\ pulmonary\ artery\ wedge\ pressure)}{cardiac\ output}}} where the pressures are measured in units of millimetres of mercury (mmHg) and the cardiac output is measured in units of litres per minute (L/min). The pulmonary artery wedge pressure (also called pulmonary artery occlusion pressure or PAOP) is a measurement in which one of the pulmonary arteries is occluded, and the pressure downstream from the occlusion is measured in order to approximately sample the left atrial pressure. Therefore, the numerator of the above equation is the pressure difference between the input to the pulmonary blood circuit (where the heart's right ventricle connects to the pulmonary trunk) and the output of the circuit (which is the input to the left atrium of the heart). The above equation contains a numerical constant to compensate for the units used, but is conceptually equivalent to the following: R = Δ P Q {\displaystyle R={\frac {\Delta P}{Q}}} where R is the pulmonary vascular resistance (fluid resistance), ΔP is the pressure difference across the pulmonary circuit, and Q is the rate of blood flow through it. As an example: If Systolic pressure: 120 mmHg, Diastolic pressure: 80 mmHg, Right atrial mean pressure: 3 mmHg, Cardiac output: 5 L/min, Then mean arterial pressure would be: (2 diastolic pressure + systolic pressure)/3 = 93.3 mmHg, and systemic vascular resistance: (93 - 3) / 5 = 18 Wood units, or equivalently 1440 dyn·s/cm5. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Procedural parameter </page_title> <path> Procedural_parameter > Example: Definite integral > Integrating over a disk </path> <section_title> Integrating over a disk </section_title> <content> Consider now the problem of integrating a given function g {\displaystyle g} , with two arguments, over a disk D {\displaystyle D} with given center ( x c , y c {\displaystyle xc,yc} ) and given radius R {\displaystyle R} . This problem can be reduced to two nested single-variable integrals by the change of variables ∫ ∫ D g ( x , y ) d x d y = ∫ 0 R z ( ∫ 0 2 π g ( x c + z cos t , y c + z sin t ) d t ) d z {\displaystyle \int \!\int _{D}g(x,y)\,\mathrm {d} x\,\mathrm {d} y=\int _{0}^{R}z\left(\int _{0}^{2\pi }g({\mathit {xc}}+z\cos t,{\mathit {yc}}+z\sin t)\,\mathrm {d} t\right)\,\mathrm {d} z} The following code implements the right-hand-side formula: procedure DiskIntg(g, xc, yc, R, n) procedure gring(z): procedure gpolar(t): float x, y x ← xc + z * cos(t) y ← yc + z * sin(t) return g(x, y) integer m ← round(n*z/R) return z * Intg(gpolar, 0, 2*π, m) return Intg(gring, 0, R, n) This code uses the integration procedure Intg in two levels. The outer level (last line) uses Intg to compute the integral of g r i n g ( z ) {\displaystyle gring(z)} for z {\displaystyle z} varying from 0 to R {\displaystyle R} . The inner level (next-to-last line) defines g r i n g ( z ) {\displaystyle gring(z)} as being the line integral of g ( x , y ) {\displaystyle g(x,y)} over the circle with center ( x c , y c ) {\displaystyle (xc,yc)} and radius z {\displaystyle z} . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Specific mass </page_title> <path> Orders_of_magnitude_(density) > Common units </path> <section_title> Common units </section_title> <content> The SI unit for density is: kilogram per cubic metre (kg/m3)The litre and tonne are not part of the SI, but are acceptable for use with it, leading to the following units: kilogram per litre (kg/L) gram per millilitre (g/mL) tonne per cubic metre (t/m3)Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m3). Liquid water has a density of about 1 kg/dm3, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm3. kilogram per cubic decimetre (kg/dm3) gram per cubic centimetre (g/cm3) 1 g/cm3 = 1000 kg/m3 megagram (metric ton) per cubic metre (Mg/m3)In US customary units density can be stated in: Avoirdupois ounce per cubic inch (1 g/cm3 ≈ 0.578036672 oz/cu in) Avoirdupois ounce per fluid ounce (1 g/cm3 ≈ 1.04317556 oz/US fl oz = 1.04317556 lb/US fl pint) Avoirdupois pound per cubic inch (1 g/cm3 ≈ 0.036127292 lb/cu in) pound per cubic foot (1 g/cm3 ≈ 62.427961 lb/cu ft) pound per cubic yard (1 g/cm3 ≈ 1685.5549 lb/cu yd) pound per US liquid gallon (1 g/cm3 ≈ 8.34540445 lb/US gal) pound per US bushel (1 g/cm3 ≈ 77.6888513 lb/bu) slug per cubic footImperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Klein–Kramers equation </page_title> <path> Klein–Kramers_equation > Solution near boundaries </path> <section_title> Solution near boundaries </section_title> <content> For a point-source boundary condition, the solution has an exact expression in terms of infinite sum and products: Here, the result is stated for the non-dimensional version of the Klein–Kramers equation: w ∂ f ( z , w ) ∂ z = ∂ ∂ w + ∂ 2 f ( z , w ) ∂ w 2 {\displaystyle w{\frac {\partial f(z,w)}{\partial z}}={\frac {\partial }{\partial w}}\left+{\frac {\partial ^{2}f(z,w)}{\partial w^{2}}}} In this representation, length and time are measured in units of ℓ = k B T / ( m ξ 2 ) {\displaystyle \ell ={\sqrt {k_{B}T/(m\xi ^{2})}}} and τ = ξ − 1 {\displaystyle \tau =\xi ^{-1}} , such that z ≡ x / ℓ {\displaystyle z\equiv x/\ell } and w ≡ p / ( m ℓ ξ ) {\displaystyle w\equiv p/(m\ell \xi )} are both dimensionless. If the boundary condition at z = 0 is g(w) = δ(w - w0), where w0 > 0, then the solution is f ( x , w ) = w 0 e − w 2 / 2 2 π {\displaystyle f(x,w)={\frac {w_{0}e^{-w^{2}/2}}{\sqrt {2\pi }}}\left} where G ± n ( w ) = ( − 1 ) n 2 − n / 2 e − n ( n ! ) − 1 / 2 e ± n w H n ( w 2 ∓ 2 n ) , n = 1 , 2 , 3 , … S n ( w 0 ) = G n ( w 0 ) 2 2 − 1 2 n Q n − ∑ m = 1 ∞ G − m ( w 0 ) 4 ( m n + m n ) Q m Q n Q n = lim N → ∞ n ! </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Cornish phonology </page_title> <path> Cornish_phonology > Historical phonology > From Proto-Brittonic to Late (Southwestern) Brittonic c. 1 — 800 AD </path> <section_title> From Proto-Brittonic to Late (Southwestern) Brittonic c. 1 — 800 AD </section_title> <content> c. 50–100: *s becomes *Σ (word-initially, before vowels) or is lost (internally)*selgā 'hunt' > *Σelgā late 1st century: *ai is monophthongized to *ɛ̄*kaitV- 'wood' > *kɛ̄tV- *eu (perhaps already merged with *ou in Proto-Celtic) and *ou are monophthongized to *ō̝*teutā 'people' > *tō̝tā *roudos 'red' > *rō̝dos *au is monophthongized to *ō̜ according to Schrijver, but to *ō̝ according to Jackson*au-beros 'vain, empty' > *ō̜-beros vowel reduction in proclitics and final syllables *ū is fronted to *ǖ (internally and word-finally) *oi is monophthongized to *ū, perhaps with *ō̝ as an intermediate step non-syllabic *i̯ is strengthened to *j by the 1st–2nd century: stress shifts from the initial syllable to the penultimate syllable end of 3rd century: *ō̝ and Latin internal *ō̝ are raised to ū 4th–early 5th centuries *j becomes *ð in certain contexts c. 400–450 word-finally, *x becomes *s final a-affection: final *ā (and perhaps also *ă from Latin loans) lowers *ĭ and *ŭ in the preceding syllable:*ĭ > *ĕ *ŭ > *ŏ c. 450: *ǖ (from Proto-Indo-European *ū and PIE and Latin word-final *ō) is fronted, and merges with *ī*dǖnən 'fort' > *dīnən c. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Epicycloid </page_title> <path> Epicycloid > Proof </path> <section_title> Proof </section_title> <content> We assume that the position of p {\displaystyle p} is what we want to solve, α {\displaystyle \alpha } is the angle from the tangential point to the moving point p {\displaystyle p} , and θ {\displaystyle \theta } is the angle from the starting point to the tangential point. Since there is no sliding between the two cycles, then we have that ℓ R = ℓ r {\displaystyle \ell _{R}=\ell _{r}} By the definition of angle (which is the rate arc over radius), then we have that ℓ R = θ R {\displaystyle \ell _{R}=\theta R} and ℓ r = α r {\displaystyle \ell _{r}=\alpha r} .From these two conditions, we get the identity θ R = α r {\displaystyle \theta R=\alpha r} .By calculating, we get the relation between α {\displaystyle \alpha } and θ {\displaystyle \theta } , which is α = R r θ {\displaystyle \alpha ={\frac {R}{r}}\theta } .From the figure, we see the position of the point p {\displaystyle p} on the small circle clearly. x = ( R + r ) cos θ − r cos ( θ + α ) = ( R + r ) cos θ − r cos ( R + r r θ ) {\displaystyle x=\left(R+r\right)\cos \theta -r\cos \left(\theta +\alpha \right)=\left(R+r\right)\cos \theta -r\cos \left({\frac {R+r}{r}}\theta \right)} y = ( R + r ) sin θ − r sin ( θ + α ) = ( R + r ) sin θ − r sin ( R + r r θ ) {\displaystyle y=\left(R+r\right)\sin \theta -r\sin \left(\theta +\alpha \right)=\left(R+r\right)\sin \theta -r\sin \left({\frac {R+r}{r}}\theta \right)} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Aerostatics </page_title> <path> Aerostatics > Basic laws </path> <section_title> Basic laws </section_title> <content> Treatment of the equations of gaseous behaviour at rest is generally taken, as in hydrostatics, to begin with a consideration of the general equations of momentum for fluid flow, which can be expressed as: ρ = − ∂ P ∂ x j − ∂ τ i j ∂ x i + ρ g j {\displaystyle \rho =-{\partial P \over \partial x_{j}}-{\partial \tau _{ij} \over \partial x_{i}}+\rho g_{j}} , where ρ {\displaystyle \rho } is the mass density of the fluid, U j {\displaystyle U_{j}} is the instantaneous velocity, P {\displaystyle P} is fluid pressure, g {\displaystyle g} are the external body forces acting on the fluid, and τ i j {\displaystyle \tau _{ij}} is the momentum transport coefficient. As the fluid's static nature mandates that U j = 0 {\displaystyle U_{j}=0} , and that τ i j = 0 {\displaystyle \tau _{ij}=0} , the following set of partial differential equations representing the basic equations of aerostatics is found. : 154 ∂ P ∂ x j = ρ g j {\displaystyle {\partial P \over \partial x_{j}}=\rho g_{j}} However, the presence of a non-constant density as is found in gaseous fluid systems (due to the compressibility of gases) requires the inclusion of the ideal gas law: P ρ = R T {\displaystyle {P \over \rho }=RT} , where R {\displaystyle R} denotes the universal gas constant, and T {\displaystyle T} the temperature of the gas, in order to render the valid aerostatic partial differential equations: ∂ P ∂ x j = ρ g j ^ = P R T g j ^ {\displaystyle {\partial P \over \partial x_{j}}=\rho {\hat {g_{j}}}={P \over \ RT}{\hat {g_{j}}}} , which can be employed to compute the pressure distribution in gases whose thermodynamic states are given by the equation of state for ideal gases. : 183 </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Hill yield criteria </page_title> <path> Hill_yield_criteria > Generalized Hill yield criterion > Generalized Hill yield criterion for anisotropic material </path> <section_title> Generalized Hill yield criterion for anisotropic material </section_title> <content> For transversely isotropic materials with 1 − 2 {\displaystyle 1-2} being the plane of symmetry, the generalized Hill yield criterion reduces to (with F = G {\displaystyle F=G} and L = M {\displaystyle L=M} ) f := F | σ 2 − σ 3 | m + G | σ 3 − σ 1 | m + H | σ 1 − σ 2 | m + L | 2 σ 1 − σ 2 − σ 3 | m + L | 2 σ 2 − σ 3 − σ 1 | m + N | 2 σ 3 − σ 1 − σ 2 | m − σ y m ≤ 0 {\displaystyle {\begin{aligned}f:=&F|\sigma _{2}-\sigma _{3}|^{m}+G|\sigma _{3}-\sigma _{1}|^{m}+H|\sigma _{1}-\sigma _{2}|^{m}+L|2\sigma _{1}-\sigma _{2}-\sigma _{3}|^{m}\\&+L|2\sigma _{2}-\sigma _{3}-\sigma _{1}|^{m}+N|2\sigma _{3}-\sigma _{1}-\sigma _{2}|^{m}-\sigma _{y}^{m}\leq 0\end{aligned}}} The R-value or Lankford coefficient can be determined by considering the situation where σ 1 > ( σ 2 = σ 3 = 0 ) {\displaystyle \sigma _{1}>(\sigma _{2}=\sigma _{3}=0)} . The R-value is then given by R = ( 2 m − 1 + 2 ) L − N + H ( 2 m − 1 − 1 ) L + 2 N + F . {\displaystyle R={\cfrac {(2^{m-1}+2)L-N+H}{(2^{m-1}-1)L+2N+F}}~.} </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Zhukovsky Air Force Engineering Academy </page_title> <path> Zhukovsky_Air_Force_Engineering_Academy > Chiefs of the academy </path> <section_title> Chiefs of the academy </section_title> <content> The following have served as chiefs of the academy: 1922—1923 — Alexander Vegener Russian: ru:Вегенер, Александр Николаевич 1924—1925 — Nikolai Sollogub 1925—1927 — Vladimir Lazarevich Russian: ru:Лазаревич, Владимир Саламанович 1927—1933 — Sergey Horkov Russian: ru:Хорьков, Сергей Григорьевич 1934—1936 — Alexander Todorsky 1936—1940 — Zinoviy Pomerantsev Russian: ru:Померанцев, Зиновий Максимович 1940—1941 — Nikolay Sokolov-Sokolenok Russian: ru:Соколов-Соколёнок, Николай Александрович 1941—1942 — Stepan Hadeev Russian: ru:Хадеев, Степан Петрович 1942—1947 — Nikolay Sokolov-Sokolenok Russian: ru:Соколов-Соколёнок, Николай Александрович 1947—1969 — Vladimir Volkov Russian: Волков, Владимир Иванович 1969—1973 — Nikolay Fedayev Russian: ru:Федяев, Николай Максимович 1973—1986 — Vasiliy Filippov Russian: ru:Филиппов, Василий Васильевич 1986—1992 — Vitaliy Kremlev Russian: ru:Кремлёв, Виталий Яковлевич 1992—2002 — Vladimir Kovalyonok с 2002 — Anatoly Maksimov Russian: ru:Максимов, Анатолий Николаевич </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Shape operator </page_title> <path> Differential_geometry_of_surfaces > Geodesic curves on a surface > Geodesics </path> <section_title> Geodesics </section_title> <content> By the Euler–Lagrange equations, if c(t) is a path minimising length, parametrized by arclength, it must satisfy the Euler equations x ¨ + Γ 11 1 x ˙ 2 + 2 Γ 12 1 x ˙ y ˙ + Γ 22 1 y ˙ 2 = 0 {\displaystyle {\ddot {x}}+\Gamma _{11}^{1}{\dot {x}}^{2}+2\Gamma _{12}^{1}{\dot {x}}{\dot {y}}+\Gamma _{22}^{1}{\dot {y}}^{2}=0} y ¨ + Γ 11 2 x ˙ 2 + 2 Γ 12 2 x ˙ y ˙ + Γ 22 2 y ˙ 2 = 0 {\displaystyle {\ddot {y}}+\Gamma _{11}^{2}{\dot {x}}^{2}+2\Gamma _{12}^{2}{\dot {x}}{\dot {y}}+\Gamma _{22}^{2}{\dot {y}}^{2}=0} where the Christoffel symbols Γkij are given by Γ i j k = 1 2 ∑ m g k m ( ∂ j g i m + ∂ i g j m − ∂ m g i j ) {\displaystyle \Gamma _{ij}^{k}={\tfrac {1}{2}}\sum _{m}g^{km}(\partial _{j}g_{im}+\partial _{i}g_{jm}-\partial _{m}g_{ij})} where g11 = E, g12 = F, g22 = G and gij is the inverse matrix to gij. A path satisfying the Euler equations is called a geodesic. By the Cauchy–Schwarz inequality a path minimising energy is just a geodesic parametrised by arc length; and, for any geodesic, the parameter t is proportional to arclength. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> PDE1 </page_title> <path> PDE1 > Inhibitors and their function </path> <section_title> Inhibitors and their function </section_title> <content> PDEs have been pursued as therapeutic targets because of the basic pharmacological principle that regulation of degradation of any ligand or second messenger can often make a more rapid and larger percentage change in concentration than comparable rates of synthesis. Another reason is that PDEs do not have to compete with very high levels of endogenous substrate to be effective since the levels of cAMP and cGMP in most cells are typically in the micromolar range.The availability of high-resolution crystal structures of the catalytic domains of PDEs makes the development of highly potent and specific inhibitors possible.Many compounds reported as PDE1 inhibitors do not interact directly with the catalytic site of PDE1 but interact during activation, either at the level of calmodulin binding sites such as compound KS505a or directly on Ca2+/calmodulin such as bepril, flunarizine and amiodarone.Those inhibitors that interact with the catalytic site occupy part of the active site, primarily around the Q pocket and occasionally close to the M pocket. A major point of interaction is a conserved hydrophobic pocket that is involved in orienting the substrate purine ring for interaction with a glutamine residue that is crucial for the catalytic mechanism of the PDEs.The interactions of inhibitors can be split into three major types: interactions with the metal ions mediated through water, H-bond interactions with the protein residues involved in nucleotide recognition and most importantly the interaction with the hydrophobic residues lining the cavity of the active site. All known inhibitors seem to exploit these three types of interactions and hence these interactions should guide the design of new types of inhibitors.Initially PDE1 inhibitors were claimed to be effective vascular relaxants. With availability of purified cloned enzymes, however, it is now known that such inhibitors are in fact equally active against PDE5. Those inhibitors include e.g. zaprinast, 8-methoxymethyl IPMX and SCH 51866.All therapeutically effective PDE inhibitors must be incorporated into the cell because all PDEs are localized in the cytoplasm and/or on intracellular membranes.Today, there is no real and effective specific PDE1 inhibitor that can be used to assess the functional role of PDE1 in tissues. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Hindu units of time </page_title> <path> Hindu_units_of_time > Cosmic metrics > Brahma > Current kalpa </path> <section_title> Current kalpa </section_title> <content> A kalpa (day of Brahma, 12 hours) lasts for 4.32 billion years, where the current (Shveta-Varaha Kalpa) is the 1st of 30 in his 1st month of his 51st year: Started in past:= elapsed 7th manvantara + 7 manvantara-sandhyas + 6 manvantaras = elapsed 28th chatur-yuga + 27 chatur-yugas + 7 manvantara-sandhyas + 6 manvantaras = chatur-yuga - Kali-yuga + elapsed Kali-yuga + 27 chatur-yugas + 7 manvantara-sandhyas + 6 manvantaras = ((4,320,000 - 432,000 + (2023 + 3102 - 1)) + 4,320,000 * 27) + 1,728,000 * 7 + 306,720,000 * 6 = 1,972,949,124 years ≈ 1.97 billion yearsEnds in future:= remaining 7th manvantara + 8 manvantara-sandhyas + 7 manvantaras = remaining 28th chatur-yuga + 43 chatur-yugas + 8 manvantara-sandhyas + 7 manvantaras = Kali-yuga - elapsed Kali-yuga + 43 chatur-yugas + 8 manvantara-sandhyas + 7 manvantaras = ((432,000 - (2023 + 3102 - 1)) + 4,320,000 * 43) + 1,728,000 * 8 + 306,720,000 * 7 = 2,347,050,876 years ≈ 2.35 billion years </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Super-Earth </page_title> <path> Super_Earth > Characteristics > Density and bulk composition </path> <section_title> Density and bulk composition </section_title> <content> For example, formation and evolution calculations of the Kepler-11 planetary system show that the two innermost planets Kepler-11b and c, whose calculated mass is ≈2 M🜨 and between ≈5 and 6 M🜨 respectively (which are within measurement errors), are extremely vulnerable to envelope loss. In particular, the complete removal of the primordial H/He envelope by energetic stellar photons appears almost inevitable in the case of Kepler-11b, regardless of its formation hypothesis.If a super-Earth is detectable by both the radial-velocity and the transit methods, then both its mass and its radius can be determined; thus its average bulk density can be calculated. The actual empirical observations are giving similar results as theoretical models, as it's found that planets larger than approximately 1.6 Earth-radius (more massive than approximately 6 Earth-masses) contain significant fractions of volatiles or H/He gas (such planets appear to have a diversity of compositions that is not well-explained by a single mass-radius relation as that found in rocky planets). After measuring 65 super-Earths smaller than 4 Earth-radii, the empirical data points out that Gas Dwarves would be the most usual composition: there is a trend where planets with radii up to 1.5 Earth-radii increase in density with increasing radius, but above 1.5 radii the average planet density rapidly decreases with increasing radius, indicating that these planets have a large fraction of volatiles by volume overlying a rocky core. Another discovery about exoplanets' composition is that about the gap or rarity observed for planets between 1.5 and 2.0 Earth-radii, which is explained by a bimodal formation of planets (rocky Super-Earths below 1.75 and sub-Neptunes with thick gas envelopes being above such radii).Additional studies, conducted with lasers at the Lawrence Livermore National Laboratory and the OMEGA laboratory at the University of Rochester, show that the magnesium-silicate internal regions of the planet would undergo phase changes under the immense pressures and temperatures of a super-Earth planet, and that the different phases of this liquid magnesium silicate would separate into layers. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Grad–Shafranov equation </page_title> <path> Grad–Shafranov_equation > Derivation (in Cartesian coordinates) </path> <section_title> Derivation (in Cartesian coordinates) </section_title> <content> This means that j ⊥ × B ⊥ = 0 {\displaystyle \mathbf {j} _{\perp }\times \mathbf {B} _{\perp }=0} , i.e. j ⊥ {\displaystyle \mathbf {j} _{\perp }} is parallel to B ⊥ {\displaystyle \mathbf {B} _{\perp }} . The right hand side of the previous equation can be considered in two parts: where the ⊥ {\displaystyle \perp } subscript denotes the component in the plane perpendicular to the z {\displaystyle z} -axis. The z {\displaystyle z} component of the current in the above equation can be written in terms of the one-dimensional vector potential as The in plane field is and using Maxwell–Ampère's equation, the in plane current is given by In order for this vector to be parallel to B ⊥ {\displaystyle \mathbf {B} _{\perp }} as required, the vector ∇ B z {\displaystyle \nabla B_{z}} must be perpendicular to B ⊥ {\displaystyle \mathbf {B} _{\perp }} , and B z {\displaystyle B_{z}} must therefore, like p {\displaystyle p} , be a field-line invariant. Rearranging the cross products above leads to and These results can be substituted into the expression for ∇ p {\displaystyle \nabla p} to yield: Since p {\displaystyle p} and B z {\displaystyle B_{z}} are constants along a field line, and functions only of A {\displaystyle A} , hence ∇ p = d p d A ∇ A {\displaystyle \nabla p={\frac {dp}{dA}}\nabla A} and ∇ B z = d B z d A ∇ A {\displaystyle \nabla B_{z}={\frac {dB_{z}}{dA}}\nabla A} . Thus, factoring out ∇ A {\displaystyle \nabla A} and rearranging terms yields the Grad–Shafranov equation: </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Inverse tangent integral </page_title> <path> Inverse_tangent_integral > Definition </path> <section_title> Definition </section_title> <content> The inverse tangent integral is defined by: Ti 2 ( x ) = ∫ 0 x arctan t t d t {\displaystyle \operatorname {Ti} _{2}(x)=\int _{0}^{x}{\frac {\arctan t}{t}}\,dt} The arctangent is taken to be the principal branch; that is, −π/2 < arctan(t) < π/2 for all real t.Its power series representation is Ti 2 ( x ) = x − x 3 3 2 + x 5 5 2 − x 7 7 2 + ⋯ {\displaystyle \operatorname {Ti} _{2}(x)=x-{\frac {x^{3}}{3^{2}}}+{\frac {x^{5}}{5^{2}}}-{\frac {x^{7}}{7^{2}}}+\cdots } which is absolutely convergent for | x | ≤ 1. {\displaystyle |x|\leq 1.} The inverse tangent integral is closely related to the dilogarithm Li 2 ( z ) = ∑ n = 1 ∞ z n n 2 {\textstyle \operatorname {Li} _{2}(z)=\sum _{n=1}^{\infty }{\frac {z^{n}}{n^{2}}}} and can be expressed simply in terms of it: Ti 2 ( z ) = 1 2 i ( Li 2 ( i z ) − Li 2 ( − i z ) ) {\displaystyle \operatorname {Ti} _{2}(z)={\frac {1}{2i}}\left(\operatorname {Li} _{2}(iz)-\operatorname {Li} _{2}(-iz)\right)} That is, Ti 2 ( x ) = Im ( Li 2 ( i x ) ) {\displaystyle \operatorname {Ti} _{2}(x)=\operatorname {Im} (\operatorname {Li} _{2}(ix))} for all real x. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Normal equations </page_title> <path> Ordinary_least_squares_regression > Linear model </path> <section_title> Linear model </section_title> <content> Suppose the data consists of n {\displaystyle n} observations { x i , y i } i = 1 n {\displaystyle \left\{\mathbf {x} _{i},y_{i}\right\}_{i=1}^{n}} . Each observation i {\displaystyle i} includes a scalar response y i {\displaystyle y_{i}} and a column vector x i {\displaystyle \mathbf {x} _{i}} of p {\displaystyle p} parameters (regressors), i.e., x i = T {\displaystyle \mathbf {x} _{i}=\left^{\mathsf {T}}} . In a linear regression model, the response variable, y i {\displaystyle y_{i}} , is a linear function of the regressors: y i = β 1 x i 1 + β 2 x i 2 + ⋯ + β p x i p + ε i , {\displaystyle y_{i}=\beta _{1}\ x_{i1}+\beta _{2}\ x_{i2}+\cdots +\beta _{p}\ x_{ip}+\varepsilon _{i},} or in vector form, y i = x i T β + ε i , {\displaystyle y_{i}=\mathbf {x} _{i}^{\mathsf {T}}{\boldsymbol {\beta }}+\varepsilon _{i},\,} where x i {\displaystyle \mathbf {x} _{i}} , as introduced previously, is a column vector of the i {\displaystyle i} -th observation of all the explanatory variables; β {\displaystyle {\boldsymbol {\beta }}} is a p × 1 {\displaystyle p\times 1} vector of unknown parameters; and the scalar ε i {\displaystyle \varepsilon _{i}} represents unobserved random variables (errors) of the i {\displaystyle i} -th observation. ε i {\displaystyle \varepsilon _{i}} accounts for the influences upon the responses y i {\displaystyle y_{i}} from sources other than the explanatory variables x i {\displaystyle \mathbf {x} _{i}} . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Vangelis </page_title> <path> Vangelis > Career > 1981–2002: Mainstream success > Solo albums and collaborations </path> <section_title> Solo albums and collaborations </section_title> <content> Vangelis collaborated in 1976 with Italian singer Patty Pravo with the album Tanto and with Italian singer Milva achieving success, especially in Germany, with the albums Ich hab' keine Angst also translated in French as Moi, Je N'ai Pas Peur (1981) and Geheimnisse in 1986 (I have no fear and Secrets), also translated in Italian as Tra due sogni.An Italian language Nana Mouskouri album featured her singing the Vangelis composition "Ti Amerò". Collaborations with lyricist Mikalis Bourboulis, sung by Maria Farantouri, included the tracks "Odi A", "San Elektra", and "Tora Xero".Vangelis released Soil Festivities in 1984. It was thematically inspired by the interaction between nature and its microscopic living creatures; Invisible Connections (1985) took inspiration from the world of elementary particles invisible to the naked eye; Mask (1985) was inspired by the theme of the mask, an obsolete artefact which was used in ancient times for concealment or amusement; and Direct (1988). The last of the aforementioned efforts was the first album to be recorded in Vangelis's post-Nemo Studios era.Vangelis performed his only concert in the U.S. on 7 November 1986 at Royce Hall on the campus of University of California, Los Angeles. It featured a special guest appearance by Jon Anderson.There were another five solo albums in the 1990s; The City (1990) was recorded during a stay in Rome in 1989, and reflected a day of bustling city life, from dawn until dusk; Voices (1995) featured sensual songs filled with nocturnal orchestrations; Oceanic (1996) thematically explored the mystery of underwater worlds and sea sailing; and two classical albums about El Greco – Foros Timis Ston Greco (1995), which had a limited release, and El Greco (1998), which was an expansion of the former. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Alternative comics </page_title> <path> Alternative_comics > From underground to alternative > List of publishers > Independent </path> <section_title> Independent </section_title> <content> ?–present) CrossGen (Cross Generation Entertainment) (1998–2004) Darby Pop Publishing (2013–present) Dark Horse Comics (1986–present) Desperado Publishing (2005–present); IDW Publishing imprint since 2009 Devil's Due Publishing (1999–present) Diego Comics Publishing (2012–present) Drawn & Quarterly (1990–present) Dynamite Entertainment (2005–present) Eclipse Comics (1978–1994) Emerald Star Comics (2013–present) Event Comics (1994–1999); absorbed by Marvel Comics FantaCo Enterprises (1978–1998) Fierce Comics (2005–present) First Comics (1983–1991) The Fourth Age (2021-present) Harrier Comics (U.K.) (1984–1989) Harris Comics (1985–2008) Hyperwerks (1997–present) IDW Publishing (2000–present) Image Comics (1992–present) In Planet Studio (2010–present) Iron Circus Comics (2007-present) keenspot (2000–present) Lion Forge Comics (2011–present) Malibu Comics (1986–1994); absorbed by Marvel Comics Markosia (2005–present) Millennium Publications (1990–2000) MonkeyBrain Books (??? ?–present) Moonstone Books (1995–present) NBM Publishing (1976, 1984–present) NOW Comics (1985–2006) Oni Press (1997–present) Papercutz (2005–present) Pendulum Press (1970–1994) Personality Comics (1991–1993) Radical Comics (2007–present) Raw Studios (??? </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Intersection (geometry) </page_title> <path> Line_segment_intersection > On a plane > Two smooth curves </path> <section_title> Two smooth curves </section_title> <content> As start values one can choose −1 and 1.5. The intersection points are: (−1.1073, −1.3578), (1.6011, 4.1046) 2: C 1: f 1 ( x , y ) = x 4 + y 4 − 1 = 0 , {\displaystyle C_{1}:f_{1}(x,y)=x^{4}+y^{4}-1=0,} C 2: f 2 ( x , y ) = ( x − 0.5 ) 2 + ( y − 0.5 ) 2 − 1 = 0 {\displaystyle C_{2}:f_{2}(x,y)=(x-0.5)^{2}+(y-0.5)^{2}-1=0} (see diagram). The Newton iteration ( x n + 1 y n + 1 ) = ( x n + δ x y n + δ y ) {\displaystyle {x_{n+1} \choose y_{n+1}}={x_{n}+\delta _{x} \choose y_{n}+\delta _{y}}} has to be performed, where ( δ x δ y ) {\displaystyle {\delta _{x} \choose \delta _{y}}} is the solution of the linear system ( ∂ f 1 ∂ x ∂ f 1 ∂ y ∂ f 2 ∂ x ∂ f 2 ∂ y ) ( δ x δ y ) = ( − f 1 − f 2 ) {\displaystyle {\begin{pmatrix}{\frac {\partial f_{1}}{\partial x}}&{\frac {\partial f_{1}}{\partial y}}\\{\frac {\partial f_{2}}{\partial x}}&{\frac {\partial f_{2}}{\partial y}}\end{pmatrix}}{\delta _{x} \choose \delta _{y}}={-f_{1} \choose -f_{2}}} at point ( x n , y n ) {\displaystyle (x_{n},y_{n})} . </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> IPhone 12 Pro Max </page_title> <path> IPhone_12_Pro_Max </path> <section_title> Summary </section_title> <content> The iPhone 12 Pro and iPhone 12 Pro Max are smartphones designed, developed, and marketed by Apple Inc. They are the flagship smartphones in the fourteenth generation of the iPhone, succeeding the iPhone 11 Pro and iPhone 11 Pro Max, respectively. They were unveiled alongside the iPhone 12 and iPhone 12 Mini at an Apple Special Event at Apple Park in Cupertino, California on October 13, 2020, with the iPhone 12 Pro being released on October 23, 2020, and the iPhone 12 Pro Max on November 13, 2020. They were discontinued on September 14, 2021, along with the iPhone XR, following the announcement of the iPhone 13 and iPhone 13 Pro. Major upgrades over the iPhone 11 Pro and iPhone 11 Pro Max include the addition of 5G support, the lidar sensor, ProRAW (DNG) allowing high quality lossless 12-bit image capture in the native photos app with the use of the new DNG v1.6 specification, the introduction of the MagSafe wireless charging and accessory system, the Apple A14 Bionic system on a chip (SoC), high-dynamic-range video Dolby Vision 10-bit 4:2:0 4K video recording at 30 or 60 fps, larger 6.1-inch and 6.7-inch displays on the iPhone 12 Pro and iPhone 12 Pro Max, respectively, and the move to a base capacity of 128 GB from the prior base capacity of 64 GB, while retaining the other storage capacities of 256 and 512 GB. The iPhone 12 Pro and iPhone 12 Pro Max, like the iPhone 12 and iPhone 12 Mini, are the first iPhone models from Apple to no longer include a power adapter or EarPods headphones found in prior iPhone models; however, a USB-C to Lightning cable is still included, and this change was retroactively applied to other iPhone models sold by Apple including the iPhone XR, iPhone 11 and iPhone SE (2nd generation). </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Exterior differentiation </page_title> <path> Exterior_differentiation > Exterior derivative in vector calculus > Invariant formulations of operators in vector calculus </path> <section_title> Invariant formulations of operators in vector calculus </section_title> <content> The standard vector calculus operators can be generalized for any pseudo-Riemannian manifold, and written in coordinate-free notation as follows: grad f ≡ ∇ f = ( d f ) ♯ div F ≡ ∇ ⋅ F = ⋆ d ⋆ ( F ♭ ) curl F ≡ ∇ × F = ( ⋆ d ( F ♭ ) ) ♯ Δ f ≡ ∇ 2 f = ⋆ d ⋆ d f ∇ 2 F = ( d ⋆ d ⋆ ( F ♭ ) − ⋆ d ⋆ d ( F ♭ ) ) ♯ , {\displaystyle {\begin{array}{rcccl}\operatorname {grad} f&\equiv &\nabla f&=&\left(df\right)^{\sharp }\\\operatorname {div} F&\equiv &\nabla \cdot F&=&{\star d{\star }{\mathord {\left(F^{\flat }\right)}}}\\\operatorname {curl} F&\equiv &\nabla \times F&=&\left({\star }d{\mathord {\left(F^{\flat }\right)}}\right)^{\sharp }\\\Delta f&\equiv &\nabla ^{2}f&=&{\star }d{\star }df\\&&\nabla ^{2}F&=&\left(d{\star }d{\star }{\mathord {\left(F^{\flat }\right)}}-{\star }d{\star }d{\mathord {\left(F^{\flat }\right)}}\right)^{\sharp },\\\end{array}}} where ⋆ is the Hodge star operator, ♭ and ♯ are the musical isomorphisms, f is a scalar field and F is a vector field. Note that the expression for curl requires ♯ to act on ⋆d(F♭), which is a form of degree n − 2. A natural generalization of ♯ to k-forms of arbitrary degree allows this expression to make sense for any n. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Random signal </page_title> <path> Stochastic_dynamics > Definitions > Stochastic process </path> <section_title> Stochastic process </section_title> <content> A stochastic process is defined as a collection of random variables defined on a common probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} , where Ω {\displaystyle \Omega } is a sample space, F {\displaystyle {\mathcal {F}}} is a σ {\displaystyle \sigma } -algebra, and P {\displaystyle P} is a probability measure; and the random variables, indexed by some set T {\displaystyle T} , all take values in the same mathematical space S {\displaystyle S} , which must be measurable with respect to some σ {\displaystyle \sigma } -algebra Σ {\displaystyle \Sigma } .In other words, for a given probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} and a measurable space ( S , Σ ) {\displaystyle (S,\Sigma )} , a stochastic process is a collection of S {\displaystyle S} -valued random variables, which can be written as: Historically, in many problems from the natural sciences a point t ∈ T {\displaystyle t\in T} had the meaning of time, so X ( t ) {\displaystyle X(t)} is a random variable representing a value observed at time t {\displaystyle t} . A stochastic process can also be written as { X ( t , ω ): t ∈ T } {\displaystyle \{X(t,\omega ):t\in T\}} to reflect that it is actually a function of two variables, t ∈ T {\displaystyle t\in T} and ω ∈ Ω {\displaystyle \omega \in \Omega } .There are other ways to consider a stochastic process, with the above definition being considered the traditional one. For example, a stochastic process can be interpreted or defined as a S T {\displaystyle S^{T}} -valued random variable, where S T {\displaystyle S^{T}} is the space of all the possible functions from the set T {\displaystyle T} into the space S {\displaystyle S} . However this alternative definition as a "function-valued random variable" in general requires additional regularity assumptions to be well-defined. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Oracle bone </page_title> <path> Dragon_bones > Publication </path> <section_title> Publication </section_title> <content> 殷墟文字甲編; Yinxu wenzi jiabian 殷墟文字乙編; Yinxu wenzi yibian 殷墟文字丙編; Yinxu wenzi bingbian 殷虛書契前編; Yin xu shu qi qian bian 集殷虛文字楹帖彙編; Ji Yin xu wen zi ying tie hui bian 殷墟萃編; Yinxu cuibian 后上; Houshang 后下; Houxia 粹編; Cuibian 殷虛書契續編; yīn xū shū qì xù biān 亀甲; Kikkō 殷契摭佚續編; Yinqizhiyi xubian 殷契遺珠; Yinqi yizhu 京都大學人文科学研究所蔵甲骨文字; Kyōto daigaku jimbunkagaku kenkyūshozō kōkotsumoji 殷契佚存; Yiqi yicun 甲骨綴合編; Jiagu zhuihebian 鐵雲藏龜拾遺; Tieyun canggui shiyi 戰後京津新獲甲骨集; Zhanhou Jingjin xinhuo jiaguji (1954) 殷墟文字存真; Yinxu wenzi cunzhen 戰後寧滬新獲甲骨集; Zhanhou Ninghu xinhuo jiaguji (1951)Observing that the citation of these different works was becoming unwieldy, an effort was made to comprehensively publish all bones hitherto discovered. The result—the Jiǎgǔwén héjí (甲骨文合集, 1978–1982) edited by Hu Houxuan, with its supplement (1999) edited by Peng Bangjiong, is the most comprehensive catalogue of oracle bone fragments. The 20 volumes contain reproductions of over 55,000 fragments. A separate work published in 1999 contains transcriptions of the inscriptions into standard characters. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Autoregressive conditional heteroskedasticity </page_title> <path> Autoregressive_conditional_heteroscedasticity > GARCH > GARCH(p, q) model specification </path> <section_title> GARCH(p, q) model specification </section_title> <content> The lag length p of a GARCH(p, q) process is established in three steps: Estimate the best fitting AR(q) model y t = a 0 + a 1 y t − 1 + ⋯ + a q y t − q + ϵ t = a 0 + ∑ i = 1 q a i y t − i + ϵ t {\displaystyle y_{t}=a_{0}+a_{1}y_{t-1}+\cdots +a_{q}y_{t-q}+\epsilon _{t}=a_{0}+\sum _{i=1}^{q}a_{i}y_{t-i}+\epsilon _{t}} . Compute and plot the autocorrelations of ϵ 2 {\displaystyle \epsilon ^{2}} by ρ = ∑ t = i + 1 T ( ϵ ^ t 2 − σ ^ t 2 ) ( ϵ ^ t − 1 2 − σ ^ t − 1 2 ) ∑ t = 1 T ( ϵ ^ t 2 − σ ^ t 2 ) 2 {\displaystyle \rho ={{\sum _{t=i+1}^{T}({\hat {\epsilon }}_{t}^{2}-{\hat {\sigma }}_{t}^{2})({\hat {\epsilon }}_{t-1}^{2}-{\hat {\sigma }}_{t-1}^{2})} \over {\sum _{t=1}^{T}({\hat {\epsilon }}_{t}^{2}-{\hat {\sigma }}_{t}^{2})^{2}}}} The asymptotic, that is for large samples, standard deviation of ρ ( i ) {\displaystyle \rho (i)} is 1 / T {\displaystyle 1/{\sqrt {T}}} . Individual values that are larger than this indicate GARCH errors. To estimate the total number of lags, use the Ljung–Box test until the value of these are less than, say, 10% significant. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Equidistant conic projection </page_title> <path> Equidistant_conic_projection > Transformation </path> <section_title> Transformation </section_title> <content> Coordinates from a spherical datum can be transformed to an equidistant conic projection with rectangular coordinates by using the following formulas, where λ is the longitude, λ0 the reference longitude, φ the latitude, φ0 the reference latitude, and φ1 and φ2 the standard parallels: x = ρ sin y = ρ 0 − ρ cos {\displaystyle {\begin{aligned}x&=\rho \sin \left\\y&=\rho _{0}-\rho \cos \left\end{aligned}}} where ρ = ( G − φ ) {\displaystyle \rho =(G-\varphi )} ρ 0 = ( G − φ 0 ) {\displaystyle \rho _{0}=(G-\varphi _{0})} G = cos φ 1 n + φ 1 {\displaystyle G={\frac {\cos {\varphi _{1}}}{n}}+\varphi _{1}} n = cos φ 1 − cos φ 2 φ 2 − φ 1 {\displaystyle n={\frac {\cos {\varphi _{1}}-\cos {\varphi _{2}}}{\varphi _{2}-\varphi _{1}}}} Constants n, G, and ρ0 need only be determined once for the entire map. If one standard parallel is used (i.e. φ1 = φ2), the formula for n above is indeterminate, but then n = sin φ 1 {\displaystyle n=\sin {\varphi _{1}}} The reference point (λ0, φ0) with longitude λ0 and latitude φ0, transforms to the x,y origin at (0,0) in the rectangular coordinate system.The Y axis maps the central meridian λ0, with y increasing northwards, which is orthogonal to the X axis mapping the central parallel φ0, with x increasing eastwards.Other versions of these transformation formulae include parameters to offset the map coordinates so that all x,y values are positive, as well as a scaling parameter relating the radius of the sphere (earth) to the units used on the map.The formulae used for ellipsoidal datums are more involved. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Dynamic discrete choice </page_title> <path> Dynamic_discrete_choice > Mathematical representation </path> <section_title> Mathematical representation </section_title> <content> Agent n {\displaystyle n} 's maximization problem can be written mathematically as follows: V ( x n 0 ) = max { d n t } t = 1 T E ( ∑ t ′ = t T ∑ i = 1 J β t ′ − t ( d n t = i ) U n i t ( x n t , ε n i t ) ) , {\displaystyle V\left(x_{n0}\right)=\max _{\left\{d_{nt}\right\}_{t=1}^{T}}\mathbb {E} \left(\sum _{t^{\prime }=t}^{T}\sum _{i=1}^{J}\beta ^{t'-t}\left(d_{nt}=i\right)U_{nit}\left(x_{nt},\varepsilon _{nit}\right)\right),} where x n t {\displaystyle x_{nt}} are state variables, with x n 0 {\displaystyle x_{n0}} the agent's initial condition d n t {\displaystyle d_{nt}} represents n {\displaystyle n} 's decision from among J {\displaystyle J} discrete alternatives β ∈ ( 0 , 1 ) {\displaystyle \beta \in \left(0,1\right)} is the discount factor U n i t {\displaystyle U_{nit}} is the flow utility n {\displaystyle n} receives from choosing alternative i {\displaystyle i} in period t {\displaystyle t} , and depends on both the state x n t {\displaystyle x_{nt}} and unobserved factors ε n i t {\displaystyle \varepsilon _{nit}} T {\displaystyle T} is the time horizon The expectation E ( ⋅ ) {\displaystyle \mathbb {E} \left(\cdot \right)} is taken over both the x n t {\displaystyle x_{nt}} 's and ε n i t {\displaystyle \varepsilon _{nit}} 's in U n i t {\displaystyle U_{nit}} . That is, the agent is uncertain about future transitions in the states, and is also uncertain about future realizations of unobserved factors. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Intangible Cultural Heritage of the Philippines </page_title> <path> Intangible_Cultural_Heritage_of_the_Philippines > National Living Treasures </path> <section_title> National Living Treasures </section_title> <content> 2015) textile weaver, Lake Sebu, South Cotabato, Weaving (T'nalak), 1998 Salinta Monon (d. 2009), weaver, Bansalan, Davao del Sur, Weaving (Abaca – ikat / Inabal), 1998 Alonzo Saclag, musician and dancer, Lubugan, Kalinga Province, Music and Dance (Kalinga), 2000 Frederico Caballero, epic chanter, Sulod- Bukidnon, Iloilo, Poetry / Epic Chant (Sugidanon), 2000 Uwang Ahadas, musician, Lamitan, Basilan, music (Yakan specifically Kulintang, kwitangan kayu, gabbang, agung, and tuntungan), 2000 Darhata Sawabi, (d. 2005), weaver, Parang, Sulu, weaving (Pis Syabit), 2004 Eduardo Mutuc, metalsmith / metal sculptor, Apalit, Pampanga, Metalwork (Bronze and Silver), 2004 Haja Amina Appi (d. 2013), weaver, Tandubas, Tawi-Tawi, Weaving (Mat), 2004 Teofilo Garcia, casque maker, San Quintin, Abra, Casque Making (Tabungaw), 2012 Magdalena Gamayo, master weaver, Pinili, Ilocos Norte, Weaving (Inabel), 2012 Ambalang Ausalin, master weaver, Lamitan, Basilan, Weaving (Yakan tennun), 2016 Estelita Tumandan Bantilan, master weaver, Malapatan, Sarangani, Weaving (B'laan igem), 2016 Yabing Masalon Dulo, master weaver, Polomolok, South Cotabato, Weaving (Ikat), 2016 </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Antonov An-225 Mriya </page_title> <path> Antonov_An-225_Mriya > Specifications </path> <section_title> Specifications </section_title> <content> Data from Antonov's Heavy Transports, and othersGeneral characteristics Crew: 6 Capacity: 190 tonnes (420,000 lb) Length: 84 m (275 ft 7 in) Wingspan: 88.4 m (290 ft 0 in) Height: 18.1 m (59 ft 5 in) Wing area: 905 m2 (9,740 sq ft) Aspect ratio: 8.6 Empty weight: 285,000 kg (628,317 lb) Max takeoff weight: 640,000 kg (1,410,958 lb) Fuel capacity: more than 300,000 kilograms (660,000 lb) 375,000 L (82,488 imp gal; 99,065 US gal) Cargo hold: volume 1,300 m3 (46,000 cu ft), 43.35 m (142.2 ft) long × 6.4 m (21 ft) wide × 4.4 m (14 ft) tall Powerplant: 6 × Progress D-18T turbofans, 229.5 kN (51,600 lbf) thrust eachPerformance Maximum speed: 850 km/h (530 mph, 460 kn) Cruise speed: 800 km/h (500 mph, 430 kn) Range: 15,400 km (9,600 mi, 8,300 nmi) with maximum fuel; range with 200 tonnes payload: 4,000 km (2,500 mi) Service ceiling: 11,000 m (36,000 ft) Wing loading: 662.9 kg/m2 (135.8 lb/sq ft) Thrust/weight: 0.234 </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Vietnamese cash coins </page_title> <path> Vietnamese_cash_coin > History > Nguyễn dynasty > Under French rule </path> <section_title> Under French rule </section_title> <content> Money changers generally tended to value the piastre based on its weight in silver, but also according to the perfection of its strike, and even according to the purity of its silver. The official exchange rates were not rigorously applied and the money changers often estimated their own values to individual piastre coins.In order to combat deflation both the Government-General of French Indochina and the imperial government of the Nguyễn dynasty fixed the exchange rate of the newly introduced Khải Định Thông Bảo at 6 zinc cash coins according to an ordonnance entitled Fixing the exchange of the new cash coins bearing the reign era of Khải Định (Fixant la valeur d'échange de la nouvelle sapèque portant la chiffre de Règne Khai-Dinh) signed on 01-09-Khải Định 5 (12 October 1920) by five of the six ministers of the Nguyễn dynasty, the Khải Định Emperor, and the Governor-General of French Indochina Maurice Long. The imperial ordonnance noted that in the French protectorate of Tonkin the Gia Long Thông Bảo (嘉隆通寶) and the Minh Mạng Thông Bảo (明命通寶) as well as zinc cash coins were unanimously accepted, while the Thiệu Trị Thông Bảo (紹治通寶) and the Tự Đức Thông Bảo (嗣德通寶) cash coins weren't accepted by the local population. Meanwhile in the provinces of Nghệ An and Thanh Hóa they would sometimes all be accepted but at other times they would be refused like they were in Tonkin. The ordonnance stated that the people of Đại Nam are "warned that cash coins are for their daily life and serve as an article of their very first necessity" and that "there is no worse malaise than the scarcity of cash coins", while emphasising that the production costs of the currency is higher than their nominal and market value and that their continued production constitutes a heavy burden both for the French Indochinese and Nguyễn dynasty governments, but that the government prefers to bear this burden than let the people suffer from the negative consequences of their scarcity.The last monarch whose name was cast on cash coins, Emperor Bảo Đại, died in 1997. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Fisons, Immingham </page_title> <path> Courtaulds,_Grimsby > Grimsby – Immingham > Background </path> <section_title> Background </section_title> <content> Neighbouring Cleethorpes also developed as a residential area for Grimsby as well as a seaside resort during the 19th century. In the 20th century, port based industries formed the main economic activities, with fishing being particularly important, influencing other industries in the town, specifically food processing, in particular frozen foods. In the late 1960s around 3,500 were employed directly in the fishing industry; 10,000 were employed in food industries of which 6,000 was fish processing activities; 2,500 in shipbuilding and repair; other lesser employment activities included engineering, and timber related businesses. Most of Grimsby's industries were concentrated on the Dock's estate, and later Pyewipe, west of the main centre.In 1911 Immingham Dock was opened, constructed for the Great Central Railway, primarily for the export of coal; the new dock was located at a point where the deep water channel of the Humber Estuary swung close to the south bank, with estuary side jetties that and could handle ships up to 30,000 deadweight tonnage. In the interwar period industry was developed on the north bank of the Humber in out of town locations: petroleum refining at Salt End (BP Saltend); smelting and cement manufacture at Melton (Capper Pass and the Humber Cement Works); and aircraft at Brough (Blackburn Aeroplane & Motor Company, later British Aerospace).During the 1970s and early 1980s the fishing industry of Grimsby declined (to less than 15% of 1970 levels by tonnage by 1983) due to fuel costs (1973 fuel crisis), decline in fish stocks, Icelandic exclusion zones (see cod war), and new EEC fishing limits, though the port's market share remained roughly constant at around 20%, imported landings from Icelandic ships (as well as from ships of Norway, Faroes, Denmark, Belgium and Holland) became important to the continuation of Grimsby's role as a 'fish port'. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Paraboloidal coordinates </page_title> <path> Paraboloidal_coordinates > Applications </path> <section_title> Applications </section_title> <content> Taking ψ = M ( μ ) N ( ν ) Λ ( λ ) {\displaystyle \psi =M(\mu )N(\nu )\Lambda (\lambda )} , the separated equations are ( μ − b ) ( μ − c ) d 2 M d μ 2 + 1 2 d M d μ + M = 0 ( b − ν ) ( c − ν ) d 2 N d ν 2 + 1 2 d N d ν + N = 0 ( b − λ ) ( λ − c ) d 2 Λ d λ 2 − 1 2 d Λ d λ − Λ = 0 {\displaystyle {\begin{aligned}&(\mu -b)(\mu -c){\frac {d^{2}M}{d\mu ^{2}}}+{\frac {1}{2}}\left{\frac {dM}{d\mu }}+\leftM=0\\&(b-\nu )(c-\nu ){\frac {d^{2}N}{d\nu ^{2}}}+{\frac {1}{2}}\left{\frac {dN}{d\nu }}+\leftN=0\\&(b-\lambda )(\lambda -c){\frac {d^{2}\Lambda }{d\lambda ^{2}}}-{\frac {1}{2}}\left{\frac {d\Lambda }{d\lambda }}-\left\Lambda =0\\\end{aligned}}} where α 2 {\displaystyle \alpha _{2}} and α 3 {\displaystyle \alpha _{3}} are the two separation constants. Similarly, the separated equations for the Laplace equation can be obtained by setting k = 0 {\displaystyle k=0} in the above. Each of the separated equations can be cast in the form of the Baer equation. Direct solution of the equations is difficult, however, in part because the separation constants α 2 {\displaystyle \alpha _{2}} and α 3 {\displaystyle \alpha _{3}} appear simultaneously in all three equations. Following the above approach, paraboloidal coordinates have been used to solve for the electric field surrounding a conducting paraboloid. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Filioque clause </page_title> <path> Filioque_clause > History > Church Fathers > Cappadocian Fathers </path> <section_title> Cappadocian Fathers </section_title> <content> Basil of Caesarea wrote: "Through the one Son is joined to the Father". He also said that the "natural goodness, inherent holiness, and royal dignity reaches from the Father through the only-begotten (διὰ τοῦ Μονογενοῦς) to the Spirit". However, Siecienski comments that "there are passages in Basil that are certainly capable of being read as advocating something like the Filioque, but to do so would be to misunderstand the inherently soteriological thrust of his work".Gregory of Nazianzus distinguished the coming forth (προϊεον) of the Spirit from the Father from that of the Son from the Father by saying that the latter is by generation, but that of the Spirit by procession (ἐκπρόρευσις), a matter on which there is no dispute between East and West, as shown also by the Latin Father Augustine of Hippo, who wrote that although biblical exegetes had not adequately discussed the individuality of the Holy Spirit: they predicate Him to be the Gift of God, God not to give a gift inferior to Himself. predicate the Holy Spirit neither as begotten, like the Son, of the Father; nor of the Son, they do not affirm Him to owe that which He is to no one, to the Father, lest we should establish two Beginnings without beginning which would be an assertion at once false and absurd, and one proper not to the catholic faith, but to the error of . Gregory of Nyssa stated: The one (i.e. the Son) is directly from the First and the other (i.e., the Spirit) is through the one who is directly from the First (τὸ δὲ ἐκ τοῦ προσεχῶς ἐκ τοῦ πρώτου) with the result that the Only-begotten remains the Son and does not negate the Spirit's being from the Father since the middle position of the Son both protects His distinction as Only-begotten and does not exclude the Spirit from His natural relation to the Father. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Inertial reference frames </page_title> <path> Inertial_reference_frames > Non-inertial frames > Inertial frames and rotation </path> <section_title> Inertial frames and rotation </section_title> <content> In an inertial frame, Newton's first law, the law of inertia, is satisfied: Any free motion has a constant magnitude and direction. Newton's second law for a particle takes the form: F = m a , {\displaystyle \mathbf {F} =m\mathbf {a} \ ,} with F the net force (a vector), m the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame. The force F is the vector sum of all "real" forces on the particle, such as contact forces, electromagnetic, gravitational, and nuclear forces. In contrast, Newton's second law in a rotating frame of reference (a non-inertial frame of reference), rotating at angular rate Ω about an axis, takes the form: F ′ = m a , {\displaystyle \mathbf {F} '=m\mathbf {a} \ ,} which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms (the paragraph following this equation presents the main points without detailed mathematics): F ′ = F − 2 m Ω × v B − m Ω × ( Ω × x B ) − m d Ω d t × x B , {\displaystyle \mathbf {F} '=\mathbf {F} -2m\mathbf {\Omega } \times \mathbf {v} _{B}-m\mathbf {\Omega } \times (\mathbf {\Omega } \times \mathbf {x} _{B})-m{\frac {d\mathbf {\Omega } }{dt}}\times \mathbf {x} _{B}\ ,} where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation Ω, symbol × denotes the vector cross product, vector xB locates the body and vector vB is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer). </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Lyapunov dimension </page_title> <path> Lyapunov_dimension > Definitions > Definition via statistical physics approach and ergodicity </path> <section_title> Definition via statistical physics approach and ergodicity </section_title> <content> Following the statistical physics approach and assuming the ergodicity the Lyapunov dimension of attractor is estimated by limit value of the local Lyapunov dimension lim t → + ∞ dim L ( t , u 0 ) {\displaystyle \lim _{t\to +\infty }\dim _{\rm {L}}(t,u_{0})} of a typical trajectory, which belongs to the attractor. In this case { lim t → + ∞ L E i ( t , u 0 ) } i n = { L E i ( u 0 ) } 1 n {\displaystyle \{\lim \limits _{t\to +\infty }{\rm {LE}}_{i}(t,u_{0})\}_{i}^{n}=\{{\rm {LE}}_{i}(u_{0})\}_{1}^{n}} and dim L u 0 = d K Y ( { L E i ( u 0 ) } i = 1 n ) = j ( u 0 ) + L E 1 ( u 0 ) + ⋯ + L E j ( u 0 ) ( u 0 ) | L E j ( u 0 ) + 1 ( u 0 ) | {\displaystyle \dim _{\rm {L}}u_{0}=d_{\rm {KY}}(\{{\rm {LE}}_{i}(u_{0})\}_{i=1}^{n})=j(u_{0})+{\frac {{\rm {LE}}_{1}(u_{0})+\cdots +{\rm {LE}}_{j(u_{0})}(u_{0})}{|{\rm {LE}}_{j(u_{0})+1}(u_{0})|}}} . From a practical point of view, the rigorous use of ergodic Oseledec theorem, verification that the considered trajectory u ( t , u 0 ) {\displaystyle u(t,u_{0})} is a typical trajectory, and the use of corresponding Kaplan–Yorke formula is a challenging task (see, e.g. discussions in). </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Intensity (heat transfer) </page_title> <path> Intensity_(heat_transfer) </path> <section_title> Summary </section_title> <content> In the field of heat transfer, intensity of radiation I {\displaystyle I} is a measure of the distribution of radiant heat flux per unit area and solid angle, in a particular direction, defined according to d q = I d ω cos θ d A {\displaystyle dq=I\,d\omega \,\cos \theta \,dA} where d A {\displaystyle dA} is the infinitesimal source area d q {\displaystyle dq} is the outgoing heat transfer from the area d A {\displaystyle dA} d ω {\displaystyle d\omega } is the solid angle subtended by the infinitesimal 'target' (or 'aperture') area d A a {\displaystyle dA_{a}} θ {\displaystyle \theta } is the angle between the source area normal vector and the line-of-sight between the source and the target areas.Typical units of intensity are W·m−2·sr−1. Intensity can sometimes be called radiance, especially in other fields of study. The emissive power of a surface can be determined by integrating the intensity of emitted radiation over a hemisphere surrounding the surface: q = ∫ ϕ = 0 2 π ∫ θ = 0 π / 2 I cos θ sin θ d θ d ϕ {\displaystyle q=\int _{\phi =0}^{2\pi }\int _{\theta =0}^{\pi /2}I\cos \theta \sin \theta d\theta d\phi } For diffuse emitters, the emitted radiation intensity is the same in all directions, with the result that E = π I {\displaystyle E=\pi I} The factor π {\displaystyle \pi } (which really should have the units of steradians) is a result of the fact that intensity is defined to exclude the effect of reduced view factor at large values θ {\displaystyle \theta } ; note that the solid angle corresponding to a hemisphere is equal to 2 π {\displaystyle 2\pi } steradians. Spectral intensity I λ {\displaystyle I_{\lambda }} is the corresponding spectral measurement of intensity; in other words, the intensity as a function of wavelength. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Hexachlorocyclohexane </page_title> <path> Hexachlorocyclohexane </path> <section_title> Summary </section_title> <content> Addition of Cl2 destroys the aromaticity of the benzene ring, and the addition of two more Cl2 molecules is rapid compared to the first. Hence, only thrice-dichlorinated product can be isolated from this reaction. Radical addition: C6H6 + 3Cl2 → C6H6Cl6Hexachlorocyclohexane isomers with more than one chlorine atom per carbon are: 1,1,2,3,4,5-hexachlorocyclohexane 1,1,2,3,4,6-hexachlorocyclohexane 1,1,2,3,5,6-hexachlorocyclohexane 1,1,2,2,3,4-hexachlorocyclohexane 1,1,2,2,3,5-hexachlorocyclohexane 1,1,2,2,3,6-hexachlorocyclohexane 1,1,2,2,4,5-hexachlorocyclohexane 1,1,2,3,3,4-hexachlorocyclohexane 1,1,2,3,3,5-hexachlorocyclohexane 1,1,2,3,4,4-hexachlorocyclohexane 1,1,3,3,5,5-hexachlorocyclohexane 1,1,2,4,4,5-hexachlorocyclohexane 1,1,2,4,4,6-hexachlorocyclohexane 1,1,2,4,5,5-hexachlorocyclohexane 1,1,2,5,6,6-hexachlorocyclohexane 1,1,2,2,3,3-hexachlorocyclohexane 1,1,2,2,4,4-hexachlorocyclohexane 1,1,3,3,5,5-hexachlorocyclohexane </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Chinese folk religion </page_title> <path> Chinese_communal_deity_religion > Features > Worship and modalities of religious practice </path> <section_title> Worship and modalities of religious practice </section_title> <content> Adam Yuet Chau identifies five styles or modalities of "doing" Chinese religion: Discursive-scriptural: involving the composition, preaching, and recitation of texts (classics, Taoist scriptures and morality books); Personal cultivation mode, involving a long-term cultivation and transformation of oneself with the goal of becoming a xian Chinese: 仙 (immortal), zhenren Chinese: 真人 ("true person"), or shengren (wise), through the practice of different "technologies of the self" (qigong Chinese: 氣功, Taoist inner and outer alchemy, charitable acts for merit, memorisation and recitation of texts); Liturgical: involving elaborate ritual procedures conducted by specialists of rites (Taoist rites, Confucian rites, Nuo rites, fengshui Chinese: 風水); Immediate practical: aiming at quick efficacious (ling Chinese: 靈) results through simple ritual and magical techniques (divination, talismans, divine medicine, consulting media and shamans); Relational: emphasising the devotional relationship between men and deities and among men themselves (organising elaborate sacrifices, making vows, organising temple festivals, pilgrimages, processions, and religious communities) in "social comings and goings" (laiwang Chinese: 來往) and "interconnectedness" (guanxi Chinese: 關係).Generally speaking, the Chinese believe that spiritual and material well-being ensues from the harmony of humanity and gods in their participation in the same cosmic power, and also believe that by taking the right path and practice anybody is able to reach the absolute reality. Religious practice is therefore regarded as the bridge to link the human world to the spiritual source, maintaining the harmony of the micro and macrocosmos, protecting the individual and the world from disruption. In this sense, the Chinese view of human life is not deterministic, but one is a master of his own life and can choose to collaborate with the deities for a harmonious world. Chinese culture being a holistic system, in which every aspect is a part of a whole, Chinese folk religious practice is often intermingled with political, educational and economic concerns. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Sea bream </page_title> <path> Sea_bream > Genera </path> <section_title> Genera </section_title> <content> The family Sparidae contains about 155 species in 38 genera: Acanthopagrus Peters, 1855 Amamiichthys Tanaka & Iwatsuki, 2015 Archosargus Gill, 1865 Argyrops Swainson, 1839 Argyrozona Smith, 1938 Boops Cuvier, 1814 Boopsoidea Castelnau, 1861 Calamus Swainson, 1839 Centracanthus Rafinesque, 1810 Cheimerius Smith, 1938 Chrysoblephus Swainson, 1839 Crenidens Valenciennes, 1830 Cymatoceps Smith, 1938 Dentex Cuvier, 1814 Diplodus Rafinesque, 1810 Evynnis Jordan & Thompson, 1912 Gymnocrotaphus Günther, 1859 Lagodon Holbrook, 1855 Lithognathus Swainson, 1839 Oblada Cuvier, 1829 Pachymetopon Günther, 1859 Pagellus Valenciennes, 1830 Pagrus Cuvier, 1816 Parargyrops Tanaka, 1916 Petrus Smith, 1938 Polyamblyodon Norman, 1935 Polysteganus Klunzinger, 1870 Porcostoma Smith, 1938 Pterogymnus Smith, 1938 Rhabdosargus Fowler, 1933 Sarpa Bonaparte, 1831 Sparidentex Munro, 1948 Sparodon Smith, 1938 Sparus Linnaeus, 1758 Spicara Rafinesque, 1810 Spondyliosoma Cantor, 1849 Stenotomus Gill, 1865 Virididentex Poll, 1971 </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Received Pronunciation </page_title> <path> Received_Pronunciation > Spoken specimen </path> <section_title> Spoken specimen </section_title> <content> Allophonic ðə ˈnɔːθ ˈw̥ɪnd ən̪n̪ə ˈsʌn wə dɪˈspj̊u̟ːtɪŋ ˈwɪʔtʃ wəz ðə ˈstɹ̥ɒŋɡə, wen ə ˈtɹ̥ævl̩ə ˌkʰeɪm əˌlɒŋ ˈɹæptʰ ɪn ə ˈwɔːm ˈkl̥əʊkˣ. ðeɪ əˈɡɹ̥iːd̥ ð̥əʔ ðə ˈwʌn ɦu ˈfɜːs səkˈsiːdɪd ɪmˈmeɪxɪŋ ðə ˈtɹ̥ævlə ˌtʰeɪk̟x̟ɪs ˈkl̥əʊk ɒf ʃʊbbi kʰənˌsɪdəd̥ ˈstɹɒŋɡə ð̥ən̪n̪i ˈʌðə. ˈðen̪n̪ə ˌnɔːθ w̥ɪnd ˈbluː əz̥ ˈhɑːd̥ əs i ˈkʊd, bət̬ ð̥ə ˈmɔː hi ˈblu̟ː ðə ˌmɔ ˈkl̥əʊsl̥i d̥ɨd ð̥ə ˈtɹ̥æv̥lə ˈfəʊld̥ hɪz̥ ˌkl̥əʊkʰ əˈɹaʊnd hɪm, ænd ət ˈl̥ɑːst ð̥ə ˈnɔːθ w̥ɪnd ˌɡ̊eɪv̥ ˈʌp ði̥ əˈtʰemʔt. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Partition coefficient </page_title> <path> Distribution_coefficient > Prediction > Log D from log P and pKa </path> <section_title> Log D from log P and pKa </section_title> <content> For cases where the molecule is un-ionized: log D ≅ log P . {\displaystyle \log D\cong \log P.} For other cases, estimation of log D at a given pH, from log P and the known mole fraction of the un-ionized form, f 0 {\displaystyle f^{0}} , in the case where partition of ionized forms into non-polar phase can be neglected, can be formulated as log D ≅ log P + log ( f 0 ) . {\displaystyle \log D\cong \log P+\log \left(f^{0}\right).} The following approximate expressions are valid only for monoprotic acids and bases: log D acids ≅ log P + log , log D bases ≅ log P + log . {\displaystyle {\begin{aligned}\log D_{\text{acids}}&\cong \log P+\log \left,\\\log D_{\text{bases}}&\cong \log P+\log \left.\end{aligned}}} Further approximations for when the compound is largely ionized: for acids with p H − p K a > 1 {\displaystyle \mathrm {pH} -\mathrm {p} K_{a}>1} , log D acids ≅ log P + p K a − p H {\displaystyle \log D_{\text{acids}}\cong \log P+\mathrm {p} K_{a}-\mathrm {pH} } , for bases with p K a − p H > 1 {\displaystyle \mathrm {p} K_{a}-\mathrm {pH} >1} , log D bases ≅ log P − p K a + p H {\displaystyle \log D_{\text{bases}}\cong \log P-\mathrm {p} K_{a}+\mathrm {pH} } .For prediction of pKa, which in turn can be used to estimate log D, Hammett type equations have frequently been applied. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Federated Moulders' (Metals) Union of Australia </page_title> <path> Federated_Moulders'_(Metals)_Union_of_Australia > History > Amalgamation </path> <section_title> Amalgamation </section_title> <content> As early as 1922 the moulders' union had participated in discussions with a view to forming one single union in the metal trade, without success. : 118 In September 1944 the federal council of the FMMUA announced its preparedness to "federated or amalgamate with any union or unions in the metal trades industry" and endorsed a proposal for amalgamation with the FIA; however, the proposal was rejected by a ballot of the moulders' union membership by 2,173 to 1,533.: 274–275 In the late 1960s the FMMUA participated in discussions with the AEU, the Boilermakers and Blacksmiths Society of Australia and the Sheet Metal Working Industrial Union regarding amalgamation. : 272 While the other three unions eventually merged in 1972 to form the Amalgamated Metal Workers Union, the moulders elected to remain independent. : 272 During the late 1970s the FMMUA again considered amalgamation with the FIA, but the proposal was rejected by a plebiscite of the membership. : 155 During the 1970s the Western Australian branch of the FMMUA split off in order to merge with the local branch of the Australian Society of Engineers, forming the Australasian Society of Engineers, Moulders and Foundry Workers, while in December 1980 the South Australian branch also seceded to form the Metal Moulders Union of South Australia before amalgamating with the Adelaide Branch of the FIA to form its Moulders and Foundry Workers Sub-Branch in 1982.Following protracted negotiations during 1980–83, including opposition from some of the moulders' state branches, the FMMUA finally merged with the Amalgamated Metal Workers and Shipwrights Union (AMWSU) to form the Amalgamated Metals, Foundry and Shipwrights' Union in February 1983.: 273 </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
<page_title> Clifford analysis </page_title> <path> Clifford_analysis > Hyperbolic Dirac type operators </path> <section_title> Hyperbolic Dirac type operators </section_title> <content> In Clifford analysis one also considers differential operators on upper half space, the disc, or hyperbola with respect to the hyperbolic, or Poincaré metric. For upper half space one splits the Clifford algebra, Cln into Cln−1 + Cln−1en. So for a in Cln one may express a as b + cen with a, b in Cln−1. One then has projection operators P and Q defined as follows P(a) = b and Q(a) = c. The Hodge–Dirac operator acting on a function f with respect to the hyperbolic metric in upper half space is now defined to be M f = D f + n − 2 x n Q ( f ) {\displaystyle Mf=Df+{\frac {n-2}{x_{n}}}Q(f)} .In this case M 2 f = − △ n P ( f ) + n − 2 x n ∂ P ( f ) ∂ x n − ( △ n Q ( f ) − n − 2 x n ∂ Q ( f ) ∂ x n + n − 2 x n 2 Q ( f ) ) e n {\displaystyle M^{2}f=-\triangle _{n}P(f)+{\frac {n-2}{x_{n}}}{\frac {\partial P(f)}{\partial x_{n}}}-\left(\triangle _{n}Q(f)-{\frac {n-2}{x_{n}}}{\frac {\partial Q(f)}{\partial x_{n}}}+{\frac {n-2}{x_{n}^{2}}}Q(f)\right)e_{n}} .The operator △ n − n − 2 x n ∂ ∂ x n {\displaystyle \triangle _{n}-{\frac {n-2}{x_{n}}}{\frac {\partial }{\partial x_{n}}}} is the Laplacian with respect to the Poincaré metric while the other operator is an example of a Weinstein operator. The hyperbolic Laplacian is invariant under actions of the conformal group, while the hyperbolic Dirac operator is covariant under such actions. </content> | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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