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<page_title> EPassport gates </page_title> <path> EPassport_gates > Eligibility </path> <section_title> Eligibility </section_title> <content> If the holder's nationality is shown as a British overseas territories citizen; a British overseas citizen; a British subject; a British national (overseas); or a British protected person then the holder will not be able to use the ePassport gates.On 22 May 2019, citizens of the following countries holding valid biometric passports became eligible to use ePassport gates, provided that they are aged either 18 and over or 12 and over travelling with an adult: Upon successfully using the ePassport gates, citizens of the above countries entering as a visitor are granted 6 months' leave to enter (subject to conditions prohibiting employment and recourse to public funds) and do not receive a passport stamp or any written notice/endorsement. However, citizens of the above countries who wish to enter the UK with a Tier 5 (Temporary Worker - Creative and Sporting) Certificate of Sponsorship (for up to 3 months) or on a permitted paid engagement are not eligible to use the ePassport gates, as a passport stamp must be obtained in these situations.In addition, citizens from the following countries/territories who are enrolled in the Registered Traveller Service can also use ePassport gates, provided that they hold valid biometric passports and are aged either 18 and over or 12 and over travelling with an adult: Upon successfully using the ePassport gates, citizens of the above countries who are enrolled in the 'Registered Traveller Service' and entering as a visitor are granted 6 months' leave to enter (subject to conditions prohibiting employment and recourse to public funds) without receiving a passport stamp or any written notice/endorsement.Practical difficulties may be faced by non-British/EU/EEA/Swiss citizens who have used an ePassport gate to enter the UK as they do not receive a passport stamp evidencing leave to enter. For example, landlords are legally required to check the immigration status of tenants before the start of a tenancy agreement. The Home Office advises that where a prospective tenant is a non-visa national who used an ePassport gate to enter the UK, the landlord should accept any documentary evidence (such as a ticket or boarding pass) that establishes the date of arrival in the UK within the past 6 months. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Chess problems </page_title> <path> Chess_problem > Example problem </path> <section_title> Example problem </section_title> <content> The full solution is as follows: 1 Rh1! 1...Bxh7, 2.Nd5# (unguards d5) 1...Bf7, 2.Qf5# (interferes with rook’s guard of f5) 1...Be6, 2.e3# (interferes with rook’s guard of e3) 1...Bd5, 2.Nxd5# (unguards d5) 1...Bxc7, 2.Rh4# (unguards h4) 1...Be7, 2.e3# (interferes with rook’s guard of e3) 1...Bf6, 2.Qf5# (interferes with rook’s guard of f5) 1...Bg5, 2.Qh2# (blocks king’s flight to g5) 1...Bh4, 2.Rxh4# (unguards h4) 1...Rf7, 2.Nd5# (interferes with bishop’s guard of d5) 1...Rf6, 2.Rh4# (interferes with bishop’s guard of h4) 1...Rf5, 2.Qxf5# (unguards f5) 1...Re7, 2.Rh4# (interferes with bishop’s guard of h4) 1...Re6, 2.Nd5# (interferes with bishop’s guard of d5) 1...Re5, 2.Qg4# (blocks king’s flight to e5) 1...Re4, 2.fxe4# (allows pawn capture discovering check) 1...Re3, 2.Bh2# (blocks king’s flight to e3) 1...Rxe2+, 2.Nxe2# (allows capture on unguarded square e2) 1...c3, 2.Nd3# (unguards d3)The thematic approach to solving is to notice then that in the original position, Black is already almost in zugzwang. If Black were compelled to play first, only Re3 and Bg5 would not allow immediate mate. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Gary Barnacle discography </page_title> <path> Gary_Barnacle_discography > Compilations, remixes and box sets </path> <section_title> Compilations, remixes and box sets </section_title> <content> by Tina Turner (album) 2008 Greatest Hits by Paul Hardcastle and The Jazzmasters 2008 The Singles Collection by Shed Seven (2 cd) 2008 The Best Of Guru's Jazzmatazz by Guru (album) 2009 The Box (33rd Anniversary Special) by Supermax 2009 Anthology: 1983–2008 by David Knopfler (album) 2009 The Collection by Paul Hardcastle (album)2010s2010 Living It Up by Level 42 2010 40 Ans De Chansons by Luc Plamondon (4 cd) 2010 1983–2009: His Greatest Hits Collection by Paul Hardcastle (3 CDs) 2010 Move Over Darling (The Complete Stiff Recordings) by Tracey Ullman (2 CDs) 2011 I Owe You Nothing - The Best Of Bros by Bros (album) 2011 Dance Classics: Take Away The Rain by Various (incl. "Run for Cover" by Steve Grant) 2011 Ruts Rules by The Ruts (album) 2011 B-Sides and Rare Tracks Volume 4 by Siouxsie and the Banshees 2012 The Collection by Kim Wilde (2 CDs) 2012 The Hits by Kajagoogoo & Limahl 2012 Backstreet Brit Funk - Compiled by Joey Negro (featuring "Summer Grooves" by Mirage) (2 CDs) 2012 Pete Waterman Presents the Hit Factory (3 CDs) (incl. "Roadblock") 2013 Best Of Electro Swing by Various (UMG 5346156) (incl. "Right Now" by The Creatures featuring Gary Barnacle - Saxophone, Peter Thoms - Trombone and Luke Tunney - Trumpet) 2019 Keychains and Snowstorms - The Soft Cell Story (9 x CD/1 X DVD Box Set) </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Quantum superpositions </page_title> <path> Quantum_superposition > Theory > Hamiltonian evolution </path> <section_title> Hamiltonian evolution </section_title> <content> The equation of motion for ψ {\displaystyle \psi } is the time differential equation: i d ψ n d t = c ∗ ψ n + 1 + c ψ n − 1 {\displaystyle i{d\psi _{n} \over dt}=c^{*}\psi _{n+1}+c\psi _{n-1}} In the case in which left and right are symmetric, c is real. By redefining the phase of the wavefunction in time, ψ → ψ e i 2 c t {\displaystyle \psi \rightarrow \psi e^{i2ct}} , the amplitudes for being at different locations are only rescaled, so that the physical situation is unchanged. But this phase rotation introduces a linear term. i d ψ n d t = c ψ n + 1 − 2 c ψ n + c ψ n − 1 , {\displaystyle i{d\psi _{n} \over dt}=c\psi _{n+1}-2c\psi _{n}+c\psi _{n-1},} which is the right choice of phase to take the continuum limit. When c {\displaystyle c} is very large and ψ {\displaystyle \psi } is slowly varying so that the lattice can be thought of as a line, this becomes the free Schrödinger equation: i ∂ ψ ∂ t = − ∂ 2 ψ ∂ x 2 {\displaystyle i{\partial \psi \over \partial t}=-{\partial ^{2}\psi \over \partial x^{2}}} If there is an additional term in the H matrix that is an extra phase rotation that varies from point to point, the continuum limit is the Schrödinger equation with a potential energy: i ∂ ψ ∂ t = − ∂ 2 ψ ∂ x 2 + V ( x ) ψ {\displaystyle i{\partial \psi \over \partial t}=-{\partial ^{2}\psi \over \partial x^{2}}+V(x)\psi } These equations describe the motion of a single particle in non-relativistic quantum mechanics. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Batterie Mirus </page_title> <path> Batterie_Mirus > Gun casemate </path> <section_title> Gun casemate </section_title> <content> Each of the four gun positions comprised the following: 21m circular concrete pit to provide a base for a turret comprising central pin, inner walkway (to take the breech recoil when gun operating at maximum elevation), thin middle wall 1.54m high, outer walkway, outer 1.5m thick 2.7m high blast wall Armoured turret, which could be rotated to allow the gun to turn 360 degrees At the rear of the circular pit is the 1.5m thick blast wall with two entrances, one on each side. The forward section of the emplacement being disconnected from the rear section to reduce concussion when the gun was fired Entrance ramp with light trolley track to bring in ammunition and supplies light trolley tracks run to ready stores, one for cordite and the other for the projectile behind the circular blast wall Two cordite stores, with reinforced concrete walls and a steel rocker delivery system that was used to deliver one 80 kg cordite charge at a time to the gun. (4.6m x 7.75m) Ammunition projectile store containing shells (4.5m x 12.6m) Ventilation room (3.0m x 7.7m) Generator room (4.6m x 10.8m) Fuel store (3.0m x 3.5m) Heating plant (3.1m x 3.4m) Officers command and sleeping quarters Crew sleeping quarters 4 x (3.6m x 8.5m) NCO sleeping quarters Shower, toilet and washing facilities Store rooms Rear entranceThe rear section measures externally 33m long by 31m wide, the external walls are 1.5m thick, the roof over the rear section being 2.7m thick.Camouflage was used in the battery, part burying a number of bunkers was common. Guns No. 1 and 3 were disguised as cottages whilst No.2 and No. 4 used netting and fake trees and bushes as camouflage. : 52 The three reserve ammunition bunkers, which were built above ground, were camouflaged as houses, given pitched roofs and painted windows and doors. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Universal space (topology) </page_title> <path> Universal_space > Definition </path> <section_title> Definition </section_title> <content> Given a class C {\displaystyle \textstyle {\mathcal {C}}} of topological spaces, U ∈ C {\displaystyle \textstyle \mathbb {U} \in {\mathcal {C}}} is universal for C {\displaystyle \textstyle {\mathcal {C}}} if each member of C {\displaystyle \textstyle {\mathcal {C}}} embeds in U {\displaystyle \textstyle \mathbb {U} } . Menger stated and proved the case d = 1 {\displaystyle \textstyle d=1} of the following theorem. The theorem in full generality was proven by Nöbeling. Theorem: The ( 2 d + 1 ) {\displaystyle \textstyle (2d+1)} -dimensional cube 2 d + 1 {\displaystyle \textstyle ^{2d+1}} is universal for the class of compact metric spaces whose Lebesgue covering dimension is less than d {\displaystyle \textstyle d} . Nöbeling went further and proved: Theorem: The subspace of 2 d + 1 {\displaystyle \textstyle ^{2d+1}} consisting of set of points, at most d {\displaystyle \textstyle d} of whose coordinates are rational, is universal for the class of separable metric spaces whose Lebesgue covering dimension is less than d {\displaystyle \textstyle d} . The last theorem was generalized by Lipscomb to the class of metric spaces of weight α {\displaystyle \textstyle \alpha } , α > ℵ 0 {\displaystyle \textstyle \alpha >\aleph _{0}}: There exist a one-dimensional metric space J α {\displaystyle \textstyle J_{\alpha }} such that the subspace of J α 2 d + 1 {\displaystyle \textstyle J_{\alpha }^{2d+1}} consisting of set of points, at most d {\displaystyle \textstyle d} of whose coordinates are "rational" (suitably defined), is universal for the class of metric spaces whose Lebesgue covering dimension is less than d {\displaystyle \textstyle d} and whose weight is less than α {\displaystyle \textstyle \alpha } . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Mellin transformation </page_title> <path> Mellin_transformation > Examples > Zeta function </path> <section_title> Zeta function </section_title> <content> It is possible to use the Mellin transform to produce one of the fundamental formulas for the Riemann zeta function, ζ ( s ) {\displaystyle \zeta (s)} . Let f ( x ) = 1 e x − 1 {\textstyle f(x)={\frac {1}{e^{x}-1}}} . Then M f ( s ) = ∫ 0 ∞ x s − 1 1 e x − 1 d x = ∫ 0 ∞ x s − 1 e − x 1 − e − x d x = ∫ 0 ∞ x s − 1 ∑ n = 1 ∞ e − n x d x = ∑ n = 1 ∞ ∫ 0 ∞ x s e − n x d x x = ∑ n = 1 ∞ 1 n s Γ ( s ) = Γ ( s ) ζ ( s ) . {\displaystyle {\mathcal {M}}f(s)=\int _{0}^{\infty }x^{s-1}{\frac {1}{e^{x}-1}}dx=\int _{0}^{\infty }x^{s-1}{\frac {e^{-x}}{1-e^{-x}}}dx=\int _{0}^{\infty }x^{s-1}\sum _{n=1}^{\infty }e^{-nx}dx=\sum _{n=1}^{\infty }\int _{0}^{\infty }x^{s}e^{-nx}{\frac {dx}{x}}=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}\Gamma (s)=\Gamma (s)\zeta (s).} Thus, ζ ( s ) = 1 Γ ( s ) ∫ 0 ∞ x s − 1 1 e x − 1 d x . {\displaystyle \zeta (s)={\frac {1}{\Gamma (s)}}\int _{0}^{\infty }x^{s-1}{\frac {1}{e^{x}-1}}dx.} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Side collision </page_title> <path> Side_collision > Occurrences and effects </path> <section_title> Occurrences and effects </section_title> <content> For fatalities, in the United States, in 2008, a total of 5,265 (22%) out of 23,888 people were killed in vehicles which were struck in the side.For speed, in Europe in 2015, it is considered that best designed cars provide serious front crash protection with speeds up to 70 km/h for car occupants wearing seat belts in frontal impacts and 50 km/h in side impacts It is considered that passenger car fatalities and seriously injured side impacts account for about 35 to 40%. In most European countries, another stakeholder is involved in the side impact, with a rate between 45% and 66%. But side impact (22% to 29%) is less common that frontal impact (61% to 69%).For European motorcyclists, side impact is the second most frequent location of impact.For European cyclist, thorax injuries are associated with side-impact injuries in urban areas and/or at junctions.In European countries, such as UK, Sweden and France, around one quarter of traffic injuries are produced by side collision, but among people subject to killing injuries the side impact account for 29 to 38% of those fatal injuries.In European vehicle side impact, 60% of casualties were "struck side", while 40% were "non struck side", in 2018.Fatal casualties count as 50% and 67% in UK and in France, in 2010Also, side collision are not well managed with child restraints which are not enough taking into account the movement of the child's head and prevent contact with the car's interior.For light vans and minibuses in 2000 in UK and Germany, between 14% and 26% of accidents with passenger cars are side impactIn Shanghai, in China, 23% of the 1097 serious accidents occurred between June 2005 and March 2013 are side impact accidents, there the leading collision mode, according to the Shanghai United Road Traffic Safety Scientific Research Center (SHUFO) database. The head and neck are involved in around 64% of the casualties. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Behavioural Insights Team </page_title> <path> Behavioural_Insights_Team > Overview > Governance and affiliations </path> <section_title> Governance and affiliations </section_title> <content> BIT is headed by psychologist David Halpern, and is now owned by the charity Nesta. It works in partnership with governments, local authorities, non-profits, and private organisations to tackle major policy problems. The organisation has a formal partnership with Harvard University’s Behavioral Insights Group (BIG) and close relationships with several universities, including University College London, Harvard University, and the Universities of Oxford, Cambridge, and Pennsylvania.As of May 2021, members of the BIT global board include: Rob Taylor – Chair David Halpern – Chief executive Janet Baker – Cabinet office Elisabeth Costa – Senior director, policy and partnerships Nathan Elstub – Nesta Nicky Kerr – Director, legal and general counsel Ian West – Director, financeAs of May 2021, academic affiliates of the BIT include: Angela Duckworth – founder and CEO of Character Lab Cass Sunstein – professor at Harvard Law School; co-author of Nudge (2008). Daniel Goldstein – principal researcher at Microsoft Research David Zendle – lecturer of computer science at the University of York Elizabeth Linos – assistant professor of public policy at UC Berkeley Gus O'Donnell – Member of the House of Lords; former Cabinet Secretary; former head of the Civil Service Michael Norton – professor of business administration at the Harvard Business School Michelle Ryan – professor of social and organisational psychology at the University of Exeter Nick Chater – professor of behavioural science at Warwick Business School Oliver Hauser – senior lecturer in economics at University of Exeter Peter John – professor of political science and public policy at University College London Peter Tufano – dean of Said Business School, University of Oxford Richard Thaler – professor of behavioural science and economics at the Chicago Booth School of Business; co-author of Nudge (2008). Rob Ranyard – visiting professor at the Centre for Decision Research, Leeds University Business School Silvia Saccardo – assistant professor at the Department of Social and Decision Sciences, Carnegie Mellon University Simon Burgess – professor of economics at the University of Bristol Thekla Morgenroth – Research Fellow of Social and Organisational Psychology, University of Exeter Theresa Marteau – director of the Behaviour and Health Research Unit, University of Cambridge Todd Rogers – professor of public policy, Harvard Kennedy School </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Radon–Nikodym set </page_title> <path> Radon–Nikodym_set > Definitions </path> <section_title> Definitions </section_title> <content> Define the following measure: V = ∑ i = 1 n V i {\displaystyle V=\sum _{i=1}^{n}V_{i}} Note that each V i {\displaystyle V_{i}} is an absolutely continuous measure with respect to V {\displaystyle V} . Therefore, by the Radon–Nikodym theorem, it has a Radon–Nikodym derivative, which is a function v i: C → [ 0 , ∞ ) {\displaystyle v_{i}:C\to [0,\infty )} such that for every measurable subset X ∈ C {\displaystyle X\in \mathbb {C} }: V i ( X ) = ∫ X v i d V {\displaystyle V_{i}(X)=\int _{X}v_{i}\,dV} The v i {\displaystyle v_{i}} are called value-density functions. They have the following properties, for almost all points of the cake x ∈ C {\displaystyle x\in C} :: 222 ∑ i = 1 n v i ( x ) = 1 {\displaystyle \sum _{i=1}^{n}v_{i}(x)=1} ∀ i: 0 ≤ v i ( x ) ≤ 1 {\displaystyle \forall i:0\leq v_{i}(x)\leq 1} For every point x ∈ C {\displaystyle x\in C} , the RNS point of x {\displaystyle x} is defined by: v ( x ) = ( v 1 ( x ) , … , v n ( x ) ) {\displaystyle v(x)=(v_{1}(x),\dots ,v_{n}(x))} Note that v ( x ) {\displaystyle v(x)} is always a point in the ( n − 1 ) {\displaystyle (n-1)} -dimensional unit simplex in R n {\displaystyle \mathbb {R} ^{n}} , denoted by Δ n − 1 {\displaystyle \Delta ^{n-1}} (or just Δ {\displaystyle \Delta } when n {\displaystyle n} is clear from the context). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Excise taxes </page_title> <path> Excise_taxes > Around the world > United Kingdom </path> <section_title> United Kingdom </section_title> <content> In the United Kingdom, the following forms of excise are levied on goods and services: Air Passenger Duty (Finance Act 1994) Aggregates Levy (Finance Act 2001) Alcohol duties (Beer Duty, Wine Duty, Cider Duty, Spirits Duty) (Alcoholic Liquor Duties Act 1979) Bingo Duty (Betting and Gaming Duties Act 1981) Climate Change Levy (Finance Act 2000) Gambling duties (General Betting Duty, Pool Betting Duty, Remote Gaming Duty) (Finance Act 2014) HGV Road User Levy (HGV Road User Levy Act 2013) Hydrocarbon Oil Duty (Hydrocarbon Oil Duties Act 1979) Landfill tax (Finance Act 1996) Machine Games Duty (Finance Act 2012) (formerly Amusement Machine Licence Duty) Tobacco Duty (Tobacco Products Duty Act 1979) Vehicle Excise Duty (Vehicle Excise and Registration Act 1994)Historically, these were collected by the Board of Excise, which was subsequently combined with the Inland Revenue (responsible for collecting direct taxes). In view of the higher likelihood of organised crime being involved in attempts at evading Excise, and its association with smuggling, compared with evasion attempts concerning direct taxation, the Board of Excise was later combined instead with the Board of Customs, to form HM Customs and Excise. In this combined form, Customs and Excise was responsible for managing the import and export of goods and services into the UK, and its officers wielded greater powers of access, arrest, and seizure, than the Police. On 18 April 2005, Customs and Excise was merged once more with the Inland Revenue to form a new department, HM Revenue and Customs (HMRC). The enormous contrast between the powers of officers of the Inland Revenue, and those of Customs and Excise, initially caused several difficulties in the early life of the new organisation. Many of the monitoring and inspection functions, and corresponding powers, were later split off to form a new UK Border Agency, while the residual organisation is now merely responsible for the financial aspects of collection. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Aortic dissection </page_title> <path> Aortic_dissection > Society and culture </path> <section_title> Society and culture </section_title> <content> A greater incidence of aortic aneurysm is seen in cigarette smokers; Ball had been a heavy smoker most of her life.Playwright Jonathan Larson, best known for the musical Rent, died in 1996 of an aortic dissection believed to be due to undiagnosed Marfan Syndrome. Days of Our Lives and Babylon 5 actor Richard Biggs died on May 22, 2004, at the age of 44 due to complications from aortic dissection.Lux Interior of The Cramps died at the Glendale Memorial Hospital on February 4, 2009, at the age of 62, following an aortic dissection which, contrary to initial reports about a pre-existing condition, was "sudden, shocking and unexpected".Alan Thicke died in 2016 of type-A aortic dissection at the Providence Saint Joseph Medical Center in Burbank, at the age of 69.Japanese actress Hiromi Tsuru died in her car from aortic dissection in 2017 at the age of 57.Taiwanese entertainer Alien Huang died in 2020 at the age of 36.Kentaro Miura, writer and artist of the manga Berserk, died from aortic dissection in 2021 at the age of 54.In August 2021, New Zealand cricketer Chris Cairns was put on full life support following an aortic dissection in his home in Canberra, Australia. He was transferred to Sydney, and became paralysed from the waist down due to sustaining a stroke during surgery. 41-year-old guitarist Richie Faulkner of the heavy metal band Judas Priest had an aortic aneurysm on September 27, 2021, in the middle of the final song of their 50-minute set at a music festival. He underwent 10+1⁄2 hours of open heart surgery to repair the aortic dissection.In May 2022, keyboardist Andy Fletcher, a founding member of the UK band Depeche Mode, died unexpectedly at home from an aortic dissection, at the age of 60. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Quadient </page_title> <path> Quadient > History </path> <section_title> History </section_title> <content> of Roneo and Hadewe (United Kingdom and Netherlands) 1981 Attached to Alcatel, subsidiary of C.G.E. (France) 1992 Foundation of Neopost Group 1997 A group of investors, advised by BC Partners and in association with management, took control of Neopost 1999 Neopost was floated on the Premier Marché of Euronext Paris on 23 February at a price of €15 per share 2002 Acquisition of Stielow and Hasler (Germany and Switzerland) 2003 Neopost completed the integration of companies acquired in 2002, sold Stielow’s non-core label printing and print finishing businesses, and strengthened its operating structures 2005 Acquisition of BTA Digital Works, a software company 2006 Neopost adopted and modified the tagline "We value your mail" at the beginning of 2006. 2007 Acquisition of PFE, a supplier of high volume folder-inserters and Valipost 2008 Acquisition of RENA, addressing systems supplier and NBG-ID, integrator of RFID technology 2009 Acquisition of Satori Software, a postal address quality management software company 2009 Acquisition of Kontur Documents Systems (Suède) and Scani (Denmark) 2011 Acquisition of GBC – Fordigraph, an Australian distributor of document finishing and mailing products 2012 Acquisition of GMC Software Technology – a Swiss-based provider of customer communications management products 2012 Acquisition of Human Inference, a Dutch provider of contact data quality services 2013 Acquisition of DMTI Spatial – a Canadian provider of location-based service provider 2014 Acquisition of Data Capture Solutions Ltd, a document management business 2016 Acquisition of icon Systemhaus 2019 The company was renamed Quadient In March 2020, Quadient sold ProShip, Inc. to FOG Software Group, a division of Constellation Software 2020 Acquisition of YayPay, an accounts receivable automation software company (United States) 2021 Acquisition of Beanworks, a Canadian accounts payable automation software company </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Sliding mode control </page_title> <path> Sliding_mode_control > Sliding mode observer </path> <section_title> Sliding mode observer </section_title> <content> In particular, the row A 12 {\displaystyle A_{12}} acts like an output vector for the error subsystem ⏞ e ˙ 2 = A 2 ⏞ e 2 + L 2 v ( e 1 ) = A 2 e 2 + L 2 v eq = A 2 e 2 + L 2 A 12 e 2 = ( A 2 + L 2 A 12 ) e 2 . {\displaystyle {\mathord {\overbrace {\begin{bmatrix}{\dot {e}}_{2}\\{\dot {e}}_{3}\\\vdots \\{\dot {e}}_{n}\end{bmatrix}} ^{{\dot {\mathbf {e} }}_{2}}}}=A_{2}{\mathord {\overbrace {\begin{bmatrix}e_{2}\\e_{3}\\\vdots \\e_{n}\end{bmatrix}} ^{\mathbf {e} _{2}}}}+L_{2}v(e_{1})=A_{2}\mathbf {e} _{2}+L_{2}v_{\text{eq}}=A_{2}\mathbf {e} _{2}+L_{2}A_{12}\mathbf {e} _{2}=(A_{2}+L_{2}A_{12})\mathbf {e} _{2}.} So, to ensure the estimator error e 2 {\displaystyle \mathbf {e} _{2}} for the unmeasured states converges to zero, the ( n − 1 ) × 1 {\displaystyle (n-1)\times 1} vector L 2 {\displaystyle L_{2}} must be chosen so that the ( n − 1 ) × ( n − 1 ) {\displaystyle (n-1)\times (n-1)} matrix ( A 2 + L 2 A 12 ) {\displaystyle (A_{2}+L_{2}A_{12})} is Hurwitz (i.e., the real part of each of its eigenvalues must be negative). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Jungle Rot </page_title> <path> Jungle_Rot > Personnel </path> <section_title> Personnel </section_title> <content> Current Dave Matrise – rhythm guitar, vocals (1994–present) James Genenz – bass (2005–present), guitars (2004–2005) Geoff Bub – lead guitar (2005–present) Spenser Syphers – drums (2019–present)Former Joe Carlino – bass (1993–1994) Brian Kuhn – bass (1994–1995) Mike LeGros – bass (1999–2000) Jim Garcia – drums (1999–2002) Joe Thomas – vocals, guitars (1992–1994) Chris "Wisco" Djuricic – bass (1995–1999, 2001–2003), guitars (2004) Jim Harte – drums (1992–1997) Jim Bell – guitars (1994–2000) Rob Pandola – drums (1997–1998) Kevin Forsythe – guitars (2000–2002) Jerry Sturino – bass (2004–2005) Eric House – drums (2004–2006 / 2008–2010) Joey Lohr – guitars (2004–2005) Neil Zacharek – drums (2006–2007) Jesse Beahler – drums (2010–2013)Touring musicians Jason Adam Borton – drums (2016) Remington Roberts – drums (2013–2016) Parker Yowell – drums (2016) Mike Miczek – drums (2014) Shawn Johnson – drums (1999) Tony Ochoa – drums (2010) Andy Vehnekamp – drums (1999) Joey Muha – drums (2015) Scott Fuller – drums (2013) Chris 'Wisco' Djuricic – guitars (2013) </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Bi-elliptic transfer </page_title> <path> Bi-elliptic_transfer > Calculation > Delta-v </path> <section_title> Delta-v </section_title> <content> The three required changes in velocity can be obtained directly from the vis-viva equation where v {\displaystyle v} is the speed of an orbiting body, μ = G M {\displaystyle \mu =GM} is the standard gravitational parameter of the primary body, r {\displaystyle r} is the distance of the orbiting body from the primary, i.e., the radius, a {\displaystyle a} is the semi-major axis of the body's orbit.In what follows, r 1 {\displaystyle r_{1}} is the radius of the initial circular orbit, r 2 {\displaystyle r_{2}} is the radius of the final circular orbit, r b {\displaystyle r_{b}} is the common apoapsis radius of the two transfer ellipses and is a free parameter of the maneuver, a 1 {\displaystyle a_{1}} and a 2 {\displaystyle a_{2}} are the semimajor axes of the two elliptical transfer orbits, which are given by and Starting from the initial circular orbit with radius r 1 {\displaystyle r_{1}} (dark blue circle in the figure to the right), a prograde burn (mark 1 in the figure) puts the spacecraft on the first elliptical transfer orbit (aqua half-ellipse). The magnitude of the required delta-v for this burn is When the apoapsis of the first transfer ellipse is reached at a distance r b {\displaystyle r_{b}} from the primary, a second prograde burn (mark 2) raises the periapsis to match the radius of the target circular orbit, putting the spacecraft on a second elliptic trajectory (orange half-ellipse). The magnitude of the required delta-v for the second burn is Lastly, when the final circular orbit with radius r 2 {\displaystyle r_{2}} is reached, a retrograde burn (mark 3) circularizes the trajectory into the final target orbit (red circle). The final retrograde burn requires a delta-v of magnitude If r b = r 2 {\displaystyle r_{b}=r_{2}} , then the maneuver reduces to a Hohmann transfer (in that case Δ v 3 {\displaystyle \Delta v_{3}} can be verified to become zero). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Stein discrepancy </page_title> <path> Stein_discrepancy > Applications of Stein discrepancy > Statistical estimation </path> <section_title> Statistical estimation </section_title> <content> Stein discrepancy has been proposed as a tool to fit parametric statistical models to data. Given a dataset { x i } i = 1 n ⊂ X {\displaystyle \{x_{i}\}_{i=1}^{n}\subset {\mathcal {X}}} , consider the associated discrete distribution Q n = 1 n ∑ i = 1 n δ ( x i ) {\displaystyle Q^{n}=\textstyle {\frac {1}{n}}\sum _{i=1}^{n}\delta (x_{i})} . For a given parametric collection { P θ } θ ∈ Θ {\displaystyle \{P_{\theta }\}_{\theta \in \Theta }} of probability distributions on X {\displaystyle {\mathcal {X}}} , one can estimate a value of the parameter θ {\displaystyle \theta } which is compatible with the dataset using a minimum Stein discrepancy estimator a r g m i n θ ∈ Θ D P θ ( Q n ) . {\displaystyle {\underset {\theta \in \Theta }{\operatorname {arg\,min} }}\;D_{P_{\theta }}(Q^{n}).} The approach is closely related to the framework of minimum distance estimation, with the role of the "distance" being played by the Stein discrepancy. Alternatively, a generalised Bayesian approach to estimation of the parameter θ {\displaystyle \theta } can be considered where, given a prior probability distribution with density function π ( θ ) {\displaystyle \pi (\theta )} , θ ∈ Θ {\displaystyle \theta \in \Theta } , (with respect to an appropriate reference measure on Θ {\displaystyle \Theta } ), one constructs a generalised posterior with probability density function π n ( θ ) ∝ π ( θ ) exp ⁡ ( − γ D P θ ( Q n ) 2 ) , {\displaystyle \pi ^{n}(\theta )\propto \pi (\theta )\exp \left(-\gamma D_{P_{\theta }}(Q^{n})^{2}\right),} for some γ > 0 {\displaystyle \gamma >0} to be specified or determined. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Composition (combinatorics) </page_title> <path> Composition_(combinatorics) > Number of compositions </path> <section_title> Number of compositions </section_title> <content> The same argument shows that the number of compositions of n into exactly k parts (a k-composition) is given by the binomial coefficient ( n − 1 k − 1 ) {\displaystyle {n-1 \choose k-1}} . Note that by summing over all possible numbers of parts we recover 2n−1 as the total number of compositions of n: ∑ k = 1 n ( n − 1 k − 1 ) = 2 n − 1 . {\displaystyle \sum _{k=1}^{n}{n-1 \choose k-1}=2^{n-1}.} For weak compositions, the number is ( n + k − 1 k − 1 ) = ( n + k − 1 n ) {\displaystyle {n+k-1 \choose k-1}={n+k-1 \choose n}} , since each k-composition of n + k corresponds to a weak one of n by the rule a 1 + a 2 + … + a k = n + k ↦ ( a 1 − 1 ) + ( a 2 − 1 ) + … + ( a k − 1 ) = n {\displaystyle a_{1}+a_{2}+\ldots +a_{k}=n+k\quad \mapsto \quad (a_{1}-1)+(a_{2}-1)+\ldots +(a_{k}-1)=n} It follows from this formula that the number of weak compositions of n into exactly k parts equals the number of weak compositions of k − 1 into exactly n + 1 parts. For A-restricted compositions, the number of compositions of n into exactly k parts is given by the extended binomial (or polynomial) coefficient ( k n ) ( 1 ) a ∈ A = ( ∑ a ∈ A x a ) k {\displaystyle {\binom {k}{n}}_{(1)_{a\in A}}=\left(\sum _{a\in A}x^{a}\right)^{k}} , where the square brackets indicate the extraction of the coefficient of x n {\displaystyle x^{n}} in the polynomial that follows it. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Point Accepted Mutation </page_title> <path> Point_Accepted_Mutation > Construction of PAM matrices > Construction of the mutation matrix </path> <section_title> Construction of the mutation matrix </section_title> <content> The non-diagonal entries are computed by the equation M ( i , j ) = λ A ( i , j ) m ( j ) ∑ i = 1 , i ≠ j 20 A ( i , j ) = λ A ( i , j ) N f ( j ) {\displaystyle M(i,j)=\lambda A(i,j){\frac {m(j)}{\sum _{i=1,i\neq j}^{20}A(i,j)}}={\frac {\lambda A(i,j)}{Nf(j)}}} where λ {\displaystyle \lambda } is a constant of proportionality. However, this equation does not compute the diagonal entries. Each column in the matrix M {\displaystyle M} lists each of the twenty possible outcomes for an amino acid — it can mutate into one of the 19 other amino acids, or remain unchanged. Since the non-diagonal entries listing the probabilities of each of the 19 mutations are known, and the sum of the probabilities of these twenty outcomes must be 1, this last probability can be calculated by M ( j , j ) = 1 − ∑ i = 1 , i ≠ j 20 M ( i , j ) {\displaystyle M(j,j)=1-\sum _{i=1,i\neq j}^{20}M(i,j)} which simplifies to M ( j , j ) = 1 − λ m ( j ) {\displaystyle M(j,j)=1-\lambda m(j)} A result of particular significance is that for the non-diagonal entries f ( j ) M ( i , j ) = λ N A ( i , j ) = λ N A ( j , i ) = f ( i ) M ( j , i ) {\displaystyle f(j)M(i,j)={\frac {\lambda }{N}}A(i,j)={\frac {\lambda }{N}}A(j,i)=f(i)M(j,i)} Which means that for all entries in the mutation matrix f ( j ) M ( i , j ) = f ( i ) M ( j , i ) {\displaystyle f(j)M(i,j)=f(i)M(j,i)} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Cross fourchy </page_title> <path> Pierced_cross_quarterly > History </path> <section_title> History </section_title> <content> The cross appears as heraldic charge in the oldest rolls of arms, from about 1250. A roll of arms of the 13th century (the reign of Henry III of England) lists the coats of arms of various noblemen distinguished by crosses of different tinctures: Le Conte de Norffolk, d'or a ung crois de goulez (viz. red on gold); Piers de Sauvoye, goules ung crois d'argent(white on red): this is attributed, Peter's funerary monument displays an eagle on his shield; Robert de Veer d'argent a la crois de goulz (red on white).Glover's Roll (British Library Add MS 29796), a 16th-century copy of a roll of arms of the 1250s has depictions of various heraldic crosses, including the or a cross gules of the earl of Norfolk, gules, a cross argent of Peter of Savoy, argent a cross gules of Robert de Veer, gules a cross flory vair of Guillaume de Forz, Comte d'Aumale, gules a cross fleury argent of Guillaume Vescy, gules a cross saltire engrele of Fulke de Escherdestone, argent a cross fleury azure of John Lexington, azure three crosses or of William de Sarren, or a cross gules, five scallops argent of Ralph Bigod, gules a cross fourchy argent of Gilbert de Vale, argent a cross fleury sable of John Lamplowe, or a cross saltire gules, a chief gules of Robert de Brus, gules a cross saltire argent of Robert de Neville, or a cross voided gules of Hamond (Robert) de Crevecoeur, and azure a cross or, four lions rampant or of Baudouin Dakeney. In addition, the Glover Roll has semy of crosses crosslet as a tincture in several coats of arms.The desire to distinguish one's coat of arms from others led to a period of substantial innovation in producing variants of the basic Christian cross by the early 14th century (in England, the reign of Edward II). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Gerodermia osteodysplastica </page_title> <path> Gerodermia_osteodysplastica > Presentation </path> <section_title> Presentation </section_title> <content> Gerodermia osteodysplastica is characterized by symptoms and features which affect the connective tissues, skin and skeletal system.These are: wrinkly, loose skin over the face, abdomen, and extremities (hands, feet) on the dorsal sides usually worsened by chronic joint laxity and hyperextensibility; fragmented elastic fibers of the skin that are reduced in number, with disorientation of collagen fibers; osteopenia and osteoporosis, with associated fractures; malar hypoplasia (underdeveloped cheek bone), maxillary hypoplasia (underdeveloped upper jaw), mandibular prognathism (protrusion of the lower jaw and chin), bowed long bones, platyspondyly (flattened spine) related to vertebral collapse; kyphoscoliosis (scoliosis with kyphosis, or "hunch back"), metaphyseal peg (an unusual outgrowth of metaphyseal tissue which protrudes into the epiphyseal region of the bone, near the knee); and the overall physical effects and facial appearance of dwarfism with premature aging.Other features and findings include: intrauterine growth retardation, congenital hip dislocations, winged scapulae (shoulder blades), pes planus (fallen arches), pseudoepiphyses of the second metacarpals (upper bone of the fingers), hypotelorism (close-set eyes), malformed ears,developmental delay,failure to thrive and abnormal electroencephalograph (EEG) readings.Dental and orthodontal abnormalities in addition to maxillary hypoplasia and mandibular prognathism have also been observed in gerodermia osteodysplastica. Including malocclusion of the dental arches (the maxilla and mandible), radiological findings in some cases have indicated significant overgrowth of the mandibular premolar and molar roots;hypercementosis (overproduction of cementum) of the molars and maxillary incisors; enlarged, funnel-shaped mandibular lingula (spiny structures on the ramus of the mandible); and a radiolucent effect on portions of many teeth, increasing their transparency to x-rays. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Ring road </page_title> <path> Ring_road > Examples > Asia-Pacific </path> <section_title> Asia-Pacific </section_title> <content> The "Four Avenues" (Bealey Avenue, Fitzgerald Avenue, Moorhouse Avenue, and Deans Avenue) serve as an inner ring around the central city. Delhi, India - Inner Ring Road, Delhi and Outer Ring Road, Delhi Erbil, Iraq - Four ring roads circulating through/around the city. Fukuoka, Japan - Fukuoka Expressway Circular Route George Town, Malaysia - George Town Inner Ring Road, Penang Middle Ring Road Hawaii Island, Hawaii - Hawaii Belt Road Hong Kong, Hong Kong - Route 9 (New Territories Circular Road) Hyderabad, India - Outer Ring Road, Hyderabad Jakarta, Indonesia - Jakarta Inner Ring Road, Jakarta Outer Ring Road, Jakarta Outer Ring Road 2 Kathmandu, Nepal - Kathmandu Ringroad Kuala Lumpur, Malaysia - Kuala Lumpur Inner Ring Road, Kuala Lumpur Middle Ring Road 1, Kuala Lumpur Middle Ring Road 2, Kuala Lumpur Outer Ring Road Lahore, Pakistan - Lahore Ring Road Manila, Philippines - EDSA, Circumferential Road 5 Medina, Saudi Arabia - King Faisal Road (1st Ring Road) and King Abdullah Road (2nd Ring Road) Nagoya, Japan - C1 Inner Ring Route Expressway, C2 Second Ring Route Expressway, C3 Third Ring Route Expressway, Japan National Route 302, Nagoya Municipal Road Nagoya Inner Ring Osaka, Japan - Loop Route Peshawar, Pakistan - Peshawar Ring Road Ranchi, India - Ranchi Ring Road Riyadh, Saudi Arabia - Riyadh Ring Road Sendai, Japan - Gurutto Sendai Seoul, South Korea - Capital Region First Ring Expressway Shanghai, China - Inner Ring Road, Middle Ring Road, S20 Outer Ring Expressway, G1501 Shanghai Ring Expressway Singapore, Singapore - Outer Ring Road System Tianjin, China - Inner, Middle and Outer Ring Roads Tokyo, Japan - C1 Inner Circular Expressway, C2 Central Circular Expressway, C3 Gaikan Expressway, C4 Ken-Ō Expressway, CA Tokyo Bay Aqua-Line/B Bayshore Route, Yokohama Ring Expressway, Japan National Route 16, Japan National Route 298, Japan National Route 357, Japan National Route 468 Hanoi, Vietnam - Ringway 3 </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> System size expansion </page_title> <path> System_size_expansion > Preliminaries > Example </path> <section_title> Example </section_title> <content> Let f 1 ( x , Ω ) = n 1 Ω = x 1 {\displaystyle f_{1}(\mathbf {x} ,\Omega )={\frac {n_{1}}{\Omega }}=x_{1}} , so that the rate of reaction 1 (the only reaction) depends on the concentration of X 1 {\displaystyle X_{1}} . The stoichiometry matrix is ( − 1 , 1 ) T {\displaystyle (-1,1)^{T}} . Then the master equation reads: ∂ P ( X , t ) ∂ t = Ω ( E − S 11 E − S 21 − 1 ) f 1 ( X Ω ) P ( X , t ) = Ω ( f 1 ( X + Δ X Ω ) P ( X + Δ X , t ) − f 1 ( X Ω ) P ( X , t ) ) , {\displaystyle {\begin{aligned}{\frac {\partial P(\mathbf {X} ,t)}{\partial t}}&=\Omega \left(\mathbb {E} ^{-S_{11}}\mathbb {E} ^{-S_{21}}-1\right)f_{1}\left({\frac {\mathbf {X} }{\Omega }}\right)P(\mathbf {X} ,t)\\&=\Omega \left(f_{1}\left({\frac {\mathbf {X} +\mathbf {\Delta X} }{\Omega }}\right)P\left(\mathbf {X} +\mathbf {\Delta X} ,t\right)-f_{1}\left({\frac {\mathbf {X} }{\Omega }}\right)P\left(\mathbf {X} ,t\right)\right),\end{aligned}}} where Δ X = { 1 , − 1 } {\displaystyle \mathbf {\Delta X} =\{1,-1\}} is the shift caused by the action of the product of step operators, required to change state X {\displaystyle \mathbf {X} } to a precursor state X ′ {\displaystyle \mathbf {X} '} . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Sight reduction </page_title> <path> Sight_reduction > Longhand haversine sight reduction > Ultra compact sight reduction </path> <section_title> Ultra compact sight reduction </section_title> <content> A practical and friendly method using only haversines was developed between 2014 and 2015, and published in NavList. A compact expression for the altitude was derived using haversines, hav ⁡ ( ) {\displaystyle \operatorname {hav} ()} , for all the terms of the equation: hav ⁡ ( Z D ) = hav ⁡ ( L a t − D e c ) + ( 1 − hav ⁡ ( L a t − D e c ) − hav ⁡ ( L a t + D e c ) ) ⋅ hav ⁡ ( L H A ) {\displaystyle \operatorname {hav} (ZD)=\operatorname {hav} (Lat-Dec)+\left(1-\operatorname {hav} (Lat-Dec)-\operatorname {hav} (Lat+Dec)\right)\cdot \operatorname {hav} (LHA)} where Z D {\displaystyle ZD} is the zenith distance, H c = ( 90 ∘ − Z D ) {\displaystyle Hc=(90^{\circ }-ZD)} is the calculated altitude. The algorithm if absolute values are used is: if same name for latitude and declination (both are North or South) n = hav(\|Lat\| − \|Dec\|) m = hav(\|Lat\| + \|Dec\|) if contrary name (one is North the other is South) n = hav(\|Lat\| + \|Dec\|) m = hav(\|Lat\| − \|Dec\|) q = n + m a = hav(LHA) hav(ZD) = n + a · (1 − q) ZD = archav() -> inverse look-up at the haversine tables Hc = 90° − ZD For the azimuth a diagram was developed for a faster solution without calculation, and with an accuracy of 1°. This diagram could be used also for star identification.An ambiguity in the value of azimuth may arise since in the diagram 0 ∘ ⩽ Z ⩽ 90 ∘ {\displaystyle 0^{\circ }\leqslant Z\leqslant 90^{\circ }} . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Holstein–Herring method </page_title> <path> Holstein–Herring_method > Theory </path> <section_title> Theory </section_title> <content> For the hydrogen molecular ion, this is: V = − e 2 4 π ε 0 ( 1 r a + 1 r b ) {\displaystyle V=-{\frac {e^{2}}{4\pi \varepsilon _{0}}}\left({\frac {1}{r_{a}}}+{\frac {1}{r_{b}}}\right)} For any gerade (or even) state, the electronic Schrödinger wave equation can be written in atomic units ( ℏ = m = e = 4 π ε 0 = 1 {\displaystyle \hbar =m=e=4\pi \varepsilon _{0}=1} ) as: ( − 1 2 ∇ 2 + V ( x ) ) ψ + = E + ψ + {\displaystyle \left(-{\frac {1}{2}}\nabla ^{2}+V({\textbf {x}})\right)\psi _{+}=E_{+}\psi _{+}} For any ungerade (or odd) state, the corresponding wave equation can be written as: ( − 1 2 ∇ 2 + V ( x ) ) ψ − = E − ψ − {\displaystyle \left(-{\frac {1}{2}}\nabla ^{2}+V({\textbf {x}})\right)\psi _{-}=E_{-}\psi _{-}} For simplicity, we assume real functions (although the result can be generalized to the complex case). We then multiply the gerade wave equation by ψ − {\displaystyle \psi _{-}} on the left and the ungerade wave equation on the left by ψ + {\displaystyle \psi _{+}} and subtract to obtain: ψ + ∇ 2 ψ − − ψ − ∇ 2 ψ + = − 2 Δ E ψ − ψ + . {\displaystyle \psi _{+}\nabla ^{2}\psi _{-}-\psi _{-}\nabla ^{2}\psi _{+}={}-2\,\Delta E\,\psi _{-}\psi _{+}\;.} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Allogene Therapeutics </page_title> <path> Allogene_Therapeutics > Development history > 2015 </path> <section_title> 2015 </section_title> <content> In January, Kite Pharma and Amgen entered into a strategic research collaboration and license agreement to develop and commercialize the next generation of novel Chimeric Antigen Receptor (CAR) T cell immunotherapies based on Kite's engineered autologous cell therapy platform and Amgen's extensive array of cancer targets.Kite Pharma announced in May, that the first patient in its Phase 1/2 clinical trial of KTE-C19 in patients with refractory aggressive Non-Hodgkin's Lymphoma has been treated.In June, Kite Pharma and bluebird bio, Inc. announced they have entered into a collaboration agreement to co-develop and co-commercialize second generation T cell receptor product candidates directed against the human papillomavirus type 16 E6 onco protein incorporating gene editing and lentiviral technologies.In July, Kite Pharma and the Leukemia & Lymphoma Society announced that they have entered into a partnership to enhance the development of Kite's lead product candidate, KTE-C19, for the treatment of patients with refractory aggressive Non-Hodgkin's Lymphoma.In September, Kite Pharma announced that it has expanded its collaboration with the Netherlands Cancer Institute (NKI). Kite and the NKI have entered into an agreement under which Kite will receive from the NKI the exclusive option to license multiple T cell receptor (TCR) gene sequences for the development and commercialization of cancer immunotherapy candidates targeting solid tumors. Kite has also expanded its access to additional resources and research facilities through a master services agreement with the NKI.In October, Kite Pharma announced that it has entered into an exclusive, worldwide license with the National Institutes of Health (NIH) for intellectual property related to T cell receptor (TCR)-based product candidates directed against MAGE A3 and A3/A6 antigens for the treatment of tumors expressing MAGE, which include lung, pancreatic, gastric, and breast cancers, among others. In the same month, Kite Pharma announced that it has entered into a worldwide research and license agreement with Alpine Immune Sciences (AIS), a privately held biotechnology startup, to discover and develop protein-based immunotherapies targeting the immune synapse to treat cancer. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Divisibility rule </page_title> <path> Divisibility_rule > Generalized divisibility rule </path> <section_title> Generalized divisibility rule </section_title> <content> Then mq+t = 10×3+91 = 121; this is divisible by 11 (with quotient 11), so 913 is also divisible by 11. As another example, to determine if 689 = 10×68 + 9 is divisible by 53, find that m = (53×3+1)÷10 = 16. Then mq+t = 16×9 + 68 = 212, which is divisible by 53 (with quotient 4); so 689 is also divisible by 53. Alternatively, any number Q = 10c + d is divisible by n = 10a + b, such that gcd(n, 2, 5) = 1, if c + D(n)d = An for some integer A, where: D ( n ) ≡ { 9 a + 1 , if n = 10a+1 3 a + 1 , if n = 10a+3 7 a + 5 , if n = 10a+7 a + 1 , if n = 10a+9 {\displaystyle D(n)\equiv {\begin{cases}9a+1,&{\mbox{if }}n{\mbox{ = 10a+1}}\\3a+1,&{\mbox{if }}n{\mbox{ = 10a+3}}\\7a+5,&{\mbox{if }}n{\mbox{ = 10a+7}}\\a+1,&{\mbox{if }}n{\mbox{ = 10a+9}}\end{cases}}\ } The first few terms of the sequence, generated by D(n), are 1, 1, 5, 1, 10, 4, 12, 2, ... (sequence A333448 in OEIS). The piece wise form of D(n) and the sequence generated by it were first published by Bulgarian mathematician Ivan Stoykov in March 2020. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Monitor lizards </page_title> <path> Monitor_lizards > Etymology </path> <section_title> Etymology </section_title> <content> But all of these explanations for the name "monitor" postdate Linnaeus giving the scientific name Lacerta monitor to the Nile monitor in 1758, which may have been based on a mistaken idea by Linnaeus that the German word Waran (borrowed from Arabic) was connected to warnen (to warn), leading him to incorrectly Latinize it as monitor ('warner', 'adviser').Austronesian languages spoken across Southeast Asia, where varanids are common, have a large number of slightly related local names for them. They are usually known as biawak (Malay, including Indonesian standard variety), bayawak (Filipino), binjawak or minjawak or nyambik (Javanese), or variations thereof. Other names include hokai (Solomon Islands); bwo, puo, or soa (Maluku); halo (Cebu); galuf or kaluf (Micronesia and the Caroline Islands); batua or butaan (Luzon); alu (Bali); hora or ghora (Komodo group of islands); phut (Burmese); and guibang (Manobo).In South Asia, they are known as hangkok in Meitei, mwpou in Boro, ghorpad घोरपड in Marathi, uḍumbu உடும்பு in Tamil and Malayalam, bilgoh in Bhojpuri, gohi (गोहि) in Maithili, in Sinhala as තලගොයා / කබරගොයා (talagoya / kabaragoya ), in Telugu as uḍumu (ఉడుము), in Kannada as uḍa (ಉಡ), in Punjabi and Magahi as गोह (goh), in Assamese as gui xaap, in Odia as ଗୋଧି (godhi), and in Bengali as গোসাপ (goshaap) or গুইসাপ (guishaap), and गोह (goh) in Hindi. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> I. I. Rabi Award </page_title> <path> I._I._Rabi_Award > Recipients </path> <section_title> Recipients </section_title> <content> 1983 - I. I. Rabi 1984 - David W. Allan 1985 - Norman Ramsey, Nobel Prize in 1989 1986 - Jerrold R. Zacharias 1987 - Louis Essen 1988 - Gernot M. R. Winkler 1989 - Leonard S. Cutler 1990 - Claude Audoin 1991 - Andrea De Marchi 1992 - James A. Barnes 1993 - Robert F. C. Vessot 1994 - Jacques Vanier 1995 - Fred L. Walls 1996 - Andre Clairon and Robert E. Drullinger 1997 - Harry E. Peters and Nikolai A. Demidov 1998 - David J. Wineland, Nobel Prize in 2012 1999 - Bernard Guinot 2000 - William J. Riley Jr. 2001 - Lute Maleki 2002 - Jon H. Shirley 2003 - Andreas Bauch 2005 - Theodor W. Hänsch, Nobel Prize in 2005 2004 - John L. Hall, Nobel Prize in 2005 2006 - James C. Bergquist 2007 - Patrick Gill and Leo Hollberg 2008 - Hidetoshi Katori 2009 - John D. Prestage 2010 - Long Sheng Ma 2011 - Fritz Riehle 2012 - James Camparo 2013 - Judah Levine 2014 - Harald R. Telle 2015 - Ulrich_L._Rohde 2016 - John Kitching 2017 - Scott Diddams 2018 - Jun Ye 2019 - Steven Jefferts 2020 - Robert Lutwak 2021 - Ekkehard Peik </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Kolmogorov–Smirnov statistic </page_title> <path> Kolmogorov–Smirnov_statistic > Kolmogorov distribution </path> <section_title> Kolmogorov distribution </section_title> <content> The Kolmogorov distribution is the distribution of the random variable K = sup t ∈ \| B ( t ) \| {\displaystyle K=\sup _{t\in }\|B(t)\|} where B(t) is the Brownian bridge. The cumulative distribution function of K is given by Pr ⁡ ( K ≤ x ) = 1 − 2 ∑ k = 1 ∞ ( − 1 ) k − 1 e − 2 k 2 x 2 = 2 π x ∑ k = 1 ∞ e − ( 2 k − 1 ) 2 π 2 / ( 8 x 2 ) , {\displaystyle \operatorname {Pr} (K\leq x)=1-2\sum _{k=1}^{\infty }(-1)^{k-1}e^{-2k^{2}x^{2}}={\frac {\sqrt {2\pi }}{x}}\sum _{k=1}^{\infty }e^{-(2k-1)^{2}\pi ^{2}/(8x^{2})},} which can also be expressed by the Jacobi theta function ϑ 01 ( z = 0 ; τ = 2 i x 2 / π ) {\displaystyle \vartheta _{01}(z=0;\tau =2ix^{2}/\pi )} . Both the form of the Kolmogorov–Smirnov test statistic and its asymptotic distribution under the null hypothesis were published by Andrey Kolmogorov, while a table of the distribution was published by Nikolai Smirnov. Recurrence relations for the distribution of the test statistic in finite samples are available.Under null hypothesis that the sample comes from the hypothesized distribution F(x), n D n → n → ∞ sup t \| B ( F ( t ) ) \| {\displaystyle {\sqrt {n}}D_{n}{\xrightarrow {n\to \infty }}\sup _{t}\|B(F(t))\|} in distribution, where B(t) is the Brownian bridge. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Appell–Humbert theorem </page_title> <path> Appell–Humbert_theorem > Statement </path> <section_title> Statement </section_title> <content> Suppose that T {\displaystyle T} is a complex torus given by V / Λ {\displaystyle V/\Lambda } where Λ {\displaystyle \Lambda } is a lattice in a complex vector space V {\displaystyle V} . If H {\displaystyle H} is a Hermitian form on V {\displaystyle V} whose imaginary part E = Im ( H ) {\displaystyle E={\text{Im}}(H)} is integral on Λ × Λ {\displaystyle \Lambda \times \Lambda } , and α {\displaystyle \alpha } is a map from Λ {\displaystyle \Lambda } to the unit circle U ( 1 ) = { z ∈ C: \| z \| = 1 } {\displaystyle U(1)=\{z\in \mathbb {C} :\|z\|=1\}} , called a semi-character, such that α ( u + v ) = e i π E ( u , v ) α ( u ) α ( v ) {\displaystyle \alpha (u+v)=e^{i\pi E(u,v)}\alpha (u)\alpha (v)\ } then α ( u ) e π H ( z , u ) + H ( u , u ) π / 2 {\displaystyle \alpha (u)e^{\pi H(z,u)+H(u,u)\pi /2}\ } is a 1-cocycle of Λ {\displaystyle \Lambda } defining a line bundle on T {\displaystyle T} . For the trivial Hermitian form, this just reduces to a character. Note that the space of character morphisms is isomorphic with a real torus Hom Ab ( Λ , U ( 1 ) ) ≅ R 2 n / Z 2 n {\displaystyle {\text{Hom}}_{\textbf {Ab}}(\Lambda ,U(1))\cong \mathbb {R} ^{2n}/\mathbb {Z} ^{2n}} if Λ ≅ Z 2 n {\displaystyle \Lambda \cong \mathbb {Z} ^{2n}} since any such character factors through R {\displaystyle \mathbb {R} } composed with the exponential map. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Maximum-flow problem </page_title> <path> Max_flow > Application > Minimum path cover in directed acyclic graph </path> <section_title> Minimum path cover in directed acyclic graph </section_title> <content> Given a directed acyclic graph G = ( V , E ) {\displaystyle G=(V,E)} , we are to find the minimum number of vertex-disjoint paths to cover each vertex in V {\displaystyle V} . We can construct a bipartite graph G ′ = ( V out ∪ V in , E ′ ) {\displaystyle G'=(V_{\textrm {out}}\cup V_{\textrm {in}},E')} from G {\displaystyle G} , where V out = { v out ∣ v ∈ V ∧ v has outgoing edge(s) } {\displaystyle V_{\textrm {out}}=\{v_{\textrm {out}}\mid v\in V\land v{\text{ has outgoing edge(s)}}\}} V in = { v in ∣ v ∈ V ∧ v has incoming edge(s) } {\displaystyle V_{\textrm {in}}=\{v_{\textrm {in}}\mid v\in V\land v{\text{ has incoming edge(s)}}\}} E ′ = { ( u out , v in ) ∈ V o u t × V i n ∣ ( u , v ) ∈ E } {\displaystyle E'=\{(u_{\textrm {out}},v_{\textrm {in}})\in V_{out}\times V_{in}\mid (u,v)\in E\}} .Then it can be shown that G ′ {\displaystyle G'} has a matching M {\displaystyle M} of size m {\displaystyle m} if and only if G {\displaystyle G} has a vertex-disjoint path cover C {\displaystyle C} containing m {\displaystyle m} edges and n − m {\displaystyle n-m} paths, where n {\displaystyle n} is the number of vertices in G {\displaystyle G} . Therefore, the problem can be solved by finding the maximum cardinality matching in G ′ {\displaystyle G'} instead. Assume we have found a matching M {\displaystyle M} of G ′ {\displaystyle G'} , and constructed the cover C {\displaystyle C} from it. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Decimal64 floating-point format </page_title> <path> Decimal64_floating-point_format > Representation of decimal64 values > Binary integer significand field </path> <section_title> Binary integer significand field </section_title> <content> This format uses a binary significand from 0 to 1016 − 1 = 9999999999999999 = 2386F26FC0FFFF16 = 1000111000011011110010011011111100000011111111111111112. The encoding, completely stored on 64 bits, can represent binary significands up to 10 × 250 − 1 = 11258999068426239 = 27FFFFFFFFFFFF16, but values larger than 1016 − 1 are illegal (and the standard requires implementations to treat them as 0, if encountered on input). As described above, the encoding varies depending on whether the most significant 4 bits of the significand are in the range 0 to 7 (00002 to 01112), or higher (10002 or 10012). If the 2 after the sign bit are "00", "01", or "10", then the exponent field consists of the 10 bits following the sign bit, and the significand is the remaining 53 bits, with an implicit leading 0 bit: s 00eeeeeeee (0)ttt tttttttttt tttttttttt tttttttttt tttttttttt tttttttttt s 01eeeeeeee (0)ttt tttttttttt tttttttttt tttttttttt tttttttttt tttttttttt s 10eeeeeeee (0)ttt tttttttttt tttttttttt tttttttttt tttttttttt tttttttttt This includes subnormal numbers where the leading significand digit is 0. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Eurasian reed warbler </page_title> <path> Eurasian_reed_warbler > Taxonomy </path> <section_title> Taxonomy </section_title> <content> The genus name Acrocephalus is from Ancient Greek akros, "highest", and kephale, "head". It is possible that the Naumanns thought akros meant "sharp-pointed". The specific scirpaceus is from Latin and means "reed".Ten subspecies are recognised: A. s. scirpaceus (Hermann, 1804) – breeds in Europe to west Russia, Ukraine and west Turkey, northwest Africa, winters in west, central Africa A. s. fuscus (Hemprich & Ehrenberg, 1833) – breeds in north Egypt and central Turkey through the Middle East to southeast European Russia, north Iran, Kazakhstan and northwest China; winters in eastern and southern Africa A. s. avicenniae Ash, Pearson, DJ, Nikolaus & Colston, 1989 – coasts of the Red Sea A. s. ammon Hering, Winkler & Steinheimer, 2016 – Oases along the Libya-Egypt border region A. s. ambiguus (Brehm, AE, 1857) – Iberian Peninsula and northwest Africa A. s. minor Lynes, 1923 – Sahel region from Senegal to west-central Sudan (Darfur) A. s. cinnamomeus Reichenow, 1908 – west Ethiopia and south Somalia south through South Sudan, Uganda, Kenya, Zambia and Mozambique; patchy distribution in west Africa from south Cameroon to possibly Niger and Mali A. s. suahelicus Grote, 1926 – east Tanzania to east Mozambique and eastern South Africa A. s. hallae White, CMN, 1960 – southwest Angola to southwest Zambia and south to western South Africa A. s. baeticatus (Vieillot, 1817) – north Botswana and Zimbabwe to southern South AfricaAn older scientific name for the reed warbler was Acrocephalus streperus (Vieill. ).The mostly resident Iberian and African subspecies are sometimes treated as a separate species, the African reed warbler (Acrocephalus baeticatus). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> John Hick (politician) </page_title> <path> John_Hick_(politician) > Education and early career </path> <section_title> Education and early career </section_title> <content> Educated at a private school near Alderley, Cheshire and Bolton Grammar School where he received a commercial and classical education, Hick entered Benjamin Hick's Soho Works from school and from a young age, management of the Bolton engineering firm Benjamin Hick and Son with his father. Following Benjamin Hick's death in 1842, Hick became senior partner in the family business, later Hick, Hargreaves, & Co and a member of the Institution of Civil Engineers in 1845.He was Church Warden for James Slade and warden for St Peter's church Belmont, Lancashire between 1862 and 1874, Governor of Bolton Grammar School, Town councillor for nine years from 1844, a member of the Society of Arts, founder member of the Institution of Mechanical Engineers from 1847 until 1852, member of the London Association of Foreman Engineers and Draughtsman, National Society for Promoting the Education of the Poor in the Principles of the Established Church in England and Wales, Justice of the Peace for the Borough of Bolton and Salford Hundred, liberal patron of the fine arts and a director of the London and North Western Railway under the chairmanship of Sir Richard Moon and Lord Stalbridge, from 1871 until his death.In 1839, age 23, while working for B. Hick and Son, John Hick Jr as he was referred to at the time, was awarded the silver medal by the Society of Arts for his novel invention of an expanding mandrel for turning lathes, it was an adaptation of a principle developed by Marc Brunel for pulley block manufacture at Portsmouth and received the praise of three eminent engineers; Bryan Donkin, Joshua Field and John Rennie.During 1842, Hick was awarded a second silver medal by the Society of Arts for his invention of an Elliptograph; conceived in 1840, the device provided a simple and accurate solution for the drawing ellipsoid forms of various proportions. Hick received further praise from James Nasmyth, William Fairbairn, Joseph Whitworth, and amongst others, Charles Holtzapffel, Chairman of the Committee of Mechanics. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Phragmén–Lindelöf principle </page_title> <path> Phragmén–Lindelöf_principle > Example of application </path> <section_title> Example of application </section_title> <content> This allows us to find an x 0 {\displaystyle x_{0}} such that \| f ( z ) h ϵ ( z ) \| ≤ 1 {\displaystyle \|f(z)h_{\epsilon }(z)\|\leq 1} whenever z ∈ S ¯ {\displaystyle z\in {\overline {S}}} and \| ℜ ( z ) \| ≥ x 0 {\displaystyle \|\Re (z)\|\geq x_{0}} . Because S x 0 {\displaystyle S_{x_{0}}} is a bounded region, and \| f ( z ) h ϵ ( z ) \| ≤ 1 {\displaystyle \|f(z)h_{\epsilon }(z)\|\leq 1} for all z ∈ ∂ S x 0 {\displaystyle z\in \partial S_{x_{0}}} , the maximum modulus principle implies that \| f ( z ) h ϵ ( z ) \| ≤ 1 {\displaystyle \|f(z)h_{\epsilon }(z)\|\leq 1} for all z ∈ S x 0 ¯ {\displaystyle z\in {\overline {S_{x_{0}}}}} . Since \| f ( z ) h ϵ ( z ) \| ≤ 1 {\displaystyle \|f(z)h_{\epsilon }(z)\|\leq 1} whenever z ∈ S {\displaystyle z\in S} and \| ℜ ( z ) \| > x 0 {\displaystyle \|\Re (z)\|>x_{0}} , \| f ( z ) h ϵ ( z ) \| ≤ 1 {\displaystyle \|f(z)h_{\epsilon }(z)\|\leq 1} in fact holds for all z ∈ S {\displaystyle z\in S} . Finally, because f h ϵ → f {\displaystyle fh_{\epsilon }\to f} as ϵ → 0 {\displaystyle \epsilon \to 0} , we conclude that \| f ( z ) \| ≤ 1 {\displaystyle \|f(z)\|\leq 1} for all z ∈ S {\displaystyle z\in S} . Q.E.D. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Black-body radiation </page_title> <path> Black-body_radiation > Applications > Temperature relation between a planet and its star </path> <section_title> Temperature relation between a planet and its star </section_title> <content> The actual temperature of the planet will likely be different, depending on its surface and atmospheric properties. Ignoring the atmosphere and greenhouse effect, the planet, since it is at a much lower temperature than the Sun, emits mostly in the infrared (IR) portion of the spectrum. In this frequency range, it emits ϵ ¯ {\displaystyle {\overline {\epsilon }}} of the radiation that a black body would emit where ϵ ¯ {\displaystyle {\overline {\epsilon }}} is the average emissivity in the IR range. The power emitted by the planet is then: P e m t = ϵ ¯ P e m t b b ( 5 ) {\displaystyle P_{\rm {emt}}={\overline {\epsilon }}\,P_{\rm {emt\,bb}}\qquad \qquad (5)} For a body in radiative exchange equilibrium with its surroundings, the rate at which it emits radiant energy is equal to the rate at which it absorbs it: P a b s = P e m t ( 6 ) {\displaystyle P_{\rm {abs}}=P_{\rm {emt}}\qquad \qquad (6)} Substituting the expressions for solar and planet power in equations 1–6 and simplifying yields the estimated temperature of the planet, ignoring greenhouse effect, TP: T P = T S R S 1 − α ε ¯ 2 D ( 7 ) {\displaystyle T_{P}=T_{S}{\sqrt {\frac {R_{S}{\sqrt {\frac {1-\alpha }{\overline {\varepsilon }}}}}{2D}}}\qquad \qquad (7)} In other words, given the assumptions made, the temperature of a planet depends only on the surface temperature of the Sun, the radius of the Sun, the distance between the planet and the Sun, the albedo and the IR emissivity of the planet. Notice that a gray (flat spectrum) ball where ( 1 − α ) = ε ¯ {\displaystyle ({1-\alpha })={\overline {\varepsilon }}} comes to the same temperature as a black body no matter how dark or light gray. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Tortoise beetle </page_title> <path> Tortoise_beetle > Taxonomy </path> <section_title> Taxonomy </section_title> <content> It includes both the former subfamily "Hispinae" (leaf-mining beetles), as well as the former more narrowly defined subfamily Cassidinae (familiar as tortoise beetles) which are now split into several tribes that include the tribe Cassidini, and in all include over 125 genera. The traditional separation of the two groups was based essentially on the habitats of the larvae and the general shapes of the adults. The name Cassidinae for the merged subfamily is considered to have priority.The former grouping of "Hispinae" (sometimes called leaf-mining beetles, or "hispoids") included the tribes Alurnini, Anisoderini, Aproidini, Arescini, Bothryonopini, Callispini, Callohispini, Cephaloleiini, Chalepini, Coelaenomenoderini, Cryptonychini, Cubispini, Eurispini, Exothispini, Gonophorini, Hispini, Hispoleptini, Hybosispini, Leptispini, Oediopalpini, Oncocephalini, Promecothecini, Prosopodontini, Sceloenoplini and Spilophorini. Most members of these tribes are elongated, slightly flattened beetles with parallel margins, and antennal bases close together on their small heads. They often have punctate elytra and pronotum, sometimes with spines both on and along the edges. The former grouping of Cassidinae (sometimes called tortoise beetles, or "cassidoids") included the tribes Aspidimorphini, Basiprionotini, Cassidini, Delocraniini, Dorynotini, Eugenysini, Goniocheniini, Hemisphaerotini, Mesomphaliini, Notosacanthini, Omocerini and Physonotini.The subfamily names Cassidinae and Hispinae are both founded by Gyllenhal in the same 1813 book, but following the Principle of the First Reviser, Chen in this case, priority is given to the name Cassidinae. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Butcher tableau </page_title> <path> Runge–Kutta_method > Implicit Runge–Kutta methods > Examples </path> <section_title> Examples </section_title> <content> Its Butcher tableau is: 0 0 0 1 1 2 1 2 1 2 1 2 1 0 {\displaystyle {\begin{array}{c\|cc}0&0&0\\1&{\frac {1}{2}}&{\frac {1}{2}}\\\hline &{\frac {1}{2}}&{\frac {1}{2}}\\&1&0\\\end{array}}} The trapezoidal rule is a collocation method (as discussed in that article). All collocation methods are implicit Runge–Kutta methods, but not all implicit Runge–Kutta methods are collocation methods.The Gauss–Legendre methods form a family of collocation methods based on Gauss quadrature. A Gauss–Legendre method with s stages has order 2s (thus, methods with arbitrarily high order can be constructed). The method with two stages (and thus order four) has Butcher tableau: 1 2 − 1 6 3 1 4 1 4 − 1 6 3 1 2 + 1 6 3 1 4 + 1 6 3 1 4 1 2 1 2 1 2 + 1 2 3 1 2 − 1 2 3 {\displaystyle {\begin{array}{c\|cc}{\frac {1}{2}}-{\frac {1}{6}}{\sqrt {3}}&{\frac {1}{4}}&{\frac {1}{4}}-{\frac {1}{6}}{\sqrt {3}}\\{\frac {1}{2}}+{\frac {1}{6}}{\sqrt {3}}&{\frac {1}{4}}+{\frac {1}{6}}{\sqrt {3}}&{\frac {1}{4}}\\\hline &{\frac {1}{2}}&{\frac {1}{2}}\\&{\frac {1}{2}}+{\frac {1}{2}}{\sqrt {3}}&{\frac {1}{2}}-{\frac {1}{2}}{\sqrt {3}}\end{array}}} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> L-140 Turbolet </page_title> <path> L-140_Turbolet > Specifications (L-410 UVP-E20) </path> <section_title> Specifications (L-410 UVP-E20) </section_title> <content> Data from LETGeneral characteristics Crew: 2 Capacity: 19 passengers / 1,800 kg (3,968 lb) payload Length: 14.42 m (47 ft 4 in) Wingspan: 19.98 m (65 ft 7 in) Height: 5.97 m (19 ft 7 in) Wing area: 34.86 m2 (375.2 sq ft) Aspect ratio: 11.45 Airfoil: root: NACA 63A418; tip: NACA 63A412 Empty weight: 4,200 kg (9,259 lb) Max takeoff weight: 6,600 kg (14,551 lb) Fuel capacity: 1,300 kg (2,866 lb) Powerplant: 2 × General Electric H80-200 turboprop engines, 597 kW (801 hp) each Propellers: 5-bladed Avia AV 725, 2.3 m (7 ft 7 in) diameterPerformance Cruise speed: 405 km/h (252 mph, 219 kn) max cruise Range: 1,500 km (930 mi, 810 nmi) 1,800 kg (3,968 lb) payload, ISA, FL140, 45 min reserve Endurance: Five hours and six minutes Service ceiling: 8,382 m (27,500 ft) Rate of climb: 8.5 m/s (1,670 ft/min) Fuel consumption: 240 kg/h (529 lb/h) Take-off run: 510 m (1,673 ft) (ISA, SL, MTOW) Landing run: 500 m (1,640 ft) (ISA, SL, MTOW) </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Matrix logarithm </page_title> <path> Logarithm_of_a_matrix > Constraints in the 2 × 2 case </path> <section_title> Constraints in the 2 × 2 case </section_title> <content> The other three quadrants are images of this one under the Klein four-group generated by ε and −1. For example, let a = log 2 ; then cosh a = 5/4 and sinh a = 3/4. For matrices, this means that A = exp ⁡ ( 0 a a 0 ) = ( cosh ⁡ a sinh ⁡ a sinh ⁡ a cosh ⁡ a ) = ( 1.25 .75 .75 1.25 ) {\displaystyle A=\exp {\begin{pmatrix}0&a\\a&0\end{pmatrix}}={\begin{pmatrix}\cosh a&\sinh a\\\sinh a&\cosh a\end{pmatrix}}={\begin{pmatrix}1.25&.75\\.75&1.25\end{pmatrix}}} .So this last matrix has logarithm log ⁡ A = ( 0 log ⁡ 2 log ⁡ 2 0 ) {\displaystyle \log A={\begin{pmatrix}0&\log 2\\\log 2&0\end{pmatrix}}} .These matrices, however, do not have a logarithm: ( 3 / 4 5 / 4 5 / 4 3 / 4 ) , ( − 3 / 4 − 5 / 4 − 5 / 4 − 3 / 4 ) , ( − 5 / 4 − 3 / 4 − 3 / 4 − 5 / 4 ) {\displaystyle {\begin{pmatrix}3/4&5/4\\5/4&3/4\end{pmatrix}},\ {\begin{pmatrix}-3/4&-5/4\\-5/4&-3/4\end{pmatrix}},\ {\begin{pmatrix}-5/4&-3/4\\-3/4&-5/4\end{pmatrix}}} .They represent the three other conjugates by the four-group of the matrix above that does have a logarithm. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Aerial surveillance </page_title> <path> Surveillance_aircraft > Current use > Business aircraft </path> <section_title> Business aircraft </section_title> <content> With smaller equipment, long-range business aircraft can be modified in surveillance aircraft to perform specialized missions cost-effectively, from ground surveillance to maritime patrol: the 99,500 lb (45,100 kg), 6,000 nmi Bombardier Global 6000 is the platform for the USAF Northrop Grumman E-11A Battlefield Airborne Communications Node, the radar-carrying ground-surveillance Raytheon Sentinel for the UK Royal Air Force, and Saab's GlobalEye AEW&C carrying its Erieye AESA radar as UK's Marshall ADG basis for Elint/Sigint for the United Arab Emirates; it is also the base for the proposed Saab AB Swordfish MPA and the USAF Lockheed Martin J-Stars Recap battlefield-surveillance program, while IAI's ELI-3360 MPA is based on the Global 5000; The 91,000 lb (41,000 kg), 6,750 nmi Gulfstream G550 was selected for the IAI EL/W-2085 Conformal Airborne Early Warning AESA radar for Italy, Singapore and Israel (which also has IAI Sigint G550s) while L3 Technologies transfers the U.S. Compass Call electronic-attack system to the G550 CAEW-based EC-37B, like the NC-37B range-support aircraft, and will modify others for Australia's AISREW program, Northrop Grumman proposes the G550 for the J-Stars Recap; Dassault Aviation developed the Falcon 900 MPA and Falcon 2000 Maritime Multirole Aircraft for France (which delayed its Avsimar requirement), South Korea and the Japan Coast Guard with a mission system developed with L3 and Thales Group; Embraer delivered several EMB-145s as a platform for AEW&C, MPA and multi-intelligence; the Beechcraft King Air 350ER is a platform for ISR versions, including L3's Spyder II and Sierra Nevada Corp.’s Scorpion and as the MC-12W for the U.S. Army. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Spring system </page_title> <path> Spring_system > Known spring lengths </path> <section_title> Known spring lengths </section_title> <content> If the nominal lengths, L, of the springs are known to be 1 and 2 units respectively, then the system can be solved as follows: Consider the simple case of three nodes connected by two springs. Then the stretching of the two springs is given as a function of the positions of the nodes by Δ L = x − L = B ⊤ x − L {\displaystyle \Delta \mathbf {L} ={\begin{bmatrix}1&-1&0\\0&1&-1\end{bmatrix}}\mathbf {x} -\mathbf {L} =B^{\top }\mathbf {x} -\mathbf {L} } where B ⊤ {\displaystyle B^{\top }} is the matrix transpose of the incidence matrix B = , {\displaystyle B={\begin{bmatrix}1&0\\-1&1\\0&-1\end{bmatrix}},} relating each degree of freedom to the direction each spring pulls on it. The forces on the springs are F springs = − W Δ L = − W ( B ⊤ x − L ) = − W B ⊤ x + W L {\displaystyle F_{\text{springs}}=-W\Delta \mathbf {L} =-W(B^{\top }\mathbf {x} -\mathbf {L} )=-WB^{\top }\mathbf {x} +W\mathbf {L} } where W is a diagonal matrix giving the stiffness of every spring. Then the force on the nodes is given by left multiplying by B {\displaystyle B} , which we set to zero to find equilibrium: F nodes = − B W B ⊤ x + B W L = 0 {\displaystyle F_{\text{nodes}}=-BWB^{\top }\mathbf {x} +BW\mathbf {L} =0} which gives the linear equation: B W B ⊤ x = B W L {\displaystyle BWB^{\top }\mathbf {x} =BW\mathbf {L} } .Now, the matrix B W B ⊤ {\displaystyle BWB^{\top }} is singular, because all solutions are equivalent up to rigid-body translation. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Ancient Greek accent </page_title> <path> Ancient_Greek_accent > Accent shift laws > Wheeler's Law </path> <section_title> Wheeler's Law </section_title> <content> Wheeler's Law, suggested in 1885, refers to a process whereby words with a dactylic ending ( ) (counting endings such as -on, -os, -oi as short), if they were oxytone in Proto-Indo-European, became paroxytone in Greek. It is also known as the "law of dactylic retraction".This law is used to explain the paroxytone accent in words such as the following: Adjectives such as ποικίλος poikílos 'multicoloured', ἐναντίος enantíos 'opposite', πλησίος plēsíos 'near' Names such as Αἰσχύλος Aiskhúlos 'Aeschylus' Perfect passive and middle participles such as δεδεγμένος dedegménos 'having received' Paroxytone compound words with active meaning such as ἀνδροκτόνος androktónos 'man-slaying', βουκόλος boukólos 'cowherd' Dative plurals such as πατράσι patrási 'fathers', ἀνδράσι andrási 'men'Similar words and endings in Sanskrit are regularly accented on the final syllable, and active compounds which do not have a dactylic rhythm often have final accent, e.g. ψυχοπομπός psukhopompós 'soul-escorting'. There are numerous exceptions to Wheeler's Law, especially words ending in -ικός -ikós or -ικόν -ikón (for example, ναυτικόν nautikón 'fleet'), which are always oxytone. There are also participles such as δεδομένος dedoménos or feminine δεδομένη dedoménē 'given', which have penultimate accent despite not being dactylic. These exceptions are usually explained as being due to analogical processes. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Uniform integrability </page_title> <path> Uniform_integrability > Probability definition </path> <section_title> Probability definition </section_title> <content> In the theory of probability, Definition A or the statement of Theorem 1 are often presented as definitions of uniform integrability using the notation expectation of random variables., that is, 1. A class C {\displaystyle {\mathcal {C}}} of random variables is called uniformly integrable if: There exists a finite M {\displaystyle M} such that, for every X {\displaystyle X} in C {\displaystyle {\mathcal {C}}} , E ⁡ ( \| X \| ) ≤ M {\displaystyle \operatorname {E} (\|X\|)\leq M} and For every ε > 0 {\displaystyle \varepsilon >0} there exists δ > 0 {\displaystyle \delta >0} such that, for every measurable A {\displaystyle A} such that P ( A ) ≤ δ {\displaystyle P(A)\leq \delta } and every X {\displaystyle X} in C {\displaystyle {\mathcal {C}}} , E ⁡ ( \| X \| I A ) ≤ ε {\displaystyle \operatorname {E} (\|X\|I_{A})\leq \varepsilon } .or alternatively 2. A class C {\displaystyle {\mathcal {C}}} of random variables is called uniformly integrable (UI) if for every ε > 0 {\displaystyle \varepsilon >0} there exists K ∈ [ 0 , ∞ ) {\displaystyle K\in [0,\infty )} such that E ⁡ ( \| X \| I \| X \| ≥ K ) ≤ ε for all X ∈ C {\displaystyle \operatorname {E} (\|X\|I_{\|X\|\geq K})\leq \varepsilon \ {\text{ for all }}X\in {\mathcal {C}}} , where I \| X \| ≥ K {\displaystyle I_{\|X\|\geq K}} is the indicator function I \| X \| ≥ K = { 1 if \| X \| ≥ K , 0 if \| X \| < K . {\displaystyle I_{\|X\|\geq K}={\begin{cases}1&{\text{if }}\|X\|\geq K,\\0&{\text{if }}\|X\| </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Reorganization plan of United States Army </page_title> <path> Reorganization_plan_of_United_States_Army > Reorganization plans by unit type > Modular combat brigades </path> <section_title> Modular combat brigades </section_title> <content> a brigade support battalion (BSB), consisting of a headquarters, medical, distribution and maintenance company, plus six forward support companies, each of which support one of the three combined arms battalions, the cavalry squadron, the engineer battalion and the field artillery battalion. 61 officers, 14 warrant officers, 1,019 enlisted personnel – total: 1,094 soldiers.Infantry Brigade Combat Team, or IBCTs, comprised around 3,300 soldiers, in the pre-2013 design, which did not include the 3rd maneuver battalion. The 2013 end-strength is now 4,413 Soldiers: Special Troops Battalion (now Brigade Engineer Battalion) Cavalry Squadron (2), later (3) Infantry Battalions Field Artillery Battalion Brigade Support BattalionStryker Brigade Combat Team or SBCTs comprised about 3,900 soldiers, making it the largest of the three combat brigade constructs in the 2006 design, and over 4,500 Soldiers in the 2013 reform. Its design includes: Headquarters Company Cavalry Squadron (with three 14-vehicle, two-120 mm mortar reconnaissance troops plus a surveillance troop with UAVs and NBC detection capability) (3) Stryker infantry battalions (each with three rifle companies with 12 infantry-carrying vehicles, 3 mobile gun platforms, 2 120 mm mortars, and around 100 infantry dismounts each, plus an HHC with scout, mortar and medical platoons and a sniper section.) Engineer Company (folded into the Brigade Engineer Battalion) Signal Company (folded into the Brigade Engineer Battalion) Military Intelligence Company (with UAV platoon) (folded into the Brigade Engineer Battalion) Anti-tank company (9 TOW-equipped Stryker vehicles) (folded into the Brigade Engineer Battalion) Field Artillery Battalion (three 6-gun 155 mm Howitzer batteries, target acquisition platoon, and a joint fires cell) Brigade Support Battalion (headquarters, medical, maintenance, and distribution companies) </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Islamic extremism </page_title> <path> Islamic_extremism > UK High Court rulings > October 2016 Shakeel Begg case </path> <section_title> October 2016 Shakeel Begg case </section_title> <content> A total, eternal 'Manichean' worldview is a central tenet of violent Islamic extremism. It divides the world strictly into 'Us' versus 'Them': those who are blessed or saved (i.e. the "right kind" of Muslim) on the one hand and those who are to be damned for eternity (i.e. the "wrong kind" of Muslim and everyone else) on the other. For violent Islamic extremists, the "wrong kind" of Muslim includes moderate Sunni Muslims, all Shia Muslims, and many others who are "mete for the sword" and can be killed, and anyone who associates or collaborates" with them... Second, the reduction of jihad (striving in God's cause) to qital (armed combat) ('the Lesser Jihad')... Third, the ignoring or flouting of the conditions for the declaration of armed jihad (qital), i.e. the established Islamic doctrinal conditions for the declaration of armed combat (qital) set out above... Fourth, the ignoring or flouting of the strict regulations governing the conduct of armed jihad, i.e. the stipulations in the Qur'an and the Sunna for the ethics of conducting qital set out above. Thus, the use of excessive violence, attacks on civilians, indiscriminate 'suicide' violence and the torture or the murder of prisoners would constitute violation of these regulations of jihad... Fifth, advocating armed fighting in defence of Islam (qital) as a universal individual religious obligation (fard al 'ayn)... Sixth, any interpretation of Shari'a (i.e. religious law laid down by the Qur'an and the Sunna) that required breaking the 'law of the land'... Seventh, the classification of all non-Muslims as unbelievers (kuffar)... Eighth, the extreme Salafist Islamism doctrine that the precepts of the Muslim faith negate and supersede all other natural ties, such as those of family, kinship and nation... Ninth, the citing with approval the fatwa (legal opinions) of Islamic scholars who espouse extremist view... Tenth, any teaching which, expressly or implicitly, encourages Muslims to engage in, or support, terrorism or violence in the name of Allah. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Press camera </page_title> <path> Press_camera > List of press cameras </path> <section_title> List of press cameras </section_title> <content> BeselerBeseler 4×5 Burke & James Press, Burke & James Inc., Chicago, U.S.A.B & J Press (4×5) Watson (2×3) Busch PressmanModel C (2×3) Model D (4×5) Tower Press (2×3, 4×5) = Sears Tower branded Busch Pressman Goerz Anschutz Ango series Graflex, the classic American press camera Speed Graphic (3¼×4¼, 4×5") Miniature Speed Graphic (2¼x3¼") Crown Graphic (3¼×4¼, 4×5") Miniature Crown Graphic (2¼x3¼") Century Graphic (2¼x3¼") Super Crown Graphic (4×5") Super Speed Graphic (4×5") Pacemaker Speed Graphic (2¼x3¼, 3¼×4¼, 4×5") Pacemaker Crown Graphic (2¼x3¼, 3¼×4¼, 4×5") Ihagee Zweiverschluss Duplex (6.5x9 cm, 9x12 cm and 10x15 cm) Kalart Press (3×4) LinhofSuper Technika Linhof Technika Press, model of both Graflex XL and Mamiya Press Linhof Press 70 Linhof Press (4×5) = Technika III with limited movements Mamiya Mamiya Press Mamiya Universal Meridan 45 (A, B, maybe C) Micro Precision Products MPP MicroPress—English design focal plane shutter camera from 1950s, based on Speed Graphic model with the rangefinder mounted horizontally at the top Omega Koni Omega Rapid Omega Plaubel Makina Polaroid Polaroid 600/600 SE Press King, B&W Manufacturing Co., Ontario, Canada Ramlose Model A (4×5) Thornton-Pickard, Topcon / Komamura Topcon Horseman (2¼ x 3¼) Models 760, 960, 970, 980, 985, VH and VHR Toyo Super Graphic (4×5) Van Neck, Wista 45RF </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Decimal expansion </page_title> <path> Decimal_representation > Types > Finite </path> <section_title> Finite </section_title> <content> The decimal expansion of non-negative real number x will end in zeros (or in nines) if, and only if, x is a rational number whose denominator is of the form 2n5m, where m and n are non-negative integers. Proof: If the decimal expansion of x will end in zeros, or x = ∑ i = 0 n a i 10 i = ∑ i = 0 n 10 n − i a i / 10 n {\textstyle x=\sum _{i=0}^{n}{\frac {a_{i}}{10^{i}}}=\sum _{i=0}^{n}10^{n-i}a_{i}/10^{n}} for some n, then the denominator of x is of the form 10n = 2n5n. Conversely, if the denominator of x is of the form 2n5m, x = p 2 n 5 m = 2 m 5 n p 2 n + m 5 n + m = 2 m 5 n p 10 n + m {\displaystyle x={\frac {p}{2^{n}5^{m}}}={\frac {2^{m}5^{n}p}{2^{n+m}5^{n+m}}}={\frac {2^{m}5^{n}p}{10^{n+m}}}} for some p. While x is of the form p 10 k {\displaystyle \textstyle {\frac {p}{10^{k}}}} , p = ∑ i = 0 n 10 i a i {\displaystyle p=\sum _{i=0}^{n}10^{i}a_{i}} for some n. By x = ∑ i = 0 n 10 n − i a i / 10 n = ∑ i = 0 n a i 10 i {\displaystyle x=\sum _{i=0}^{n}10^{n-i}a_{i}/10^{n}=\sum _{i=0}^{n}{\frac {a_{i}}{10^{i}}}} , x will end in zeros. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Fantasista Doll </page_title> <path> Fantasista_Doll > Characters > Mutual Dream Association Group </path> <section_title> Mutual Dream Association Group </section_title> <content> Komachi Seishou (清正小町, Seishou Komachi) Voiced by: Kaori Nazuka Uzume's upperclassman, who is a top fashion model and often gives Uzume advice whenever she is down. She is later revealed to be the chairman of the Mutual Dream Association Group who desires Uzume's cards for some reason. She was the original owner of the Uzume's dolls. She formed the MDAG after her doll, Sonnet, was destroyed in a traffic accident, hoping to use the data from Uzume's dolls to rebuild Sonnet using her personal doll, Proto-Zero (プロトゼロ, Puroto Zero, Voiced by: Kotori Koiwai).Anne (アンヌ, Annu) Voiced by: Satomi Akesaka A dark-haired spectacled woman, who is initially thought to be the director of the MDAG.Kazunari Kira (吉良一成, Kira Kazunari) Voiced by: Yoshitsugu Matsuoka A man who sought out the MDAG to reunite with his ex-girlfriend, using any means necessary to win.Umihiro Yamada (山田海洋, Yamada Umihiro) Voiced by: Megumi Matsumoto A young boy from the MDAG.Miina Rurukawa (瑠々川みいな, Rurukawa Miina) Voiced by: Megumi Han A girl who saw her dolls as her masters as opposed to their servants.Kiyoshi Kiyomizu (清水潔, Kiyomizu Kiyoshi) Voiced by: Susumu Chiba A rugby player who sought out the MDAG so that people would appreciate rugby as a true sport instead of a way to meet girls.Rin (リン) Voiced by: Haruna Ikezawa An amateur model who is jealous of Komachi always being ahead of her.Jun Fujihisa (藤玖純, Fujihisa Jun) Voiced by: Natsuki Hanae A novice filmmaker who sought out the MDAG to get people to watch his experimental film, that tends to go under-appreciated by the general viewing public. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> UV Stabilizers in plastics </page_title> <path> UV_stabilizer > Susceptible polymers > Polyolefins </path> <section_title> Polyolefins </section_title> <content> Chain initiation Polymer ⟶ P ∙ + P ∙ {\displaystyle {\ce {Polymer->P\bullet +\ P\bullet }}} Chain propagation P ∙ + O 2 ⟶ POO ∙ {\displaystyle {\ce {P\bullet +\ O2->POO\bullet }}} POO ∙ + PH ⟶ POOH + P ∙ {\displaystyle {\ce {POO\bullet +\ PH->{POOH}+\ P\bullet }}} Chain branching POOH ⟶ PO ∙ + OH ∙ {\displaystyle {\ce {POOH->PO\bullet +\ OH\bullet }}} PH + OH ∙ ⟶ P ∙ + H 2 O {\displaystyle {\ce {{PH}+OH\bullet ->P\bullet +\ H2O}}} PO ∙ ⟶ Chain scission reactions {\displaystyle {\ce {PO\bullet ->Chain\ scission\ reactions}}} Termination POO ∙ + POO ∙ ⟶ cross linking reaction to non − radical product {\displaystyle {\ce {POO\bullet +\ POO\bullet ->cross\ linking\ reaction\ to\ non-radical\ product}}} POO ∙ + P ∙ ⟶ cross linking reaction to non − radical product {\displaystyle {\ce {POO\bullet +\ P\bullet ->cross\ linking\ reaction\ to\ non-radical\ product}}} P ∙ + P ∙ ⟶ cross linking reaction to non − radical product {\displaystyle {\ce {P\bullet +\ P\bullet ->cross\ linking\ reaction\ to\ non-radical\ product}}} Classically the carbon-centred macroradicals (P•) rapidly react with oxygen to form hydroperoxyl radicals (POO•), which in turn abstract an H atom from the polymer chain to give a hydroperoxide (POOH) and a fresh macroradical. Hydroperoxides readily undergo photolysis to give an alkoxyl macroradical radical (PO•) and a hydroxyl radical (HO•), both of which may go on to form new polymer radicals via hydrogen abstraction. Non-classical alternatives to these steps have been proposed. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Country Airplay </page_title> <path> Country_Airplay > Chart achievements > Most weeks at number one </path> <section_title> Most weeks at number one </section_title> <content> 10 weeks "You Proof" – Morgan Wallen (2022–2023)8 weeks "Amazed" – Lonestar (1999) "It's Five O'Clock Somewhere" – Alan Jackson and Jimmy Buffett (2003) "Last Night" – Morgan Wallen (2023)7 weeks "The Good Stuff" – Kenny Chesney (2002) "Have You Forgotten?" – Darryl Worley (2003) "There Goes My Life" – Kenny Chesney (2003–2004) "Live Like You Were Dying" – Tim McGraw (2004) "Beautiful Crazy" – Luke Combs (2019)6 weeks "It's Your Love" – Tim McGraw with Faith Hill (1997) "Just to See You Smile" – Tim McGraw (1998) "How Forever Feels" – Kenny Chesney (1999) "Breathe" – Faith Hill (1999–2000) "Ain't Nothing 'bout You" – Brooks & Dunn (2001) "I'm Already There" – Lonestar (2001) "Somebody Like You" – Keith Urban (2002) "19 Somethin'" – Mark Wills (2003) "Beer for My Horses" – Toby Keith duet with Willie Nelson (2003) "As Good as I Once Was" – Toby Keith (2005) "Better Life" – Keith Urban (2005) "Jesus, Take the Wheel" – Carrie Underwood (2006) "Our Song" – Taylor Swift (2007–2008) "Die a Happy Man" – Thomas Rhett (2016) "Forever After All" – Luke Combs (2021) "Thinking 'Bout You" – Dustin Lynch featuring MacKenzie Porter (2021–2022) "Rock and a Hard Place" – Bailey Zimmerman (2023)Sources: </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> 28 (number) </page_title> <path> 28_(number) > In mathematics </path> <section_title> In mathematics </section_title> <content> Twenty-eight is the sum of the totient function for the first nine integers.Since the greatest prime factor of 28 2 + 1 = 785 {\displaystyle 28^{2}+1=785} is 157, which is more than 28 twice, 28 is a Størmer number.Twenty-eight is a harmonic divisor number, a happy number, a triangular number, a hexagonal number, a Leyland number of the second kind and a centered nonagonal number.It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, 18, 28...Twenty-eight is the ninth and last number in early Indian magic square of order 3. There are twenty-eight convex uniform honeycombs. Twenty-eight is the only positive integer that has a unique Kayles nim-value. Twenty-eight is the only known number that can be expressed as a sum of the first nonnegative (or positive) integers ( 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 {\displaystyle 0+1+2+3+4+5+6+7} ), a sum of the first primes ( 2 + 3 + 5 + 7 + 11 {\displaystyle 2+3+5+7+11} ) and a sum of the first nonprimes ( 1 + 4 + 6 + 8 + 9 {\displaystyle 1+4+6+8+9} ), and it is unlikely that any other number has this property.There are twenty-eight oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.There are 28 elements of the cuboid: 8 vertices, 12 edges, 6 faces, 2 3-dimensional elements (interior and exterior). There are 28 non-equivalent ways of expressing 1000 as the sum of two prime numbers </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Discrete choice </page_title> <path> Discrete_choice > Prominent types of discrete choice models > Multinomial choice with correlation among alternatives > H. Multinomial probit </path> <section_title> H. Multinomial probit </section_title> <content> The model is the same as model G except that the unobserved terms are distributed jointly normal, which allows any pattern of correlation and heteroscedasticity: { U n i = β z n i + ε n i ε n ≡ ( ε n 1 , ⋯ , ε n J ) ∼ N ( 0 , Ω ) ⇒ P n i = Pr ( ⋂ j ≠ i β z n i + ε n i > β z n j + ε n j ) = ∫ I ( ⋂ j ≠ i β z n i + ε n i > β z n j + ε n j ) ϕ ( ε n \| Ω ) d ε n , {\displaystyle {\begin{cases}U_{ni}=\beta z_{ni}+\varepsilon _{ni}\\\varepsilon _{n}\equiv (\varepsilon _{n1},\cdots ,\varepsilon _{nJ})\sim N(0,\Omega )\end{cases}}\quad \Rightarrow \quad P_{ni}=\Pr \left(\bigcap _{j\neq i}\beta z_{ni}+\varepsilon _{ni}>\beta z_{nj}+\varepsilon _{nj}\right)=\int I\left(\bigcap _{j\neq i}\beta z_{ni}+\varepsilon _{ni}>\beta z_{nj}+\varepsilon _{nj}\right)\phi (\varepsilon _{n}\|\Omega )\;d\varepsilon _{n},} where ϕ ( ε n \| Ω ) {\displaystyle \phi (\varepsilon _{n}\|\Omega )} is the joint normal density with mean zero and covariance Ω {\displaystyle \Omega } . The integral for this choice probability does not have a closed form, and so the probability is approximated by quadrature or simulation. When Ω {\displaystyle \Omega } is the identity matrix (such that there is no correlation or heteroscedasticity), the model is called independent probit. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Alien hand syndrome </page_title> <path> Alien_hand_syndrome > Cause > Loss of inhibitions </path> <section_title> Loss of inhibitions </section_title> <content> These two intrahemispheric systems, each of which activates an opposing cortical "tropism", interact through mutual inhibition that maintains a dynamic balance between approaching toward (in other words, with "intent-to-capture" in which contact with and grasping onto the attended object is sought) versus withdrawing from (that is, with "intent-to-escape" in which distancing from the attended object is sought) environmental stimuli in the behavior of the contralateral limbs. Together, these two intrahemispheric agency systems form an integrated trans-hemispheric agency system.When the anteromedial frontal "escape" system is damaged, involuntary but purposive movements of an exploratory reach-and-grasp nature – what Denny-Brown referred to as a positive cortical tropism – are released in the contralateral limb. This is referred to as a positive cortical tropism because eliciting sensory stimuli, such as would result from tactile contact on the volar aspect of the fingers and palm of the hand, are linked to the activation of movement that increases or enhances the eliciting stimulation through a positive feedback connection (see discussion above in section entitled "Parietal and Occipital Lobes").When the posterolateral parieto-occipital "approach" system is damaged, involuntary purposive movements of a release-and-retract nature, such as levitation and instinctive avoidance – what Denny-Brown referred to as a negative cortical tropism – are released in the contralateral limb. This is referred to as a negative cortical tropism because eliciting sensory stimuli, such as would result from tactile contact on the volar aspect of the fingers and palm of the hand, are linked to the activation of movement that reduces or eliminates the eliciting stimulation through a negative feedback connection (see discussion above in section entitled "Parietal and Occipital Lobes").Each intrahemispheric agency system has the potential capability of acting autonomously in its control over the contralateral limb although unitary integrative control of the two hands is maintained through interhemispheric communication between these systems via the projections traversing the corpus callosum at the cortical level and other interhemispheric commissures linking the two hemispheres at the subcortical level. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Dominical Letter </page_title> <path> Dominical_Letter > Calculating Easter Sunday > Week table: Julian and Gregorian calendars for AD years since March 1 AD 4 </path> <section_title> Week table: Julian and Gregorian calendars for AD years since March 1 AD 4 </section_title> <content> Note that this table does not work for AD years at the early stage of the real Julian calendar before March 1 AD 4 or for any BC year, except when using the Julian calendar rules for proleptic dates (which are different from effective historic dates, whose effective calendar in use depended on the location of dated events or the location of the person using the calendar, sometimes differently between political/civil or religious purposes in places where both calendars still coexisted). The duration of months, and the number and placement of intercalated days also changed inconsistently before AD 42 in the early local Julian calendars which used native names for the months, depending on places and years, causing finally a lot of confusion in the population (so dating events precisely in that period is often difficult, unless they are correlated with observed lunar cycles, or with days of the week, or with another calendar). In these early AD years and in all BC years, with the effective Julian calendars used locally to align the counting of years (but still with the tradition inherited from the earlier Roman calendar for noting days in each year), a variable number of days at end of the months (after the last day of its ides but before the last day of calends which started the next month) were also still counted relatively from the start of the next named month (on the last day of its calends), and years were theoretically starting on March 1 (but with the last days of the year in February also counted from the New Year's Day in March). As well, all these early years were effectively counted inclusively and positively from a different, much earlier epoch in other eras, such as the supposed foundation of Rome, or the accession to power of a local ruler (and still not relatively to the supposed date of birth of Christ, which was fixed later arbitrarily by a Christian reform for the modern Julian calendar so that this epoch for the Christian era starts now on January 1 in proleptic year AD 1 of the modern Julian calendar, but the real date of birth of Christ is still not known precisely but certainly falls before, somewhere in the last few BC years). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Selenicereus hamatus </page_title> <path> Selenicereus_hamatus > Description </path> <section_title> Description </section_title> <content> Stems scandent, clambering or sprawling, branching, producing few aerial roots, very vigorous, to 5–12 m long or more, often growing 2 m or more in a season, 16–22 mm thick; ribs 4 or rarely 3-5, strong, later terete, acute; areoles small, brownish or black, remote, on the upper edges of knubby projections, these often forming obtuse, deflexed spurs about 1 cm long, internodes 4–5 cm; spines 5-6, ca 5 mm long, whitish, bristle like, 1-3 lower or central spines usually brown or black; epidermis glossy grass or light green. Flowers produced one by one over a longer period than most other species, born sparingly near tips of mature stems, 30–40 cm long, 20–30 cm in Ø, nocturnal and strongly scented with an aromatic fragrance, tepals rotate, inner ones forming a broad cup; pericarpel oval, knobby, ca 4 cm thick, covered with white spines and brown or black hairs, bracteoles green with white tips. ; receptacle ca 10–14 cm long, green, purplish towards the apex, ca 22 mm in Ø, its areoles with short, retuse, 1–12 mm long bracteoles, long black hairs and spines, upper bracteoles longer, the uppermost tipped purple; outer tepals 15 cm long, in 4 series, the outermost more narrow, reddish purple outside, chrome yellow inside, innermost broader, to 2 cm, acute to acuminate, greenish yellow outside, chrome yellow inside; inner tepals 12 cm, in 3 series, very broad, retuse, mucronate, white; stamens creamy white, anthers yellow; style thick, longer than the stamens, yellowish, lobes 15-18. Fruit oval, 10x8 cm, green or yellow, covered densely with yellowish spines, 2,5 cm long. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> 100% renewable energy </page_title> <path> 100%_renewable_energy > Feasibility > Energy transition </path> <section_title> Energy transition </section_title> <content> At the national level, at least 30 nations already have renewable energy contributing more than 20% of the energy supply.According to a review of the 181 peer-reviewed papers on 100% renewable energy which were published until 2018, "he great majority of all publications highlights the technical feasibility and economic viability of 100% RE systems." While there are still many publications which focus on electricity only, there is a growing number of papers that cover different energy sectors and sector-coupled, integrated energy systems. This cross-sectoral, holistic approach is seen as an important feature of 100% renewable energy systems and is based on the assumption "that the best solutions can be found only if one focuses on the synergies between the sectors" of the energy system such as electricity, heat, transport or industry.Stephen W. Pacala and Robert H. Socolow of Princeton University have developed a series of "climate stabilization wedges" that can allow us to maintain our quality of life while avoiding catastrophic climate change, and "renewable energy sources", in aggregate, constitute the largest number of their "wedges".Similarly, in the United States, the independent National Research Council has noted that "sufficient domestic renewable resources exist to allow renewable electricity to play a significant role in future electricity generation and thus help confront issues related to climate change, energy security, and the escalation of energy costs ... Renewable energy is an attractive option because renewable resources available in the United States, taken collectively, can supply significantly greater amounts of electricity than the total current or projected domestic demand. "The main barriers to the widespread implementation of large-scale renewable energy and low-carbon energy strategies are political rather than technological. According to the 2013 Post Carbon Pathways report, which reviewed many international studies, the key roadblocks are: climate change denial, the fossil fuels lobby, political inaction, unsustainable energy consumption, outdated energy infrastructure, and financial constraints.Studies have shown that Southeast Asia countries could achieve almost 100% renewable elecitricity based on solar, wind, and off-river pumped hydro energy storage at a competitive LCOE of around US$55-115/MWh. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> PragerU </page_title> <path> PragerU > Reception </path> <section_title> Reception </section_title> <content> In this way, viewers identifying as mainline conservatives gain "easy access to white supremacist logic." She also demonstrated an algorithmic connection on YouTube between PragerU, Fox News, and alt-right personalities.A Buzzfeed News article published in 2018 attributed PragerU's success to the quality of its production values compared to similar outlets and to its use of popular presenters with established audiences. The article also noted that it had received comparatively little attention from news and media analysts due to PragerU's lack of coverage of topical issues, such as Donald Trump.An August 2019 article by Drew Anderson in GLAAD, noted PragerU's "interviews with many controversial public figures who are often hailed by the white supremacist movement" and accused it of a "horrific anti-LGBTQ record. "Reason has criticized PragerU's claims of being censored by big tech companies for being false, as the company's content had not been removed from any social media platforms, and that they indicate a misunderstanding of the First Amendment as protecting a party from any type of censorship, when that law merely protects content from censorship by the government.Climate Feedback, Reuters and the Weather Channel have found that PragerU's videos promote inaccurate and misleading claims about climate change.PragerU's coverage of COVID-19 has been criticized for spreading false and misleading information about the pandemic.In 2019, Mike Gravel, a former United States Senator from Alaska, launched The Gravel Institute, a progressive left-leaning think tank, to counteract PragerU.Mother Jones said PragerU videos assert that there is no gender pay gap, and that there is not discrimination in policing of African-Americans.On race, Pam Nilan, in her 2021 book Young People and the Far Right, says that PragerU "pretends to sidestep" white supremacy, but that "the message is always that white culture is better than other cultures. "A case study of PragerU by McCarthy & Brewer claimed that "PragerU has fundamental overlapping ideologies to the extreme right" and detailed the methods of persuasion PragerU uses which "combine in a way that reflects information laundering and persuasion techniques used on online platforms by white supremacists who similarly hide racist propaganda behind more politically correct wording and professional-looking websites" </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Potential vorticity </page_title> <path> Potential_vorticity_unit > Bjerknes circulation theorem </path> <section_title> Bjerknes circulation theorem </section_title> <content> Vilhelm Bjerknes generalized Helmholtz's vorticity equation (1858) and Kelvin's circulation theorem (1869) to inviscid, geostrophic, and baroclinic fluids, i.e., fluids of varying density in a rotational frame which has a constant angular speed. If we define circulation as the integral of the tangent component of velocity around a closed fluid loop and take the integral of a closed chain of fluid parcels, we obtain D C D t = − ∮ 1 ρ ∇ p ⋅ d r − 2 Ω D A e D t , {\displaystyle {\frac {DC}{Dt}}=-\oint {\frac {1}{\rho }}\nabla p\cdot \mathrm {d} \mathbf {r} -2\Omega {\frac {DA_{e}}{Dt}},} (1)where D D t {\textstyle {\frac {D}{Dt}}} is the time derivative in the rotational frame (not inertial frame), C {\displaystyle C} is the relative circulation, A e {\displaystyle A_{e}} is projection of the area surrounded by the fluid loop on the equatorial plane, ρ {\displaystyle \rho } is density, p {\displaystyle p} is pressure, and Ω {\displaystyle \Omega } is the frame's angular speed. With Stokes' theorem, the first term on the right-hand-side can be rewritten as D C D t = ∫ A ∇ ρ × ∇ p ρ 2 ⋅ d A − 2 Ω D A e D t , {\displaystyle {\frac {DC}{Dt}}=\int _{A}{\frac {\nabla \rho \times \nabla p}{\rho ^{2}}}\cdot \mathrm {d} \mathbf {A} -2\Omega {\frac {DA_{e}}{Dt}},} (2)which states that the rate of the change of the circulation is governed by the variation of density in pressure coordinates and the equatorial projection of its area, corresponding to the first and second terms on the right hand side. The first term is also called the "solenoid term". </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Commemorative coins of the United Kingdom </page_title> <path> Commemorative_coins_of_the_United_Kingdom > Two pounds > Bimetallic > Non-circulating </path> <section_title> Non-circulating </section_title> <content> 2017: First World War Aviation 2017: 200th anniversary of the death of Jane Austen 2018: 200th anniversary of Mary Shelley's Frankenstein; or, The Modern Prometheus 2018: 250th anniversary of Captain Cook's Voyage of Discovery (1st coin) 2018: 100th anniversary of the World War One Armistice 2018: 100th anniversary of the Royal Air Force (5 coins) - Badge, Vulcan, Spitfire, Sea King, Lightning II 2019: 75th anniversary of D-Day 2019: 260th anniversary of Wedgwood 2019: 250th anniversary of Samuel Pepys' final diary entry 2019: 250th anniversary of Captain Cook's Voyage of Discovery (2nd coin) 2020: 75th anniversary of Victory in Europe Day 2020: 400th anniversary of the Mayflower voyage 2020: 100th anniversary of Agatha Christie's first book 2020: 250th anniversary of Captain Cook's Voyage of Discovery (3rd coin) 2021: 75th anniversary of the death of H. G. Wells 2021: 250th anniversary of the birth of Sir Walter Scott 2022: Dame Vera Lynn 2022: 150th anniversary of the FA Cup 2022: 100th anniversary of the death of Alexander Graham Bell 2022: 25th anniversary of the bimetallic £2 coin 2023: 50th anniversary of the death of JRR Tolkien 2023: 100th anniversary of the Flying Scotsman 2023: 200th anniversary of the death of Edward Jenner 2023: Ada Lovelace </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Newton Lacy Pierce Prize in Astronomy </page_title> <path> Newton_Lacy_Pierce_Prize_in_Astronomy > Pierce Prize winners </path> <section_title> Pierce Prize winners </section_title> <content> Source: AAS 1974 Edwin M. Kellogg 1975 Eric Becklin 1976 James Roger Angel 1977 Donald N.B. Hall 1978 James M. Moran, Jr. 1979 D. Harper 1980 Jack Baldwin 1981 Bruce Margon 1982 Marc Davis 1983 Alan Dressler 1984 Marc Aaronson, Jeremy Mould 1985 Richard G. Kron 1986 Reinhard Genzel 1987 Donald E. Winget 1988 Sallie L. Baliunas 1989 Harriet Dinerstein 1990 Kristen Sellgren 1991 Kenneth G. Libbrecht 1992 Alexei Filippenko 1993 Arlin P.S. Crotts 1994 No award 1995 Andrew McWilliam 1996 Michael Strauss 1997 Alyssa A. Goodman 1998 Andrea Ghez 1999 Dennis F. Zaritsky 2000 Kirpal Nandra 2001 Kenneth R. Sembach 2002 Amy Barger 2003 Xiaohui Fan 2004 Niel Brandt 2005 Andrew Blain 2006 Bryan Gaensler 2007 No award 2008 Lisa Kewley 2009 Joshua Bloom 2010 Tommaso Treu 2011 Gaspar Bakos 2012 John A. Johnson 2013 Jason Kalirai 2014 Nadia L. Zakamska 2015 Heather A. Knutson 2016 Karin Öberg 2017 Evan Kirby 2018 Caitlin Casey 2019 Daniel R. Weisz 2020 Emily Levesque 2021 Courtney Dressing 2022 Erin Kara 2023 Renee Ludlam </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> APG III system </page_title> <path> APG_III_system > Organization </path> <section_title> Organization </section_title> <content> These figures were produced by simply counting the families in the text of the paper that established APG III.ORDERS: Amborellales (1), Nymphaeales (3), Austrobaileyales (3), Chloranthales (1), Canellales (2), Piperales (5), Magnoliales (6), Laurales (7), Acorales (1), Alismatales (13), Petrosaviales (1), Dioscoreales (3), Pandanales (5), Liliales (10), Asparagales (14), Arecales (1), Poales (16), Commelinales (5), Zingiberales (8), Ceratophyllales (1), Ranunculales (7), Proteales (3), Trochodendrales (1), Buxales (2), Gunnerales (2), Saxifragales (14), Vitales (1), Zygophyllales (2), Celastrales (2), Oxalidales (7), Malpighiales (35), Fabales (4), Rosales (9), Fagales (7), Cucurbitales (7), Geraniales (3), Myrtales (9), Crossosomatales (7), Picramniales (1), Sapindales (9), Huerteales (3), Brassicales (17), Malvales (10), Berberidopsidales (2), Santalales (7), Caryophyllales (34), Cornales (6), Ericales (22), Garryales (2), Gentianales (5), Solanales (5), Lamiales (23), Aquifoliales (5), Asterales (11), Escalloniales (1), Bruniales (2), Apiales (7), Paracryphiales (1), Dipsacales (2). SUPRA-ORDINAL GROUPS: commelinids (1), basal eudicots (1), Pentapetalae (1), lamiids incertae sedis (3), core lamiids (2), angiosperms incertae sedis (2). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Ionic polymer–metal composites </page_title> <path> Ionic_polymer-metal_composite </path> <section_title> Summary </section_title> <content> 25, pp. 5504–5511, (1992) 6-Oguro, K., K. Asaka, and H. Takenaka, "Polymer film actuator driven by low voltage",In Proceedings of the 4th International Symposium of Micro Machines and Human Science", Nagoya, pp. 38–40, (1993) 7-Adolf D., Shahinpoor M., Segalman D., Witkowski W.,"Electrically Controlled Polymeric Gel Actuators", US Patent Office, US Patent No. 5,250,167, Issued October 5, (1993) 8-Oguro K., Kawami Y.and Takenaka H.,"Actuator Element", US Patent Office, US Patent No. 5,268,082, Issued December 7, (1993) These patents were followed by additional related patents: 9-Shahinpoor, M., "Spring-Loaded Ionic Polymeric Gel Linear Actuator", US Patent Office, US Patent No. 5,389,222, Issued February 14,(1995) 10-Shahinpoor, M. and Mojarrad, M., "Soft Actuators and Artificial Muscles", US Patent Office, United States Patent 6,109,852, Issued August 29,(2000) 11-Shahinpoor, M. and Mojarrad, M.,"Ionic Polymer Sensors and Actuators", US Patent Office, No. 6,475,639, Issued November 5, (2002) 12-Shahinpoor, M. and Kim, K.J.,“Method of Fabricating a Dry Electro-Active Polymeric Synthetic Muscle”, US Patent Office, Patent No. 7,276,090, Issued October 2,(2007) It should also be mentioned that Tanaka, Nishio and Sun introduced the phenomenon of ionic gel collapse in an electric field: 13-T. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Log-lin plot </page_title> <path> Semi-log_graph > Equations > Finding the function from the semi–log plot > Linear–log plot </path> <section_title> Linear–log plot </section_title> <content> On a linear–log plot, pick some fixed point (x0, F0), where F0 is shorthand for F(x0), somewhere on the straight line in the above graph, and further some other arbitrary point (x1, F1) on the same graph. The slope formula of the plot is: m = F 1 − F 0 log n ⁡ ( x 1 / x 0 ) {\displaystyle m={\frac {F_{1}-F_{0}}{\log _{n}(x_{1}/x_{0})}}} which leads to F 1 − F 0 = m log n ⁡ ( x 1 / x 0 ) {\displaystyle F_{1}-F_{0}=m\log _{n}(x_{1}/x_{0})} or F 1 = m log n ⁡ ( x 1 / x 0 ) + F 0 = m log n ⁡ ( x 1 ) − m log n ⁡ ( x 0 ) + F 0 {\displaystyle F_{1}=m\log _{n}(x_{1}/x_{0})+F_{0}=m\log _{n}(x_{1})-m\log _{n}(x_{0})+F_{0}} which means that In other words, F is proportional to the logarithm of x times the slope of the straight line of its lin–log graph, plus a constant. Specifically, a straight line on a lin–log plot containing points (F0, x0) and (F1, x1) will have the function: F ( x ) = ( F 1 − F 0 ) + F 0 = ( F 1 − F 0 ) log x 1 x 0 ⁡ ( x x 0 ) + F 0 {\displaystyle F(x)=(F_{1}-F_{0}){\left}+F_{0}=(F_{1}-F_{0})\log _{\frac {x_{1}}{x_{0}}}{\left({\frac {x}{x_{0}}}\right)}+F_{0}} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Degree of a mapping </page_title> <path> Degree_of_a_mapping > Definitions of the degree > Maps from closed region </path> <section_title> Maps from closed region </section_title> <content> If Ω ⊂ R n {\displaystyle \Omega \subset \mathbb {R} ^{n}} is a bounded region, f: Ω ¯ → R n {\displaystyle f:{\bar {\Omega }}\to \mathbb {R} ^{n}} smooth, p {\displaystyle p} a regular value of f {\displaystyle f} and p ∉ f ( ∂ Ω ) {\displaystyle p\notin f(\partial \Omega )} , then the degree deg ⁡ ( f , Ω , p ) {\displaystyle \deg(f,\Omega ,p)} is defined by the formula deg ⁡ ( f , Ω , p ) := ∑ y ∈ f − 1 ( p ) sgn ⁡ det ( D f ( y ) ) {\displaystyle \deg(f,\Omega ,p):=\sum _{y\in f^{-1}(p)}\operatorname {sgn} \det(Df(y))} where D f ( y ) {\displaystyle Df(y)} is the Jacobian matrix of f {\displaystyle f} in y {\displaystyle y} . This definition of the degree may be naturally extended for non-regular values p {\displaystyle p} such that deg ⁡ ( f , Ω , p ) = deg ⁡ ( f , Ω , p ′ ) {\displaystyle \deg(f,\Omega ,p)=\deg \left(f,\Omega ,p'\right)} where p ′ {\displaystyle p'} is a point close to p {\displaystyle p} . The degree satisfies the following properties: If deg ⁡ ( f , Ω ¯ , p ) ≠ 0 {\displaystyle \deg \left(f,{\bar {\Omega }},p\right)\neq 0} , then there exists x ∈ Ω {\displaystyle x\in \Omega } such that f ( x ) = p {\displaystyle f(x)=p} . deg ⁡ ( id , Ω , y ) = 1 {\displaystyle \deg(\operatorname {id} ,\Omega ,y)=1} for all y ∈ Ω {\displaystyle y\in \Omega } . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Generalized logistic distribution </page_title> <path> Generalized_logistic_distribution > Type IV (logistic-beta) properties > Cumulants and skewness </path> <section_title> Cumulants and skewness </section_title> <content> The cumulant generating function is K ( t ) = ln ⁡ M ( t ) {\displaystyle K(t)=\ln M(t)} , where the moment generating function M ( t ) {\displaystyle M(t)} is given above. The cumulants, κ n {\displaystyle \kappa _{n}} , are the n {\displaystyle n} -th derivatives of K ( t ) {\displaystyle K(t)} , evaluated at t = 0 {\displaystyle t=0}: κ n = K ( n ) ( 0 ) = ψ ( n − 1 ) ( α ) + ( − 1 ) n ψ ( n − 1 ) ( β ) {\displaystyle \kappa _{n}=K^{(n)}(0)=\psi ^{(n-1)}(\alpha )+(-1)^{n}\psi ^{(n-1)}(\beta )} where ψ ( 0 ) = ψ {\displaystyle \psi ^{(0)}=\psi } and ψ ( n − 1 ) {\displaystyle \psi ^{(n-1)}} are the digamma and polygamma functions. In agreement with the derivation above, the first cumulant, κ 1 {\displaystyle \kappa _{1}} , is the mean and the second, κ 2 {\displaystyle \kappa _{2}} , is the variance. The third cumulant, κ 3 {\displaystyle \kappa _{3}} , is the third central moment E ) 3 ] {\displaystyle E)^{3}]} , which when scaled by the third power of the standard deviation gives the skewness: skew = ψ ( 2 ) ( α ) − ψ ( 2 ) ( β ) var 3 {\displaystyle {\text{skew}}={\frac {\psi ^{(2)}(\alpha )-\psi ^{(2)}(\beta )}{{\sqrt {{\text{var}}}}^{3}}}} The sign (and therefore the handedness) of the skewness is the same as the sign of α − β {\displaystyle \alpha -\beta } . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Type 912 degaussing/deperming ship </page_title> <path> Type_912_degaussing/deperming_ship > Origin </path> <section_title> Origin </section_title> <content> The origin of Type 912 rooted from the need to replace very first batch of degaussing/deperming ships in PLAN service, all of which were converted from other wooden hulled ships: Since most of the wooden hulled degaussing/deperming ships have already been in service for prolonged period of time prior to their conversion, and needed to be replaced, PLAN thus converted other steel hulled ships as their successors. Most units were converted from large infantry landing craft (LCIL)and a minesweeper Qiu-Feng (秋风 in Chinese, meaning Autumn Wind),which was a IJN No.1-class auxiliary minesweeper (MSA) No. 14 given to Republic of China on October 4, 1947,along with No. 19 and 22 as part of war reparations, and respectively entered Republic of China Navy (RoCN) as Minesweeping (Sao-Lei, or 扫雷 in Chinese) 201, 202, and 203 on May 1, 1948, after rearmed with US weaponry.During the Chinese Civil War, crew of RoCN Minesweeping 201 defected to the communists in the absence of the captain on February 17, 1949, with ship being renamed as Autumn Wind afterward, and also used as a training ship in addition to degaussing/deperming ship by PLAN, until its final retirement in 1976.The three LCILs were sold to China after World War II as surplus material for civilian use, such as custom patrol boats,and were taken over by PLAN,initially converted as minesweepers,but subsequently converted again to a degaussing/deperming ship. Molded after Soviet SR barges, these converted degaussing/deperming ships carried sixty KSM-type accumulator batteries providing ten-volt external and a hundred ten-volt or two hundred twenty-volt for internal coils and cable reels for two hundred forty-millimeter diameter cables. Additional equipment needed for degaussing/deperming duties such as magnetometer to measure horizontal and vertical magnetic field is also carried on board. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Ring lasers </page_title> <path> Ring_Lasers_for_Research > The laser beam: theoretical tools > Beam characteristics > Curvature radius and width </path> <section_title> Curvature radius and width </section_title> <content> The matrices have \| M 1 \| = \| M 2 \| = 1 {\displaystyle \left\|M_{1}\right\|=\left\|M_{2}\right\|=1} . A typical design of a rectangular ring has the following form: ( r r ′ ) 4 = ( r r ′ ) 1 = ( M 1 ⋅ M 2 ) 4 ⋅ ( M 1 ⋅ M 2 ) 3 ⋅ ( M 1 ⋅ M 2 ) 2 ⋅ ( M 1 ⋅ M 2 ) 1 ⋅ ( r r ′ ) 1 {\displaystyle \left({\begin{matrix}r\\r'\\\end{matrix}}\right)_{4}=\left({\begin{matrix}r\\r'\\\end{matrix}}\right)_{1}=\left(M_{1}\cdot M_{2}\right)_{4}\cdot \left(M_{1}\cdot M_{2}\right)_{3}\cdot \left(M_{1}\cdot M_{2}\right)_{2}\cdot \left(M_{1}\cdot M_{2}\right)_{1}\cdot \left({\begin{matrix}r\\r'\\\end{matrix}}\right)_{1}} ( A B C D ) ⋅ ( r r ′ ) 1 {\displaystyle \left({\begin{matrix}A&B\\C&D\\\end{matrix}}\right)\cdot \left({\begin{matrix}r\\r'\\\end{matrix}}\right)_{1}} (for the equivalent rays where r = distance of equivalent ray from the axis, r’ = the slope against the axis). Note that in order for the ray to close on itself, the input column matrix has to equal the output column. This round-trip matrix is actually called ABCD matrix in the literature.The requirement that the ray is to be closed is therefore \| A B C D \| = 1 {\displaystyle \left\|{\begin{matrix}A&B\\C&D\\\end{matrix}}\right\|=1} . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Elliptic Curve DSA </page_title> <path> Elliptic_Curve_Digital_Signature_Algorithm > Signature verification algorithm > Correctness of the algorithm </path> <section_title> Correctness of the algorithm </section_title> <content> It is not immediately obvious why verification even functions correctly. To see why, denote as C the curve point computed in step 5 of verification, C = u 1 × G + u 2 × Q A {\displaystyle C=u_{1}\times G+u_{2}\times Q_{A}} From the definition of the public key as Q A = d A × G {\displaystyle Q_{A}=d_{A}\times G} , C = u 1 × G + u 2 d A × G {\displaystyle C=u_{1}\times G+u_{2}d_{A}\times G} Because elliptic curve scalar multiplication distributes over addition, C = ( u 1 + u 2 d A ) × G {\displaystyle C=(u_{1}+u_{2}d_{A})\times G} Expanding the definition of u 1 {\displaystyle u_{1}} and u 2 {\displaystyle u_{2}} from verification step 4, C = ( z s − 1 + r d A s − 1 ) × G {\displaystyle C=(zs^{-1}+rd_{A}s^{-1})\times G} Collecting the common term s − 1 {\displaystyle s^{-1}} , C = ( z + r d A ) s − 1 × G {\displaystyle C=(z+rd_{A})s^{-1}\times G} Expanding the definition of s from signature step 6, C = ( z + r d A ) ( z + r d A ) − 1 ( k − 1 ) − 1 × G {\displaystyle C=(z+rd_{A})(z+rd_{A})^{-1}(k^{-1})^{-1}\times G} Since the inverse of an inverse is the original element, and the product of an element's inverse and the element is the identity, we are left with C = k × G {\displaystyle C=k\times G} From the definition of r, this is verification step 6. This shows only that a correctly signed message will verify correctly; many other properties are required for a secure signature algorithm. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Allied Command Transformation </page_title> <path> Allied_Command_Transformation > Organization > NATO Centres of Excellence </path> <section_title> NATO Centres of Excellence </section_title> <content> The JAPCC succeeds the Reaction Forces (Air) Staff, originally activated in 1993. The RFAS Memorandum of Understanding was terminated and all RFAS activities ceased on the formal activation of the Joint Air Power Competence Centre on 1 January 2005. The Joint Chemical, Biological, Radiation, & Nuclear Defence Centre of Excellence (JCBRN Defence) COE in Vyškov, Czech Republic The Military Engineering Centre of Excellence in Ingolstadt, Germany The Military Medical Centre of Excellence (MILMED) COE in Budapest, Hungary The Modelling and Simulation (M&S) COE in Rome, Italy The Naval Mine Warfare Centre of Excellence (EGUERMIN) COE in Ostend, Belgium The Centre of Excellence for Operations in Confined and Shallow Waters in Kiel, Germany (supported by the German Navy's Einsatzflottille 1.) The Strategic Communications Centre of Excellence (STRATCOM) COE in Riga, Latvia The Crisis Management for Disaster Response (CMDR) COE in Sofia, Bulgaria The NATO Military Police (MP) COE in Bydgoszcz, Poland NATO Mountain Warfare Centre of Excellence in Begunje na Gorenjskem, Slovenia NATO Stability Policing Centre of Excellence in Vicenza, Italy NATO Counter Intelligence Centre of Excellence in Krakow, Poland / Slovakia NATO Security Force Assistance (SFA) Centre of Excellence in Rome, Italy The Integrated Air & Missile Defence Centre of Excellence (IAMD COE) in Crete, Greece The Maritime, Geospatial, Meteorological, & Oceanographic Centre of Excellence (MGEOMETOC COE) in Lisbon, Portugal The Maritime Security Centre of Excellence (MARSEC COE) in Istanbul, Turkey The Centre of Excellence for naval Visit, Board, Search and Seizure, NATO Maritime Interdiction Operational Training Centre (NMIOTC) [https://web.archive.org/web/20200214003715/http://nmiotc.nato.int/ Archived 2020-02-14 at the Wayback Machine, Souda Bay, Crete; supported by the Hellenic Navy. NATO Space Centre of Excellence in Toulouse, France </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Bending </page_title> <path> Beam_bending > Quasistatic bending of plates > Mindlin–Reissner theory of plates </path> <section_title> Mindlin–Reissner theory of plates </section_title> <content> The special assumption of this theory is that normals to the mid-surface remain straight and inextensible but not necessarily normal to the mid-surface after deformation. The displacements of the plate are given by u α ( x ) = − x 3 φ α ; α = 1 , 2 u 3 ( x ) = w 0 ( x 1 , x 2 ) {\displaystyle {\begin{aligned}u_{\alpha }(\mathbf {x} )&=-x_{3}~\varphi _{\alpha }~;~~\alpha =1,2\\u_{3}(\mathbf {x} )&=w^{0}(x_{1},x_{2})\end{aligned}}} where φ α {\displaystyle \varphi _{\alpha }} are the rotations of the normal. The strain-displacement relations that result from these assumptions are ε α β = − x 3 φ α , β ε α 3 = 1 2 κ ( w , α 0 − φ α ) ε 33 = 0 {\displaystyle {\begin{aligned}\varepsilon _{\alpha \beta }&=-x_{3}~\varphi _{\alpha ,\beta }\\\varepsilon _{\alpha 3}&={\cfrac {1}{2}}~\kappa \left(w_{,\alpha }^{0}-\varphi _{\alpha }\right)\\\varepsilon _{33}&=0\end{aligned}}} where κ {\displaystyle \kappa } is a shear correction factor. The equilibrium equations are M α β , β − Q α = 0 Q α , α + q = 0 {\displaystyle {\begin{aligned}&M_{\alpha \beta ,\beta }-Q_{\alpha }=0\\&Q_{\alpha ,\alpha }+q=0\end{aligned}}} where Q α := κ ∫ − h h σ α 3 d x 3 {\displaystyle Q_{\alpha }:=\kappa ~\int _{-h}^{h}\sigma _{\alpha 3}~dx_{3}} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Islamic extremism </page_title> <path> Islamic_extremism > UK High Court rulings > October 2016 Shakeel Begg case </path> <section_title> October 2016 Shakeel Begg case </section_title> <content> A total, eternal 'Manichean' worldview is a central tenet of violent Islamic extremism. It divides the world strictly into 'Us' versus 'Them': those who are blessed or saved (i.e. the "right kind" of Muslim) on the one hand and those who are to be damned for eternity (i.e. the "wrong kind" of Muslim and everyone else) on the other. For violent Islamic extremists, the "wrong kind" of Muslim includes moderate Sunni Muslims, all Shia Muslims, and many others who are "mete for the sword" and can be killed, and anyone who associates or collaborates" with them... Second, the reduction of jihad (striving in God's cause) to qital (armed combat) ('the Lesser Jihad')... Third, the ignoring or flouting of the conditions for the declaration of armed jihad (qital), i.e. the established Islamic doctrinal conditions for the declaration of armed combat (qital) set out above... Fourth, the ignoring or flouting of the strict regulations governing the conduct of armed jihad, i.e. the stipulations in the Qur'an and the Sunna for the ethics of conducting qital set out above. Thus, the use of excessive violence, attacks on civilians, indiscriminate 'suicide' violence and the torture or the murder of prisoners would constitute violation of these regulations of jihad... Fifth, advocating armed fighting in defence of Islam (qital) as a universal individual religious obligation (fard al 'ayn)... Sixth, any interpretation of Shari'a (i.e. religious law laid down by the Qur'an and the Sunna) that required breaking the 'law of the land'... Seventh, the classification of all non-Muslims as unbelievers (kuffar)... Eighth, the extreme Salafist Islamism doctrine that the precepts of the Muslim faith negate and supersede all other natural ties, such as those of family, kinship and nation... Ninth, the citing with approval the fatwa (legal opinions) of Islamic scholars who espouse extremist view... Tenth, any teaching which, expressly or implicitly, encourages Muslims to engage in, or support, terrorism or violence in the name of Allah. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Electronic Municipal Market Access </page_title> <path> Electronic_Municipal_Market_Access </path> <section_title> Summary </section_title> <content> The Electronic Municipal Market Access (EMMA) system, operated by the Municipal Securities Rulemaking Board (MSRB), serves as the official source for municipal securities disclosures and related financial data in the United States. EMMA provides free on-line access to centralized new issue municipal securities disclosure documents (known as official statements), on-going continuing disclosures for all municipal securities, escrow deposit agreements for advance refundings (i.e., refinancings) of outstanding bonds, real-time municipal bond trade price information, interest rates and auction results for municipal auction rate securities (the first free source for this kind of information on the auction rate securities market) and interest rate reset information for variable rate demand obligations, together with daily statistics on trading activity and investor education materials.EMMA's disclosure collection operates in coordination with the MSRB's investor protection rules mandating that securities firms and banks selling municipal securities to customers provide them with complete disclosure of all important information about the investment. EMMA also is the central information utility through which municipal securities disclosures mandated by the Securities and Exchange Commission (SEC) through its Rule 15c2-12 are made freely available to the general public. The EMMA continuing disclosure service provides access to audited financial statements, default notices, taxability notices, notices of rating changes, and approximately 30 additional categories of financial and other updates relating to municipal securities. The MSRB and SEC continue to work toward expanding the types and timeliness of disclosures available through EMMA.Public access to the integrated collection of primary market and secondary market disclosure provided through EMMA parallels the centralized disclosure currently available for securities offerings by public companies through the SEC's EDGAR system, although EMMA provides additional items of information beyond the base disclosures provided by EDGAR, such as trade prices, interest rates, market statistics and educational materials. The collection of disclosure documents available through EMMA for municipal securities is not identical to what is available through EDGAR for registered offerings of corporate or other securities since municipal securities and their state & local governmental issuers are afforded broad exemptions from most provisions of the federal securities laws (such as the Securities Act of 1933, the Securities Exchange Act of 1934 and the Investment Company Act of 1940) otherwise applicable to private-sector issuers of corporate and other types of securities. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Cantor set </page_title> <path> Cantor_set > Properties > Descriptive set theory </path> <section_title> Descriptive set theory </section_title> <content> However, unlike Q ∩ {\displaystyle \mathbb {Q} \cap } , which is countable and has a "small" cardinality, ℵ 0 {\displaystyle \aleph _{0}} , the cardinality of C {\displaystyle {\mathcal {C}}} is the same as that of , the continuum c {\displaystyle {\mathfrak {c}}} , and is "large" in the sense of cardinality. In fact, it is also possible to construct a subset of that is meagre but of positive measure and a subset that is non-meagre but of measure zero: By taking the countable union of "fat" Cantor sets C ( n ) {\displaystyle {\mathcal {C}}^{(n)}} of measure λ = ( n − 1 ) / n {\displaystyle \lambda =(n-1)/n} (see Smith–Volterra–Cantor set below for the construction), we obtain a set A := ⋃ n = 1 ∞ C ( n ) {\textstyle {\mathcal {A}}:=\bigcup _{n=1}^{\infty }{\mathcal {C}}^{(n)}} which has a positive measure (equal to 1) but is meagre in , since each C ( n ) {\displaystyle {\mathcal {C}}^{(n)}} is nowhere dense. Then consider the set A c = ∖ ⋃ n = 1 ∞ C ( n ) {\textstyle {\mathcal {A}}^{\mathrm {c} }=\setminus \bigcup _{n=1}^{\infty }{\mathcal {C}}^{(n)}} . Since A ∪ A c = {\displaystyle {\mathcal {A}}\cup {\mathcal {A}}^{\mathrm {c} }=} , A c {\displaystyle {\mathcal {A}}^{\mathrm {c} }} cannot be meagre, but since μ ( A ) = 1 {\displaystyle \mu ({\mathcal {A}})=1} , A c {\displaystyle {\mathcal {A}}^{\mathrm {c} }} must have measure zero. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Centers for Disease Control and Prevention </page_title> <path> Centers_for_Disease_Control_and_Prevention > Controversies > COVID-19 </path> <section_title> COVID-19 </section_title> <content> Officials said that a CDC document in July arguing for "the importance of reopening schools" was also crafted outside the CDC. On August 16, the chief of staff, Kyle McGowan, and his deputy, Amanda Campbell, resigned from the agency. The testing guidelines were reversed on September 18, 2020, after public controversy.In September 2020, the CDC drafted an order requiring masks on all public transportation in the United States, but the White House Coronavirus Task Force blocked the order, refusing to discuss it, according to two federal health officials.In October 2020, it was disclosed that White House advisers had repeatedly altered the writings of CDC scientists about COVID-19, including recommendations on church choirs, social distancing in bars and restaurants, and summaries of public-health reports.In the lead up to 2020 Thanksgiving, the CDC advised Americans not to travel for the holiday saying, "It's not a requirement. It's a recommendation for the American public to consider." The White House coronavirus task force had its first public briefing in months on that date but travel was not mentioned.The New York Times later concluded that the CDC's decisions to "ben to political pressure from the Trump White House to alter key public health guidance or withhold it from the public cost it a measure of public trust that experts say it still has not recaptured" as of 2022.In May 2021, following criticism by scientists, the CDC updated its COVID-19 guidance to acknowledge airborne transmission of COVID-19, after having previously claimed that the majority of infections occurred via "close contact, not airborne transmission".Until 2022, the CDC withheld critical data about COVID-19 vaccine boosters, hospitalizations and wastewater data.On June 10, 2022, the Biden Administration ordered the CDC to remove the COVID-19 testing requirement for air travelers entering the United States.In January 2022, it was revealed that the CDC had communicated with moderators at Facebook and Instagram over COVID-19 information and discussion on the platforms, including information that the CDC considered false or misleading and that might influence people not to get the COVID-19 vaccines. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> 12-Hydroxyeicosatetraenoic acid </page_title> <path> 12-Hydroxyeicosatetraenoic_acid > Further metabolism </path> <section_title> Further metabolism </section_title> <content> The majority of reports on hepoxilin formation have not defined the pathways evolved. Human and other mammalian cytochrome P450 enzymes convert 12(S)-HpETE to 12-oxo-ETE. 12-HETE (stereoisomer not determined), 12(S)-HETE, 12-oxo-ETE, hepoxilin B3, and trioxilin B3 are found in the sn-2 position of phospholipids isolated from normal human epidermis and human psoriatic scales. This indicates that the metabolites are acylated into the sn-2 position after being formed and/or directly produced by the metabolism of the arachidonic acid at the sn-2 position of these phospholipids. These acylation reactions may sequester and thereby inactivate or store the metabolites for release during cell stimulation.12(S)-HETE and 12(R)-HETE are converted to 12-oxo-ETE by microsomal NAD+-dependent 12-hydroxyeicosanoid dehydrogenase in porcine polymophonuclear leukocytes; a similar pathway may be active in rabbit corneal epithelium, cow corneal epithelium, and mouse keratinocytes although this pathway has not been described in human tissues.12-oxo-ETE is metabolised by cytosolic NADH-dependent 12-oxoeicosinoid Δ10-reductase to 12-oxo-5Z,8Z,14Z-eicosatrienoic acid (12-oxo-ETrE); 12-ketoreductase may then reduce this 12-oxo-ETrE to 12(R)-hydroxy-5Z,8Z,14Z-eicosatrienoic acid (12(R)-HETrE) and to a lesser extent 12(S)-hydroxy-5Z,8Z,14Z-eicosatrienoic acid (12(S)-HETrE). </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> The Holocaust in curricula </page_title> <path> The_Holocaust_in_curricula > Direct reference </path> <section_title> Direct reference </section_title> <content> "Direct reference" refers to countries whose curricula stipulate teaching about the Holocaust by using the term "Holocaust" or "Shoah", or by using alternative terminologies such as "genocide against the Jews", or "Nazi persecution of minorities": The terms "Holocaust" and "Shoah" are used explicitly. While most curricula employ the term "Holocaust" (in Albania, Australia, Denmark, Ethiopia and Poland, for example), some use "Shoah" (Belgium (Flanders), Côte d'Ivoire, Italy and Luxembourg); or the two terms are used as synonyms (in Switzerland (canton of Bern), in Germany (Saxony) and in Argentina). In many countries, the two terms appear within the context of the Second World War (this is the most frequent category found in the majority of European countries, in Australia, in several US states, in Chile, Ethiopia, Singapore, South Africa, and Trinidad and Tobago). Additionally, in some cases, the Holocaust is mentioned in teaching units devoted to genocidal crimes (in Canada (Ontario), in Panama and in the US (Arkansas)). The Holocaust is referred to directly, but using alternative terms such as "the singularity of the Jewish genocide" in Spain, the "Nazi policy of extermination" in Andorra, the "extermination of Jews" (Belgium (Wallonia)), "genocide of the Jews" (France, Germany (Lower Saxony)), "mass murder of Jews" (Trinidad and Tobago), "persecution of Jews" (Singapore) and "Final Solution" (Namibia). Another country in which there is no direct reference to the Holocaust, but where the contextualization of themes related to the Holocaust or local terminological usage makes it clear that the Holocaust is in fact stipulated, is Turkey, where soykırım (genocide) is the standard term used to refer to the Holocaust, and where terms analogous to "Holocaust" or "Shoah" are strictly avoided to emphasize the uniqueness of the genocide against the Jews in contradistinction to the massacre of Armenians in 1915 and 1916, which occurred at a time before the term genocide came into use. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Tadpole goby </page_title> <path> Tadpole_goby > Species </path> <section_title> Species </section_title> <content> There are currently 20 recognized species in this genus: Benthophilus abdurahmanovi Ragimov, 1978 (Abdurahmanov's pugolovka) Benthophilus baeri Kessler, 1877 (Baer pugolovka) Benthophilus casachicus Ragimov, 1978 Benthophilus ctenolepidus Kessler, 1877 Benthophilus durrelli Boldyrev & Bogutskaya, 2004 (Don tadpole-goby) Benthophilus granulosus Kessler, 1877 (Granular pugolovka) Benthophilus grimmi Kessler, 1877 Benthophilus kessleri L. S. Berg, 1927 Benthophilus leobergius L. S. Berg, 1949 (Caspian stellate tadpole-goby) Benthophilus leptocephalus Kessler, 1877 Benthophilus leptorhynchus Kessler, 1877 (Short-snout pugolovka) Benthophilus macrocephalus (Pallas, 1787) (Caspian tadpole goby) Benthophilus magistri Iljin, 1927 (Azov tadpole goby) Benthophilus mahmudbejovi Ragimov, 1976 (Small-spine tadpole-goby) Benthophilus nudus L. S. Berg, 1898 (Black Sea tadpole-goby) Benthophilus pinchuki Ragimov, 1982 Benthophilus ragimovi Boldyrev & Bogutskaya, 2004 Benthophilus spinosus Kessler, 1877 (Spiny pugolovka) Benthophilus stellatus (Sauvage, 1874) (Stellate tadpole-goby) Benthophilus svetovidovi Pinchuk & Ragimov, 1979 == References == </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Chaotic mixing </page_title> <path> Chaotic_mixing > Characterization of chaotic advection > Filament growth versus evolution of the tracer gradient </path> <section_title> Filament growth versus evolution of the tracer gradient </section_title> <content> The following, exact equation can be derived from an advection-diffusion equation (see below), with a diffusion term (D=0) of zero: d ∇ q d t = − ∇ q ⋅ ∇ v → {\displaystyle {\frac {\mathrm {d} \nabla q}{\mathrm {d} t}}=-\nabla q\cdot \nabla {\vec {v}}} In parallel with the definition of the Lyapunov exponent, we define the matrix H ′ {\displaystyle {\boldsymbol {H}}^{\prime }} , as follows: d H ′ d t = − ∇ H ′ ⋅ ∇ v → H ′ ( t = 0 ) = I {\displaystyle {\frac {\mathrm {d} {\boldsymbol {H^{\prime }}}}{\mathrm {d} t}}=-\nabla {\boldsymbol {H^{\prime }}}\cdot \nabla {\vec {v}}\qquad {\boldsymbol {H^{\prime }}}(t=0)={\boldsymbol {I}}} It is easy to show that: H ′ = H − 1 {\displaystyle {\boldsymbol {H^{\prime }}}={\boldsymbol {H}}^{-1}} If we define { h i ′ } {\displaystyle \lbrace h_{i}^{\prime }\rbrace } as the squared lengths of the principal components of the tracer gradient matrix, H ′ {\displaystyle {\boldsymbol {H}}^{\prime }} , then: h i ′ = 1 / h i {\displaystyle h_{i}^{\prime }=1/h_{i}} where the { h i ′ } {\displaystyle \lbrace h_{i}^{\prime }\rbrace } 's are arranged, as before, from largest to smallest. Therefore, growth in the error vector will cause a corresponding decrease in the tracer gradient and vice versa. This can be understood very simply and intuitively by considering two nearby points: since the difference in tracer concentration will be fixed, the only source of variation in the gradients between them will be their separation. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Separation principle in stochastic control </page_title> <path> Separation_principle_in_stochastic_control > Issues on feedback in linear stochastic systems </path> <section_title> Issues on feedback in linear stochastic systems </section_title> <content> At this point it is suitable to consider a more general class of controlled linear stochastic systems that also covers systems with time delays, namely z ( t ) = z 0 ( t ) + ∫ 0 t G ( t , s ) u ( s ) d s y ( t ) = H z ( t ) {\displaystyle {\begin{aligned}z(t)&=z_{0}(t)+\int _{0}^{t}G(t,s)u(s)\,ds\\y(t)&=Hz(t)\end{aligned}}} with z 0 {\displaystyle {\begin{aligned}z_{0}\end{aligned}}} a stochastic vector process which does not depend on the control. The standard stochastic system is then obtained as a special case where z = ′ {\displaystyle z='} , z 0 = ′ {\displaystyle z_{0}='} and H = {\displaystyle H=} . We shall use the short-hand notation z = z 0 + g π H z {\displaystyle z=z_{0}+g\pi Hz} for the feedback system, where g: ( t , u ) ↦ ∫ 0 t G ( t , τ ) u ( τ ) d τ {\displaystyle g\;:\;(t,u)\mapsto \int _{0}^{t}G(t,\tau )u(\tau )\,d\tau } is a Volterra operator. In this more general formulation the embedding procedure of Lindquist defines the class Π {\displaystyle \Pi } of admissible feedback laws π {\displaystyle \pi } as the class of non-anticipatory functions u := π ( y ) {\displaystyle u:=\pi (y)} such that the feedback equation z = z 0 + g π H z {\displaystyle z=z_{0}+g\pi Hz} has a unique solution z π {\displaystyle z_{\pi }} and u = π ( H z π ) {\displaystyle u=\pi (Hz_{\pi })} is adapted to { Y t 0 } {\displaystyle \{{\mathcal {Y}}_{t}^{0}\}} . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Risk management framework </page_title> <path> Risk_management_framework > History </path> <section_title> History </section_title> <content> The E-Government Act of 2002 (Public Law 107-347) entitled FISMA 2002 (Federal Information Security Management Act) was a law passed in 2002 to protect the economic and national security interests of the United States related to information security.Congress later passed FISMA 2014 (Federal Information Security Modernization Act) to provide improvements over FISMA 2002 by: Codifying Department of Homeland Security (DHS) authority to administer the implementation of information security policies for non-national security federal Executive Branch systems, including providing technical assistance and deploying technologies to such systems; Amending and clarifying the Office of Management and Budget's (OMB) oversight authority over federal agency information security practices; and by Requiring OMB to amend or revise OMB A-130 to "eliminate inefficient and wasteful reporting. "FISMA required the protecting information and information systems from unauthorized access, use, disclosure, disruption, modification, or destruction in order to provide Confidentiality, Integrity and Availability. Title III of FISMA 2002 tasked NIST with responsibilities for standards and guidelines, including the development of: Standards to be used by all federal agencies to categorize all information and information systems collected or maintained by or on behalf of each agency based on the objectives of providing appropriate levels of information security according to a range of risk levels. This task was satisfied by FIPS Publication 199; Guidelines recommending the types of information and information systems to be included in each category. This task was satisfied by NIST Special Publication 800-60, Volumes 1 and 2; and Minimum information security requirements (i.e., management, operational, and technical controls), for information and information systems in each such category. This task was satisfied by the development of FIPS Publication 200.NIST 800-37 (Risk Management Framework or RMF) was developed to help organizations manage security and privacy risk, and to satisfy the requirements in the Federal Information Security Modernization Act of 2014 (FISMA), the Privacy Act of 1974, OMB policies, and Federal Information Processing Standards, among other laws, regulations, and policies. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Refractory status epilepticus </page_title> <path> Refractory_status_epilepticus > Prognosis </path> <section_title> Prognosis </section_title> <content> While sources vary, about 16 to 20% of first-time SE patients die; with other sources indicating between 10 and 30% of such patients die within 30 days. Further, 10-50% of first-time SE patients experience lifelong disabilities. In the 30% mortality figure, the great majority of these people have an underlying brain condition causing their status seizure such as brain tumor, brain infection, brain trauma, or stroke. People with diagnosed epilepsy who have a status seizure also have an increased risk of death if their condition is not stabilized quickly, their medication and sleep regimen adapted and adhered to, and stress and other stimulant (seizure trigger) levels controlled. However, with optimal neurological care, adherence to the medication regimen, and a good prognosis (no other underlying uncontrolled brain or other organic disease), the person—even people who have been diagnosed with epilepsy—in otherwise good health can survive with minimal or no brain damage, and can decrease risk of death and even avoid future seizures.Prognosis of Refractory status epilepticus A special prognosis for Refractory Status Epilepticus (RSE) was crucial to be studied; since it represent the severe and urgent form of status epilepticus, therefore, studies have indicated that New-onset Refractory Status Epilepticus (NORSE), prognosis studies have shown that there is no clear structure of the symptoms; since they range from gastrointestinal to flu-like symptoms, which are considered to be mild and only represent 10% , while the remaining majority of 90% of the clinical cases were unknown, also, it was found that it takes a period of 1 to 14 days for the patient to reach the prodromal stage in which the episode is yet to come for the first time, add to that, it was found that the frequency of those initial seizures initially starts from a short and inconsistent seizures that lasts for a few hours and may extend to few days, however, it can simply strike to hundreds of seizures per day, which is the stage that needed an urgent medical intervene in which the patient expected to be in the ICU as soon as possible, and typically focal seizures are the most common among those cases. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Ampère's force law </page_title> <path> Ampère's_force_law > Equation > General case </path> <section_title> General case </section_title> <content> The general formulation of the magnetic force for arbitrary geometries is based on iterated line integrals and combines the Biot–Savart law and Lorentz force in one equation as shown below. where F 12 {\displaystyle \mathbf {F} _{12}} is the total magnetic force felt by wire 1 due to wire 2 (usually measured in newtons), I 1 {\displaystyle I_{1}} and I 2 {\displaystyle I_{2}} are the currents running through wires 1 and 2, respectively (usually measured in amperes), The double line integration sums the force upon each element of wire 1 due to the magnetic field of each element of wire 2, d ℓ 1 {\displaystyle d{\boldsymbol {\ell }}_{1}} and d ℓ 2 {\displaystyle d{\boldsymbol {\ell }}_{2}} are infinitesimal vectors associated with wire 1 and wire 2 respectively (usually measured in metres); see line integral for a detailed definition, The vector r ^ 21 {\displaystyle {\hat {\mathbf {r} }}_{21}} is the unit vector pointing from the differential element on wire 2 towards the differential element on wire 1, and \|r\| is the distance separating these elements, The multiplication × is a vector cross product, The sign of I n {\displaystyle I_{n}} is relative to the orientation d ℓ n {\displaystyle d{\boldsymbol {\ell }}_{n}} (for example, if d ℓ 1 {\displaystyle d{\boldsymbol {\ell }}_{1}} points in the direction of conventional current, then I 1 > 0 {\displaystyle I_{1}>0} ).To determine the force between wires in a material medium, the magnetic constant is replaced by the actual permeability of the medium. For the case of two separate closed wires, the law can be rewritten in the following equivalent way by expanding the vector triple product and applying Stokes' theorem: In this form, it is immediately obvious that the force on wire 1 due to wire 2 is equal and opposite the force on wire 2 due to wire 1, in accordance with Newton's 3rd law. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Distributed source coding </page_title> <path> Distributed_source_coding > Practical distributed source coding > Slepian–Wolf coding – lossless distributed coding > General theorem of Slepian–Wolf coding with syndromes for two sources </path> <section_title> General theorem of Slepian–Wolf coding with syndromes for two sources </section_title> <content> Theorem: Any pair of correlated uniformly distributed sources, X , Y ∈ { 0 , 1 } n {\displaystyle X,Y\in \left\{0,1\right\}^{n}} , with d H ( X , Y ) ≤ t {\displaystyle \mathbf {d_{H}} (X,Y)\leq t} , can be compressed separately at a rate pair ( R 1 , R 2 ) {\displaystyle (R_{1},R_{2})} such that R 1 , R 2 ≥ n − k , R 1 + R 2 ≥ 2 n − k {\displaystyle R_{1},R_{2}\geq n-k,R_{1}+R_{2}\geq 2n-k} , where R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} are integers, and k ≤ n − log ⁡ ( ∑ i = 0 t ( n i ) ) {\displaystyle k\leq n-\log(\sum _{i=0}^{t}{n \choose i})} . This can be achieved using an ( n , k , 2 t + 1 ) {\displaystyle (n,k,2t+1)} binary linear code. Proof: The Hamming bound for an ( n , k , 2 t + 1 ) {\displaystyle (n,k,2t+1)} binary linear code is k ≤ n − log ⁡ ( ∑ i = 0 t ( n i ) ) {\displaystyle k\leq n-\log(\sum _{i=0}^{t}{n \choose i})} , and we have Hamming code achieving this bound, therefore we have such a binary linear code C {\displaystyle \mathbf {C} } with k × n {\displaystyle k\times n} generator matrix G {\displaystyle \mathbf {G} } . Next we will show how to construct syndrome encoding based on this linear code. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Per-unit system </page_title> <path> Per-unit_system > Example of per-unit </path> <section_title> Example of per-unit </section_title> <content> As an example of how per-unit is used, consider a three-phase power transmission system that deals with powers of the order of 500 MW and uses a nominal voltage of 138 kV for transmission. We arbitrarily select S b a s e = 500 M V A {\displaystyle S_{\mathrm {base} }=500\,\mathrm {MVA} } , and use the nominal voltage 138 kV as the base voltage V b a s e {\displaystyle V_{\mathrm {base} }} . We then have: I base = S base V base × 3 = 2.09 k A {\displaystyle I_{\text{base}}={\frac {S_{\text{base}}}{V_{\text{base}}\times {\sqrt {3}}}}=2.09\,\mathrm {kA} } Z base = V base I base × 3 = V base 2 S base = 38.1 Ω {\displaystyle Z_{\text{base}}={\frac {V_{\text{base}}}{I_{\text{base}}\times {\sqrt {3}}}}={\frac {V_{\text{base}}^{2}}{S_{\text{base}}}}=38.1\,\Omega } Y b a s e = 1 Z b a s e = 26.3 m S {\displaystyle Y_{\mathrm {base} }={\frac {1}{Z_{\mathrm {base} }}}=26.3\,\mathrm {mS} } If, for example, the actual voltage at one of the buses is measured to be 136 kV, we have: V p u = V V b a s e = 136 k V 138 k V = 0.9855 p u {\displaystyle V_{\mathrm {pu} }={\frac {V}{V_{\mathrm {base} }}}={\frac {136\,\mathrm {kV} }{138\,\mathrm {kV} }}=0.9855\,\mathrm {pu} } </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Engel expansion </page_title> <path> Engel_expansion </path> <section_title> Summary </section_title> <content> The Engel expansion of a positive real number x is the unique non-decreasing sequence of positive integers ( a 1 , a 2 , a 3 , … ) {\displaystyle (a_{1},a_{2},a_{3},\dots )} such that x = 1 a 1 + 1 a 1 a 2 + 1 a 1 a 2 a 3 + ⋯ = 1 a 1 ( 1 + 1 a 2 ( 1 + 1 a 3 ( 1 + ⋯ ) ) ) {\displaystyle x={\frac {1}{a_{1}}}+{\frac {1}{a_{1}a_{2}}}+{\frac {1}{a_{1}a_{2}a_{3}}}+\cdots ={\frac {1}{a_{1}}}\!\left(1+{\frac {1}{a_{2}}}\!\left(1+{\frac {1}{a_{3}}}\left(1+\cdots \right)\right)\right)} For instance, Euler's number e has the Engel expansion 1, 1, 2, 3, 4, 5, 6, 7, 8, ...corresponding to the infinite series e = 1 1 + 1 1 + 1 1 ⋅ 2 + 1 1 ⋅ 2 ⋅ 3 + 1 1 ⋅ 2 ⋅ 3 ⋅ 4 + ⋯ {\displaystyle e={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{1\cdot 2}}+{\frac {1}{1\cdot 2\cdot 3}}+{\frac {1}{1\cdot 2\cdot 3\cdot 4}}+\cdots } Rational numbers have a finite Engel expansion, while irrational numbers have an infinite Engel expansion. If x is rational, its Engel expansion provides a representation of x as an Egyptian fraction. Engel expansions are named after Friedrich Engel, who studied them in 1913. An expansion analogous to an Engel expansion, in which alternating terms are negative, is called a Pierce expansion. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Force concentration </page_title> <path> Force_concentration > Mathematical model </path> <section_title> Mathematical model </section_title> <content> The sizes of both armies decrease at different rates depending on the size of the other, and casualties of the superior army approach zero as the size of the inferior army approaches zero. This can be written in equations: d d t N 1 = − c 2 N 2 {\displaystyle {\frac {d}{dt}}N_{1}=-c_{2}N_{2}} d d t N 2 = − c 1 N 1 {\displaystyle {\frac {d}{dt}}N_{2}=-c_{1}N_{1}} N 1 {\displaystyle N_{1}} is the number of units in the first army d d t N 2 {\displaystyle {\frac {d}{dt}}N_{2}} is the rate in which army 1 damages army 2 (affected by unit quality or other advantage) c 1 {\displaystyle c_{1}} is a coefficient which describes army 1's ability to inflict damage per unit per time.The above equations result in the following homogeneous second-order linear ordinary differential equations: d 2 d t 2 N 1 = c 2 c 1 N 1 {\displaystyle {\frac {d^{2}}{dt^{2}}}N_{1}=c_{2}c_{1}N_{1}} d 2 d t 2 N 2 = c 2 c 1 N 2 {\displaystyle {\frac {d^{2}}{dt^{2}}}N_{2}=c_{2}c_{1}N_{2}} To determine the time evolution of N 1 {\displaystyle N_{1}} and N 2 {\displaystyle N_{2}} , these equations need to be solved using the known initial conditions (the initial size of the two armies prior to combat). This model clearly demonstrates (see picture) that an inferior force can suffer devastating losses even when the superior force is only slightly larger, in case of equal per-unit qualitative capabilities: in the first example (see picture, top plot) the superior force starts only 40% larger, yet it brings about the total annihilation of the inferior force while suffering only 40% losses. Quality of the force may outweigh the quantitative inferiority of the force (middle plot) when it comes to battle outcomes. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> MacMahon master theorem </page_title> <path> MacMahon_master_theorem > Derivation of Dixon's identity </path> <section_title> Derivation of Dixon's identity </section_title> <content> Consider a matrix A = ( 0 1 − 1 − 1 0 1 1 − 1 0 ) . {\displaystyle A={\begin{pmatrix}0&1&-1\\-1&0&1\\1&-1&0\end{pmatrix}}.} Compute the coefficients G(2n, 2n, 2n) directly from the definition: G ( 2 n , 2 n , 2 n ) = ( x 2 − x 3 ) 2 n ( x 3 − x 1 ) 2 n ( x 1 − x 2 ) 2 n = ∑ k = 0 2 n ( − 1 ) k ( 2 n k ) 3 , {\displaystyle {\begin{aligned}G(2n,2n,2n)&={\bigl }(x_{2}-x_{3})^{2n}(x_{3}-x_{1})^{2n}(x_{1}-x_{2})^{2n}\\&=\,\sum _{k=0}^{2n}(-1)^{k}{\binom {2n}{k}}^{3},\end{aligned}}} where the last equality follows from the fact that on the right-hand side we have the product of the following coefficients: ( x 2 − x 3 ) 2 n , ( x 3 − x 1 ) 2 n , ( x 1 − x 2 ) 2 n , {\displaystyle (x_{2}-x_{3})^{2n},\ \ (x_{3}-x_{1})^{2n},\ \ (x_{1}-x_{2})^{2n},} which are computed from the binomial theorem. On the other hand, we can compute the determinant explicitly: det ( I − T A ) = det ( 1 − t 1 t 1 t 2 1 − t 2 − t 3 t 3 1 ) = 1 + ( t 1 t 2 + t 1 t 3 + t 2 t 3 ) . </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Five points determine a conic </page_title> <path> Five_points_determine_a_conic > Proofs > Dimension counting </path> <section_title> Dimension counting </section_title> <content> Intuitively, passing through five points in general linear position specifies five independent linear constraints on the (projective) linear space of conics, and hence specifies a unique conic, though this brief statement ignores subtleties. More precisely, this is seen as follows: conics correspond to points in the five-dimensional projective space P 5 ; {\displaystyle \mathbf {P} ^{5};} requiring a conic to pass through a point imposes a linear condition on the coordinates: for a fixed ( x , y ) , {\displaystyle (x,y),} the equation A x 2 + B x y + C y 2 + D x + E y + F = 0 {\displaystyle Ax^{2}+Bxy+Cy^{2}+Dx+Ey+F=0} is a linear equation in ( A , B , C , D , E , F ) ; {\displaystyle (A,B,C,D,E,F);} by dimension counting, five constraints (that the curve passes through five points) are necessary to specify a conic, as each constraint cuts the dimension of possibilities by 1, and one starts with 5 dimensions; in 5 dimensions, the intersection of 5 (independent) hyperplanes is a single point (formally, by Bézout's theorem); general linear position of the points means that the constraints are independent, and thus do specify a unique conic; the resulting conic is non-degenerate because it is a curve (since it has more than 1 point), and does not contain a line (else it would split as two lines, at least one of which must contain 3 of the 5 points, by the pigeonhole principle), so it is irreducible.The two subtleties in the above analysis are that the resulting point is a quadratic equation (not a linear equation), and that the constraints are independent. The first is simple: if A, B, and C all vanish, then the equation D x + E y + F = 0 {\displaystyle Dx+Ey+F=0} defines a line, and any 3 points on this (indeed any number of points) lie on a line – thus general linear position ensures a conic. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Verma module </page_title> <path> Verma_module > Definition of Verma modules > As a quotient of the enveloping algebra </path> <section_title> As a quotient of the enveloping algebra </section_title> <content> Since, also, v {\displaystyle v} is supposed to be a weight vector with weight λ {\displaystyle \lambda } , the kernel of Φ {\displaystyle \Phi } should include all vectors of the form H − λ ( H ) 1 , H ∈ h {\displaystyle H-\lambda (H)1,\quad H\in {\mathfrak {h}}} .Finally, the kernel of Φ {\displaystyle \Phi } should be a left ideal in U ( g ) {\displaystyle U({\mathfrak {g}})} ; after all, if x ⋅ v = 0 {\displaystyle x\cdot v=0} then ( y x ) ⋅ v = y ⋅ ( x ⋅ v ) = 0 {\displaystyle (yx)\cdot v=y\cdot (x\cdot v)=0} for all y ∈ U ( g ) {\displaystyle y\in U({\mathfrak {g}})} . The previous discussion motivates the following construction of Verma module. We define W λ {\displaystyle W_{\lambda }} as the quotient vector space W λ = U ( g ) / I λ {\displaystyle W_{\lambda }=U({\mathfrak {g}})/I_{\lambda }} ,where I λ {\displaystyle I_{\lambda }} is the left ideal generated by all elements of the form X α , α ∈ R + , {\displaystyle X_{\alpha },\quad \alpha \in R^{+},} and H − λ ( H ) 1 , H ∈ h {\displaystyle H-\lambda (H)1,\quad H\in {\mathfrak {h}}} .Because I λ {\displaystyle I_{\lambda }} is a left ideal, the natural left action of U ( g ) {\displaystyle U({\mathfrak {g}})} on itself carries over to the quotient. Thus, W λ {\displaystyle W_{\lambda }} is a U ( g ) {\displaystyle U({\mathfrak {g}})} -module and therefore also a g {\displaystyle {\mathfrak {g}}} -module. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Quasi-random sequences </page_title> <path> Quasi-random_sequence > The formula of Hlawka–Zaremba </path> <section_title> The formula of Hlawka–Zaremba </section_title> <content> Let D = { 1 , 2 , … , d } {\displaystyle D=\{1,2,\ldots ,d\}} . For ∅ ≠ u ⊆ D {\displaystyle \emptyset \neq u\subseteq D} we write d x u := ∏ j ∈ u d x j {\displaystyle dx_{u}:=\prod _{j\in u}dx_{j}} and denote by ( x u , 1 ) {\displaystyle (x_{u},1)} the point obtained from x by replacing the coordinates not in u by 1 {\displaystyle 1} . Then 1 N ∑ i = 1 N f ( x i ) − ∫ I ¯ s f ( u ) d u = ∑ ∅ ≠ u ⊆ D ( − 1 ) \| u \| ∫ \| u \| disc ⁡ ( x u , 1 ) ∂ \| u \| ∂ x u f ( x u , 1 ) d x u , {\displaystyle {\frac {1}{N}}\sum _{i=1}^{N}f(x_{i})-\int _{{\bar {I}}^{s}}f(u)\,du=\sum _{\emptyset \neq u\subseteq D}(-1)^{\|u\|}\int _{^{\|u\|}}\operatorname {disc} (x_{u},1){\frac {\partial ^{\|u\|}}{\partial x_{u}}}f(x_{u},1)\,dx_{u},} where disc ⁡ ( z ) = 1 N ∑ i = 1 N ∏ j = 1 d 1 [ 0 , z j ) ( x i , j ) − ∏ j = 1 d z i {\displaystyle \operatorname {disc} (z)={\frac {1}{N}}\sum _{i=1}^{N}\prod _{j=1}^{d}1_{[0,z_{j})}(x_{i,j})-\prod _{j=1}^{d}z_{i}} is the discrepancy function. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Effective population </page_title> <path> Effective_population_size > Inbreeding effective size > Theoretical example: overlapping generations and age-structured populations > Diploid </path> <section_title> Diploid </section_title> <content> Similarly, the inbreeding effective number can be calculated for a diploid population with discrete age structure. This was first given by Johnson, but the notation more closely resembles Emigh and Pollak.Assume the same basic parameters for the life table as given for the haploid case, but distinguishing between male and female, such as N0ƒ and N0m for the number of newborn females and males, respectively (notice lower case ƒ for females, compared to upper case F for inbreeding). The inbreeding effective number is 1 N e ( F ) = 1 4 T { 1 N 0 f + 1 N 0 m + ∑ i ( ℓ i + 1 f ) 2 ( v i + 1 f ) 2 ( 1 ℓ i + 1 f − 1 ℓ i f ) + ∑ i ( ℓ i + 1 m ) 2 ( v i + 1 m ) 2 ( 1 ℓ i + 1 m − 1 ℓ i m ) } . {\displaystyle {\begin{aligned}{\frac {1}{N_{e}^{(F)}}}={\frac {1}{4T}}\left\{{\frac {1}{N_{0}^{f}}}+{\frac {1}{N_{0}^{m}}}+\sum _{i}\left(\ell _{i+1}^{f}\right)^{2}\left(v_{i+1}^{f}\right)^{2}\left({\frac {1}{\ell _{i+1}^{f}}}-{\frac {1}{\ell _{i}^{f}}}\right)\right.\,\,\,\,\,\,\,\,&\\\left. {}+\sum _{i}\left(\ell _{i+1}^{m}\right)^{2}\left(v_{i+1}^{m}\right)^{2}\left({\frac {1}{\ell _{i+1}^{m}}}-{\frac {1}{\ell _{i}^{m}}}\right)\right\}.&\end{aligned}}} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Förster resonance energy transfer </page_title> <path> Electronic_energy_transfer > Theoretical basis </path> <section_title> Theoretical basis </section_title> <content> J {\displaystyle J} obtained from these units will have unit M − 1 c m − 1 n m 4 {\displaystyle M^{-1}cm^{-1}nm^{4}} . To use unit Å ( 10 − 10 m {\displaystyle 10^{-10}m} ) for the R 0 {\displaystyle R_{0}} , the equation is adjusted to R 0 6 = 8.785 × 10 − 5 κ 2 Q D n 4 J {\displaystyle {R_{0}}^{6}=8.785\times 10^{-5}{\frac {\kappa ^{2}\,Q_{D}}{n^{4}}}J} (Å 6 {\displaystyle ^{6}} )For time-dependent analyses of FRET, the rate of energy transfer ( k ET {\displaystyle k_{\text{ET}}} ) can be used directly instead: k ET = ( R 0 r ) 6 1 τ D {\displaystyle k_{\text{ET}}=({\frac {R_{0}}{r}})^{6}\,{\frac {1}{\tau _{D}}}} where τ D {\displaystyle \tau _{D}} is the donor's fluorescence lifetime in the absence of the acceptor. The FRET efficiency relates to the quantum yield and the fluorescence lifetime of the donor molecule as follows: E = 1 − τ D ′ / τ D , {\displaystyle E=1-\tau '_{\text{D}}/\tau _{\text{D}},} where τ D ′ {\displaystyle \tau _{\text{D}}'} and τ D {\displaystyle \tau _{\text{D}}} are the donor fluorescence lifetimes in the presence and absence of an acceptor respectively, or as E = 1 − F D ′ / F D , {\displaystyle E=1-F_{\text{D}}'/F_{\text{D}},} where F D ′ {\displaystyle F_{\text{D}}'} and F D {\displaystyle F_{\text{D}}} are the donor fluorescence intensities with and without an acceptor respectively. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Thermal boundary layer thickness and shape </page_title> <path> Thermal_boundary_layer_thickness_and_shape > Moment method </path> <section_title> Moment method </section_title> <content> Consider the first derivative temperature profile central moments given by: ϵ n = ∫ 0 ∞ ( y − β ∗ ) n d θ ( x , y ) d y d y {\displaystyle {\epsilon _{n}}=\int _{0}^{\infty }{(y-{\beta ^{}})^{n}{d\theta (x,y) \over dy}\mathrm {d} y}} where the mean location is the thermal displacement thickness β ∗ {\displaystyle \beta ^{}} . Finally the second derivative temperature profile central moments are given by: ϕ n = μ T ∫ 0 ∞ ( y − μ T ) n d 2 θ ( x , y ) d y 2 d y {\displaystyle {\phi _{n}}=\mu _{T}\int _{0}^{\infty }{(y-{\mu _{T}})^{n}{d^{2}\theta (x,y) \over dy^{2}}\mathrm {d} y}} where the mean location, μ T {\displaystyle \mu _{T}} , is given by: 1 μ T = − ( d θ ( x , y ) d y ) y = 0 {\displaystyle {1 \over \mu _{T}}=-\left({\frac {d\theta (x,y)}{dy}}\right)_{y=0}} With the moments and the thermal mean location defined, the boundary layer thickness and shape can be described in terms of the thermal boundary layer width (variance), thermal skewnesses, and thermal excess (excess kurtosis). For the Pohlhausen solution for laminar flow on a heated flat plate, it is found that thermal boundary layer thickness defined as δ T = m T + 4 σ T {\displaystyle \delta _{T}=m_{T}+4\sigma _{T}} where σ T = ξ 2 1 / 2 {\displaystyle \sigma _{T}=\xi _{2}^{1/2}} , tracks the 99% thickness very well.For laminar flow, the three different moment cases all give similar values for the thermal boundary layer thickness. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Windows Spotlight </page_title> <path> Windows_Spotlight > Photo locations > North America </path> <section_title> North America </section_title> <content> Kananaskis Country, Alberta, Canada Moraine Lake, Alberta, Canada Lake Louise, Alberta, Canada Banff National Park, Alberta, Canada Vancouver from Burnaby Mountain, BC, Canada Numa Falls, British Columbia, Canada Landing Lake in Manitoba, Canada Peggy's Cove Lighthouse, Nova Scotia, Canada Niagara Falls, Ontario, Canada and New York, US Tobermory, Ontario, Canada Perce Rock Quebec, Canada Havana, Cuba Punta Gorda, Florida Antigua Guatemala, Guatemala Lake Atitlan Guatemala Durango, Mexico Tamul and Tamasopo waterfalls, Aquismón, near the Cave of Swallows, Huasteca Potosina, Mexico Philipsburg, Sint Maarten Antelope Canyon, Arizona, US Cathedral Rock, Arizona, US The Wave, Vermillion Cliffs National Monument, Arizona, US Badwater Basin, Death Valley, California, US Golden Gate Bridge, California, US Convict Lake, California, US Natural Bridges State Beach, Santa Cruz, California, US Yosemite National Park, California, US Zabriske Point, Death Valley, California, US Bixby Creek Bridge, Big Sur Coast, California, US Griffith Observatory and Los Angeles, California, US South Dakota Highway 87 Needle Eye natural granite tunnel, South Dakota, US Brasstown Bald, Georgia, US Kailua Pier, Hawaii, Hawaii, US Na Pali Coast, Kauai, Hawaii, US Oahu, Hawaii, Hawaii, US Chicago Lakefront, Illinois, US Acadia National Park, Maine, US St Joseph Lighthouse, Michigan, US Gateway Arch, St. Louis, Missouri, US Grinnell Point on Swiftcurrent Lake, Glacier National Park, Montana, US Bisti/De-Na-Zin Wilderness, New Mexico, US Valley of Fire State Park, Nevada, US Bethesda Terrace and Fountain, Central Park, New York City, New York, US Castilleja Indivisa wild flowers field, Oklahoma, US Vista House, Columbia River Gorge, Oregon, US Mesa Arch, Canyonlands National Park, Utah, US Teton Range, Wyoming, US Grand Prismatic Spring, Yellowstone National Park, Wyoming, US Pennybacker Bridge, Austin, Texas, US Bryce Canyon National park, Utah, US Silver Falls State Park, Oregon, US </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Comparison of multi-paradigm programming languages </page_title> <path> Comparison_of_multi-paradigm_programming_languages > Paradigm summaries </path> <section_title> Paradigm summaries </section_title> <content> A concise reference for the programming paradigms listed in this article. Concurrent programming – have language constructs for concurrency, these may involve multi-threading, support for distributed computing, message passing, shared resources (including shared memory), or futures Actor programming – concurrent computation with actors that make local decisions in response to the environment (capable of selfish or competitive behaviour) Constraint programming – relations between variables are expressed as constraints (or constraint networks), directing allowable solutions (uses constraint satisfaction or simplex algorithm) Dataflow programming – forced recalculation of formulas when data values change (e.g. spreadsheets) Declarative programming – describes what computation should perform, without specifying detailed state changes c.f. imperative programming (functional and logic programming are major subgroups of declarative programming) Distributed programming – have support for multiple autonomous computers that communicate via computer networks Functional programming – uses evaluation of mathematical functions and avoids state and mutable data Generic programming – uses algorithms written in terms of to-be-specified-later types that are then instantiated as needed for specific types provided as parameters Imperative programming – explicit statements that change a program state Logic programming – uses explicit mathematical logic for programming Metaprogramming – writing programs that write or manipulate other programs (or themselves) as their data, or that do part of the work at compile time that would otherwise be done at runtime Template metaprogramming – metaprogramming methods in which a compiler uses templates to generate temporary source code, which is merged by the compiler with the rest of the source code and then compiled Reflective programming – metaprogramming methods in which a program modifies or extends itself Object-oriented programming – uses data structures consisting of data fields and methods together with their interactions (objects) to design programs Class-based – object-oriented programming in which inheritance is achieved by defining classes of objects, versus the objects themselves Prototype-based – object-oriented programming that avoids classes and implements inheritance via cloning of instances Pipeline programming – a simple syntax change to add syntax to nest function calls to language originally designed with none Rule-based programming – a network of rules of thumb that comprise a knowledge base and can be used for expert systems and problem deduction & resolution Visual programming – manipulating program elements graphically rather than by specifying them textually (e.g. Simulink); also termed diagrammatic programming </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Pearson's correlation coefficient </page_title> <path> Pearson_coefficient > Interpretation > Geometric interpretation </path> <section_title> Geometric interpretation </section_title> <content> By the usual procedure for finding the angle θ between two vectors (see dot product), the uncentered correlation coefficient is cos ⁡ θ = x ⋅ y ‖ x ‖ ‖ y ‖ = 2.93 103 0.0983 = 0.920814711. {\displaystyle \cos \theta ={\frac {\mathbf {x} \cdot \mathbf {y} }{\left\\|\mathbf {x} \right\\|\left\\|\mathbf {y} \right\\|}}={\frac {2.93}{{\sqrt {103}}{\sqrt {0.0983}}}}=0.920814711.} This uncentered correlation coefficient is identical with the cosine similarity. The above data were deliberately chosen to be perfectly correlated: y = 0.10 + 0.01 x. The Pearson correlation coefficient must therefore be exactly one. Centering the data (shifting x by ℰ(x) = 3.8 and y by ℰ(y) = 0.138) yields x = (−2.8, −1.8, −0.8, 1.2, 4.2) and y = (−0.028, −0.018, −0.008, 0.012, 0.042), from which cos ⁡ θ = x ⋅ y ‖ x ‖ ‖ y ‖ = 0.308 30.8 0.00308 = 1 = ρ x y , {\displaystyle \cos \theta ={\frac {\mathbf {x} \cdot \mathbf {y} }{\left\\|\mathbf {x} \right\\|\left\\|\mathbf {y} \right\\|}}={\frac {0.308}{{\sqrt {30.8}}{\sqrt {0.00308}}}}=1=\rho _{xy},} as expected. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Outline of oceanography </page_title> <path> Outline_of_oceanography > Geological oceanography > Seamounts > Seamounts of the Pacific Ocean </path> <section_title> Seamounts of the Pacific Ocean </section_title> <content> Hawaii hotspot – A volcanic hotspot located near the Hawaiian Islands, in the northern Pacific Ocean Jingū Seamount – A guyot of the Hawaiian-Emperor seamount chain in the Pacific Ocean Kaena Ridge – A submerged remnant of an ancient shield volcano to the north of the Hawaiian Island of Oʻahu Kamaʻehuakanaloa Seamount (formerly Lōʻihi) – An active submarine volcano off the southeast coast of the island of Hawaii Kammu Seamount – A seamount in the Hawaiian-Emperor seamount chain in the Pacific Ocean Kaʻula – A small, crescent-shaped offshore islet in the Hawaiian Islands Kimmei Seamount – A seamount of the Hawaiian-Emperor seamount chain in the northern Pacific Ocean. Koko Guyot – A guyot near the southern end of the Emperor seamounts north of the bend in the Hawaiian-Emperor seamount chain. Kure Atoll – An atoll in the Pacific Ocean in the Northwestern Hawaiian Islands Lanai – The sixth-largest of the Hawaiian Islands Laysan – One of the Northwestern Hawaiian Islands Lisianski Island – One of the Northwestern Hawaiian Islands Māhukona – A submerged shield volcano on the northwestern flank of the Island of Hawaiʻi Maro Reef – A largely submerged coral atoll in the Northwestern Hawaiian Islands Meiji Seamount – The oldest seamount in the Hawaiian-Emperor seamount chain Midway Atoll – One of the United States Minor Outlying Islands in the Hawaiian archipelago Necker Island (Hawaii) – A small island in the Northwestern Hawaiian Islands Nihoa – The tallest of ten islands and atolls in the uninhabited Northwestern Hawaiian Islands Niihau – The westernmost and seventh largest inhabited island in Hawaiʻi Nintoku Seamount – A flat topped seamount in the Hawaiian-Emperor seamount chain Ojin Seamount – A guyot of the Hawaiian-Emperor seamount chain in the Pacific Ocean Pearl and Hermes Atoll – Part of the Northwestern Hawaiian Islands Penguin Bank – A now-submerged shield volcano of the Hawaiian Islands Suiko Seamount – A guyot of the Hawaiian-Emperor seamount chain in the Pacific Ocean. </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
<page_title> Availability (system) </page_title> <path> Availability_(system) > Definition > Availability </path> <section_title> Availability </section_title> <content> A p = T m T m + T d { A p = P r e d i c t e d A v a i l a b i l i t y T m = M i s s i o n D u r a t i o n T d = M o d e l D o w n T i m e {\displaystyle A_{p}={\frac {T_{m}}{T_{m}+T_{d}}}{\begin{cases}A_{p}=Predicted\ Availability\\T_{m}=Mission\ Duration\\T_{d}=Model\ Down\ Time\end{cases}}} Downtime is the total of all of the different contributions that compromise operation. For modeling, these are different aspects of the model, such as human-system interface for MTTR and reliability modeling for MTBF. For observation, these reflect the different areas of the organization, such as maintenance personnel and documentation for MTTR, and manufacturers and shippers for MLDT. T d = T m × M T T R + M L D T + M A M D T M T B F { T d = D o w n T i m e T m = M i s s i o n D u r a t i o n M T T R = M e a n T i m e T o R e c o v e r M L D T = M e a n L o g i s t i c s D e l a y T i m e M A M D T = M e a n A c t i v e M a i n t e n a n c e D o w n T i m e M T B F = M e a n T i m e B e t w e e n F a i l u r e {\displaystyle T_{d}=T_{m}\times {\frac {MTTR+MLDT+MAMDT}{MTBF}}{\begin{cases}T_{d}=Down\ Time\\T_{m}=Mission\ Duration\\MTTR=Mean\ Time\ To\ Recover\\MLDT=Mean\ Logistics\ Delay\ Time\\MAMDT=Mean\ Active\ Maintenance\ Down\ Time\\MTBF=Mean\ Time\ Between\ Failure\end{cases}}} </content>	https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus

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