vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Digboi
Digboi town Nickname ( s ) : The Oil Town Digboi Location in Assam , India Digboi Digboi ( India ) Show map of Assam Show map of India Show all Coordinates : 27 ° 23 ′ N 95 ° 38 ′ E ﻿ / ﻿ 27.38 ° N 95.63 ° E ﻿ / 27.38 ; 95.63 Coordinates : 27 ° 23 ′ N 95 ° 38 ′ E ﻿ / ﻿ 27.38 ° N 95.63 ° E ﻿ / 27.38 ; 95.63 Country India State Assam District Tinsukia Government Body Digboi Municipality Elevation 165 m ( 541 ft ) Population ( 2001 ) Total 20,405 Languages Official Assamese Time zone IST ( UTC + 5 : 30 ) PIN 786171 ISO 3166 code IN - AS Vehicle registration AS - 23
River Thames
Thames River The Thames in London Country England Counties Gloucestershire , Wiltshire , Oxfordshire , Berkshire , Buckinghamshire , Surrey , Middlesex , London , Kent , Essex Towns / Cities Cricklade , Lechlade , Oxford , Abingdon , Wallingford , Reading , Henley - on - Thames , Marlow , Maidenhead , Windsor , Staines - upon - Thames , Walton - on - Thames , Kingston upon Thames , Teddington , Richmond , London , London Source - location Thames Head , Gloucestershire , UK - elevation 110 m ( 361 ft ) - coordinates 51 ° 41 ′ 39 '' N 2 ° 01 ′ 47 '' W ﻿ / ﻿ 51.694262 ° N 2.029724 ° W ﻿ / 51.694262 ; - 2.029724 Mouth Thames Estuary , North Sea - location Southend - on - Sea , Essex , UK - elevation 0 m ( 0 ft ) - coordinates 51 ° 29 ′ 56 '' N 0 ° 36 ′ 31 '' E ﻿ / ﻿ 51.4989 ° N 0.6087 ° E ﻿ / 51.4989 ; 0.6087 Coordinates : 51 ° 29 ′ 56 '' N 0 ° 36 ′ 31 '' E ﻿ / ﻿ 51.4989 ° N 0.6087 ° E ﻿ / 51.4989 ; 0.6087 Length 346 km ( 215 mi ) Basin 12,935 km ( 4,994 sq mi ) Discharge for London - average 65.8 m / s ( 2,324 cu ft / s ) - max 370 m / s ( 13,066 cu ft / s ) Discharge elsewhere ( average ) - entering Oxford 17.6 m / s ( 622 cu ft / s ) - leaving Oxford 24.8 m / s ( 876 cu ft / s ) - Reading 39.7 m / s ( 1,402 cu ft / s ) - Windsor 59.3 m / s ( 2,094 cu ft / s ) Map of the Thames within southern England
Capital asset pricing model
E ( R i ) ( \ displaystyle E ( R_ ( i ) ) ) is required return on security i R f ( \ displaystyle R_ ( f ) ) is risk - free rate R P m ( \ displaystyle RP_ ( m ) ) is general market risk premium R P s ( \ displaystyle RP_ ( s ) ) is risk premium for small size R P u ( \ displaystyle RP_ ( u ) ) is risk premium due to company - specific risk factor ''
Hoarders
Hoarders Genre Reality Show Country of origin United States Original language ( s ) English No. of seasons 9 No. of episodes 118 ( list of episodes ) Production Executive producer ( s ) Dave Severson Andrew Berg David McKillop Elaine Frontain Bryant George Butts Jessica Morgan Matt Chan Mike Kelly Camera setup Multiple Running time 42 to 48 minutes Production company ( s ) Screaming Flea Productions Distributor A + E Networks Release Original network A&E , Lifetime Picture format 480i ( SDTV ) 1080i ( HDTV ) Original release August 17 , 2009 ( 2009 - 08 - 17 ) -- present External links Website www.aetv.com/hoarders/
River Welland
River Welland The river at Stamford Country United Kingdom Country within the UK England Counties Northamptonshire , Leicestershire , Rutland , Lincolnshire Towns Market Harborough , Stamford , Crowland , Spalding Tributaries - left Eye Brook , River Chater , River Gwash , River Glen - right River Jordan Source - location Hothorpe Hills , Sibbertoft , Northamptonshire - elevation 157 m ( 515 ft ) - coordinates 52 ° 26 ′ 24 '' N 1 ° 00 ′ 35 '' W ﻿ / ﻿ 52.4399 ° N 1.0098 ° W ﻿ / 52.4399 ; - 1.0098 Mouth Fosdyke Wash - location The Wash , Lincolnshire - elevation 1 m ( 3 ft ) - coordinates 52 ° 53 ′ 54 '' N 0 ° 01 ′ 51 '' E ﻿ / ﻿ 52.8983 ° N 0.0308 ° E ﻿ / 52.8983 ; 0.0308 Coordinates : 52 ° 53 ′ 54 '' N 0 ° 01 ′ 51 '' E ﻿ / ﻿ 52.8983 ° N 0.0308 ° E ﻿ / 52.8983 ; 0.0308 Length 105 km ( 65 mi ) Basin 1,580 km ( 610 sq mi ) Discharge for Tallington - average 3.7 m / s ( 131 cu ft / s ) - max 94.5 m / s ( 3,337 cu ft / s ) Wikimedia Commons : River Welland Progression : Welland -- The Wash -- North Sea
Aihole
Group of monuments At Aihole Durga temple cluster at Aihole Location Bagalkot , Karnataka , India Nearest city Badami Coordinates 16 ° 1 ′ 08 '' N 75 ° 52 ′ 55 '' E ﻿ / ﻿ 16.01889 ° N 75.88194 ° E ﻿ / 16.01889 ; 75.88194 Coordinates : 16 ° 1 ′ 08 '' N 75 ° 52 ′ 55 '' E ﻿ / ﻿ 16.01889 ° N 75.88194 ° E ﻿ / 16.01889 ; 75.88194 Area 5 square kilometres ( 1.9 sq mi ) Elevation 810 m ( 2,657 ft ) Built 4th -- 12th century CE Architectural style ( s ) Hindu , Jain , Buddhist temples and monasteries Governing body Archaeological Survey of India Location of Aihole Aihole ( Karnataka ) Show map of India Show map of Karnataka Show all
Bias of an estimator
Since this is an orthogonal decomposition , Pythagorean theorem says C → 2 = A → 2 + B → 2 ( \ displaystyle ( \ vec ( C ) ) ^ ( 2 ) = ( \ vec ( A ) ) ^ ( 2 ) + ( \ vec ( B ) ) ^ ( 2 ) ) , and taking expectations we get n σ 2 = n E ⁡ ( ( X ̄ − μ ) 2 ) + n E ⁡ ( S 2 ) ( \ displaystyle n \ sigma ^ ( 2 ) = n \ operatorname ( E ) \ left ( ( ( \ overline ( X ) ) - \ mu ) ^ ( 2 ) \ right ) + n \ operatorname ( E ) ( S ^ ( 2 ) ) ) , as above ( but times n ( \ displaystyle n ) ) . If the distribution of C → ( \ displaystyle ( \ vec ( C ) ) ) is rotationally symmetric , as in the case when X i ( \ displaystyle X_ ( i ) ) are sampled from a Gaussian , then on average , the dimension along u → ( \ displaystyle ( \ vec ( u ) ) ) contributes to C → 2 ( \ displaystyle ( \ vec ( C ) ) ^ ( 2 ) ) equally as the n − 1 ( \ displaystyle n - 1 ) directions perpendicular to u → ( \ displaystyle ( \ vec ( u ) ) ) , so that E ⁡ ( ( X ̄ − μ ) 2 ) = σ 2 n ( \ displaystyle \ operatorname ( E ) \ left ( ( ( \ overline ( X ) ) - \ mu ) ^ ( 2 ) \ right ) = ( \ frac ( \ sigma ^ ( 2 ) ) ( n ) ) ) and E ⁡ ( S 2 ) = ( n − 1 ) σ 2 n ( \ displaystyle \ operatorname ( E ) ( S ^ ( 2 ) ) = ( \ frac ( ( n - 1 ) \ sigma ^ ( 2 ) ) ( n ) ) ) . This is in fact true in general , as explained above .
Bias of an estimator
E ⁡ ( n S 2 ) = ( n − 1 ) σ 2 and Var ⁡ ( n S 2 ) = 2 ( n − 1 ) σ 4 . ( \ displaystyle \ operatorname ( E ) ( nS ^ ( 2 ) ) = ( n - 1 ) \ sigma ^ ( 2 ) ( \ text ( and ) ) \ operatorname ( Var ) ( nS ^ ( 2 ) ) = 2 ( n - 1 ) \ sigma ^ ( 4 ) . )
Bipolar junction transistor
text ( S ) ) \ left ( ( \ frac ( 1 ) ( \ beta _ ( F ) ) ) \ left ( e ^ ( \ frac ( V_ ( \ text ( BE ) ) ) ( V_ ( \ text ( T ) ) ) ) - 1 \ right ) + ( \ frac ( 1 ) ( \ beta _ ( R ) ) ) \ left ( e ^ ( \ frac ( V_ ( \ text ( BC ) ) ) ( V_ ( \ text ( T ) ) ) ) - 1 \ right ) \ right ) \ \ i_ ( \ text ( E ) ) & = I_ ( \ text ( S ) ) \ left ( \ left ( e ^ ( \ frac ( V_ ( \ text ( BE ) ) ) ( V_ ( \ text ( T ) ) ) ) - e ^ ( \ frac ( V_ ( \ text ( BC ) ) ) ( V_ ( \ text ( T ) ) ) ) \ right ) + ( \ frac ( 1 ) ( \ beta _ ( F ) ) ) \ left ( e ^ ( \ frac ( V_ ( \ text ( BE ) ) ) ( V_ ( \ text ( T ) ) ) ) - 1 \ right ) \ right ) \ end ( aligned ) ) )
Heat
Δ S o v e r a l l > 0 . ( \ displaystyle \ Delta S_ ( \ mathrm ( overall ) ) > 0 . )
Heat
T d S ≥ δ Q ( s e c o n d l a w ) . ( \ displaystyle T \ , \ mathrm ( d ) S \ geq \ delta Q \ quad ( \ rm ( ( second \ , \ , law ) ) ) \ , . )
Cardinal direction
North ( N ) : 0 ° = 360 ° East ( E ) : 90 ° South ( S ) : 180 ° West ( W ) : 270 °
Leaning Tower of Pisa
Leaning Tower of Pisa Torre pendente di Pisa Leaning Tower of Pisa Basic information Location Pisa , Italy Geographic coordinates 43 ° 43 ′ 23 '' N 10 ° 23 ′ 47 '' E ﻿ / ﻿ 43.72306 ° N 10.39639 ° E ﻿ / 43.72306 ; 10.39639 Coordinates : 43 ° 43 ′ 23 '' N 10 ° 23 ′ 47 '' E ﻿ / ﻿ 43.72306 ° N 10.39639 ° E ﻿ / 43.72306 ; 10.39639 Affiliation Roman Catholic Country Italy Website www.opapisa.it Architectural description Architect ( s ) Bonanno Pisano Architectural style Romanesque Groundbreaking 1173 Completed 1372 Specifications Height ( max ) 55.86 metres ( 183.3 ft ) Materials marble stone UNESCO World Heritage Site Criteria Cultural : ( i ) , ( ii ) , ( iv ) , ( vi ) Reference 395 Inscription 1987 ( 11th Session ) ( edit on Wikidata )
Physics of magnetic resonance imaging
S ( t ) = ρ ~ e f f ( k → ( t ) ) ≡ ∫ − ∞ ∞ d x → ρ ( x → ) ⋅ e 2 π ı k → ( t ) ⋅ x → ( \ displaystyle S ( t ) = ( \ tilde ( \ rho ) ) _ ( \ mathrm ( eff ) ) \ left ( ( \ vec ( k ) ) ( t ) \ right ) \ equiv \ int _ ( - \ infty ) ^ ( \ infty ) \ mathrm ( d ) ( \ vec ( x ) ) \ \ rho ( ( \ vec ( x ) ) ) \ cdot e ^ ( 2 \ pi \ imath \ ( \ vec ( k ) ) ( t ) \ cdot ( \ vec ( x ) ) ) )
Bowen Hills railway station
Bowen Hills Northbound view from Platform 2 in July 2012 Location Abbotsford Road , Bowen Hills Coordinates 27 ° 26 ′ 43 '' S 153 ° 02 ′ 15 '' E ﻿ / ﻿ 27.4454 ° S 153.0376 ° E ﻿ / - 27.4454 ; 153.0376 Coordinates : 27 ° 26 ′ 43 '' S 153 ° 02 ′ 15 '' E ﻿ / ﻿ 27.4454 ° S 153.0376 ° E ﻿ / - 27.4454 ; 153.0376 Owned by Queensland Rail Operated by City network Line ( s ) North Coast Ferny Grove Distance 2.66 kilometres from Central Platforms 4 ( 2 islands ) Construction Structure type Ground Disabled access Yes Other information Status Staffed Station code 600005 ( platform 1 ) 600000 ( platform 2 ) 600002 ( platform 3 ) 600007 ( platform 4 ) Fare zone go card 1 Website Queensland Rail History Opened 1973 Electrified Yes Services Preceding station Queensland Rail Following station Fortitude Valley toward Roma Street Airport Line Albion toward Domestic Terminal Terminus Beenleigh Line Fortitude Valley toward Beenleigh Fortitude Valley toward Roma Street Caboolture Line Eagle Junction toward Caboolture Terminus Cleveland Line Fortitude Valley toward Cleveland Fortitude Valley toward Roma Street Doomben Line Albion toward Doomben Fortitude Valley toward Roma Street Ferny Grove Line Windsor toward Ferny Grove Terminus Gold Coast Line Fortitude Valley toward Varsity Lakes Terminus Ipswich & Rosewood Line Fortitude Valley toward Rosewood Fortitude Valley toward Roma Street Redcliffe Peninsula Line Eagle Junction toward Kippa - Ring Fortitude Valley toward Roma Street Shorncliffe Line Albion toward Shorncliffe Terminus Springfield Line Fortitude Valley toward Springfield Central Fortitude Valley toward Roma Street Sunshine Coast Line Eagle Junction toward Nambour Northgate toward Gympie North
Time dilation
f d e t e c t e d = f r e s t ( 1 − v c cos ⁡ φ ) / 1 − v 2 / c 2 ( \ displaystyle f_ ( \ mathrm ( detected ) ) = f_ ( \ mathrm ( rest ) ) ( \ left ( 1 - ( \ frac ( v ) ( c ) ) \ cos \ phi \ right ) / ( \ sqrt ( 1 - ( v ^ ( 2 ) ) / ( c ^ ( 2 ) ) ) ) ) ) as deduced by Einstein ( 1905 ) . For φ = 90 ° ( cosφ = 0 ) this reduces to f = f γ . This lower frequency from the moving source can be attributed to the time dilation effect and is often called the transverse Doppler effect and was predicted by relativity .
Bias of an estimator
Thus E ⁡ ( S 2 ) = σ 2 ( \ displaystyle \ operatorname ( E ) ( S ^ ( 2 ) ) = \ sigma ^ ( 2 ) ) , and therefore S 2 = 1 n − 1 ∑ i = 1 n ( X i − X  ̄ ) 2 ( \ displaystyle S ^ ( 2 ) = ( \ frac ( 1 ) ( n - 1 ) ) \ sum _ ( i = 1 ) ^ ( n ) ( X_ ( i ) - ( \ overline ( X ) ) \ , ) ^ ( 2 ) ) is an unbiased estimator of the population variance , σ . The ratio between the biased ( uncorrected ) and unbiased estimates of the variance is known as Bessel 's correction .
Mid-Atlantic Ridge
Ascension Island ( The Peak , Green Mountain , 859 m , at 07 ° 59 ′ S 14 ° 25 ′ W ﻿ / ﻿ 7.983 ° S 14.417 ° W ﻿ / - 7.983 ; - 14.417 ) Saint Helena ( Diana 's Peak , 818 m at 15 ° 57 ′ S 5 ° 41 ′ W ﻿ / ﻿ 15.950 ° S 5.683 ° W ﻿ / - 15.950 ; - 5.683 ) Tristan da Cunha ( Queen Mary 's Peak , 2062 m , at 37 ° 05 ′ S 12 ° 17 ′ W ﻿ / ﻿ 37.083 ° S 12.283 ° W ﻿ / - 37.083 ; - 12.283 ) Gough Island ( Edinburgh Peak , 909 m , at 40 ° 20 ′ S 10 ° 00 ′ W ﻿ / ﻿ 40.333 ° S 10.000 ° W ﻿ / - 40.333 ; - 10.000 ) Bouvet Island ( Olavtoppen , 780 m , at 54 ° 24 ′ S 03 ° 21 ′ E ﻿ / ﻿ 54.400 ° S 3.350 ° E ﻿ / - 54.400 ; 3.350 )
Command-line interface
Operating system Command Valid alternative Notes OpenVMS directory / owner Dir / Owner instruct the directory command to also display the ownership of the files . Note the Directory command name is not case sensitive , and can be abbreviated to as few letters as required to remain unique . DOS dir / Q / O :S d * diR / qd * / o :s display ownership of files whose names begin with `` D '' , sorted by size , smallest first . Note spaces around argument d * are required . Unix - like systems ls - lS D * ls - S - l D * display in long format files and directories beginning with `` D '' ( but not `` d '' ) , sorted by size ( largest first ) . Note spaces are required around all arguments and options , but some can be run together , e.g. - lS is the same as - l - S . Data General RDOS CLI list / e / s 04 - 26 - 80 / b List / S / E 4 - 26 - 80 / B list every attribute for files created before 26 April 1980 . Note the / B at the end of the date argument is a local switch , that modifies the meaning of that argument , while / S and / E are global switches , i.e. apply to the whole command . Abbreviating
Bias of an estimator
E ⁡ ( S 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − X ̄ ) 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( ( X i − μ ) − ( X ̄ − μ ) ) 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( ( X i − μ ) 2 − 2 ( X ̄ − μ ) ( X i − μ ) + ( X ̄ − μ ) 2 ) ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 − 2 n ( X ̄ − μ ) ∑ i = 1 n ( X i − μ ) + 1 n ( X ̄ − μ ) 2 ∑ i = 1 n 1 ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 − 2 n ( X ̄ − μ ) ∑ i = 1 n ( X i − μ ) + 1 n ( X ̄ − μ ) 2 ⋅ n ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 − 2 n ( X ̄ − μ ) ∑ i = 1 n ( X i − μ ) + ( X ̄ − μ ) 2 ) ( \ displaystyle ( \ begin ( aligned ) \ operatorname ( E ) ( S ^ ( 2 ) ) & = \ operatorname ( E ) \ left ( ( \ frac ( 1 ) ( n ) ) \ sum _ ( i = 1 ) ^ ( n ) ( \ big ( ) X_ ( i ) - ( \ overline ( X ) ) ( \ big ) ) ^ ( 2 ) \ right ) = \ operatorname ( E ) ( \ bigg ( ) ( \ frac ( 1 ) ( n ) ) \ sum _ ( i = 1 ) ^ ( n ) ( \ bigg ( ) ( X_ ( i ) - \ mu ) - ( ( \ overline ( X ) ) - \ mu ) ( \ bigg ) ) ^ ( 2 ) ( \ bigg ) ) \ \ ( 8pt ) & = \ operatorname ( E ) ( \ bigg ( ) ( \ frac ( 1 ) ( n ) ) \ sum _ ( i = 1 ) ^ ( n ) ( \ bigg ( ) ( X_ ( i ) - \ mu ) ^ (
Tashan-e-Ishq
No . Title Singer ( s ) Length 1 . `` Tashan E Ishq '' Arpita Chakraborty 3 : 53 2 . `` Sajna Ve '' Mamta Raut , Rahul Pandit and Altamash Faridi 5 : 13
Student's t-test
α ^ , β ^ = least - squares estimators , S E α ^ , S E β ^ = the standard errors of least - squares estimators . ( \ displaystyle ( \ begin ( aligned ) ( \ hat ( \ alpha ) ) , ( \ hat ( \ beta ) ) & = ( \ text ( least - squares estimators ) ) , \ \ SE_ ( \ hat ( \ alpha ) ) , SE_ ( \ hat ( \ beta ) ) & = ( \ text ( the standard errors of least - squares estimators ) ). \ end ( aligned ) ) )
List of mathematical symbols
σ A g e ≥ 34 ( P e r s o n ) ( \ displaystyle \ sigma _ ( \ mathrm ( Age ) \ geq 34 ) ( \ mathrm ( Person ) ) ) σ A g e = W e i g h t ( P e r s o n ) ( \ displaystyle \ sigma _ ( \ mathrm ( Age ) = \ mathrm ( Weight ) ) ( \ mathrm ( Person ) ) ) ∑ ∑ ( \ displaystyle \ sum ) \ sum summation sum over ... from ... to ... of arithmetic ∑ k = 1 n a k ( \ displaystyle \ sum _ ( k = 1 ) ^ ( n ) ( a_ ( k ) ) ) means a 1 + a 2 + ⋯ + a n ( \ displaystyle a_ ( 1 ) + a_ ( 2 ) + \ cdots + a_ ( n ) ) . ∑ k = 1 4 k 2 = 1 2 + 2 2 + 3 2 + 4 2 = 1 + 4 + 9 + 16 = 30 ( \ displaystyle \ sum _ ( k = 1 ) ^ ( 4 ) ( k ^ ( 2 ) ) = 1 ^ ( 2 ) + 2 ^ ( 2 ) + 3 ^ ( 2 ) + 4 ^ ( 2 ) = 1 + 4 + 9 + 16 = 30 )
Speed of sound
c s o l i d , p = K + 4 3 G ρ = E ( 1 − ν ) ρ ( 1 + ν ) ( 1 − 2 ν ) , ( \ displaystyle c_ ( \ mathrm ( solid , p ) ) = ( \ sqrt ( \ frac ( K+ ( \ frac ( 4 ) ( 3 ) ) G ) ( \ rho ) ) ) = ( \ sqrt ( \ frac ( E ( 1 - \ nu ) ) ( \ rho ( 1 + \ nu ) ( 1 - 2 \ nu ) ) ) ) , ) c s o l i d , s = G ρ , ( \ displaystyle c_ ( \ mathrm ( solid , s ) ) = ( \ sqrt ( \ frac ( G ) ( \ rho ) ) ) , )
Unbiased estimation of standard deviation
E ( s 2 ) = σ 2 ( 1 − 2 n − 1 ∑ k = 1 n − 1 ( 1 − k n ) ρ k ) ( \ displaystyle ( \ rm ( E ) ) \ left ( s ^ ( 2 ) \ right ) = \ sigma ^ ( 2 ) \ left ( 1 - ( \ frac ( 2 ) ( n - 1 ) ) \ sum _ ( k = 1 ) ^ ( n - 1 ) \ left ( 1 - ( \ frac ( k ) ( n ) ) \ right ) \ rho _ ( k ) \ right ) )
To Autumn
On 19 September 1819 , Keats walked near Winchester along the River Itchen . In a letter to his friend John Hamilton Reynolds written on 21 September , Keats described the impression the scene had made upon him and its influence on the composition of `` To Autumn '' : `` How beautiful the season is now -- How fine the air . A temperate sharpness about it ( ... ) I never lik 'd stubble fields so much as now ( ... ) Somehow a stubble plain looks warm -- in the same way that some pictures look warm -- this struck me so much in my sunday 's walk that I composed upon it . '' Not everything on Keats 's mind at the time was bright ; the poet knew in September that he would have to finally abandon Hyperion . Thus , in the letter that he wrote to Reynolds , Keats also included a note saying that he abandoned his long poem . Keats did not send `` To Autumn '' to Reynolds , but did include the poem within a letter to Richard Woodhouse , Keats 's publisher and friend , and dated it on the same day .
Bias of an estimator
E ⁡ ( S 2 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − X ̄ ) 2 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( ( X i − μ ) − ( X ̄ − μ ) ) 2 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( ( X i − μ ) 2 − 2 ( X ̄ − μ ) ( X i − μ ) + ( X ̄ − μ ) 2 ) ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − μ ) 2 − 2 n − 1 ( X ̄ − μ ) ∑ i = 1 n ( X i − μ ) + 1 n − 1 ( X ̄ − μ ) 2 ∑ i = 1 n 1 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − μ ) 2 − 2 n − 1 ( X ̄ − μ ) ∑ i = 1 n ( X i − μ ) + 1 n − 1 ( X ̄ − μ ) 2 ⋅ n ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − μ ) 2 − 2 n − 1 ( X ̄ − μ ) ∑ i = 1 n ( X i − μ ) + n n − 1 ( X ̄ − μ ) 2 ) ( \ displaystyle ( \ begin ( aligned ) \ operatorname ( E ) ( S ^ ( 2 ) ) & = \ operatorname ( E ) \ left ( ( \ frac ( 1 ) ( n - 1 ) ) \ sum _ ( i = 1 ) ^ ( n ) ( \ big ( ) X_ ( i ) - ( \ overline ( X ) ) ( \ big ) ) ^ ( 2 ) \ right ) = \ operatorname ( E ) ( \ bigg ( ) ( \ frac ( 1 ) ( n - 1 ) ) \ sum _ ( i = 1 ) ^ ( n ) ( \ bigg ( ) ( X_ ( i ) - \ mu ) - ( ( \ overline ( X ) ) - \ mu ) ( \ bigg ) ) ^ ( 2 ) ( \ bigg ) ) \ \ ( 8pt ) & = \ operatorname ( E ) ( \ bigg ( ) ( \ frac ( 1 ) ( n - 1 ) ) \ sum _ ( i = 1 ) ^ ( n ) ( \ bigg ( ) ( X_ ( i ) - \ mu )
Spark plug
( E ) Exhaust camshaft ( I ) Intake camshaft ( S ) Spark plug ( V ) Valves ( P ) Piston ( R ) Connecting rod ( C ) Crankshaft ( W ) Water jacket for coolant flow
Chennai
Chennai Madras Metropolis Clockwise from top right : Chennai Central , Marina Beach , Madras High Court , TIDEL Park , Ripon Building , San Thome Basilica , Kapaleeshwarar Temple , Classical dance Bharata Natyam and Valluvar Kottam Nickname ( s ) : Detroit of Asia Gateway of South India India 's Health Capital , City of flyover Chennai Location of Chennai in Tamil Nadu Coordinates : 13 ° 5 ′ N 80 ° 16 ′ E ﻿ / ﻿ 13.083 ° N 80.267 ° E ﻿ / 13.083 ; 80.267 Coordinates : 13 ° 5 ′ N 80 ° 16 ′ E ﻿ / ﻿ 13.083 ° N 80.267 ° E ﻿ / 13.083 ; 80.267 Country India State Tamil Nadu District Chennai , Kanchipuram Tiruvallur Former name Madras Established 1639 Government Type Mayor -- Council Body Greater Chennai Corporation Mayor Saidai Duraisamy Corporation Commissioner D Karthikeyan IAS Police Commissioner Karan Sinha IPS Area Metropolis 426 km ( 164.5 sq mi ) Metro 1,189 km ( 459.07 sq mi ) Elevation 6 m ( 20 ft ) Population ( 2011 ) Metropolis 7,088,000 Rank 5th Metro 8,653,521 8,917,749 ( Extended UA ) Metro rank 4th Demonym ( s ) Chennaiite Languages Native Tamil Official Tamil , and English Time zone IST ( UTC + 05 : 30 ) Pincode ( s ) 600xxx Area code ( s ) + 91 - 44 Vehicle registration TN - 01 to TN - 14 , TN - 18 , TN - 22 , TN - 85 Metro GDP $59 to $66 billion ( PPP ) Website Chennai Corporation Jump up ^ The Chennai metropolitan area also includes portions of Kanchipuram and Tiruvallur districts adjoining the Chennai District .
Currencies of Puerto Rico
Puerto Rican dollar Dólar Puertoriqueño ( Spanish ) Bilingual 200 pesos banknote ( series E ) Denominations Subunit 1 / 100 centavo Banknotes 5 , 10 , 20 , 50 , 100 , 200 dollars series E ( 1904 ) , series F ( 1909 ) Coins 5 , 10 , 20 , 40 centavos Demographics User ( s ) Puerto Rico ( U.S. ) Issuance Central bank Bank of Porto Rico ( 1898 - 1913 ) Printer American Bank Note Co . N.Y. Website www.abnote.com Valuation Pegged with United States dollar
Dr Narla Tata Rao Thermal Power Station
Dr Narla Tata Rao Thermal Power Station Narla Tata Rao Power Station in January 2015 Location of Dr Narla Tata Rao Thermal Power Station Country India Location Vijayawada , Krishna , Andhra Pradesh Coordinates 16 ° 35 ′ 27 '' N 80 ° 32 ′ 00 '' E ﻿ / ﻿ 16.5907 ° N 80.5332 ° E ﻿ / 16.5907 ; 80.5332 Coordinates : 16 ° 35 ′ 27 '' N 80 ° 32 ′ 00 '' E ﻿ / ﻿ 16.5907 ° N 80.5332 ° E ﻿ / 16.5907 ; 80.5332 Status Operational Commission date Unit 1 : November 1 , 1979 Unit 2 : October 10 , 1980 Unit 3 : October 5 , 1980 Unit 4 : August 23 , 1990 Unit 5 : March 31 , 1994 Unit 6 : February 24 , 1995 Unit 7 : April 6 , 2009 Operator ( s ) APGENCO Thermal power station Primary fuel Coal - fired Power generation Units operational 6 X 210 MW 1 X 500 MW Nameplate capacity 1760.00 MW
List of mathematical symbols
P ( r , t ) = χ ⋮ E ( r , t 1 ) E ( r , t 2 ) E ( r , t 3 ) ( \ displaystyle P ( r , t ) = \ chi \ vdots E ( r , t_ ( 1 ) ) E ( r , t_ ( 2 ) ) E ( r , t_ ( 3 ) ) ) ≀ ≀ ( \ displaystyle \ wr \ ! \ , ) \ wr \ ! \ , wreath product wreath product of ... by ... group theory A ≀ H means the wreath product of the group A by the group H . This may also be written A H . S n ≀ Z 2 ( \ displaystyle \ mathrm ( S ) _ ( n ) \ wr \ mathrm ( Z ) _ ( 2 ) ) is isomorphic to the automorphism group of the complete bipartite graph on ( n , n ) vertices . ↯ ⨳ ⇒ ⇐ \ blitza \ lighting : requires \ usepackage ( stmaryd ) . \ smashtimes requires \ usepackage ( unicode - math ) and \ setmathfont ( XITS Math ) or another Open Type Math Font . ⇒ ⇐ ( \ displaystyle \ Rightarrow \ Leftarrow ) \ Rightarrow \ Leftarrow ⊥ ( \ displaystyle \ bot ) \ bot ↮ ( \ displaystyle \ nleftrightarrow ) \ nleftrightarrow \ textreferencemark Contradiction ! downwards zigzag arrow contradiction ; this contradicts that everywhere Denotes that contradictory statements have been inferred . For clarity , the exact point of contradiction can be appended . x + 4 = x − 3 ※ Statement : Every finite , non-empty , ordered set has a largest element . Otherwise , let 's assume that X ( \ displaystyle X ) is a finite , non-empty , ordered set with no largest element .
Internal energy
Internal energy Common symbols U SI unit In SI base units m * kg / s Derivations from other quantities U = ∑ i E i ( \ displaystyle U = \ sum _ ( i ) E_ ( i ) \ ! )
Cheruthoni Dam
Cheruthoni Dam Cheruthoni dam Location of Cheruthoni Dam in India Cheruthoni Dam ( Kerala ) Cheruthoni Dam ( Tamil Nadu ) Show map of India Show map of Kerala Show map of Tamil Nadu Show all Country India Location Idukki , Kerala , India Coordinates 9 ° 50 ′ 43 '' N 76 ° 58 ′ 01 '' E ﻿ / ﻿ 9.84528 ° N 76.96694 ° E ﻿ / 9.84528 ; 76.96694 Coordinates : 9 ° 50 ′ 43 '' N 76 ° 58 ′ 01 '' E ﻿ / ﻿ 9.84528 ° N 76.96694 ° E ﻿ / 9.84528 ; 76.96694 Status Operational Opening date 1976 Owner ( s ) Kerala State Electricity Board Dam and spillways Type of dam Straight gravity concrete Impounds Periyar River Height 138.2 m ( 453 ft ) Length 650.9 m ( 2,135 ft ) Dam volume 17 , 00,000 cu. m Spillways 7 no. s ( 5 radial floodgates gates Ft. and 2 vertical flood gates ( river bed level ) ) Spillway type Chute type spillway Reservoir Creates Idukki Reservoir Total capacity 1,996,000,000 m ( 1,618,184 acre ⋅ ft ) Active capacity 1,459,000,000 m ( 1,182,831 acre ⋅ ft ) Inactive capacity 536,000,000 m ( 434,542 acre ⋅ ft ) Catchment area 649.3 km ( 251 sq mi ) Surface area 60 km ( 23 sq mi ) Normal elevation 732.62 m ( 2,404 ft )
Physics of magnetic resonance imaging
I ( x → ) = ∫ − ∞ ∞ d k → S ( k → ( t ) ) ⋅ e − 2 π ı k → ( t ) ⋅ x → ( \ displaystyle I \ left ( ( \ vec ( x ) ) \ right ) = \ int _ ( - \ infty ) ^ ( \ infty ) \ mathrm ( d ) ( \ vec ( k ) ) \ S \ left ( ( \ vec ( k ) ) ( t ) \ right ) \ cdot e ^ ( - 2 \ pi \ imath \ ( \ vec ( k ) ) ( t ) \ cdot ( \ vec ( x ) ) ) )