vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Time dilation
v ∥ ( \ displaystyle v_ ( \ shortparallel ) ) is the radial velocity , v e = 2 G M i r i ( \ displaystyle v_ ( e ) = ( \ sqrt ( \ frac ( 2GM_ ( i ) ) ( r_ ( i ) ) ) ) ) is the escape velocity , β = v / c ( \ displaystyle \ beta = v / c ) , β e = v e / c ( \ displaystyle \ beta _ ( e ) = v_ ( e ) / c ) and β ∥ = v ∥ / c ( \ displaystyle \ beta _ ( \ shortparallel ) = v_ ( \ shortparallel ) / c ) are velocities as a percentage of speed of light c , U = G M i r i ( \ displaystyle U = ( \ frac ( GM_ ( i ) ) ( r_ ( i ) ) ) ) is the Newtonian potential , equivalent to half of the escape velocity squared .
Time dilation
d t E d t c = 1 − 2 U c 2 − v 2 c 2 − ( c 2 2 U − 1 ) − 1 v ∥ 2 c 2 = 1 − ( β 2 + β e 2 + β ∥ 2 β e 2 1 − β e 2 ) ( \ displaystyle ( \ frac ( dt_ ( \ text ( E ) ) ) ( dt_ ( \ text ( c ) ) ) ) = ( \ sqrt ( 1 - ( \ frac ( 2U ) ( c ^ ( 2 ) ) ) - ( \ frac ( v ^ ( 2 ) ) ( c ^ ( 2 ) ) ) - \ left ( ( \ frac ( c ^ ( 2 ) ) ( 2U ) ) - 1 \ right ) ^ ( - 1 ) ( \ frac ( ( v_ ( \ shortparallel ) ) ^ ( 2 ) ) ( c ^ ( 2 ) ) ) ) ) = ( \ sqrt ( 1 - \ left ( \ beta ^ ( 2 ) + \ beta _ ( e ) ^ ( 2 ) + ( \ frac ( \ beta _ ( \ shortparallel ) ^ ( 2 ) \ beta _ ( e ) ^ ( 2 ) ) ( 1 - \ beta _ ( e ) ^ ( 2 ) ) ) \ right ) ) ) \ , )
Heat
δ Q = T d S e and d S i ≡ d S u n c o m p e n s a t e d . ( \ displaystyle \ delta Q = T \ , \ mathrm ( d ) S_ ( \ mathrm ( e ) ) \ , \ , \ , \ , \ , ( \ text ( and ) ) \ , \ , \ , \ , \ , \ mathrm ( d ) S_ ( \ mathrm ( i ) ) \ equiv \ mathrm ( d ) S_ ( \ mathrm ( uncompensated ) ) . )
Kashi Vishwanath Temple
Kashi Vishwanath Temple Kashi Vishwanath Temple , ca . 1915 Location within Uttar Pradesh Geography Coordinates 25 ° 18 ′ 38.79 '' N 83 ° 0 ′ 38.21 '' E ﻿ / ﻿ 25.3107750 ° N 83.0106139 ° E ﻿ / 25.3107750 ; 83.0106139 Coordinates : 25 ° 18 ′ 38.79 '' N 83 ° 0 ′ 38.21 '' E ﻿ / ﻿ 25.3107750 ° N 83.0106139 ° E ﻿ / 25.3107750 ; 83.0106139 Country India State Uttar Pradesh District Varanasi Locale Varanasi Culture Sanctum Vishwanath ( Shiva ) Major festivals Maha Shivaratri Architecture Architecture Mandir History Date built 1780 Creator Maharani Ahilyabai Holkar Website shrikashivishwanath.org
Romance languages
Haitian Creole Li toujou fèmen fenèt la avan li mange . Mauritian Creole Li pou touzour ferm lafnet la avan ( li ) manze . Seychellois Creole Y pou touzour ferm lafnet aven y manze . Chavacano Ta cerrá él con el puerta antes de cená . Papiamento E muhe semper ta sera e bentana promé ku e kome . Cape Verdean Creole Êl fechâ porta antes de jantâ .
Band gap
E g ( T ) = E g ( 0 ) − α T 2 T + β ( \ displaystyle E_ ( g ) ( T ) = E_ ( g ) ( 0 ) - ( \ frac ( \ alpha T ^ ( 2 ) ) ( T+ \ beta ) ) ) , where E ( 0 ) , α and β are material constants .
Nuclear fusion
σ ≈ σ g e o m e t r y ∗ T ∗ R ( \ displaystyle \ sigma \ approx \ sigma _ ( geometry ) * T * R )
Nuclear fusion
5 → He + 2 n + He + p , E = 4.03 + 17.6 + 3.27 = 24.9 MeV , E = 4.03 + 3.5 + 0.82 = 8.35 MeV .
Conic section
r = l 1 + e cos ⁡ θ , ( \ displaystyle r = ( \ frac ( l ) ( 1 + e \ cos \ theta ) ) , )
Radioactive decay
N A = N A 0 e − λ t . ( \ displaystyle N_ ( A ) = N_ ( A0 ) e ^ ( - \ lambda t ) . )
Circular motion
F n e t = m a F n e t = m a r F n e t = m v 2 r F n e t = F c ( \ displaystyle ( \ begin ( aligned ) F_ ( net ) & = ma \ , \ \ F_ ( net ) & = ma_ ( r ) \ , \ \ F_ ( net ) & = ( \ frac ( mv ^ ( 2 ) ) ( r ) ) \ , \ \ F_ ( net ) & = F_ ( c ) \ , \ end ( aligned ) ) )
Medjugorje
Međugorje Међугорје April 2012 view of St. James Church and Medjugorje Međugorje Location of Medjugorje within Bosnia and Herzegovina . Coordinates : 43 ° 12 ′ N 17 ° 41 ′ E ﻿ / ﻿ 43.200 ° N 17.683 ° E ﻿ / 43.200 ; 17.683 Coordinates : 43 ° 12 ′ N 17 ° 41 ′ E ﻿ / ﻿ 43.200 ° N 17.683 ° E ﻿ / 43.200 ; 17.683 Country Bosnia and Herzegovina Entity Federation of Bosnia and Herzegovina Canton Herzegovina - Neretva Municipality Čitluk Population Total 2,306 Time zone UTC + 1 ( CET ) Summer ( DST ) UTC + 2 ( CEST )
Speed of sound
c s = ( γ Z k T e / m i ) 1 / 2 = 9.79 × 10 3 ( γ Z T e / μ ) 1 / 2 m / s , ( \ displaystyle c_ ( s ) = ( \ gamma ZkT_ ( \ mathrm ( e ) ) / m_ ( \ mathrm ( i ) ) ) ^ ( 1 / 2 ) = 9.79 \ times 10 ^ ( 3 ) ( \ gamma ZT_ ( e ) / \ mu ) ^ ( 1 / 2 ) ~ \ mathrm ( m / s ) , )
All You Need Is Love
After the verse `` learn how to play the game , it 's easy '' , the bass alters the prolonged V ( D ) chord with F ♯ , E , C and B notes . The song is notable for a dramatic use of a dominant or V chord ( here D ) on `` It 's easy . '' The `` Love , love , love '' chant involves chords in a I -- V7 -- vi shift ( G -- D -- Em ) and simultaneous descending B , A , G notes with the concluding G note corresponding not to the tonic G chord , but acting as the third of the E minor chord ; this also introducing the E note of the Em chord as a 6th of the tonic G scale . Supporting the same melody note with different and unexpected chords has been termed a characteristic Beatles technique .
PageRank
PageRank is a link analysis algorithm and it assigns a numerical weighting to each element of a hyperlinked set of documents , such as the World Wide Web , with the purpose of `` measuring '' its relative importance within the set . The algorithm may be applied to any collection of entities with reciprocal quotations and references . The numerical weight that it assigns to any given element E is referred to as the PageRank of E and denoted by P R ( E ) . ( \ displaystyle PR ( E ) . ) Other factors like Author Rank can contribute to the importance of an entity .
Democratic Republic of the Congo
Coordinates : 2 ° 52 ′ 48 '' S 23 ° 39 ′ 22 '' E ﻿ / ﻿ 2.88 ° S 23.656 ° E ﻿ / - 2.88 ; 23.656
PageRank
If the matrix M ( \ displaystyle ( \ mathcal ( M ) ) ) is a transition probability , i.e. , column - stochastic and R ( \ displaystyle \ mathbf ( R ) ) is a probability distribution ( i.e. , R = 1 ( \ displaystyle \ mathbf ( R ) = 1 ) , E R = 1 ( \ displaystyle \ mathbf ( E ) \ mathbf ( R ) = \ mathbf ( 1 ) ) where E ( \ displaystyle \ mathbf ( E ) ) is matrix of all ones ) , Eq. ( * * ) is equivalent to
One Tree Hill (New Zealand)
Maungakiekie One Tree Hill Maungakiekie / One Tree Hill after the removal of the `` one tree '' . Highest point Elevation 182 m ( 597 ft ) Coordinates 36 ° 54 ′ 0 '' S 174 ° 46 ′ 59 '' E ﻿ / ﻿ 36.90000 ° S 174.78306 ° E ﻿ / - 36.90000 ; 174.78306 Coordinates : 36 ° 54 ′ 0 '' S 174 ° 46 ′ 59 '' E ﻿ / ﻿ 36.90000 ° S 174.78306 ° E ﻿ / - 36.90000 ; 174.78306 Geography Location North Island , New Zealand Geology Volcanic arc / belt Auckland volcanic field Location
Sahara
Sahara The Great Desert Desert A satellite image of the Sahara by NASA World Wind Countries Algeria , Chad , Egypt , Libya , Mali , Mauritania , Morocco , Niger , Sudan , Tunisia Highest point Emi Koussi 3,415 m ( 11,204 ft ) - coordinates 19 ° 47 ′ 36 '' N 18 ° 33 ′ 6 '' E ﻿ / ﻿ 19.79333 ° N 18.55167 ° E ﻿ / 19.79333 ; 18.55167 Lowest point Qattara Depression − 133 m ( − 436 ft ) - coordinates 30 ° 0 ′ 0 '' N 27 ° 5 ′ 0 '' E ﻿ / ﻿ 30.00000 ° N 27.08333 ° E ﻿ / 30.00000 ; 27.08333 Length 4,800 km ( 2,983 mi ) , E / W Width 1,800 km ( 1,118 mi ) , N / S Area 9,200,000 km ( 3,552,140 sq mi ) Biome Desert
List of earthquakes in New Zealand
Date Location Region Magnitude ( M ) Magnitude ( M ) Depth Latitude Longitude Fatalities Further information 10 Feb 1951 Porangahau Hawke 's Bay 6.1 33 km 40.21 ° S 177.04 ° E Felt throughout North Island 24 Jun 1951 Toaroa Junction Manawatu 6.3 33 km 39.45 ° S 176.20 ° E Felt throughout North Island 29 Sep 1953 Tauranga Bay of Plenty 7.2 273 km 37.59 ° S 176.48 ° E Felt throughout North Island 27 Feb 1955 Raoul Island Kermadec Islands 7.8 18 km 28.40 ° S 175.37 ° W Felt in the East half of North Island 29 Dec 1956 Matawai Gisborne 6.1 6.1 33 km 39.72 ° S 176.87 ° E Felt strongly along the East Coast of the North Island 31 Jan 1958 Waipawa Hawke 's Bay 6.1 12 km 30.30 ° S 177.50 ° E 14 Sep 1959 Raoul Island Kermadec Islands 7.8 35 km 28.82 ° S 177.07 ° W Felt in the East half of North Island 28 Mar 1960 Mokau Taranaki 6.6 237 km 39.04 ° S 174.81 ° E Doublet earthquake to
Channel Tunnel
Channel Tunnel Map of the Channel Tunnel Overview Location English Channel ( Strait of Dover ) Coordinates 51 ° 00 ′ 45 '' N 1 ° 30 ′ 15 '' E ﻿ / ﻿ 51.0125 ° N 1.5041 ° E ﻿ / 51.0125 ; 1.5041 Coordinates : 51 ° 00 ′ 45 '' N 1 ° 30 ′ 15 '' E ﻿ / ﻿ 51.0125 ° N 1.5041 ° E ﻿ / 51.0125 ; 1.5041 Status Active Start Folkestone , Kent , England , United Kingdom ( 51 ° 5 ′ 49.5 '' N 1 ° 9 ′ 21 '' E ﻿ / ﻿ 51.097083 ° N 1.15583 ° E ﻿ / 51.097083 ; 1.15583 ﻿ ( Folkestone Portal ) ) End Coquelles , Pas - de-Calais , Hauts - de-France , France ( 50 ° 55 ′ 22 '' N 1 ° 46 ′ 50.16 '' E ﻿ / ﻿ 50.92278 ° N 1.7806000 ° E ﻿ / 50.92278 ; 1.7806000 ﻿ ( Coquelles Portal ) ) Operation Opened 6 May 1994 ( 1994 - 05 - 06 ) ( tunnel ) 14 November 1994 ( passenger service ) Owner Getlink Operator DB Cargo UK Eurostar Getlink Character Through - rail passenger and freight . Vehicle shuttle . Technical Line length 50.45 km ( 31.35 mi ) No. of tracks 2 single track tunnels 1 service tunnel Track gauge 1,435 mm ( 4 ft 8 ⁄ in ) ( standard gauge ) Electrified 25 kV AC OHLE , 5.87 m Operating speed 160 kilometres per hour ( 99 mph )
Forecasting
However , they have the disadvantage of being infinite or undefined if Y is close to or equal to zero . Mean absolute percentage error ( MAPE ) or mean absolute percentage deviation ( MAPD ) M A P E = 100 ∗ ∑ t = 1 N E t Y t N ( \ displaystyle \ MAPE = 100 * ( \ frac ( \ sum _ ( t = 1 ) ^ ( N ) ( \ frac ( E_ ( t ) ) ( Y_ ( t ) ) ) ) ( N ) ) ) M A P D = ∑ t = 1 N E t ∑ t = 1 N Y t ( \ displaystyle \ MAPD = ( \ frac ( \ sum _ ( t = 1 ) ^ ( N ) E_ ( t ) ) ( \ sum _ ( t = 1 ) ^ ( N ) Y_ ( t ) ) ) ) Scaled Errors : Hyndman and Koehler ( 2006 ) proposed using scaled errors as an alternative to percentage errors . Mean absolute scaled error ( MASE ) M A S E = ∑ t = 1 N E t 1 N − m ∑ t = m + 1 N Y t − Y t − m N ( \ displaystyle MASE = ( \ frac ( \ sum _ ( t = 1 ) ^ ( N ) ( \ frac ( E_ ( t ) ) ( ( \ frac ( 1 ) ( N-m ) ) \ sum _ ( t = m + 1 ) ^ ( N ) Y_ ( t ) - Y_ ( t-m ) ) ) ) ( N ) ) ) * m = s e a s o n a l p e r i o d ( \ displaystyle m = seasonalperiod ) or 1 if non-seasonal Other Measures : Forecast skill ( SS ) S S = 1 − M S E f o r e c a s t M S E r e f ( \ displaystyle \ SS = 1 - ( \ frac ( MSE_ ( forecast ) ) ( MSE_ ( ref ) ) ) )
Eyepiece
f O ( \ displaystyle f_ ( O ) ) is the focal length of the objective , f E ( \ displaystyle f_ ( E ) ) is the focal length of the eyepiece .
Natural logarithm
e ln ⁡ x = x if x > 0 ( \ displaystyle e ^ ( \ ln x ) = x \ qquad ( \ text ( if ) ) x > 0 )
Eyepiece
M A = P E × P O ( \ displaystyle \ mathrm ( MA ) = P_ ( \ mathrm ( E ) ) \ times P_ ( \ mathrm ( O ) ) )
Pi
e i φ = cos ⁡ φ + i sin ⁡ φ , ( \ displaystyle e ^ ( i \ varphi ) = \ cos \ varphi + i \ sin \ varphi , )
Magnetic field
∇ ⋅ B = 0 , ∇ ⋅ E = ρ ε 0 , ∇ × B = μ 0 J + μ 0 ε 0 ∂ E ∂ t , ∇ × E = − ∂ B ∂ t , ( \ displaystyle ( \ begin ( aligned ) \ nabla \ cdot \ mathbf ( B ) & = 0 , \ \ \ nabla \ cdot \ mathbf ( E ) & = ( \ frac ( \ rho ) ( \ varepsilon _ ( 0 ) ) ) , \ \ \ nabla \ times \ mathbf ( B ) & = \ mu _ ( 0 ) \ mathbf ( J ) + \ mu _ ( 0 ) \ varepsilon _ ( 0 ) ( \ frac ( \ partial \ mathbf ( E ) ) ( \ partial t ) ) , \ \ \ nabla \ times \ mathbf ( E ) & = - ( \ frac ( \ partial \ mathbf ( B ) ) ( \ partial t ) ) , \ end ( aligned ) ) )
List of United States Air Force installations
Name Location Coordinates Unit Emblem Unit Designation Notes / Mission Ankara Support Facility Turkey 39th Air Base Wing 717th Air Base Squadron A GSU of Incirlik Air Base , operates the Ankara Support Facility providing support to the American Community in the Ankara Area including the diverse military community and the U.S. Embassy . Ankara Support Element was a portion of the former Ankara Air Station ; in Balgat , three miles from the centre of the city . ( Globalsecurity.org ) Aviano Air Base Italy 46 ° 01 ′ 53 '' N 012 ° 35 ′ 49 '' E ﻿ / ﻿ 46.03139 ° N 12.59694 ° E ﻿ / 46.03139 ; 12.59694 ﻿ ( Aviano AB ) 31st Fighter Wing F - 16 Fighting Falcon supporting NATO and deployments to US Air Forces Central . Büchel Air Base Germany 50 ° 10 ′ 35 '' N 007 ° 03 ′ 28 '' E ﻿ / ﻿ 50.17639 ° N 7.05778 ° E ﻿ / 50.17639 ; 7.05778 ﻿ ( Büchel AB ) 52d Fighter Wing 702nd Munitions Support Squadron . Chièvres Air Base Belgium 50 ° 35 ′ 9.58 '' N 003 ° 50 ′ 37.47 '' E ﻿ / ﻿ 50.5859944 ° N 3.8437417 ° E ﻿ / 50.5859944 ; 3.8437417 ﻿ ( Chievres AB ) 86th Airlift Wing GSU of Ramstein Air Base . Ghedi Air Base Italy 45 ° 25 ′ 52.57 '' N 10 ° 16 ′ 48.40 '' E ﻿ / ﻿ 45.4312694 ° N 10.2801111 ° E ﻿ / 45.4312694 ; 10.2801111 ﻿ ( Ghedi AB ) 52d Fighter Wing 704th Munitions Support Squadron . Incirlik Air Base Turkey 37 ° 00 ′ 07 '' N 035 ° 25 ′ 33 '' E ﻿ / ﻿ 37.00194 ° N 35.42583 ° E ﻿ / 37.00194 ; 35.42583 ﻿ ( Incirlik Air Base ) 39th Air Base Wing No permanent aircraft assigned . Supports USAF / NATO aircraft deployed to Southern Europe supporting NATO and deployments to US Air Forces Central .
Life in a Northern Town
The song , which took a year to record , also includes elements of classical music , an `` African-esque '' chant ( which was later sampled by dance duo Dario G for their track `` Sunchyme '' ) , and hints of psychedelia . It is in the key of E major with a main chord pattern of E-A - E and a vocal range from B to E .
Time dilation
d t E ( \ displaystyle dt_ ( \ text ( E ) ) ) is a small increment of proper time t E ( \ displaystyle t_ ( \ text ( E ) ) ) ( an interval that could be recorded on an atomic clock ) , d t c ( \ displaystyle dt_ ( \ text ( c ) ) ) is a small increment in the coordinate t c ( \ displaystyle t_ ( \ text ( c ) ) ) ( coordinate time ) , d x , d y , d z ( \ displaystyle dx , dy , dz ) are small increments in the three coordinates x , y , z ( \ displaystyle x , y , z ) of the clock 's position , G M i r i ( \ displaystyle ( \ frac ( GM_ ( i ) ) ( r_ ( i ) ) ) ) represents the sum of the Newtonian gravitational potentials due to the masses in the neighborhood , based on their distances r i ( \ displaystyle r_ ( i ) ) from the clock . This sum includes any tidal potentials .
Normal distribution
f ( x ) = e a x 2 + b x + c ( \ displaystyle f ( x ) = e ^ ( ax ^ ( 2 ) + bx + c ) )
PID controller
P out = K p e ( t ) . ( \ displaystyle P_ ( \ text ( out ) ) = K_ ( \ text ( p ) ) e ( t ) . )
Test probe
t r ( c o m b i n e d ) = t r ( p r o b e ) 2 + t r ( s c o p e ) 2 ( \ displaystyle t_ ( r ) ( combined ) = ( \ sqrt ( t_ ( r ) ( probe ) ^ ( 2 ) + t_ ( r ) ( scope ) ^ ( 2 ) ) ) )
Dark matter halo
where r is the spatial ( i.e. , not projected ) radius . The term d n ( \ displaystyle d_ ( n ) ) is a function of n such that ρ e ( \ displaystyle \ rho _ ( e ) ) is the density at the radius r e ( \ displaystyle r_ ( e ) ) that defines a volume containing half of the total mass . While the addition of a third parameter provides a slightly improved description of the results from numerical simulations , it is not observationally distinguishable from the 2 parameter NFW halo , and does nothing to alleviate the cuspy halo problem .
Hammersmith & City line
51 ° 32 ′ 20 '' N 000 ° 03 ′ 06 '' E ﻿ / ﻿ 51.53889 ° N 0.05167 ° E ﻿ / 51.53889 ; 0.05167 ﻿ ( 28 - East Ham tube station ) Barking 2 June 1902 Connects with c2c , London Overground , and District line services to Upminster . Main - line station opened in 1854 . District Railway service withdrawn 1905 -- 8 . Metropolitan service began in 1936 . 51 ° 32 ′ 21 '' N 000 ° 04 ′ 54 '' E ﻿ / ﻿ 51.53917 ° N 0.08167 ° E ﻿ / 51.53917 ; 0.08167 ﻿ ( 29 - Barking station )
Vredefort crater
Vredefort Crater Vredefort Dome ( centre ) Vredefort Dome , seen from space by STS - 51 - I Impact crater / structure Confidence Confirmed Diameter 300 km ( 190 mi ) Age 2023 ± 4 Ma Paleoproterozoic Exposed Yes Drilled Yes Location Coordinates 27 ° 0 ′ 0 '' S 27 ° 30 ′ 0 '' E ﻿ / ﻿ 27.00000 ° S 27.50000 ° E ﻿ / - 27.00000 ; 27.50000 Coordinates : 27 ° 0 ′ 0 '' S 27 ° 30 ′ 0 '' E ﻿ / ﻿ 27.00000 ° S 27.50000 ° E ﻿ / - 27.00000 ; 27.50000 Country South Africa Province Free State Province Location of Vredefort crater
Tropical cyclone
Tropical cyclone basins and official warning centers Basin Warning center Area of responsibility Notes Northern Hemisphere North Atlantic Eastern Pacific United States National Hurricane Center United States Central Pacific Hurricane Center Equator northward , African Coast -- 140 ° W Equator northward , 140 ° W - 180 Western Pacific Japan Meteorological Agency Equator - 60 ° N , 180 - 100 ° E North Indian Ocean India Meteorological Department Equator northward , 100 ° E-45 ° E Southern Hemisphere South - West Indian Ocean Météo - France Reunion Equator - 40 ° S , African Coast - 90 ° E Australian region Indonesian Agency for Meteorology , Climatology and Geophysics ( BMKG ) Papua New Guinea National Weather Service , Australian Bureau of Meteorology Equator - 10 ° S , 90 ° E-141 ° E Equator - 10 ° S , 141 ° E-160 ° E 10 ° S - 36 ° S , 90 ° E-160 ° E Southern Pacific Fiji Meteorological Service Meteorological Service of New Zealand Equator - 25 ° S , 160 ° E-120 ° W 25 ° S - 40 ° S , 160 ° E-120 ° W
Unbiased estimation of standard deviation
E ⁡ ( s ) = c 4 ( n ) σ ( \ displaystyle \ operatorname ( E ) ( s ) = c_ ( 4 ) ( n ) \ sigma )
Radioactive decay
N A = N A 0 e − λ t ( \ displaystyle N_ ( A ) = N_ ( A0 ) e ^ ( - ( \ lambda ) t ) \ , \ ! )
Thebes, Egypt
Thebes Waset Θῆβαι Pillars of the Great Hypostyle Hall Shown within Egypt Location Luxor , Luxor Governorate , Egypt Region Upper Egypt Coordinates 25 ° 43 ′ 14 '' N 32 ° 36 ′ 37 '' E ﻿ / ﻿ 25.72056 ° N 32.61028 ° E ﻿ / 25.72056 ; 32.61028 Coordinates : 25 ° 43 ′ 14 '' N 32 ° 36 ′ 37 '' E ﻿ / ﻿ 25.72056 ° N 32.61028 ° E ﻿ / 25.72056 ; 32.61028 Type Settlement UNESCO World Heritage Site Official name Ancient Thebes with its Necropolis Type Cultural Criteria I , III , VI Designated 1979 ( 3rd session ) Reference no . 87 Region Arab States
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 ) 2 ) = σ 2 . ( \ displaystyle ( \ begin ( aligned ) \ operatorname ( E ) ( S ^ ( 2 ) ) & = \ operatorname ( E ) ( \ bigg ( ) ( \ frac ( 1 ) ( n ) ) \ sum _ ( i = 1 ) ^ ( n ) ( X_ ( i ) - ( \ overline ( X ) ) ) ^ ( 2 ) ( \ bigg ) ) < \ operatorname ( E ) ( \ bigg ( ) ( \ frac ( 1 ) ( n ) ) \ sum _ ( i = 1 ) ^ ( n ) ( X_ ( i ) - \ mu ) ^ ( 2 ) ( \ bigg ) ) = \ sigma ^ ( 2 ). \ end ( aligned ) ) )
Southern Ocean
In the second edition , the Southern Ocean then extended from Antarctica northwards to latitude 40 ° S between Cape Agulhas in Africa ( long . 20 ° E ) and Cape Leeuwin in Western Australia ( long . 115 ° E ) , and extended to latitude 55 ° S between Auckland Island of New Zealand ( 165 or 166 ° E east ) and Cape Horn in South America ( 67 ° W ) .
Red Sea
Red Sea Coordinates 22 ° N 38 ° E ﻿ / ﻿ 22 ° N 38 ° E ﻿ / 22 ; 38 Coordinates : 22 ° N 38 ° E ﻿ / ﻿ 22 ° N 38 ° E ﻿ / 22 ; 38 Primary inflows Barka River , Haddas River , Anseba River , Wadi Gasus Primary outflows Bab el Mandeb Max. length 2,250 km ( 1,400 mi ) Max . width 355 km ( 221 mi ) Surface area 438,000 km ( 169,000 sq mi ) Average depth 490 m ( 1,610 ft ) Max . depth 3,040 m ( 9,970 ft ) Water volume 233,000 km ( 56,000 cu mi ) Play
Monte Carlo
Monte Carlo Quarter and Ward of Monaco Monte Carlo in Monaco ( Ward shown ) Monte Carlo Location in relation to France Coordinates : 43 ° 44 ′ 23 '' N 7 ° 25 ′ 38 '' E ﻿ / ﻿ 43.73972 ° N 7.42722 ° E ﻿ / 43.73972 ; 7.42722 Coordinates : 43 ° 44 ′ 23 '' N 7 ° 25 ′ 38 '' E ﻿ / ﻿ 43.73972 ° N 7.42722 ° E ﻿ / 43.73972 ; 7.42722 Country Monaco Government Type Principality Area Urban 0.61 km (. 234 sq mi ) Population Quarter and Ward of Monaco 15,200 ( in the quarter ) 3,500 ( in the ward ) Postcode 98000
Sundial
H E = 15 ∘ × t ( hours ) . ( \ displaystyle H_ ( E ) = 15 ^ ( \ circ ) \ times t ( \ text ( ( hours ) ) ) . )
Particle in a box
The energy gap of a quantum dot is the energy gap between its valence and conduction bands . This energy gap Δ E ( r ) ( \ displaystyle \ Delta E ( r ) ) is equal to the band gap of the bulk material E gap ( \ displaystyle E_ ( \ text ( gap ) ) ) plus the energy equation derived from particle - in - a-box , which gives the energy for electrons and holes . This can be seen in the following equation , where m e ∗ ( \ displaystyle m_ ( e ) ^ ( * ) ) and m h ∗ ( \ displaystyle m_ ( h ) ^ ( * ) ) are the effective masses of the electron and hole , r ( \ displaystyle r ) is radius of the dot , and h ( \ displaystyle h ) is Planck 's constant :
List of earthquakes in New Zealand
14 Mar 2005 Opunake Manawatu - Wanganui 6.4 154 km 40.17 ° S 173.63 ° E Felt strongly throughout central New Zealand 16 May 2006 L'Esperance Rock Kermadec Islands 7.5 7.4 150 km 31.56 ° S , 179.30 ° W Felt in East half of New Zealand 16 May 2006 Raoul Island Kermadec Islands 7.1 33 km 31.98 ° S , 177.21 ° W Felt in East half on North Island 16 Oct 2007 Fiordland Southland 6.7 6.7 5 km 44.72 ° S 167.39 ° E Felt lower half of South Island 9 Dec 2007 Raoul Island Kermadec Islands 7.8 152 km 25.99 ° S 177.51 ° W Felt in East half of New Zealand 20 Dec 2007 Gisborne East Cape 6.7 6.6 44 km 38.89 ° S 178.44 ° E 2007 Gisborne earthquake 25 Aug 2008 Hastings Hawke 's Bay 5.9 31 km 39.71 ° S 176.85 ° E 2008 Hastings earthquake 15 Jul 2009 Puysegur Trench South of New Zealand 6.1 33 km 46.07 ° S 165.75 ° E Felt throughout Southland and Otago 15 Jul 2009 Dusky Sound Southland 7.8 12 km 45.76 ° S 166.58 ° E 2009 Fiordland earthquake
Malaysia
Flag Coat of arms Motto : `` Bersekutu Bertambah Mutu '' `` Unity Is Strength '' Anthem : Negaraku My Country Capital Kuala Lumpur 3 ° 8 ′ N 101 ° 41 ′ E ﻿ / ﻿ 3.133 ° N 101.683 ° E ﻿ / 3.133 ; 101.683 Putrajaya ( administrative ) 2 ° 56 ′ 35 '' N 101 ° 41 ′ 58 '' E ﻿ / ﻿ 2.9430952 ° N 101.699373 ° E ﻿ / 2.9430952 ; 101.699373 Largest city Kuala Lumpur 3 ° 8 ′ N 101 ° 41 ′ E ﻿ / ﻿ 3.133 ° N 101.683 ° E ﻿ / 3.133 ; 101.683 Official languages Malaysian Official script Malay ( Latin ) alphabet Recognised languages English Ethnic groups ( ) 50.1 % Malay 22.6 % Chinese 11.8 % Indigenous 6.7 % Indian 8.8 % other Religion Official : 61.3 % Islam ( Sunni ) Other religions : 19.8 % Buddhist 9.2 % Christian 6.2 % Hindu 3.4 % other Demonym Malaysian Government Federal parliamentary elective constitutional monarchy Yang di - Pertuan Agong Muhammad V Prime Minister Najib Razak Chief Justice Md Raus Sharif President of the Dewan Negara S. Vigneswaran Speaker of the Dewan Rakyat Pandikar
Challenger Deep
The maximum surveyed depth of the Challenger Deep was reported in 1957 by the Soviet Research vessel Vityaz recording a spot 11,034 metres ( 36,201 ft ) ± 50 m ( 164 ft ) deep at 11 ° 20.9 ′ N 142 ° 11.5 ′ E ﻿ / ﻿ 11.3483 ° N 142.1917 ° E ﻿ / 11.3483 ; 142.1917 . It was dubbed the Mariana Hollow and is listed in many reference sources , including the Encyclopædia Britannica , articles in National Geographic and on maps . The pressure at this depth is approximately 1,099 times that at the surface , or 111 MPa ( 16,099 psi ) . In 1959 , the US Navy research vessel RV Stranger using bomb - sounding surveyed a maximum depth of 10,915 m ( 35,810 ft ) ± 10 m ( 33 ft ) at 11 ° 20.0 ′ N 142 ° 11.8 ′ E ﻿ / ﻿ 11.3333 ° N 142.1967 ° E ﻿ / 11.3333 ; 142.1967 . In 1962 , the US Navy research vessel RV Spencer F. Baird using a frequency - controlled depth recorder surveyed a maximum depth of 10,915 m ( 35,810 ft ) ± 10 m ( 33 ft ) at 11 ° 20.0 ′ N 142 ° 11.8 ′ E ﻿ / ﻿ 11.3333 ° N 142.1967 ° E ﻿ / 11.3333 ; 142.1967 . In 1975 and 1980 , the US Navy research vessel RV Thomas Washington using a precision depth recorder with satellite positioning surveyed a maximum depth of 10,915 m ( 35,810 ft ) ± 10 m ( 33 ft ) at 11 ° 20.0 ′ N 142 ° 11.8 ′ E ﻿ / ﻿ 11.3333 ° N 142.1967 ° E ﻿ / 11.3333 ; 142.1967 . In 1984 , the survey vessel Takuyo from the Hydrographic Department of Japan , used a narrow , multibeam echo sounder to take a measurement of 10,924 m ( 35,840 ft ) ± 10 m ( 33 ft ) at 11 ° 22.4 ′ N 142 ° 35.5 ′ E ﻿ / ﻿ 11.3733 ° N 142.5917 ° E ﻿ / 11.3733 ; 142.5917 . Deep