vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Red Sea
On the North . The Southern limits of the Gulfs of Suez ( A line running from Ràs Muhammed ( 27 ° 43'N ) to the South point of Shadwan Island ( 34 ° 02'E ) and thence Westward on a parallel ( 27 ° 27'N ) to the coast of Africa ) and Aqaba ( A line running from Ràs al Fasma Southwesterly to Requin Island ( 27 ° 57 ′ N 34 ° 36 ′ E ﻿ / ﻿ 27.950 ° N 34.600 ° E ﻿ / 27.950 ; 34.600 ) through Tiran Island to the Southwest point thereof and thence Westward on a parallel ( 27 ° 54'N ) to the coast of the Sinaï Peninsula ) . On the South . A line joining Husn Murad ( 12 ° 40 ′ N 43 ° 30 ′ E ﻿ / ﻿ 12.667 ° N 43.500 ° E ﻿ / 12.667 ; 43.500 ) and Ras Siyyan ( 12 ° 29 ′ N 43 ° 20 ′ E ﻿ / ﻿ 12.483 ° N 43.333 ° E ﻿ / 12.483 ; 43.333 ) .
Exponential function
one may use the Taylor series of e x − 1 : ( \ displaystyle e ^ ( x ) - 1 : )
Rub' al Khali
Coordinates : 20 ° N 50 ° E ﻿ / ﻿ 20 ° N 50 ° E ﻿ / 20 ; 50
Quantum mechanics
H n ( x ) = ( − 1 ) n e x 2 d n d x n ( e − x 2 ) , ( \ displaystyle H_ ( n ) ( x ) = ( - 1 ) ^ ( n ) e ^ ( x ^ ( 2 ) ) ( \ frac ( d ^ ( n ) ) ( dx ^ ( n ) ) ) \ left ( e ^ ( - x ^ ( 2 ) ) \ right ) , )
Bias of an estimator
E ⁡ ( S 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 − 2 n ( X ̄ − μ ) ∑ i = 1 n ( X i − μ ) + ( X ̄ − μ ) 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 − 2 n ( X ̄ − μ ) ⋅ n ⋅ ( X ̄ − μ ) + ( X ̄ − μ ) 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 − 2 ( X ̄ − μ ) 2 + ( X ̄ − μ ) 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 − ( X ̄ − μ ) 2 ) = E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 ) − E ⁡ ( ( X ̄ − μ ) 2 ) = σ 2 − E ⁡ ( ( X ̄ − μ ) 2 ) = ( 1 − 1 n ) σ 2 < σ 2 .
Radioactive decay
lim λ B → 0 ( N A 0 λ A λ B − λ A ( e − λ A t − e − λ B t ) ) = N A 0 λ A 0 − λ A ( e − λ A t − 1 ) = N A 0 ( 1 − e − λ A t ) , ( \ displaystyle \ lim _ ( \ lambda _ ( B ) \ rightarrow 0 ) \ left ( ( \ frac ( N_ ( A0 ) \ lambda _ ( A ) ) ( \ lambda _ ( B ) - \ lambda _ ( A ) ) ) \ left ( e ^ ( - \ lambda _ ( A ) t ) - e ^ ( - \ lambda _ ( B ) t ) \ right ) \ right ) = ( \ frac ( N_ ( A0 ) \ lambda _ ( A ) ) ( 0 - \ lambda _ ( A ) ) ) \ left ( e ^ ( - \ lambda _ ( A ) t ) - 1 \ right ) = N_ ( A0 ) \ left ( 1 - e ^ ( - \ lambda _ ( A ) t ) \ right ) , )
Nepanagar
Nepanagar Town Nepanagar Location in Madhya Pradesh , India Coordinates : 21 ° 27 ′ 21 '' N 76 ° 26 ′ 58 '' E ﻿ / ﻿ 21.45583 ° N 76.44944 ° E ﻿ / 21.45583 ; 76.44944 Coordinates : 21 ° 27 ′ 21 '' N 76 ° 26 ′ 58 '' E ﻿ / ﻿ 21.45583 ° N 76.44944 ° E ﻿ / 21.45583 ; 76.44944 Country India State Madhya Pradesh District Burhanpur Population ( 2011 ) Total 29,682 Time zone IST ( UTC + 5 : 30 )
Degrees of freedom (physics and chemistry)
If E = X 1 4 + X 1 3 X 2 + X 2 4 ( \ displaystyle E = X_ ( 1 ) ^ ( 4 ) + X_ ( 1 ) ^ ( 3 ) X_ ( 2 ) + X_ ( 2 ) ^ ( 4 ) ) , then the two degrees of freedom are not independent and non-quadratic . If E = X 1 4 + X 2 4 ( \ displaystyle E = X_ ( 1 ) ^ ( 4 ) + X_ ( 2 ) ^ ( 4 ) ) , then the two degrees of freedom are independent and non-quadratic . If E = X 1 2 + X 1 X 2 + 2 X 2 2 ( \ displaystyle E = X_ ( 1 ) ^ ( 2 ) + X_ ( 1 ) X_ ( 2 ) + 2X_ ( 2 ) ^ ( 2 ) ) , then the two degrees of freedom are not independent but are quadratic . If E = X 1 2 + 2 X 2 2 ( \ displaystyle E = X_ ( 1 ) ^ ( 2 ) + 2X_ ( 2 ) ^ ( 2 ) ) , then the two degrees of freedom are independent and quadratic .
Siberia
Coordinates : 60 ° 0 ′ N 105 ° 0 ′ E ﻿ / ﻿ 60.000 ° N 105.000 ° E ﻿ / 60.000 ; 105.000
Natural logarithm
ln ⁡ ( e x ) = x . ( \ displaystyle \ ln ( e ^ ( x ) ) = x . )
Malaysia
Coordinates : 2 ° 30 ′ N 112 ° 30 ′ E ﻿ / ﻿ 2.500 ° N 112.500 ° E ﻿ / 2.500 ; 112.500
Lebanon
Coordinates : 33 ° 50 ′ N 35 ° 50 ′ E ﻿ / ﻿ 33.833 ° N 35.833 ° E ﻿ / 33.833 ; 35.833
Challenger Deep
On 24 March 1995 , the Japanese robotic deep - sea probe Kaikō broke the depth record for unmanned probes when it reached close to the surveyed bottom of the Challenger Deep . Created by the Japan Agency for Marine - Earth Science and Technology ( JAMSTEC ) , it was one of the few unmanned deep - sea probes in operation that could dive deeper than 6,000 metres ( 20,000 ft ) . The manometer measured depth of 10,911 m ( 35,797 ft ) ± 3 m ( 10 ft ) at 11 ° 22.39 ′ N 142 ° 35.54 ′ E ﻿ / ﻿ 11.37317 ° N 142.59233 ° E ﻿ / 11.37317 ; 142.59233 for the Challenger Deep is believed to be the most accurate measurement taken yet . Kaikō also collected sediment cores containing marine organisms from the bottom of the deep . Kaikō made many unmanned descents to the Mariana Trench during three expeditions in 1995 , 1996 and 1998 . The greatest depth measured by Kaikō in 1996 was 10,898 m ( 35,755 ft ) at 11 ° 22.10 ′ N 142 ° 25.85 ′ E ﻿ / ﻿ 11.36833 ° N 142.43083 ° E ﻿ / 11.36833 ; 142.43083 and in 1998 10,907 m ( 35,784 ft ) at 11 ° 22.95 ′ N 142 ° 12.42 ′ E ﻿ / ﻿ 11.38250 ° N 142.20700 ° E ﻿ / 11.38250 ; 142.20700 . It was lost at sea off Shikoku Island during Typhoon Chan - Hom on 29 May 2003 . ABISMO
Nile
Nile The river in Uganda Countries Egypt , Sudan , South Sudan , Ethiopia , Uganda , Congo , Kenya , Tanzania , Rwanda , Burundi , Eritrea Major cities Jinja , Juba , Khartoum , Cairo Physical characteristics Main source White Nile Rwanda 2,700 m ( 8,900 ft ) 02 ° 16 ′ 56 '' S 29 ° 19 ′ 53 '' E ﻿ / ﻿ 2.28222 ° S 29.33139 ° E ﻿ / - 2.28222 ; 29.33139 2nd source Blue Nile Lake Tana , Ethiopia 12 ° 02 ′ 09 '' N 037 ° 15 ′ 53 '' E ﻿ / ﻿ 12.03583 ° N 37.26472 ° E ﻿ / 12.03583 ; 37.26472 River mouth Mediterranean Sea Egypt Sea level 30 ° 10 ′ N 31 ° 09 ′ E ﻿ / ﻿ 30.167 ° N 31.150 ° E ﻿ / 30.167 ; 31.150 Coordinates : 30 ° 10 ′ N 31 ° 09 ′ E ﻿ / ﻿ 30.167 ° N 31.150 ° E ﻿ / 30.167 ; 31.150 Length 6,853 km ( 4,258 mi ) Width Maximum width : 2.8 km ( 1.7 mi ) Depth Average depth : 8 -- 11 m ( 26 -- 36 ft ) Discharge Average rate : 2,830 m / s ( 100,000 cu ft / s ) Basin features Basin size 3,400,000 km ( 1,300,000 sq mi )
Bias of an estimator
1 − e − 4 λ . ( \ displaystyle 1 - e ^ ( - 4 \ lambda ). \ , )
Exponential function
z w = e w log ⁡ z ( \ displaystyle z ^ ( w ) = e ^ ( w \ log z ) )
Moment-generating function
Distribution Moment - generating function M ( t ) Characteristic function φ ( t ) Bernoulli P ( X = 1 ) = p ( \ displaystyle \ , P ( X = 1 ) = p ) 1 − p + p e t ( \ displaystyle \ , 1 - p + pe ^ ( t ) ) 1 − p + p e i t ( \ displaystyle \ , 1 - p + pe ^ ( it ) ) Geometric ( 1 − p ) k − 1 p ( \ displaystyle ( 1 - p ) ^ ( k - 1 ) \ , p \ ! ) p e t 1 − ( 1 − p ) e t ( \ displaystyle ( \ frac ( pe ^ ( t ) ) ( 1 - ( 1 - p ) e ^ ( t ) ) ) \ ! ) ∀ t < − ln ⁡ ( 1 − p ) ( \ displaystyle \ forall t < - \ ln ( 1 - p ) \ ! ) p e i t 1 − ( 1 − p ) e i t ( \ displaystyle ( \ frac ( pe ^ ( it ) ) ( 1 - ( 1 - p ) \ , e ^ ( it ) ) ) \ !
Planck's law
⟨ E ⟩ = − d log ⁡ ( Z ) d β = ε 2 + ε e β ε − 1 . ( \ displaystyle \ left \ langle E \ right \ rangle = - ( \ frac ( d \ log \ left ( Z \ right ) ) ( d \ beta ) ) = ( \ frac ( \ varepsilon ) ( 2 ) ) + ( \ frac ( \ varepsilon ) ( e ^ ( \ beta \ varepsilon ) - 1 ) ) . )
Italian Australians
È la dura quotidiana fatica del lavoro e la resistenza alle lotte degli Australiani che essi debbono sostenere per il prestigio di essere Italiani di Mussolini . ( ... ) Gli Italiani formarono quel fronte unico di resistenza che va considerato una delle più belle vittorie del fascismo in terra straniera . Altra cosa è fare gl'Italiani in Italia altra è all'estero , dove chi ti dà da mangiare dimentica che tu lavori per lui , e solo per questo crede di essere padrone delle tue braccia e del tuo spirito . ( Italians have to sustain the daily hard work and the resistance to the claims of Australians , to bear the prestige to be Italians of Mussolini . ( ... ) Italians formed that strong front of resistance , which can be considered one of the best victories of fascism in foreign land . One thing is to form Italians in Italy and another is abroad , where those who feed you forget that you all work for them , and just for this reason they think to be the owners of your arms and spirits ) .
Mariana Trench
Coordinates : 11 ° 21 ′ N 142 ° 12 ′ E ﻿ / ﻿ 11.350 ° N 142.200 ° E ﻿ / 11.350 ; 142.200 Location
Particle in a box
λ = h c Δ E ( \ displaystyle \ lambda = ( \ tfrac ( hc ) ( \ Delta E ) ) )
Particle in a box
λ = h c Δ E ( \ displaystyle \ lambda = ( \ frac ( hc ) ( \ Delta E ) ) )
Cross product
The cross product is used to describe the Lorentz force experienced by a moving electric charge q e ( \ displaystyle q_ ( e ) ) :
Planck's law
E 2 − E 1 = h ν ( \ displaystyle E_ ( 2 ) - E_ ( 1 ) = h \ nu ) .
Conic section
A property that the conic sections share is often presented as the following definition . A conic section is the locus of all points P whose distance to a fixed point F ( called the focus of the conic ) is a constant multiple ( called the eccentricity , e ) of the distance from P to a fixed line L ( called the directrix of the conic ) . For 0 < e < 1 we obtain an ellipse , for e = 1 a parabola , and for e > 1 a hyperbola .
Radioactive decay
N B = N A 0 − N A = N A 0 − N A 0 e − λ t = N A 0 ( 1 − e − λ t ) . ( \ displaystyle N_ ( B ) = N_ ( A0 ) - N_ ( A ) = N_ ( A0 ) - N_ ( A0 ) e ^ ( - ( \ lambda ) t ) = N_ ( A0 ) \ left ( 1 - e ^ ( - ( \ lambda ) t ) \ right ) . )
Electromagnetic radiation
∇ × E = k ^ × E 0 f ′ ( k ^ ⋅ x − c 0 t ) = − ∂ B ∂ t ( \ displaystyle \ nabla \ times \ mathbf ( E ) = ( \ hat ( \ mathbf ( k ) ) ) \ times \ mathbf ( E ) _ ( 0 ) f ' \ left ( ( \ hat ( \ mathbf ( k ) ) ) \ cdot \ mathbf ( x ) - c_ ( 0 ) t \ right ) = - ( \ frac ( \ partial \ mathbf ( B ) ) ( \ partial t ) ) ) B = 1 c 0 k ^ × E ( \ displaystyle \ mathbf ( B ) = ( \ frac ( 1 ) ( c_ ( 0 ) ) ) ( \ hat ( \ mathbf ( k ) ) ) \ times \ mathbf ( E ) )
Equator
E ﻿ / 0.000 ; 120.083 ﻿ ( Gulf of Tomini ) Gulf of Tomini 0 ° 0 ′ N 124 ° 0 ′ E ﻿ / ﻿ 0.000 ° N 124.000 ° E ﻿ / 0.000 ; 124.000 ﻿ ( Molucca Sea ) Molucca Sea 0 ° 0 ′ N 127 ° 24 ′ E ﻿ / ﻿ 0.000 ° N 127.400 ° E ﻿ / 0.000 ; 127.400 ﻿ ( Indonesia ) Indonesia Kayoa and Halmahera islands 0 ° 0 ′ N 127 ° 53 ′ E ﻿ / ﻿ 0.000 ° N 127.883 ° E ﻿ / 0.000 ; 127.883 ﻿ ( Halmahera Sea ) Halmahera Sea 0 ° 0 ′ N 129 ° 20 ′ E ﻿ / ﻿ 0.000 ° N 129.333 ° E ﻿ / 0.000 ; 129.333 ﻿ ( Indonesia ) Indonesia Gebe and Kawe islands 0 ° 0 ′ N 129 ° 21 ′ E ﻿ / ﻿ 0.000 ° N 129.350 ° E ﻿ / 0.000 ; 129.350 ﻿ ( Pacific Ocean ) Pacific Ocean Passing between Aranuka and Nonouti atolls , Kiribati ( at 0 ° 0 ′ N 173 ° 40 ′ E ﻿ / ﻿ 0.000 ° N 173.667 ° E ﻿ / 0.000 ; 173.667 ) 0 ° 0 ′ N 80 ° 6 ′ W ﻿ / ﻿ 0.000 ° N 80.100 ° W ﻿ / 0.000 ; - 80.100 ﻿ ( Ecuador ) Ecuador Passing 24 km ( 15 mi ) north of central Quito , near Mitad del Mundo , and precisely at the location of Catequilla , a pre-Columbian ruin Also , Isabela Island in the Galápagos Islands 0 ° 0 ′ N 75 ° 32 ′ W ﻿ / ﻿ 0.000 ° N 75.533 ° W ﻿ / 0.000 ; - 75.533 ﻿ ( Colombia ) Colombia Passing 4.3 km ( 2.7 mi ) north of the border with Peru 0 ° 0 ′ N 70 ° 3 ′ W ﻿ / ﻿ 0.000 ° N 70.050 ° W ﻿ / 0.000 ; - 70.050 ﻿ ( Brazil ) Brazil Amazonas Roraima Pará Amapá ( passing slightly south of the city center of the state capital Macapá ) 0 ° 0 ′ N 49 ° 21 ′ W ﻿ / ﻿ 0.000 ° N 49.350 ° W ﻿ / 0.000 ; - 49.350 ﻿ ( Atlantic Ocean ) Atlantic Ocean At the Perigoso Canal on the mouth of the Amazon River
Bias of an estimator
E ⁡ ( S 2 ) = 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 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − μ ) 2 − 2 n − 1 ( X ̄ − μ ) ⋅ n ⋅ ( X ̄ − μ ) + n n − 1 ( X ̄ − μ ) 2 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − μ ) 2 − 2 n n − 1 ( X ̄ − μ ) 2 + n n − 1 ( X ̄ − μ ) 2 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − μ ) 2 − n n − 1 ( X ̄ − μ ) 2 ) = E ⁡ ( 1 n − 1 ∑ i = 1 n ( X i − μ ) 2 ) − E ⁡ ( n n − 1 ( X ̄ − μ ) 2 ) = E ⁡ ( n n − 1 ⋅ 1 n ∑ i = 1 n ( X i − μ ) 2 ) − E ⁡ ( n n − 1 ( X ̄ − μ ) 2 ) = n n − 1 E ⁡ ( 1 n ∑ i = 1 n ( X i − μ ) 2 ) − n n − 1 E ⁡ ( ( X ̄ − μ ) 2 ) = n n − 1 ⋅ σ 2 − n n − 1 ⋅ 1 n σ 2 = n n − 1 ⋅ σ 2 − 1
Romance languages
In Tuscan ( including standard Italian ) , final / u / merged into / o / . In the Western Romance languages , final / i / eventually merged into / e / ( although final / i / triggered metaphony before that , e.g. Spanish hice , Portuguese fiz `` I did '' < * fize < Latin fēcī ) . Conservative languages like Spanish largely maintain that system , but drop final / e / after certain single consonants , e.g. / r / , / l / , / n / , / d / , / z / ( < palatalized c ) . In the Gallo - Romance languages ( part of Western Romance ) , final / o / and / e / were dropped entirely unless that produced an impossible final cluster ( e.g. / tr / ) , in which case a `` prop vowel '' / e / was added . This left only two final vowels : / a / and prop vowel / e / . Catalan preserves this system . Loss of final stressless vowels in Venetian shows a pattern intermediate between Central Italian and the Gallo - Italic branch , and the environments for vowel deletion vary considerably depending on the dialect . In the table above , final / e / is uniformly absent in mar , absent in some dialects in part ( e ) / part ( e ) / and set ( e ) / sɛt ( e ) / , but retained in mare ( < Latin mātrem ) as a relic of the earlier cluster * dr . In primitive Old French ( one of the Gallo - Romance languages ) , these two remaining vowels merged into / ə / .
Electromagnetic radiation
E = B = 0 , ( \ displaystyle \ mathbf ( E ) = \ mathbf ( B ) = \ mathbf ( 0 ) , )
Conic section
p e = l ( \ displaystyle pe = \ ell \ , ) a e = c . ( \ displaystyle ae = c. \ , )
Internal energy
Δ U = Q + W p r e s s u r e − v o l u m e + W i s o c h o r i c ( c l o s e d s y s t e m , n o t r a n s f e r o f m a t t e r ) . ( \ displaystyle \ Delta U = Q + W_ ( \ mathrm ( pressure - volume ) ) + W_ ( \ mathrm ( isochoric ) ) \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ , \ mathrm ( ( closed \ , \ , system , \ , \ , no \ , \ , transfer \ , \ , of \ , \ , matter ) ) . )
List of United States Air Force installations
Kabul International Airport Afghanistan 34 ° 33 ′ 56 '' N 069 ° 12 ′ 39 '' E ﻿ / ﻿ 34.56556 ° N 69.21083 ° E ﻿ / 34.56556 ; 69.21083 ﻿ ( Kabul IAP ) 438th Air Expeditionary Wing 438th Air Expeditionary Advisory Group Provides the International Security Assistance Force with responsive airpower as part of Operation Enduring Freedom . Kandahar Airfield Afghanistan 31 ° 30 ′ 21 '' N 065 ° 50 ′ 52 '' E ﻿ / ﻿ 31.50583 ° N 65.84778 ° E ﻿ / 31.50583 ; 65.84778 ﻿ ( Kandahar AFLD ) 451st Air Expeditionary Group 651st Air Expeditionary Group 738th Air Expeditionary Advisory Group Provides the International Security Assistance Force with responsive airpower as part of Operation Enduring Freedom . 738th AEAG is a detached component of the 438th AEW at Kabul IAP Sheik Isa Air Base Bahrain 25 ° 55 ′ 05 '' N 50 ° 35 ′ 26 '' E ﻿ / ﻿ 25.91806 ° N 50.59056 ° E ﻿ / 25.91806 ; 50.59056 ﻿ ( Sheik Isa AB ) Detachment of the 379th Air Expeditionary Wing Logistical hub . Shindand Air Base Afghanistan 33 ° 23 ′ 28.79 '' N 62 ° 15 ′ 39.51 '' E ﻿ / ﻿ 33.3913306 ° N 62.2609750 ° E ﻿ / 33.3913306 ; 62.2609750 ﻿ ( Shindand AB ) 838th Air Expeditionary Advisory Group Being developed into a major flying training base for the Afghanistan Air Force . 838th AEAG is a detached component of the 438th AEW at Kabul IAP RAFO Thumrait Oman 17 ° 39 ′ 56 '' N 54 ° 01 ′ 28 '' E ﻿ / ﻿ 17.66556 ° N 54.02444 ° E ﻿ / 17.66556 ; 54.02444 ﻿ ( RAFO Thumrait ) 405th Air Expeditionary Wing Primary AFCENT Deployment Base .
Strait of Dover
Dover Strait View from France across the Strait of Dover towards the English coast Location North Sea -- English Channel ( Atlantic Ocean ) Coordinates 51 ° 00 ′ N 1 ° 27 ′ E ﻿ / ﻿ 51.000 ° N 1.450 ° E ﻿ / 51.000 ; 1.450 Coordinates : 51 ° 00 ′ N 1 ° 27 ′ E ﻿ / ﻿ 51.000 ° N 1.450 ° E ﻿ / 51.000 ; 1.450 Type Strait Basin countries France England Max . width 33.3 km ( 20.7 mi ) Average depth 30 m ( 98 ft )
Radioactive decay
N B = N A 0 λ A λ B − λ A ( e − λ A t − e − λ B t ) . ( \ displaystyle N_ ( B ) = ( \ frac ( N_ ( A0 ) \ lambda _ ( A ) ) ( \ lambda _ ( B ) - \ lambda _ ( A ) ) ) \ left ( e ^ ( - \ lambda _ ( A ) t ) - e ^ ( - \ lambda _ ( B ) t ) \ right ) . )
Irrational number
It is not known whether π + e or π − e is irrational or not . In fact , there is no pair of non-zero integers m and n for which it is known whether mπ + ne is irrational or not . Moreover , it is not known whether the set ( π , e ) is algebraically independent over Q .
Dasht-e Kavir
Dasht - e Kavir ( Persian : دشت كوير ‎ ‎ , lit . ' Low Plains ' in classical Persian , from khwar ( low ) , and dasht ( plain ) , flatland ) , also known as Kavir - e Namak ( lit . ' salty lowlands ' ) and the Great Salt Desert , is a large desert lying in the middle of the Iranian plateau . It is about 800 km ( 500 mi ) by 320 km ( 200 mi ) with a total surface area of about 77,600 km ( 30,000 sq mi ) , making it the Earth 's 26th largest desert . The area of this desert stretches from the Alborz mountain range in the north - west to the Dasht - e Lut in the south - east and is partitioned between the Iranian provinces of Khorasan , Semnan , Tehran , Isfahan and Yazd
Parthenon
Coordinates : 37 ° 58 ′ 17 '' N 23 ° 43 ′ 35 '' E ﻿ / ﻿ 37.9714 ° N 23.7265 ° E ﻿ / 37.9714 ; 23.7265
Quantum mechanics
with state ψ ( \ displaystyle \ psi ) in this case having energy E ( \ displaystyle E ) coincident with the kinetic energy of the particle .
Unbiased estimation of standard deviation
E ( s 2 ) = σ 2 γ 1 ⇒ E ( s 2 γ 1 ) = σ 2 ( \ displaystyle ( \ rm ( E ) ) \ left ( s ^ ( 2 ) \ right ) = \ sigma ^ ( 2 ) \ gamma _ ( 1 ) \ Rightarrow ( \ rm ( E ) ) \ left ( ( \ frac ( s ^ ( 2 ) ) ( \ gamma _ ( 1 ) ) ) \ right ) = \ sigma ^ ( 2 ) )
Carthage
Carthage Baths of Antoninus , Carthage Shown within Tunisia Location Tunisia Region Tunis Governorate Coordinates 36 ° 51 ′ 10 '' N 10 ° 19 ′ 24 '' E ﻿ / ﻿ 36.8528 ° N 10.3233 ° E ﻿ / 36.8528 ; 10.3233 Coordinates : 36 ° 51 ′ 10 '' N 10 ° 19 ′ 24 '' E ﻿ / ﻿ 36.8528 ° N 10.3233 ° E ﻿ / 36.8528 ; 10.3233 UNESCO World Heritage Site Type Cultural Criteria ii , iii , vi Designated 1979 ( 3rd session ) Reference no . 37 State Party Tunisia Region Arab States
Tsar Bomba
Coordinates : 73 ° 48 ′ 26 '' N 54 ° 58 ′ 54 '' E ﻿ / ﻿ 73.80722 ° N 54.98167 ° E ﻿ / 73.80722 ; 54.98167
Gethsemane
Coordinates : 31 ° 46 ′ 46 '' N 35 ° 14 ′ 25 '' E ﻿ / ﻿ 31.779402 ° N 35.240197 ° E ﻿ / 31.779402 ; 35.240197 Garden
Quantum mechanics
ψ 1 ( x ) = 1 k 1 ( A → e i k 1 x + A ← e − i k 1 x ) x < 0 ( \ displaystyle \ psi _ ( 1 ) ( x ) = ( \ frac ( 1 ) ( \ sqrt ( k_ ( 1 ) ) ) ) \ left ( A_ ( \ rightarrow ) e ^ ( ik_ ( 1 ) x ) + A_ ( \ leftarrow ) e ^ ( - ik_ ( 1 ) x ) \ right ) \ qquad x < 0 )
Romance languages
Examples of evolution of final unstressed vowels : From least - to most - changed languages English Latin Proto - Italo - Western Conservative Central Italian Italian Spanish Catalan Old French a , e , i , o , u a , e , i , o , u a , e , i , o a , e / - , o a , - / e e , - / e one ( fem . ) ūnam ˈuna una una una una une door portam ˈpɔrta pɔrta porta puerta porta porte seven septem ˈsɛtte sɛtte sette siete set set sea mare ˈmare mare mare mar mar mer peace pācem ˈpatʃe pace pace paz pau paiz part partem ˈparte parte parte parte part part mother mātrem ˈmatre matre madre madre mare meḍre twenty vīgintī veˈenti vinti venti veinte vint vint four quattuor ˈkwattro quattro quattro cuatro quatre quatre eight octō ˈɔkto ɔtto otto ocho vuit huit when quandō ˈkwando quando quando cuando quan quant fourth quartum ˈkwartu quartu quarto cuarto quart quart one ( masc . ) ūnum ˈunu unu uno uno un un port portum ˈpɔrtu portu porto puerto port port These columns use IPA symbols / ɔ , ɛ / to indicate open - mid vowels .
Quantum mechanics
ψ 2 ( x ) = 1 k 2 ( B → e i k 2 x + B ← e − i k 2 x ) x > 0 ( \ displaystyle \ psi _ ( 2 ) ( x ) = ( \ frac ( 1 ) ( \ sqrt ( k_ ( 2 ) ) ) ) \ left ( B_ ( \ rightarrow ) e ^ ( ik_ ( 2 ) x ) + B_ ( \ leftarrow ) e ^ ( - ik_ ( 2 ) x ) \ right ) \ qquad x > 0 ) ,
Jarmo
Jarmo The Neolithic village of Jarmo in Iraqi , 1954 Shown within Iraq Location Chamchamal , Kirkuk Province , Iraq Region Mesopotamia Coordinates 35 ° 32 ′ 56 '' N 44 ° 57 ′ 1 '' E ﻿ / ﻿ 35.54889 ° N 44.95028 ° E ﻿ / 35.54889 ; 44.95028 Coordinates : 35 ° 32 ′ 56 '' N 44 ° 57 ′ 1 '' E ﻿ / ﻿ 35.54889 ° N 44.95028 ° E ﻿ / 35.54889 ; 44.95028 Type Settlement Area 12,000 to 16,000 m ( 170,000 sq ft ) History Founded Approximately 7090 BC Abandoned Approximately 4950 BC Periods Neolithic
Electromagnetic radiation
E = h f = h c λ ( \ displaystyle E = hf = ( \ frac ( hc ) ( \ lambda ) ) \ , \ ! )
Exponential function
For n distinct complex numbers ( a , ... , a ) , the set ( e , ... , e ) is linearly independent over C ( z ) .
Moment-generating function
M X ( t ) ≥ e μ t , ( \ displaystyle M_ ( X ) ( t ) \ geq e ^ ( \ mu t ) , )
Bias of an estimator
Algebraically speaking , E ⁡ ( S 2 ) ( \ displaystyle \ operatorname ( E ) ( S ^ ( 2 ) ) ) is unbiased because :
The O2
Coordinates : 51 ° 30 ′ 10.14 '' N 0 ° 0 ′ 11.22 '' E ﻿ / ﻿ 51.5028167 ° N 0.0031167 ° E ﻿ / 51.5028167 ; 0.0031167 ``
Russian Orthodox Church
Coordinates : 55 ° 42 ′ 40 '' N 37 ° 37 ′ 45 '' E ﻿ / ﻿ 55.71111 ° N 37.62917 ° E ﻿ / 55.71111 ; 37.62917
Circular motion
v = z  ̇ = d ( R e i θ ( t ) ) d t = R d ( e i θ ( t ) ) d t = R e i θ ( t ) d ( i θ ( t ) ) d t = i R θ  ̇ ( t ) e i θ ( t ) = i ω R e i θ ( t ) = i ω z ( \ displaystyle v = ( \ dot ( z ) ) = ( \ frac ( d \ left ( Re ^ ( i \ theta ( t ) ) \ right ) ) ( dt ) ) = R ( \ frac ( d \ left ( e ^ ( i \ theta ( t ) ) \ right ) ) ( dt ) ) = Re ^ ( i \ theta ( t ) ) ( \ frac ( d ( i \ theta ( t ) ) ) ( dt ) ) = iR ( \ dot ( \ theta ) ) ( t ) e ^ ( i \ theta ( t ) ) = i \ omega Re ^ ( i \ theta ( t ) ) = i \ omega z )
List of Super Bowl commercials
Product Type Product / Title Plot / Notes Beer Bud Light `` Cavemen '' Three cavemen are trying to carry a cooler of Bud Light to a party . A friend says that he has invented the wheel . But the wheel is not working when they use it as hoister to carry the Bud Light . Beer Budweiser `` Training '' For the Budweiser Clydesdales this year , Hank the Clydesdale is not picked . A dalmatian sees this and offers to train Hank for next year . In a tribute to Rocky , the two train like the training in the famous movie . The year after that , Hank becomes a Budweiser Clydesdale and gives a high five to his trainer . Car Audi `` The Godfather '' Spoofing The Godfather , the horse 's head is replaced with the front of a Rolls - Royce . Film Iron Man TV promo . Film Jumper TV promo . Film The Chronicles of Narnia : Prince Caspian TV promo . Film Wanted TV promo . Film You Do n't Mess with the Zohan TV promo . Soft drink Coca - Cola `` It 's Mine '' At the Macy 's Thanksgiving Day Parade , the Underdog and Stewie Griffin balloons chase after a Coke balloon , with New Yorkers watching from many places . But instead , Charlie Brown triumphantly catches the Coke . Soft drink SoBe `` Thriller '' Naomi Campbell and lizards do the famous Thriller dance . Website E * Trade `` Baby '' The birth of the E * Trade baby , the baby explains that he can use E * Trade , you can use it too . Website E * Trade `` Clown '' The E * Trade Baby has rented a clown with his savings .
Chemiosmosis
Note that for spontaneous proton import from the P side ( relatively more positive and acidic ) to the N side ( relatively more negative and alkaline ) , Δ μ H + ( \ displaystyle \ Delta \ ! \ mu _ ( \ mathrm ( H ) ^ ( + ) ) ) is negative ( similar to Δ G ( \ displaystyle \ Delta \ ! G ) ) whereas PMF is positive ( similar to redox cell potential Δ E ( \ displaystyle \ Delta E ) ) .
Eyepiece
M A = f O f E ( \ displaystyle \ mathrm ( MA ) = ( \ frac ( f_ ( O ) ) ( f_ ( E ) ) ) )
Normal distribution
φ ( x ) = e − π x 2 ( \ displaystyle \ varphi ( x ) = e ^ ( - \ pi x ^ ( 2 ) ) )
Belvedere, Vienna
Coordinates : 48 ° 11 ′ 29 '' N 16 ° 22 ′ 51 '' E ﻿ / ﻿ 48.191439 ° N 16.380787 ° E ﻿ / 48.191439 ; 16.380787 Upper
Nuclear fusion
fuel Z E ( MeV ) E ( MeV ) neutronicity - 17.6 3.5 0.80 - 12.5 4.2 0.66 - He 18.3 18.3 ≈ 0.05 p - 5 8.7 8.7 ≈ 0.001
Radioactive decay
N = N 0 e − t / τ , ( \ displaystyle N = N_ ( 0 ) \ , e ^ ( - t / \ tau ) , )