vania-janet/multiturn-rag-retrieval-data huggingface dataset:
Bipolar junction transistor
Applied voltages B-E junction bias ( NPN ) B-C junction bias ( NPN ) Mode ( NPN ) E < B < C Forward Reverse Forward - active E < B > C Forward Forward Saturation E > B < C Reverse Reverse Cut - off E > B > C Reverse Forward Reverse - active Applied voltages B-E junction bias ( PNP ) B-C junction bias ( PNP ) Mode ( PNP ) E < B < C Reverse Forward Reverse - active E < B > C Reverse Reverse Cut - off E > B < C Forward Forward Saturation E > B > C Forward Reverse Forward - active
Arctic Ocean
Murmansk ( 68 ° 58 ′ N 033 ° 05 ′ E ﻿ / ﻿ 68.967 ° N 33.083 ° E ﻿ / 68.967 ; 33.083 ﻿ ( Murmansk ) ) in the Barents Sea Arkhangelsk ( 64 ° 32 ′ N 040 ° 32 ′ E ﻿ / ﻿ 64.533 ° N 40.533 ° E ﻿ / 64.533 ; 40.533 ﻿ ( Arkhangelsk ) ) in the White Sea Labytnangi ( 66 ° 39 ′ 26 '' N 066 ° 25 ′ 06 '' E ﻿ / ﻿ 66.65722 ° N 66.41833 ° E ﻿ / 66.65722 ; 66.41833 ﻿ ( Labytnangi ) ) Salekhard ( 66 ° 32 ′ N 066 ° 36 ′ E ﻿ / ﻿ 66.533 ° N 66.600 ° E ﻿ / 66.533 ; 66.600 ﻿ ( Salekhard ) ) , Dudinka ( 69 ° 24 ′ N 086 ° 11 ′ E ﻿ / ﻿ 69.400 ° N 86.183 ° E ﻿ / 69.400 ; 86.183 ﻿ ( Dudinka ) ) , Igarka ( 67 ° 28 ′ N 86 ° 35 ′ E ﻿ / ﻿ 67.467 ° N 86.583 ° E ﻿ / 67.467 ; 86.583 ﻿ ( Igarka ) ) and Dikson ( 73 ° 30 ′ N 080 ° 31 ′ E ﻿ / ﻿ 73.500 ° N 80.517 ° E ﻿ / 73.500 ; 80.517 ﻿ ( Dikson ) ) in the Kara Sea Tiksi ( 71 ° 38 ′ N 128 ° 52 ′ E ﻿ / ﻿ 71.633 ° N 128.867 ° E ﻿ / 71.633 ; 128.867 ﻿ ( Tiksi ) ) in the Laptev Sea Pevek ( 69 ° 42 ′ N 170 ° 17 ′ E ﻿ / ﻿ 69.700 ° N 170.283 ° E ﻿ / 69.700 ; 170.283 ﻿ ( Pevek ) ) in the East Siberian Sea
Equator
0 ° 0 ′ N 17 ° 46 ′ E ﻿ / ﻿ 0.000 ° N 17.767 ° E ﻿ / 0.000 ; 17.767 ﻿ ( Democratic Republic of the Congo ) Democratic Republic of the Congo Passing 9 km ( 5.6 mi ) south of central Butembo 0 ° 0 ′ N 29 ° 43 ′ E ﻿ / ﻿ 0.000 ° N 29.717 ° E ﻿ / 0.000 ; 29.717 ﻿ ( Uganda ) Uganda Passing 32 km ( 20 mi ) south of central Kampala 0 ° 0 ′ N 32 ° 22 ′ E ﻿ / ﻿ 0.000 ° N 32.367 ° E ﻿ / 0.000 ; 32.367 ﻿ ( Lake Victoria ) Lake Victoria Passing through some islands of Uganda 0 ° 0 ′ N 34 ° 0 ′ E ﻿ / ﻿ 0.000 ° N 34.000 ° E ﻿ / 0.000 ; 34.000 ﻿ ( Kenya ) Kenya Passing 6 km ( 3.7 mi ) north of central Kisumu 0 ° 0 ′ N 41 ° 0 ′ E ﻿ / ﻿ 0.000 ° N 41.000 ° E ﻿ / 0.000 ; 41.000 ﻿ ( Somalia ) Somalia 0 ° 0 ′ N 42 ° 53 ′ E ﻿ / ﻿ 0.000 ° N 42.883 ° E ﻿ / 0.000 ; 42.883 ﻿ ( Indian Ocean ) Indian Ocean Passing between Huvadhu Atoll and Fuvahmulah of the Maldives 0 ° 0 ′ N 98 ° 12 ′ E ﻿ / ﻿ 0.000 ° N 98.200 ° E ﻿ / 0.000 ; 98.200 ﻿ ( Indonesia ) Indonesia The Batu Islands , Sumatra and the Lingga Islands 0 ° 0 ′ N 104 ° 34 ′ E ﻿ / ﻿ 0.000 ° N 104.567 ° E ﻿ / 0.000 ; 104.567 ﻿ ( Karimata Strait ) Karimata Strait 0 ° 0 ′ N 109 ° 9 ′ E ﻿ / ﻿ 0.000 ° N 109.150 ° E ﻿ / 0.000 ; 109.150 ﻿ ( Indonesia ) Indonesia Borneo 0 ° 0 ′ N 117 ° 30 ′ E ﻿ / ﻿ 0.000 ° N 117.500 ° E ﻿ / 0.000 ; 117.500 ﻿ ( Makassar Strait ) Makassar Strait 0 ° 0 ′ N 119 ° 40 ′ E ﻿ / ﻿ 0.000 ° N 119.667 ° E ﻿ / 0.000 ; 119.667 ﻿ ( Indonesia ) Indonesia Sulawesi ( Celebes ) 0 ° 0 ′ N 120 ° 5 ′ E ﻿ / ﻿ 0.000 ° N 120.083 °
Oil drop experiment
F E = q E ( \ displaystyle F_ ( E ) = qE \ , )
List of volcanoes in the United States
Name Elevation Location Last eruption meters feet Coordinates Agrigan 965 3165 18 ° 48 ′ N 145 ° 42 ′ E ﻿ / ﻿ 18.8 ° N 145.7 ° E ﻿ / 18.8 ; 145.7 ﻿ ( Agrigan ) - Ahyi Seamount - 137 - 449 20 ° 25 ′ N 145 ° 02 ′ E ﻿ / ﻿ 20.42 ° N 145.03 ° E ﻿ / 20.42 ; 145.03 ﻿ ( Ahyi ) 2001 Alamagan 744 2441 17 ° 36 ′ N 145 ° 50 ′ E ﻿ / ﻿ 17.60 ° N 145.83 ° E ﻿ / 17.60 ; 145.83 ﻿ ( Dante Rodondi ) 1887 Anatahan 788 2592 16 ° 21 ′ N 145 ° 40 ′ E ﻿ / ﻿ 16.35 ° N 145.67 ° E ﻿ / 16.35 ; 145.67 ﻿ ( Veronica Rodondi ) 2006 Asuncion Island 857 2810 19 ° 42 ′ N 145 ° 24 ′ E ﻿ / ﻿ 19.7 ° N 145.4 ° E ﻿ / 19.7 ; 145.4 ﻿ ( Asuncion ) - Esmeralda Bank - 43 - 141 15 ° 00 ′ N 145 ° 15 ′ E ﻿ / ﻿ 15.00 ° N 145.25 ° E ﻿ / 15.00 ; 145.25 ﻿ ( Ashley Rodondi ) - Farallon de Pajaros 360 1,180 20 ° 30 ′ N 144 ° 54 ′ E ﻿ / ﻿ 20.5 ° N 144.9 ° E ﻿ /
Conic section
As above , for e = 0 , we have a circle , for 0 < e < 1 we obtain an ellipse , for e = 1 a parabola , and for e > 1 a hyperbola .
List of earthquakes in New Zealand
Date Location Region Magnitude ( M ) Magnitude ( M ) Depth Latitude Longitude Fatalities Further information 1815 New Plymouth Taranaki 7.0 25 km 38.99 ° S 174.00 ° E 1817 Fiordland South Island 7.0 25 km 45.99 ° S 167.00 ° E 1826 Fiordland South Island 8.0 8.0 25 km 44.99 ° S 167.00 ° E 1835 South Auckland Auckland 7.0 25 km 36.99 ° S 175.00 ° E Apparently a large shallow earthquake followed by aftershocks . Evidence rests on a single report that has so far not been verified 1838 Waitotara Forest Manawatu 7.0 25 km 39.39 ° S 176.10 ° E 26 May 1840 Paraparaumu Wellington 6.0 25 km 41.00 ° S 175.00 ° E 8 Jul 1843 Near Taihape Manawatu 7.6 7.6 12 km 39.59 ° S 176.20 ° E 1843 Wanganui earthquake 13 Jul 1846 Snares Islands Southland 6.3 25 km 47.00 ° S 166.00 ° E 19 Nov 1846 Karamea West Coast 6.5 25 km 41.00 ° S 172.00 ° E 4 Dec 1846 Wellington Wellington 6.0 25 km 41.00 ° S 174.50 ° E 16 Oct 1848 Blenheim Marlborough 7.4 7.8 12 km 41.89 ° S 173.60 ° E 1848 Marlborough earthquake 27 Jul 1851 Motueka Tasman 6.0 25 km 41.00 ° S 173.00 ° E 23 Jan 1855 Lake Wairarapa Wairarapa 8.2 8.2 33 km 41.198 ° S 175.20 ° E 9 1855 Wairarapa earthquake 23 Feb 1863 Waipukurau Hawke 's Bay 7.5 25 km 40.00 ° S 176.50 ° E 1863 Hawke 's Bay earthquake 19 Oct 1868 Cape Farewell Tasman 7.2 12 km 40.20 ° S 173.00 ° E Felt
pH
E = E 0 + R T F ln ⁡ ( a H + ) = E 0 − 2.303 R T F p H ( \ displaystyle E = E ^ ( 0 ) + ( \ frac ( RT ) ( F ) ) \ ln ( a_ ( ( \ textrm ( H ) ) ^ ( + ) ) ) = E ^ ( 0 ) - ( \ frac ( 2.303 RT ) ( F ) ) \ mathrm ( pH ) )
Moment-generating function
M X ( t ) = E ( e t X ) = ∫ − ∞ ∞ e t x f X ( x ) d x . ( \ displaystyle M_ ( X ) ( t ) = \ mathbb ( E ) \ ! \ left ( e ^ ( tX ) \ right ) = \ int _ ( - \ infty ) ^ ( \ infty ) e ^ ( tx ) f_ ( X ) ( x ) \ , dx . )
Moment-generating function
M X ( t ) = E ( e ⟨ t , X ⟩ ) ( \ displaystyle M_ ( X ) ( t ) = E \ left ( e ^ ( \ langle t , X \ rangle ) \ right ) )
List of earthquakes in New Zealand
5 Mar 1934 Pahiatua Manawatu 7.2 12 km 40.54 ° S 176.29 ° E 1934 Pahiatua earthquake 15 Mar 1934 Wairoa Hawke 's Bay 6.3 25 km 39.31 ° S 177.23 ° E Felt strongly in Hawke 's Bay and Gisborne 24 May 1936 Whakatane Bay of Plenty 6.5 150 km 37.99 ° S 177.00 ° E Felt in North Island 16 Dec 1938 Fiordland Southland 7.0 60 km 44.99 ° S 167.00 ° E Felt throughout South Island 11 Feb 1939 Fiordland Southland 7.0 25 km 45.00 ° S 167.50 ° E Felt throughout South Island 26 Feb 1940 Hastings Hawke 's Bay 6.0 25 km 39.50 ° S 176.50 ° E Felt throughout North Island 24 Jun 1942 Masterton Wairarapa 6.9 12 km 40.96 ° S 175.69 ° E June 1942 Wairarapa earthquake 1 Aug 1942 Masterton Wairarapa 6.8 40 km 41.01 ° S 175.52 ° E August 1942 Wairarapa earthquake 17 Feb 1943 Te Anau Southland 6.5 123 km 45.29 ° S 168.00 ° E Felt throughout South Island 2 Aug 1943 Te Anau Southland 6.1 33 km 45.64 ° S 166.67 ° E Felt throughout South Island 2 Sep 1945 Stewart Island Southland 6.5 12 km 47.47 ° S , 166.12 ° E Felt throughout Southland and Otago 26 Jun 1946 Lake Coleridge Canterbury 6.5 12 km 43.30 ° S 171.47 ° E Mainshock 26 Mar 1947 Offshore Poverty Bay Gisborne 7.1 38.55 ° S 178.42 ° E 1947 Gisborne earthquakes and tsunami 17 May 1947 Offshore Tolaga Bay Gisborne 7.1 38.21 ° S 178.60 ° E 1947 Gisborne earthquakes and tsunami 22 May 1948 Hanmer Springs North Canterbury 6.4 12 km 42.49 ° S 173.00 ° E Mainshock 22 May 1948 Cheviot North Canterbury 6.2 12 km 42.83 ° S 173.05 ° E Separate event triggered by the M 6.4 earthquake 5 minutes prior 9 Feb 1949 Hawera Taranaki 6.4 199 km 39.67 ° S 174.35 ° E Felt throughout North Island
Exponential function
Plots of the exponential function on the complex plane z = Re ( e ) z = Im ( e ) z = e
Eyepiece
M A = D D E O f O f E = D f E × D E O f O ( \ displaystyle \ mathrm ( MA ) = ( \ frac ( DD_ ( \ mathrm ( EO ) ) ) ( f_ ( O ) f_ ( E ) ) ) = ( \ frac ( D ) ( f_ ( E ) ) ) \ times ( \ frac ( D_ ( \ mathrm ( EO ) ) ) ( f_ ( O ) ) ) )
Cross product
This is the unique multilinear , alternating product which evaluates to e 1 × ⋯ × e n − 1 = e n ( \ displaystyle e_ ( 1 ) \ times \ cdots \ times e_ ( n - 1 ) = e_ ( n ) ) , e 2 × ⋯ × e n = e 1 , ( \ displaystyle e_ ( 2 ) \ times \ cdots \ times e_ ( n ) = e_ ( 1 ) , ) and so forth for cyclic permutations of indices .
Dasht-e Kavir
Dasht - e Kavir ( دشت كوير ) Desert Sand dunes in the Rig - e Jenn in the Dasht - e Kavir Country Iran Region Khorasan , Semnan , Tehran , Isfahan , Yazd Coordinates 34 ° 44 ′ 15.2 '' N 54 ° 49 ′ 37.56 '' E ﻿ / ﻿ 34.737556 ° N 54.8271000 ° E ﻿ / 34.737556 ; 54.8271000 Coordinates : 34 ° 44 ′ 15.2 '' N 54 ° 49 ′ 37.56 '' E ﻿ / ﻿ 34.737556 ° N 54.8271000 ° E ﻿ / 34.737556 ; 54.8271000 Length 800 km ( 497 mi ) Width 500 km ( 311 mi ) Area 77,600 km ( 29,962 sq mi )
Substrate (chemistry)
E + S ↽ − − ⇀ ES ⟶ EP ↽ − − ⇀ E + P ( \ displaystyle ( \ ce ( ( E ) + S < = > ES - > EP < = > ( E ) + P ) ) )
Cross product
F = q e ( E + v × B ) ( \ displaystyle \ mathbf ( F ) = q_ ( e ) \ left ( \ mathbf ( E ) + \ mathbf ( v ) \ times \ mathbf ( B ) \ right ) )
Eyepiece
P E = D f E , P O = D E O f O ( \ displaystyle P_ ( \ mathrm ( E ) ) = ( \ frac ( D ) ( f_ ( E ) ) ) , \ qquad P_ ( \ mathrm ( O ) ) = ( \ frac ( D_ ( \ mathrm ( EO ) ) ) ( f_ ( O ) ) ) )
PID controller
d e ( t k ) d t = e ( t k ) − e ( t k − 1 ) Δ t ( \ displaystyle ( \ dfrac ( de ( t_ ( k ) ) ) ( dt ) ) = ( \ dfrac ( e ( t_ ( k ) ) - e ( t_ ( k - 1 ) ) ) ( \ Delta t ) ) )
List of volcanoes in the United States
20.5 ; 144.9 ﻿ ( Farallon de Pajaros ) 1967 Guguan 287 942 17 ° 19 ′ N 145 ° 50 ′ E ﻿ / ﻿ 17.32 ° N 145.83 ° E ﻿ / 17.32 ; 145.83 ﻿ ( Guguan ) 1883 Maug Islands 227 745 20 ° 01 ′ N 145 ° 13 ′ E ﻿ / ﻿ 20.02 ° N 145.22 ° E ﻿ / 20.02 ; 145.22 ﻿ ( Maug Islands ) Quaternary Mount Tapochau 474 1554 - - Northwest Rota - 1 - 517 - 1696 14 ° 36 ′ 04 '' N 144 ° 46 ′ 30 '' E ﻿ / ﻿ 14.601 ° N 144.775 ° E ﻿ / 14.601 ; 144.775 ﻿ ( Northwest Rota - 1 ) Pagan Island 570 1870 18 ° 06 ′ N 145 ° 46 ′ E ﻿ / ﻿ 18.10 ° N 145.76 ° E ﻿ / 18.10 ; 145.76 ﻿ ( Pagan Island ) 1993 Mount Rodondi Island Sarigan 538 1765 16 ° 42 ′ 29 '' N 145 ° 46 ′ 48 '' E ﻿ / ﻿ 16.708 ° N 145.78 ° E ﻿ / 16.708 ; 145.78 ﻿ ( Sarigan ) - Supply Reef - 8 - 26 20 ° 08 ′ N 145 ° 06 ′ E ﻿ / ﻿ 20.13 ° N 145.10 ° E ﻿ / 20.13 ; 145.10 ﻿ ( Supply Reef ) 1989
You're So Vain
Over the years Simon has divulged `` letter clues '' and has claimed that the subject 's name contains the letters A , E , and R .
List of airports in the Melbourne area
Community Airport name Type ICAO IATA Avalon Avalon Airport Public YMAV AVV 38 ° 02 ′ 22 '' S 144 ° 28 ′ 10 '' E ﻿ / ﻿ 38.03944 ° S 144.46944 ° E ﻿ / - 38.03944 ; 144.46944 ﻿ ( Avalon Airport ) Coldstream Coldstream Airport Private YCEM 37 ° 43 ′ 42 '' S 145 ° 24 ′ 30 '' E ﻿ / ﻿ 37.72833 ° S 145.40833 ° E ﻿ / - 37.72833 ; 145.40833 ﻿ ( Coldstream Airport ) Essendon Essendon Airport Public YMEN MEB 37 ° 43 ′ 41 '' S 144 ° 54 ′ 07 '' E ﻿ / ﻿ 37.72806 ° S 144.90194 ° E ﻿ / - 37.72806 ; 144.90194 ﻿ ( Essendon Airport ) Lilydale Lilydale Airport Private YLIL 37 ° 41 ′ 30 '' S 145 ° 22 ′ 00 '' E ﻿ / ﻿ 37.69167 ° S 145.36667 ° E ﻿ / - 37.69167 ; 145.36667 ﻿ ( Lilydale Airport ) Moorabbin Moorabbin Airport Public YMMB MBW 37 ° 58 ′ 33 '' S 145 ° 06 ′ 08 '' E ﻿ / ﻿ 37.97583 ° S 145.10222 ° E ﻿ / - 37.97583 ; 145.10222 ﻿ ( Moorabbin Airport ) Point Cook RAAF Williams Military YMPC 37 ° 55 ′ 54 '' S 144 ° 45 ′ 12 '' E ﻿ / ﻿ 37.93167 ° S 144.75333 ° E ﻿ / - 37.93167 ; 144.75333 ﻿ ( RAAF Williams ) Melbourne Airport Melbourne Airport Public YMML MEL 37 ° 40 ′ 24 '' S 144 ° 50 ′ 36 '' E ﻿ / ﻿ 37.67333 ° S 144.84333 ° E ﻿ / - 37.67333 ; 144.84333 ﻿ ( Melbourne Airport )
Bias of an estimator
E ⁡ ( δ ( X ) ) = ∑ x = 0 ∞ δ ( x ) λ x e − λ x ! = e − 2 λ , ( \ displaystyle \ operatorname ( E ) ( \ delta ( X ) ) = \ sum _ ( x = 0 ) ^ ( \ infty ) \ delta ( x ) ( \ frac ( \ lambda ^ ( x ) e ^ ( - \ lambda ) ) ( x ! ) ) = e ^ ( - 2 \ lambda ) , )
pH
E = E 0 + f 2.303 R T F log ⁡ ( H + ) ( \ displaystyle E = E ^ ( 0 ) + f ( \ frac ( 2.303 RT ) ( F ) ) \ log ( ( \ mbox ( H ) ) ^ ( + ) ) )
Natural logarithm
The exponential function can be extended to a function which gives a complex number as e for any arbitrary complex number x ; simply use the infinite series with x complex . This exponential function can be inverted to form a complex logarithm that exhibits most of the properties of the ordinary logarithm . There are two difficulties involved : no x has e = 0 ; and it turns out that e = 1 = e . Since the multiplicative property still works for the complex exponential function , e = e , for all complex z and integers k .
Magnetic domain
Some sources define a wall energy E equal to the sum of the exchange energy and the magnetocrystalline anisotropy energy , which replaces E and E in the above equation .
PID controller
U ( t ) = K p e ( t ) + K i ∫ 0 t e ( τ ) d τ + K d d d t e ( t ) ( \ displaystyle \ mathrm ( U ( t ) ) = K_ ( p ) ( e ( t ) ) + K_ ( i ) \ int _ ( 0 ) ^ ( t ) ( e ( \ tau ) ) \ , ( d \ tau ) + K_ ( d ) ( \ frac ( d ) ( dt ) ) e ( t ) )
Natural logarithm
Part of a series of articles on the mathematical constant e Properties Natural logarithm Exponential function Applications compound interest Euler 's identity Euler 's formula half - lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann -- Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel 's conjecture
Exponential function
Part of a series of articles on the mathematical constant e Properties Natural logarithm Exponential function Applications compound interest Euler 's identity Euler 's formula half - lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann -- Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel 's conjecture
Exponential function
d d x e f ( x ) = f ′ ( x ) e f ( x ) . ( \ displaystyle ( \ frac ( d ) ( dx ) ) e ^ ( f ( x ) ) = f ' ( x ) e ^ ( f ( x ) ) . )
PageRank
D = 1 2 E ( d e g ( p 1 ) d e g ( p 2 ) ⋮ d e g ( p N ) ) ( \ displaystyle D = ( 1 \ over 2 E ) ( \ begin ( bmatrix ) deg ( p_ ( 1 ) ) \ \ deg ( p_ ( 2 ) ) \ \ \ vdots \ \ deg ( p_ ( N ) ) \ end ( bmatrix ) ) )
Degrees of freedom (physics and chemistry)
p i ( X i ) = e − E i k B T ∫ d X i e − E i k B T ( \ displaystyle p_ ( i ) ( X_ ( i ) ) = ( \ frac ( e ^ ( - ( \ frac ( E_ ( i ) ) ( k_ ( B ) T ) ) ) ) ( \ int dX_ ( i ) \ , e ^ ( - ( \ frac ( E_ ( i ) ) ( k_ ( B ) T ) ) ) ) ) ) ,
Bipolar junction transistor
i C = I S ( ( e V BE V T − e V BC V T ) − 1 β R ( e V BC V T − 1 ) ) i B = I S ( 1 β F ( e V BE V T − 1 ) + 1 β R ( e V BC V T − 1 ) ) i E = I S ( ( e V BE V T − e V BC V T ) + 1 β F ( e V BE V T − 1 ) ) ( \ displaystyle ( \ begin ( aligned ) i_ ( \ text ( C ) ) & = 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 _ ( R ) ) ) \ left ( e ^ ( \ frac ( V_ ( \ text ( BC ) ) ) ( V_ ( \ text ( T ) ) ) ) - 1 \ right ) \ right ) \ \ i_ ( \ text ( B ) ) & = I_ ( \
Treaty of Waitangi
Na ko te Kuini e hiahia ana kia wakaritea te Kawanatanga kia kaua ai nga kino e puta mai ki te tangata Maori ki te Pakeha e noho ture kore ana .
Conic section
M = ( A B D B C E D E F ) , ( \ displaystyle M = \ left ( ( \ begin ( matrix ) A&B&D \ \ B&C&E \ \ D&E&F \ end ( matrix ) ) \ right ) , )
Mental calculation
Exponent Value Error Application ≈ 20 + π 0.004 % Spherical wave attenuation ≈ 10 0.0003 % 1 ° C , 274 Kelvin ≈ 4 x 10 0.00003 % e / e = e near ambient , Kelvin ≈ 2 x 10 0.000004 % Accurate thermal temperature k e ≈ 10 1.4 % k = Boltzmann 's constant
New Zealand
English is the predominant language in New Zealand , spoken by 96.1 % of the population . New Zealand English is similar to Australian English and many speakers from the Northern Hemisphere are unable to tell the accents apart . The most prominent differences between the New Zealand English dialect and other English dialects are the shifts in the short front vowels : the short - `` i '' sound ( as in `` kit '' ) has centralised towards the schwa sound ( the `` a '' in `` comma '' and `` about '' ) ; the short - `` e '' sound ( as in `` dress '' ) has moved towards the short - `` i '' sound ; and the short - `` a '' sound ( as in `` trap '' ) has moved to the short - `` e '' sound .
List of earthquakes in New Zealand
South of New Zealand 8.2 Felt in the South Island 31 May 1989 Doubtful Sound Southland 6.1 23 km 45.33 ° S 166.87 ° E 13 May 1990 Weber Manawatu 6.2 6.4 29 km 40.42 S 176.47 ° E Mainshock 28 Jan 1991 Buller Ranges West Coast 6.1 9.9 km 41.90 ° S 171.65 ° E Foreshock to M 6.3 event 29 Jan 1991 Buller Ranges West Coast 6.3 17.3 km 41.90 ° S 171.72 ° E Mainshock 8 Sep 1991 South Taranaki Bight Manawatu 6.3 86 km 40.24 ° S 175.16 ° E Felt throughout North Island 27 May 1992 Wairau Valley Marlborough 6.8 79 km 41.60 ° S 173.66 ° E Felt in Central New Zealand 21 June 1992 White Island Bay of Plenty 6.1 5 km 37.57 ° S 176.82 ° E Felt in Bay of Plenty 10 Aug 1993 Secretary Island Southland 6.7 7.0 5 km 45.21 ° S 166.70 ° E Felt as far away as Australia 10 Aug 1993 Gisborne East Cape 6.3 45 km 38.52 ° S 177.90 ° E Felt strongly in Gisborne .
Bipolar junction transistor
I E = I ES ( e V BE V T − 1 ) I C = α F I E I B = ( 1 − α F ) I E ( \ displaystyle ( \ begin ( aligned ) I_ ( \ text ( E ) ) & = I_ ( \ text ( ES ) ) \ left ( e ^ ( \ frac ( V_ ( \ text ( BE ) ) ) ( V_ ( \ text ( T ) ) ) ) - 1 \ right ) \ \ I_ ( \ text ( C ) ) & = \ alpha _ ( F ) I_ ( \ text ( E ) ) \ \ I_ ( \ text ( B ) ) & = \ left ( 1 - \ alpha _ ( F ) \ right ) I_ ( \ text ( E ) ) \ end ( aligned ) ) )
Radioactive decay
N = N 0 e − λ t = N 0 e − t / τ , ( \ displaystyle N = N_ ( 0 ) \ , e ^ ( - ( \ lambda ) t ) = N_ ( 0 ) \ , e ^ ( - t / \ tau ) , \ , \ ! )
Moment-generating function
M X ( t ) : = E ( e t X ) , t ∈ R , ( \ displaystyle M_ ( X ) ( t ) : = \ mathbb ( E ) \ ! \ left ( e ^ ( tX ) \ right ) , \ quad t \ in \ mathbb ( R ) , )
Sum of normally distributed random variables
φ X + Y ( t ) = E ⁡ ( e i t ( X + Y ) ) ( \ displaystyle \ varphi _ ( X + Y ) ( t ) = \ operatorname ( E ) \ left ( e ^ ( it ( X + Y ) ) \ right ) )
List of earthquakes in New Zealand
22 Oct 2011 Raoul Island Kermadec Islands 7.3 7.4 6.5 33 km 28.99 ° S 176.18 ° W Felt in eastern half of the North Island . 23 Dec 2011 Christchurch Canterbury 6.0 5.9 5.7 7 km 43.52 ° S 172.74 ° E Caused damage in the Christchurch region . 3 Jul 2012 South Taranaki Bight Taranaki 6.5 6.3 5.9 254 km 40.00 ° S 173.75 ° E 2012 Opunake earthquake 21 Jul 2013 Cook Strait Marlborough 6.5 6.5 6.1 17 km 41.61 ° S 174.33 ° E 2013 Seddon earthquake 16 Aug 2013 Lake Grassmere Marlborough 6.6 6.5 6.0 8 km 41.73 ° S 174.15 ° E 2013 Lake Grassmere earthquake 16 Aug 2013 Lake Grassmere Marlborough 6.0 5.9 5.8 8 km 41.67 ° S 174.26 ° E Largest aftershock to 2013 Lake Grassmere earthquake 20 Jan 2014 Eketahuna Wairarapa 6.2 6.1 5.8 34 km 40.62 ° S 175.85 ° E 2014 Eketahuna earthquake 13 Oct 2014 Fiordland Southland 6.2 5.8 5.4 9 km 46.29 ° S 165.87 ° E 14 Oct 2014 NE of Whakatane Bay of Plenty 6.5 5.7 82 km 34.90 ° S 179.65 ° E 17 Nov 2014 NE of Gisborne Gisborne 6.5 6.7 6.2 22 km 37.68 ° S 179.68 ° E Felt strongly across the North Island 6 Jan 2015 W of Arthur 's Pass Canterbury 6.0 5.6 5.5 5 km 43.06 ° S 171.25 ° E Felt throughout the South Island 24 Apr 2015 SE of St Arnaud Marlborough 6.2 6.1 6.0 52 km 42.09 ° S 173.07 ° E Felt throughout New Zealand 2 Feb 2016 E of Macauley Island Kermadec Islands 6.6 6.2 6.3 366 km 31.65 ° S 177.74 ° E Felt widely in the North Island .
Normal distribution
f ^ ( t ) = ∫ − ∞ ∞ f ( x ) e − i t x d x = e − i μ t e − 1 2 ( σ t ) 2 ( \ displaystyle ( \ hat ( f ) ) ( t ) = \ int _ ( - \ infty ) ^ ( \ infty ) \ ! f ( x ) e ^ ( - itx ) \ , dx = e ^ ( - i \ mu t ) e ^ ( - ( \ frac ( 1 ) ( 2 ) ) ( \ sigma t ) ^ ( 2 ) ) )
Nuclear force
V Reid ( r ) = − 10.463 e − μ r μ r + 1650.6 e − 4 μ r μ r + 6484.2 e − 7 μ r μ r ( \ displaystyle V_ ( \ text ( Reid ) ) ( r ) = - 10.463 ( \ frac ( e ^ ( - \ mu r ) ) ( \ mu r ) ) + 1650.6 ( \ frac ( e ^ ( - 4 \ mu r ) ) ( \ mu r ) ) + 6484.2 ( \ frac ( e ^ ( - 7 \ mu r ) ) ( \ mu r ) ) )
List of earthquakes in New Zealand
11 Apr 1993 Hastings Hawke 's Bay 6.1 37 km 39.72 ° S 176.71 ° E Felt strongly throughout Hawke 's Bay 18 Jun 1994 Arthur 's Pass Canterbury 6.7 6.7 4 km 43.00 ° S 171.47 ° E Mainshock 19 Jun 1994 Lake Coleridge Canterbury 6.1 5 km 43.16 ° S , 171.47 ° E Triggered from the M 6.7 Arthur 's Pass event 24 Nov 1995 Arthur 's Pass Canterbury 6.3 7 km 42.95 ° S , 171.81 ° E Felt strongly in the South Island 6 Feb 1995 NE of New Zealand East Cape 7.0 12 km 37.7 ° 7S 179.68 ° E Mainshock 10 Feb 1995 NE of New Zealand East Cape 6.6 12 km 37.92 ° 7S 179.51 ° E 25 May 1997 Raoul Island Kermadec Islands 7.9 339 km 33.61 ° S 177.80 ° E Felt throughout North Island and upper half of South Island 20 Apr 1998 Taumaranui Manawatu 6.7 232 km 39 , 02S 174.92 ° E Felt throughout the North Island 25 Oct 1999 Taupo Waikato 7.0 160 km 38.56 S 175.91 ° E Felt throughout New Zealand
Capital asset pricing model
E ( R i ) − R f = β i ( E ( R m ) − R f ) ( \ displaystyle E ( R_ ( i ) ) - R_ ( f ) = \ beta _ ( i ) ( E ( R_ ( m ) ) - R_ ( f ) ) \ , )
Capital asset pricing model
E ( R i ) = R f + β i ( E ( R m ) − R f ) ( \ displaystyle E ( R_ ( i ) ) = R_ ( f ) + \ beta _ ( i ) ( E ( R_ ( m ) ) - R_ ( f ) ) \ , )
Nessun dorma
Nessun dorma ! Nessun dorma ! Tu pure , o Principessa , nella tua fredda stanza , guardi le stelle che tremano d'amore , e di speranza ! None shall sleep ! None shall sleep ! Not even you , oh Princess , in your cold bedroom , watching the stars that tremble with love and with hope ! Ma il mio mistero è chiuso in me ; il nome mio nessun saprà ! No , No ! Sulla tua bocca lo dirò quando la luce splenderà ! But my secret is hidden within me ; no one will know my name ! No , no ! On your mouth I will say it when the light shines ! Ed il mio bacio scioglierà il silenzio che ti fa mia ! And my kiss will dissolve the silence that makes you mine !
Equator
Co-ordinates Country , territory or sea Notes 0 ° N 0 ° E ﻿ / ﻿ 0 ° N 0 ° E ﻿ / 0 ; 0 ﻿ ( Prime Meridian ) Atlantic Ocean Gulf of Guinea 0 ° 0 ′ N 6 ° 31 ′ E ﻿ / ﻿ 0.000 ° N 6.517 ° E ﻿ / 0.000 ; 6.517 ﻿ ( São Tomé and Príncipe ) São Tomé and Príncipe Ilhéu das Rolas 0 ° 0 ′ N 9 ° 21 ′ E ﻿ / ﻿ 0.000 ° N 9.350 ° E ﻿ / 0.000 ; 9.350 ﻿ ( Gabon ) Gabon passes 8.9 km ( 5.5 mi ) south of Ayem , 10.6 km ( 6.6 mi ) north of Mayene , Booue 0 ° 0 ′ N 13 ° 56 ′ E ﻿ / ﻿ 0.000 ° N 13.933 ° E ﻿ / 0.000 ; 13.933 ﻿ ( Republic of the Congo ) Republic of the Congo Passing through the town of Makoua .
List of earthquakes in New Zealand
throughout Central New Zealand 5 Jun 1869 Christchurch Canterbury 4.7 -- 5.7 5 km 43.55 ° S 172.60 ° E 1869 Christchurch earthquake 18 Jul 1876 Palmerston North Manawatu 6.8 50 km 40.19 ° S 175.80 ° E Felt strongly in Palmerston North 25 Jun 1881 Palmerston North Manawatu 6.7 33 km 40.39 ° S 175.60 ° E Felt strongly in Palmerston North 5 Dec 1881 Castle Hill Canterbury 6.0 12 km 43.13 ° S 171.77 ° E Damaged stone buildings in Christchurch , including ChristChurch Cathedral 1 Sep 1888 Lewis Pass Canterbury 7.0 7.1 12 km 42.59 ° S 172.55 ° E 1888 North Canterbury earthquake 23 Jun 1891 Port Waikato Auckland 6.2 12 km 37.43 ° S 174.43 ° E Felt in Auckland / Waikato 12 Feb 1893 Nelson Tasman Bay 6.7 70 km 40.99 ° S 173.80 ° E Felt throughout Central New Zealand 18 Aug 1895 Taupo Bay of Plenty 6.0 12 km 38.80 ° S 176.80 ° E Felt throughout Central New Zealand 8 Dec 1897 Wanganui Manawatu 6.5 40 km 39.99 ° S , 175.00 ° E Felt throughout North Island , Strong in Wanganui
Capital asset pricing model
E ( R i ) − R f β i = E ( R m ) − R f ( \ displaystyle ( \ frac ( E ( R_ ( i ) ) - R_ ( f ) ) ( \ beta _ ( i ) ) ) = E ( R_ ( m ) ) - R_ ( f ) )
Romance languages
Outcome of Classical Latin vowels Classical Latin Proto - Romance Sardinian Eastern Romance Italo - Western short A / a / / a / / a / / a / long A short E / ɛ / / e / / ɛ / / ɛ / long E / e / / e / / e / short I / ɪ / / i / long I / i / / i / / i / short O / ɔ / / o / / o / / ɔ / long O / o / / o / short U / ʊ / / u / / u / long U / u / / u /