vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Radioactive decay
The factor of ln ( 2 ) in the above relations results from the fact that the concept of `` half - life '' is merely a way of selecting a different base other than the natural base e for the lifetime expression . The time constant τ is the e - 1 - life , the time until only 1 / e remains , about 36.8 % , rather than the 50 % in the half - life of a radionuclide . Thus , τ is longer than t . The following equation can be shown to be valid :
Electromagnetic radiation
E = E 0 f ( k ^ ⋅ x − c 0 t ) ( \ displaystyle \ mathbf ( E ) = \ mathbf ( E ) _ ( 0 ) f \ left ( ( \ hat ( \ mathbf ( k ) ) ) \ cdot \ mathbf ( x ) - c_ ( 0 ) t \ right ) )
Exponential function
( In fact , this identity extends to complex - valued exponents . ) It can be shown that every continuous , nonzero solution of the functional equation f ( x + y ) = f ( x ) f ( y ) ( \ displaystyle f ( x + y ) = f ( x ) f ( y ) ) is an exponential function , f : R → R , x ↦ b x ( \ displaystyle f : \ mathbb ( R ) \ to \ mathbb ( R ) , \ x \ mapsto b ^ ( x ) ) , with b > 0 ( \ displaystyle b > 0 ) . The fundamental multiplicative identity , along with the definition of the number e as e , shows that e n = e × ⋯ × e ⏟ n t e r m s ( \ displaystyle e ^ ( n ) = \ underbrace ( e \ times \ cdots \ times e ) _ ( n \ \ mathrm ( terms ) ) ) for positive integers n and relates the exponential function to the elementary notion of exponentiation .
Forecasting
Scaled Errors : The forecast error , E , is on the same scale as the data , as such , these accuracy measures are scale - dependent and can not be used to make comparisons between series on different scales . Mean absolute error ( MAE ) or mean absolute deviation ( MAD ) M A E = ∑ t = 1 N E t N ( \ displaystyle \ MAE = ( \ frac ( \ sum _ ( t = 1 ) ^ ( N ) E_ ( t ) ) ( N ) ) ) M A D = ∑ t = 1 N E t N ( \ displaystyle \ MAD = ( \ frac ( \ sum _ ( t = 1 ) ^ ( N ) E_ ( t ) ) ( N ) ) ) Mean squared error ( MSE ) or mean squared prediction error ( MSPE ) M S E = ∑ t = 1 N E t 2 N ( \ displaystyle \ MSE = ( \ frac ( \ sum _ ( t = 1 ) ^ ( N ) ( E_ ( t ) ^ ( 2 ) ) ) ( N ) ) ) Root mean squared error ( RMSE ) R M S E = ∑ t = 1 N E t 2 N ( \ displaystyle \ RMSE = ( \ sqrt ( \ frac ( \ sum _ ( t = 1 ) ^ ( N ) ( E_ ( t ) ^ ( 2 ) ) ) ( N ) ) ) ) Average of Errors ( E ) E ̄ = ∑ i = 1 N E i N ( \ displaystyle \ ( \ bar ( E ) ) = ( \ frac ( \ sum _ ( i = 1 ) ^ ( N ) ( E_ ( i ) ) ) ( N ) ) ) Percentage Errors : These are more frequently used to compare forecast performance between different data sets because they are scale - independent . However , they have the disadvantage of being infinite or undefined if Y is close to or equal to zero .
Radioactive decay
N ( t ) = N 0 e − λ t = N 0 e − t / τ , ( \ displaystyle N ( t ) = N_ ( 0 ) \ , e ^ ( - ( \ lambda ) t ) = N_ ( 0 ) \ , e ^ ( - t / \ tau ) , \ , \ ! )
Resting potential
E m = g K + E e q , K + + g N a + E e q , N a + + g C l − E e q , C l − g K + + g N a + + g C l − ( \ displaystyle E_ ( m ) = ( \ frac ( g_ ( K ^ ( + ) ) E_ ( eq , K ^ ( + ) ) + g_ ( Na ^ ( + ) ) E_ ( eq , Na ^ ( + ) ) + g_ ( Cl ^ ( - ) ) E_ ( eq , Cl ^ ( - ) ) ) ( g_ ( K ^ ( + ) ) + g_ ( Na ^ ( + ) ) + g_ ( Cl ^ ( - ) ) ) ) )
Resting potential
E m = g K + g t o t E e q , K + + g N a + g t o t E e q , N a + + g C l − g t o t E e q , C l − ( \ displaystyle E_ ( m ) = ( \ frac ( g_ ( K ^ ( + ) ) ) ( g_ ( tot ) ) ) E_ ( eq , K ^ ( + ) ) + ( \ frac ( g_ ( Na ^ ( + ) ) ) ( g_ ( tot ) ) ) E_ ( eq , Na ^ ( + ) ) + ( \ frac ( g_ ( Cl ^ ( - ) ) ) ( g_ ( tot ) ) ) E_ ( eq , Cl ^ ( - ) ) )
Electromagnetic radiation
∇ 2 E = μ 0 ε 0 ∂ 2 E ∂ t 2 ( \ displaystyle \ nabla ^ ( 2 ) \ mathbf ( E ) = \ mu _ ( 0 ) \ epsilon _ ( 0 ) ( \ frac ( \ partial ^ ( 2 ) \ mathbf ( E ) ) ( \ partial t ^ ( 2 ) ) ) )
Electromagnetic radiation
∇ ⋅ E = k ^ ⋅ E 0 f ′ ( k ^ ⋅ x − c 0 t ) = 0 ( \ displaystyle \ nabla \ cdot \ mathbf ( E ) = ( \ hat ( \ mathbf ( k ) ) ) \ cdot \ mathbf ( E ) _ ( 0 ) f ' \ left ( ( \ hat ( \ mathbf ( k ) ) ) \ cdot \ mathbf ( x ) - c_ ( 0 ) t \ right ) = 0 ) E ⋅ k ^ = 0 ( \ displaystyle \ mathbf ( E ) \ cdot ( \ hat ( \ mathbf ( k ) ) ) = 0 )
Moment-generating function
at ) - e ^ ( ( b + 1 ) t ) ) ( ( b - a + 1 ) ( 1 - e ^ ( t ) ) ) ) ) e a i t − e ( b + 1 ) i t ( b − a + 1 ) ( 1 − e i t ) ( \ displaystyle \ , ( \ frac ( e ^ ( ait ) - e ^ ( ( b + 1 ) it ) ) ( ( b - a + 1 ) ( 1 - e ^ ( it ) ) ) ) ) Normal N ( μ , σ ) e t μ + 1 2 σ 2 t 2 ( \ displaystyle \ , e ^ ( t \ mu + ( \ frac ( 1 ) ( 2 ) ) \ sigma ^ ( 2 ) t ^ ( 2 ) ) ) e i t μ − 1 2 σ 2 t 2 ( \ displaystyle \ , e ^ ( it \ mu - ( \ frac ( 1 ) ( 2 ) ) \ sigma ^ ( 2 ) t ^ ( 2 ) ) ) Chi - squared χ ( 1 − 2 t ) − k 2 ( \ displaystyle \ , ( 1 - 2t ) ^ ( - ( \ frac ( k ) ( 2 ) ) ) ) ( 1 − 2 i t ) − k 2 ( \ displaystyle \ , ( 1 - 2it ) ^ ( - ( \ frac ( k ) ( 2 ) ) ) ) Gamma Γ ( k , θ ) ( 1 −
List of earthquakes in New Zealand
25 Dec 1922 Motunau North Canterbury 6.4 20 km 42.99 ° S 173.00 ° E Felt throughout Upper half of South Island 9 Mar 1929 Arthur 's Pass Canterbury 7.0 12 km 42.83 ° S 171.83 ° E 1929 Arthur 's Pass earthquake 17 Jun 1929 Murchison West Coast 7.3 7.8 20 km 41.69 ° S 172.20 ° E 17 1929 Murchison earthquake 23 Jun 1929 Murchison West Coast 6.5 12 km 41.78 ° S 172.32 ° E 12 Feb 1930 Porangahau Hawke 's Bay 6.2 33 km 40.39 ° S 176.55 ° E Felt throughout lower half of North Island 3 Feb 1931 North of Napier Hawke 's Bay 7.4 7.8 20 km 39.29 ° S 177.00 ° E 256 1931 Hawke 's Bay earthquake 13 Feb 1931 East of Napier Hawke 's Bay 7.3 30 km 39.55 ° S 177.31 ° E Aftershock to M 7.4 event 16 Sep 1932 Wairoa Hawke 's Bay 6.9 12 km 38.95 ° S 177.59 ° E Caused further damage to the already devastated Hawke 's Bay .
PID controller
M V ( t ) = K p ( e ( t ) + 1 T i ∫ 0 t e ( τ ) d τ + T d d d t e ( t ) ) ( \ displaystyle \ mathrm ( MV ( t ) ) = K_ ( p ) \ left ( \ , ( e ( t ) ) + ( \ frac ( 1 ) ( T_ ( i ) ) ) \ int _ ( 0 ) ^ ( t ) ( e ( \ tau ) ) \ , ( d \ tau ) + T_ ( d ) ( \ frac ( d ) ( dt ) ) e ( t ) \ right ) )
Moment-generating function
M X ( t ) : = E ( e t T X ) . ( \ displaystyle M_ ( \ mathbf ( X ) ) ( \ mathbf ( t ) ) : = \ mathbb ( E ) \ ! \ left ( e ^ ( \ mathbf ( t ) ^ ( \ mathrm ( T ) ) \ mathbf ( X ) ) \ right ) . )
List of earthquakes in New Zealand
6.5 event 28 Mar 1960 Mokau Taranaki 6.5 209 km 39.04 ° S 174.77 ° E Doublet earthquake to 6.6 event 25 May 1960 Milford Sound Southland 6.3 12 km 44.17 ° S 167.72 ° E 27 Dec 1961 Martinborough Wellington 6.2 12 km 41.51 ° S 176.11 ° E Struck offshore , 65 km east of Martinborough 18 Dec 1963 Raoul Islands Kermadec Islands 7.7 35 km 24.77 ° S 176.52 ° W Felt in the East half of North Island 11 April 1965 Kaikoura North Canterbury 6.1 12 km 42.76 ° S 173.87 ° E Felt in Kaikoura / North Canterbury 21 May 1965 George Sound Southland 6.4 101 km 44.94 ° S 167.36 ° E 4 Mar 1966 Gisborne East Cape 6.0 33 km 38.73 ° S 178.11 ° E Felt in Gisborne 23 April 1966 Cook Strait Marlborough 5.8 5.8 12 km 41.64 ° S 174.54 ° E Caused damage in Wellington 24 May 1968 Inangahua Junction West Coast 6.7 7.1 12 km 41.75 ° S 172.04 ° E 1968 Inangahua earthquake 6 Jan 1973 Taupo Waikato 7.0
Unbiased estimation of standard deviation
E ( s ) ≠ E ( s 2 ) ≠ σ γ 1 ( \ displaystyle ( \ rm ( E ) ) ( s ) \ neq ( \ sqrt ( ( \ rm ( E ) ) \ left ( s ^ ( 2 ) \ right ) ) ) \ neq \ sigma ( \ sqrt ( \ gamma _ ( 1 ) ) ) )
Hyperinflation
Price doubling time = log e ⁡ 2 log e ⁡ ( 1 + inflation 100 ) ( \ displaystyle ( \ hbox ( Price doubling time ) ) = ( \ frac ( \ log _ ( e ) 2 ) ( \ log _ ( e ) \ left ( 1 + ( \ frac ( \ hbox ( inflation ) ) ( 100 ) ) \ right ) ) ) )
Quantum mechanics
ψ ( x ) = A e i k x + B e − i k x E = ħ 2 k 2 2 m ( \ displaystyle \ psi ( x ) = Ae ^ ( ikx ) + Be ^ ( - ikx ) \ qquad \ qquad E = ( \ frac ( \ hbar ^ ( 2 ) k ^ ( 2 ) ) ( 2m ) ) )
Pi
Γ ( z ) = e − γ z ∏ n = 1 ∞ e z / n 1 + z / n ( \ displaystyle \ Gamma ( z ) = e ^ ( - \ gamma z ) \ prod _ ( n = 1 ) ^ ( \ infty ) ( \ frac ( e ^ ( z / n ) ) ( 1 + z / n ) ) )
Capital asset pricing model
S M L : E ( R i ) = R f + β i ( E ( R M ) − R f ) . ( \ displaystyle \ mathrm ( SML ) : E ( R_ ( i ) ) = R_ ( f ) + \ beta _ ( i ) ( E ( R_ ( M ) ) - R_ ( f ) ). ~ )
Italian Australians
With particular reference to Western Australia , as previously stated , Italians began to arrive in more notable number after the discovery of gold in the Eastern Goldfields , in the early 1890s . The Australian Census of 1911 records the presence of over 2,000 Italians in Western Australia . Only two years before , the Italian writer Capra had visited the state and reported : `` L'attuale emigrazione italiana in Australia e ' poca cosa , e consta quasi esclusivamente di operai per le miniere e pel taglio della legna nella parte occidentale , e di lavoratori della canna da zucchero nel Queensland '' . ( Present Italian migration to Australia is negligible , almost exclusively limited to miners and woodcutters in the western state , and sugarcane cutters in Queensland ) .
Quantum mechanics
E = h ν ( \ displaystyle E = h \ nu \ ) , Max
Arctic Ocean
In Norway , Kirkenes ( 69 ° 43 ′ 37 '' N 030 ° 02 ′ 44 '' E ﻿ / ﻿ 69.72694 ° N 30.04556 ° E ﻿ / 69.72694 ; 30.04556 ﻿ ( Kirkenes ) ) and Vardø ( 70 ° 22 ′ 14 '' N 031 ° 06 ′ 27 '' E ﻿ / ﻿ 70.37056 ° N 31.10750 ° E ﻿ / 70.37056 ; 31.10750 ﻿ ( Vardø ) ) are ports on the mainland . Also , there is Longyearbyen ( 78 ° 13 ′ 12 '' N 15 ° 39 ′ 00 '' E ﻿ / ﻿ 78.22000 ° N 15.65000 ° E ﻿ / 78.22000 ; 15.65000 ﻿ ( Longyearbyen ) ) on Svalbard , a Norwegian archipelago , next to Fram Strait . Russia
List of earthquakes in New Zealand
Date Location Region Magnitude ( M ) Magnitude ( M ) Depth Latitude Longitude Fatalities Further information 15 Aug 2000 L'Esperance Rock Kermadec Islands 7.6 436 km 31.94 ° S 178.55 ° E Felt in Christchurch 1 Nov 2000 Fiordland Southland 6.2 9 km 45.12 ° S 166.95 ° E 21 Aug 2001 NE of New Zealand East Cape 7.1 7.1 33 km 36.98 ° S 179.16 ° E Felt in the Gisborne area 21 Oct 2001 NE of New Zealand East Cape 6.3 12 km 36.89 ° S 179.86 ° E Felt in the Gisborne area 8 Dec 2001 Haast West Coast 6.2 5 km 44.11 ° S 168.60 ° E Mainshock 22 Aug 2003 Fiordland Southland 7.0 7.2 24 km 45.19 ° S , 166.83 ° E Felt throughout South Island 22 Nov 2004 Puysegur Trench South of New Zealand 7.1 7.0 12 km 46.57 ° S 165.08 ° E Reportedly felt as far north as Hamilton .
Chicxulub crater
The Chicxulub impactor had an estimated diameter of 15 kilometres ( 9.3 mi ) , and delivered an estimated energy of 10 billion Hiroshima A-bombs ( about 1 × e 23 ( \ displaystyle 1 \ times e ^ ( 23 ) ) Joules , or 100,000 EJ ) . By contrast , the most powerful man - made explosive device ever detonated , the Tsar Bomba , had an energy of only 210 peta joules ( 2.10 × e 17 ( \ displaystyle 2.10 \ times e ^ ( 17 ) ) joules , the yield of 50 megatons of TNT ) . The object dug a hole 100 kilometres ( 62 mi ) wide and 30 kilometres ( 19 mi ) deep , leaving a crater mainly under the sea and covered by 600 metres ( 2,000 ft ) of sediment in the 21st century .
PID controller
u ( t ) = K p e ( t ) + K i ∫ 0 t e ( t ′ ) d t ′ + K d d e ( t ) d t , ( \ displaystyle u ( t ) = K_ ( \ text ( p ) ) e ( t ) + K_ ( \ text ( i ) ) \ int _ ( 0 ) ^ ( t ) e ( t ' ) \ , dt'+ K_ ( \ text ( d ) ) ( \ frac ( de ( t ) ) ( dt ) ) , )
Moment-generating function
M X ( t ) = E ( e t X ) = 1 + t E ( X ) + t 2 E ( X 2 ) 2 ! + t 3 E ( X 3 ) 3 ! + ⋯ + t n E ( X n ) n ! + ⋯ = 1 + t m 1 + t 2 m 2 2 ! + t 3 m 3 3 ! + ⋯ + t n m n n ! + ⋯ , ( \ displaystyle ( \ begin ( aligned ) M_ ( X ) ( t ) = \ mathbb ( E ) ( e ^ ( t \ , X ) ) & = 1 + t \ , \ mathbb ( E ) ( X ) + ( \ frac ( t ^ ( 2 ) \ , \ mathbb ( E ) ( X ^ ( 2 ) ) ) ( 2 ! ) ) + ( \ frac ( t ^ ( 3 ) \ , \ mathbb ( E ) ( X ^ ( 3 ) ) ) ( 3 ! ) ) + \ cdots + ( \ frac ( t ^ ( n ) \ , \ mathbb ( E ) ( X ^ ( n ) ) ) ( n ! ) ) + \ cdots \ \ & = 1 + tm_ ( 1 ) + ( \ frac ( t ^ ( 2 ) m_ ( 2 ) ) ( 2 ! ) ) + ( \ frac ( t ^ ( 3 ) m_ ( 3 ) ) ( 3 ! ) ) + \ cdots + ( \ frac ( t ^ ( n ) m_ ( n ) ) ( n ! ) ) + \ cdots , \ end ( aligned ) ) )
PID controller
∫ 0 t k e ( τ ) d τ = ∑ i = 1 k e ( t i ) Δ t ( \ displaystyle \ int _ ( 0 ) ^ ( t_ ( k ) ) ( e ( \ tau ) ) \ , ( d \ tau ) = \ sum _ ( i = 1 ) ^ ( k ) e ( t_ ( i ) ) \ Delta t )
Dasht-e Kavir
Central in the desert lies the Kavir Buzurg ( Great Kavir ) , which is about 320 km long and 160 km ( 99 mi ) wide . In the west lies the Daryahcheh - e Namak ( `` salt lake '' ) , of 1,800 km ( 690 sq mi ) . It contains some large salt plates in a mosaic - like shape . It is part of a 4,000 km ( 1,500 sq mi ) protected ecological zone , the Kavir National Park . One of the most desolate places of Dasht - e Kavir is the Rig - e Jenn ( `` devil 's dunes ) .
Magnetic domain
H e = α M ( \ displaystyle H_ ( e ) = \ alpha \ M )
Nairobi
The city is situated at 1 ° 09 ′ S 36 ° 39 ′ E ﻿ / ﻿ 1.150 ° S 36.650 ° E ﻿ / - 1.150 ; 36.650 ﻿ ( Nairobi , Kenya ) and 1 ° 27 ′ S 37 ° 06 ′ E ﻿ / ﻿ 1.450 ° S 37.100 ° E ﻿ / - 1.450 ; 37.100 ﻿ ( Nairobi , Kenya ) and occupies 696 square kilometres ( 270 sq mi ) .
Exponential function
a b = ( r e θ i ) b = ( e ln ⁡ ( r ) + θ i ) b = e ( ln ⁡ ( r ) + θ i ) b ( \ displaystyle a ^ ( b ) = \ left ( re ^ ( \ theta i ) \ right ) ^ ( b ) = \ left ( e ^ ( \ ln ( r ) + \ theta i ) \ right ) ^ ( b ) = e ^ ( \ left ( \ ln ( r ) + \ theta i \ right ) b ) )
Moment-generating function
\ displaystyle \ , e ^ ( ta ) ) e i t a ( \ displaystyle \ , e ^ ( ita ) ) Laplace L ( μ , b ) e t μ 1 − b 2 t 2 ; for t < 1 / b ( \ displaystyle \ , ( \ frac ( e ^ ( t \ mu ) ) ( 1 - b ^ ( 2 ) t ^ ( 2 ) ) ) ; ( \ text ( for ) ) t < 1 / b \ , ) e i t μ 1 + b 2 t 2 ( \ displaystyle \ , ( \ frac ( e ^ ( it \ mu ) ) ( 1 + b ^ ( 2 ) t ^ ( 2 ) ) ) ) Negative Binomial NB ( r , p ) ( 1 − p ) r ( 1 − p e t ) r ( \ displaystyle \ , ( \ frac ( ( 1 - p ) ^ ( r ) ) ( \ left ( 1 - pe ^ ( t ) \ right ) ^ ( r ) ) ) ) ( 1 − p ) r ( 1 − p e i t ) r ( \ displaystyle \ , ( \ frac ( ( 1 - p ) ^ ( r ) ) ( \ left ( 1 - pe ^ ( it ) \ right ) ^ ( r ) ) ) ) Cauchy Cauchy ( μ , θ ) Does not exist e i t μ − θ t ( \ displaystyle \ , e ^ ( it \ mu - \ theta t ) )
Degrees of freedom (physics and chemistry)
E = ∑ i = 1 N E i ( X i ) , ( \ displaystyle E = \ sum _ ( i = 1 ) ^ ( N ) E_ ( i ) ( X_ ( i ) ) , )
Romance languages
These diphthongizations had the effect of reducing or eliminating the distinctions between open - mid and close - mid vowels in many languages . In Spanish and Romanian , all open - mid vowels were diphthongized , and the distinction disappeared entirely . Portuguese is the most conservative in this respect , keeping the seven - vowel system more or less unchanged ( but with changes in particular circumstances , e.g. due to metaphony ) . Other than before palatalized consonants , Catalan keeps / ɔ o / intact , but / ɛ e / split in a complex fashion into / ɛ e ə / and then coalesced again in the standard dialect ( Eastern Catalan ) in such a way that most original / ɛ e / have reversed their quality to become / e ɛ / .
Pi
E = − ∇ V . ( \ displaystyle \ mathbf ( E ) = - \ nabla V . )
Degrees of freedom (physics and chemistry)
⟨ E ⟩ = ∑ i = 1 N ⟨ E i ⟩ . ( \ displaystyle \ langle E \ rangle = \ sum _ ( i = 1 ) ^ ( N ) \ langle E_ ( i ) \ rangle . )
Planck's law
E = ( 3 + W ( − 3 e 3 ) ) k B T ≈ 2.821 k B T , ( \ displaystyle E = \ left ( 3 + W \ left ( ( \ frac ( - 3 ) ( e ^ ( 3 ) ) ) \ right ) \ right ) k_ ( \ mathrm ( B ) ) T \ approx 2.821 \ k_ ( \ mathrm ( B ) ) T , )
Planck's law
E = ( 5 + W ( − 5 e 5 ) ) k B T ≈ 4.965 k B T , ( \ displaystyle E = \ left ( 5 + W \ left ( ( \ frac ( - 5 ) ( e ^ ( 5 ) ) ) \ right ) \ right ) k_ ( \ mathrm ( B ) ) T \ approx 4.965 \ k_ ( \ mathrm ( B ) ) T , )
Particle in a box
Δ E ( r ) = E gap + ( h 2 8 r 2 ) ( 1 m e ∗ + 1 m h ∗ ) ( \ displaystyle \ Delta E ( r ) = E_ ( \ text ( gap ) ) + \ left ( ( \ frac ( h ^ ( 2 ) ) ( 8r ^ ( 2 ) ) ) \ right ) \ left ( ( \ frac ( 1 ) ( m_ ( e ) ^ ( * ) ) ) + ( \ frac ( 1 ) ( m_ ( h ) ^ ( * ) ) ) \ right ) )
Conic section
Δ e 4 + ( ( A + C ) 2 − 4 Δ ) e 2 − ( ( A + C ) 2 − 4 Δ ) = 0 , ( \ displaystyle \ Delta e ^ ( 4 ) + ( ( A + C ) ^ ( 2 ) - 4 \ Delta ) e ^ ( 2 ) - ( ( A + C ) ^ ( 2 ) - 4 \ Delta ) = 0 , )
Execution of the Romanov family
Early next morning , when rumours spread in Yekaterinburg about the disposal site , Yurovsky removed the bodies and hid them elsewhere ( 56 ° 56 ′ 32 '' N 60 ° 28 ′ 24 '' E ﻿ / ﻿ 56.942222 ° N 60.473333 ° E ﻿ / 56.942222 ; 60.473333 ) . When the vehicle carrying the bodies broke down on the way to the next chosen site , Yurovsky made new arrangements , and buried most of the acid - covered bodies in a pit sealed and concealed with rubble , covered over with railroad ties and then earth ( 56 ° 54 ′ 41 '' N 60 ° 29 ′ 44 '' E ﻿ / ﻿ 56.9113628 ° N 60.4954326 ° E ﻿ / 56.9113628 ; 60.4954326 ) on Koptyaki Road , a cart track ( subsequently abandoned ) 19 kilometres ( 12 mi ) north of Yekaterinburg .
Nun River
Nun River 2005 satellite view of Niger Delta . Nun River in the center Niger Delta in 1898 . The Niger flows from the north , and bifurcates just below Abo . The Forçados flows west and the Nun continues south . Country Nigeria State Rivers State Physical characteristics Main source 5 ° 17 ′ 56 '' N 6 ° 24 ′ 52 '' E ﻿ / ﻿ 5.298847 ° N 6.414350 ° E ﻿ / 5.298847 ; 6.414350 River mouth 5 ° 18 ′ 30 '' N 6 ° 25 ′ 00 '' E ﻿ / ﻿ 5.308333 ° N 6.416667 ° E ﻿ / 5.308333 ; 6.416667 Coordinates : 5 ° 18 ′ 30 '' N 6 ° 25 ′ 00 '' E ﻿ / ﻿ 5.308333 ° N 6.416667 ° E ﻿ / 5.308333 ; 6.416667 Length 160 km ( 99 mi )
Philippines
Coordinates : 13 ° N 122 ° E ﻿ / ﻿ 13 ° N 122 ° E ﻿ / 13 ; 122
Afghanistan
Coordinates : 33 ° N 65 ° E ﻿ / ﻿ 33 ° N 65 ° E ﻿ / 33 ; 65
Bias of an estimator
e − 2 X ( \ displaystyle e ^ ( - 2 ( X ) ) \ quad )
Israel
Coordinates : 31 ° N 35 ° E ﻿ / ﻿ 31 ° N 35 ° E ﻿ / 31 ; 35
Kenya
Coordinates : 1 ° N 38 ° E ﻿ / ﻿ 1 ° N 38 ° E ﻿ / 1 ; 38
Lithuania
Coordinates : 55 ° N 24 ° E ﻿ / ﻿ 55 ° N 24 ° E ﻿ / 55 ; 24
Yemen
Coordinates : 15 ° N 48 ° E ﻿ / ﻿ 15 ° N 48 ° E ﻿ / 15 ; 48
Ural Mountains
The Ural Mountains The Ural Mountains Highest point Peak Mount Narodnaya Elevation 1,895 m ( 6,217 ft ) Coordinates 60 ° N 60 ° E ﻿ / ﻿ 60 ° N 60 ° E ﻿ / 60 ; 60 Coordinates : 60 ° N 60 ° E ﻿ / ﻿ 60 ° N 60 ° E ﻿ / 60 ; 60 Length 2,500 km ( 1,600 mi ) Width 150 km ( 93 mi ) Geography Countries Russia and Kazakhstan Geology Age of rock Carboniferous
List of earthquakes in New Zealand
14 Feb 2016 Christchurch Canterbury 5.7 5.8 15 km 43.5 ° S 172.83 ° E 2016 Christchurch earthquake 2 Sep 2016 NE of East Cape East Cape 7.1 7.1 55 km 37.01 ° S 179.63 ° E 2016 Te Araroa earthquake 14 Nov 2016 Culverden North Canterbury 7.8 7.8 15 km 42.757 ° S 173.077 ° E 2016 Kaikoura earthquake 11 Jul 2017 NW of Auckland Island South Tasman Sea 6.6 6.6 6.3 10 km 49.546 ° S 164.031 ° E
List of earthquakes in New Zealand
Date Location Region Magnitude ( M ) Magnitude ( M ) Depth Latitude Longitude Fatalities Further information 16 Nov 1901 Cheviot North Canterbury 6.8 12 km 42.74 ° S 173.35 ° E 1901 Cheviot earthquake 9 Aug 1904 Cape Turnagain Hawke 's Bay 7.0 7.2 16 km 40.40 ° S 176.40 ° E 1904 Cape Turnagain earthquake 7 Oct 1914 East Cape Gisborne 6.6 12 km 37.80 ° S 178.20 ° E Felt throughout eastern North Island 22 Nov 1914 Tauranga Bay of Plenty 7.3 300 km 37.49 ° S 176.50 ° E Felt throughout North Island 1 May 1917 Raoul Island Kermadec Islands 8.0 50 km 29.00 ° S 177.00 ° W Felt throughout New Zealand 6 Aug 1917 Castlepoint Manawatu 6.8 12 km 40.80 ° S 176.00 ° E Felt throughout North Island 3 Nov 1918 Puysegur Trench South of New Zealand 6.8 50 km 47.00 ° S 165.40 ° E Felt throughout Southland 29 Jun 1921 Kaweka Forest Hawke 's Bay 7.0 80 km 39.29 ° S 176.40 ° E Felt throughout North Island
Zimbabwe
Coordinates : 20 ° S 30 ° E ﻿ / ﻿ 20 ° S 30 ° E ﻿ / - 20 ; 30
Magnetic domain
H e = α M s ( \ displaystyle H_ ( e ) = \ alpha \ M_ ( s ) )
Mach Five
Control E = Zircon - tipped cutter blades ( C in the original , E originally activated the special Evening Eye )
Romance languages
Evolution of unstressed vowels in early Italo - Western Romance Latin Proto - Romance Stressed Non-final unstressed Final - unstressed Original Later Italo - Romance Later Western - Romance Gallo - Romance Primitive French IPA Acad . IPA a , ā / a / / a / / a / / ə / e , ae / ɛ / ę / ɛ / / e / / e / / e / ∅ ; / e / ( prop ) ∅ ; / ə / ( prop ) ē , oe / e / ẹ / e / i , y / ɪ / ī , ȳ / i / i / i / / i / o / ɔ / ǫ / ɔ / / o / / o / / o / ō , ( au ) / o / ọ / o / u / ʊ / / u / ū / u / u / u / au ( most words ) / aw / au / aw / N / A Traditional academic transcription in Romance studies .
Both Sides, Now
`` Both Sides , Now '' is written in F - sharp major . Mitchell used a guitar tuning of E -- B -- E -- G ♯ -- B -- E with a capo at the second fret . The song uses a modified I -- IV -- V chord progression .
Pi
e i π + 1 = 0 . ( \ displaystyle e ^ ( i \ pi ) + 1 = 0 . )
Oil drop experiment
E = V d ( \ displaystyle E = ( \ frac ( V ) ( d ) ) \ , )
East China Sea
Coordinates : 30 ° N 125 ° E ﻿ / ﻿ 30 ° N 125 ° E ﻿ / 30 ; 125
Jura Mountains
Jura Mountains Looking towards Lélex from near the Crêt de la Neige Highest point Peak Crêt de la Neige Elevation 1,720 m ( 5,640 ft ) Coordinates 46 ° 16 ′ 15 '' N 5 ° 56 ′ 22 '' E ﻿ / ﻿ 46.27083 ° N 5.93944 ° E ﻿ / 46.27083 ; 5.93944 Geography Satellite image of the Jura Mountains ( upper left half of the image ) Countries France and Switzerland States / Provinces List ( show ) Auvergne - Rhône - Alpes Bourgogne - Franche - Comté Vaud Canton of Neuchâtel Canton of Jura Basel - Landschaft Range coordinates 46 ° 40 ′ N 6 ° 15 ′ E ﻿ / ﻿ 46.667 ° N 6.250 ° E ﻿ / 46.667 ; 6.250 Coordinates : 46 ° 40 ′ N 6 ° 15 ′ E ﻿ / ﻿ 46.667 ° N 6.250 ° E ﻿ / 46.667 ; 6.250
Planck's law
Nowadays , as a statement of the energy of a light quantum , often one finds the formula E = ħω , where ħ = h / 2π , and ω = 2πν denotes angular frequency , and less often the equivalent formula E = hν . This statement about a really existing and propagating light quantum , based on Einstein 's , has a physical meaning different from that of Planck 's above statement ε = hν about the abstract energy units to be distributed amongst his hypothetical resonant material oscillators .
List of earthquakes in New Zealand
163 km 39.03 ° S 175.26 ° E Felt throughout New Zealand 5 May 1976 Milford Sound Southland 6.6 12 km 44.67 ° S 167.38 ° E 15 Jan 1976 Raoul Island Kermadec Islands 7.8 43 km 29.21 ° S 177.63 ° W Foreshock to M 8.2 event 15 Jan 1976 Raoul Island Kermadec Islands 8.2 31 km 29.17 ° S 177.31 ° W Main shock 18 Jan 1977 Cook Strait Marlborough 6.0 33 km 41.84 ° S 174.58 ° E 12 Oct 1979 Puysegur Trench South of New Zealand 6.5 12 km 46.70 ° S 166.03 ° E 31 Dec 1984 White Island Bay of Plenty 6.3 12 km 36.59 ° S 177.55 ° E Felt around the Bay of Plenty 21 Oct 1986 Raoul Island Kermadec Islands 8.3 33 km 28.15 ° S 176.29 ° W Felt throughout New Zealand 2 Mar 1987 Edgecumbe Bay of Plenty 6.1 6.5 10 km 37.88 ° S 176.80 ° E 1987 Edgecumbe earthquake 4 Jun 1988 Te Anau Southland 6.1 73 km 45.12 ° S 167.29 ° E 24 May 1989 Puysegur Trench
Symmetry of second derivatives
If f : E → R ( \ displaystyle f : E \ to \ mathbb ( R ) ) is defined on an open set E ⊂ R 2 ( \ displaystyle E \ subset \ mathbb ( R ) ^ ( 2 ) ) and D 1 f , D 2 f , D 2 , 1 f ( \ displaystyle D_ ( 1 ) f , D_ ( 2 ) f , D_ ( 2 , 1 ) f ) exist everywhere on E ( \ displaystyle E ) , and D 2 , 1 f ( \ displaystyle D_ ( 2 , 1 ) f ) is continuous at ( a , b ) ∈ E ( \ displaystyle ( a , b ) \ in E ) , then D 1 , 2 f ( \ displaystyle D_ ( 1 , 2 ) f ) exists at ( a , b ) ( \ displaystyle ( a , b ) ) and D 1 , 2 f ( a , b ) = D 2 , 1 f ( a , b ) ( \ displaystyle D_ ( 1 , 2 ) f ( a , b ) = D_ ( 2 , 1 ) f ( a , b ) ) .
PID controller
u ( t ) = M V ( t ) = K p e ( t ) + K i ∫ 0 t e ( τ ) d τ + K d d e ( t ) d t , ( \ displaystyle u ( t ) = \ mathrm ( MV ) ( t ) = K_ ( \ text ( p ) ) e ( t ) + K_ ( \ text ( i ) ) \ int _ ( 0 ) ^ ( t ) e ( \ tau ) \ , d \ tau + K_ ( \ text ( d ) ) ( \ frac ( de ( t ) ) ( dt ) ) , )