formulasearchengine - User contributions [en]

Gaussian integral

2015-01-11T14:39:43Z

87.115.115.203: mismatch between definite and indefinite integrals

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Kermack–McKendrick theory

2015-01-06T00:46:48Z

87.115.9.107: Spelling

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XOR cipher

2014-01-28T18:07:34Z

87.115.241.113: /* Example implementation */ ever so slightly simpler still

[[File:Population curve.svg|thumb|550px|The estimated size of human population from 10,000 [[Common Era|BCE]]–2000 CE.]]

'''Population growth''' is the change in a [[population]] over time, and can be quantified as the change in the number of individuals of any [[species]] in a population using "per unit time" for measurement.
In [[biology]], the term ''population growth'' is likely to refer to any known [[organism]], but this article deals mostly with the application of the term to [[human]] populations in [[demography]].

Population growth rates might have declined, but in 2013 every 60 minutes there are another 8,000 people in the world: about 75 million every year.<ref>[http://www.theguardian.com/commentisfree/2013/nov/11/typhoon-haiyan-there-is-worse-to-come Typhoon Haiyan: there is worse to come, The first disaster to kill more than a million people could happen within our lifetimes] The Guardian, Monday 11 November 2013</ref>

In demography, ''population growth'' is used informally for the more specific term '''population growth rate''' (see below), and is often used to refer specifically to the growth of the human [[World population|population of the world]].

Simple models of population growth include the Malthusian Growth Model and the [[logistic function|logistic model]].

The world population grew from 1 billion to 7 billion from 1800 to 2011. During the year 2011, according to [[World population estimates|estimates]], 135 million people were born and 57 million died, for an increase in population of 78 million.<ref name=hesa2011>7. miljardis ihminen, Helsingin Sanomat editor Mr Timo Paukku 5.9.2011 D1 {{fi}}</ref>

{| class="wikitable" style="float: right; clear:right; margin-left: 10px"
! colspan=3 align="center" style="background-color: #cfb;" | Population<ref name="hesa2011"/>
|-
! style="background-color: #cfb;" | Years Passed
! style="background-color: #cfb;" | Year
! style="background-color: #cfb;" | Billion
|----
| align="left" | - || 1800 || align="right"| 1
|----
| align="left" | 127 || 1927 || align="right"| 2
|----
| align="left" | 33 || 1960 || align="right"| 3
|----
| align="left" | 14 || 1974 || align="right"| 4
|----
| align="left" | 13 || 1987 || align="right"| 5
|----
| align="left" | 12 || 1999 || align="right"| 6
|----
| align="left" | 12 || 2011 || align="right"| 7
|----
| align="left" | 14 || 2025* || align="right"| 8
|----
| align="left" | 18 || 2043* || align="right"| 9
|----
| align="left" | 40 || 2083* || align="right"| 10
|-----
| align="left" colspan=3 | * [[UNFPA]]United Nations Population Fund estimate 31.10.2011 
|}

==Determinants of population growth==

Four factors determine population growth for a given geographical area - births ('''B'''), deaths ('''D'''), immigration rate ('''I'''), and emigration rate ('''E'''):

growth rate of population = (B-D)+(I-E)

In other words, the population growth of a period can be calculated in two parts, [[natural growth]] of population (B-D) and [[mechanical growth]] of population (I-E), in which mechanical growth of population is mainly affected by social factors, e.g. advanced economies may grow faster while backward economies grow slowly or even experience negative growth. (Growth can be both positive or negative i.e. growth can increase or decrease.)

==Population growth rate==
In demographics and [[ecology]], the "population growth rate" is the rate at which the number of individuals in a population increases in a given time period as a fraction of the initial population. Specifically, population growth rate refers to the change in population over a unit time period, often expressed as a [[percentage]] of the number of individuals in the population at the beginning of that period. This can be written as the formula:

:<math>pop\ growth\ rate = \frac{ P(t_2) - P(t_1)} {P(t_1)}</math>

The most common way to express population growth is as a percentage. That is:

:<math>\mathrm{percentage\ growth} = \mathrm{pop\ growth\ rate} \times 100.</math>

A positive growth ratio (or rate) indicates that the population is increasing, while a negative growth ratio indicates the population is decreasing. A growth ratio of zero indicates that there were the same number of people at the two times—net difference between births, deaths a growth rate may be zero even when there are significant changes in the [[birth rate]]s, [[death rate]]s, [[immigration rate]]s, and age distribution between the two times.<ref>[http://www.apheo.ca/index.php?pid=61 Association of Public Health Epidemiologists in Ontario]</ref>

A related measure is the [[net reproduction rate]]. In the absence of migration, a net reproduction rate of more than one indicates that the population of women is increasing, while a net reproduction rate less than one ([[sub-replacement fertility]]) indicates that the population of women is decreasing.

==Excessive growth and decline==
{{main|Human overpopulation|Population decline}}

Population exceeding the [[carrying capacity]] of an area or environment is called [[overpopulation (biology)|overpopulation]]. It may be caused by growth in population or by reduction in capacity. Spikes in human population can cause problems such as [[pollution]] and [[traffic congestion]], these might be resolved or worsened by technological and economic changes. Conversely, such areas may be considered "underpopulated" if the population is not large enough to maintain an [[economic system]] (see [[population decline]]). Between these two extremes sits the notion of the [[optimum population]].

==Human population growth rate==
{{Main|Total fertility rate}}

[[File:Countriesbyfertilityrate.svg|thumb|350px|A world map showing global variations in [[fertility rate]] per woman, according to the [[The World Factbook|CIA World Factbook]]'s 2013 data.
{{col-begin}}
{{col-break}}
{{legend|#AE23AE|7–8 children}}
{{legend|#FF00FF|6–7 children}}
{{col-break}}
{{legend|#FF0000|5–6 children}}
{{legend|#FF6600|4–5 children}}
{{col-break}}
{{legend|#FFFF00|3–4 children}}
{{legend|#00FF00|2–3 children}}
{{col-break}}
{{legend|#20DFD8|1–2 children}}
{{legend|#35B0E3|0–1 children}}
{{col-end}}]]
[[File:World population (UN).svg|thumb|350px|Estimates of population evolution in different [[continent]]s between 1950 and 2050, according to the United Nations. The vertical axis is [[Logarithmic scale|logarithmic]] and is in millions of people.]]
[[File:World population growth rate 1950–2050.svg|thumb|350px|Growth rate of world population (1950–2050).]]

Globally, the growth rate of the [[World population|human population]] has been declining since peaking in 1962 and 1963 at 2.20% per annum. In 2009, the estimated annual growth rate was 1.1%.<ref name="U.S. Census Bureau, January 2010">[http://www.census.gov/ipc/www/idb/worldpop.php U.S. Census Bureau, January 2010]</ref> The [[CIA World Factbook]] gives the world annual birthrate, mortality rate, and growth rate as 1.89%, 0.79%, and 1.096% respectively.<ref>[https://www.cia.gov/library/publications/the-world-factbook/geos/xx.html World Factbook ]</ref> The last 100 years have seen a rapid increase in population due to [[History of medicine#Modern medicine|medical advances]] and massive increase in agricultural productivity<ref>[http://news.bbc.co.uk/1/hi/world/south_asia/4994590.stm BBC NEWS | The end of India's green revolution?]</ref> made possible by the [[Green Revolution]].<ref>[http://www.foodfirst.org/media/opeds/2000/4-greenrev.html Food First/Institute for Food and Development Policy]</ref><ref>[http://www.csmonitor.com/2007/0724/p01s01-wogi.html Rising food prices curb aid to global poor]</ref><ref>[http://www.finfacts.com/irelandbusinessnews/publish/article_1011078.shtml Record rise in wheat price prompts UN official to warn that surge in food prices may trigger social unrest in developing countries]</ref>

The trend is shown in the graph at right. Actual measured data are given to 2010 and extrapolated estimates beyond that. If the linear trend holds and growth rate continues to decline, population growth rate will fall to zero in about 2080. Population will peak and begin declining thereafter. The Malthus exponential model, modified to reflect the linear growth rate trend, suggests that world population will peak at about 10.3 billion. This, of course, is speculative but is consistent with other models showing a population peak in the latter part of the 21st century.

The actual annual growth in the number of humans fell from its peak of 88.0 million in 1989, to a low of 73.9 million in 2003, after which it rose again to 75.2 million in 2006. Since then, annual growth has declined. In 2009, the human population increased by 74.6 million, which is projected to fall steadily to about 41 million per annum in 2050, at which time the population will have increased to about 9.2 billion.<ref name="U.S. Census Bureau, January 2010"/> Each region of the globe has seen great reductions in growth rate in recent decades, though growth rates remain above 2% in some countries of the [[Middle East]] and [[Sub-Saharan Africa]], and also in [[South Asia]], [[Southeast Asia]], and [[Latin America]].<ref>[http://www.census.gov/ipc/www/idb/worldpop.php U.S. Census Bureau, June 2009]</ref>

Some countries experience [[Population decline|negative population growth]], especially in [[Eastern Europe]] mainly due to low [[Total fertility rate|fertility rate]]s, high death rates and [[emigration]]. In [[Southern Africa]], growth is slowing due to the high number of [[HIV]]-related deaths. Some [[Western Europe]] countries might also encounter negative population growth.<ref>[http://esa.un.org/unpp/index.asp?panel=2 UN population projections]</ref> [[Japan]]'s population began decreasing in 2005.<ref>[http://www.guardian.co.uk/world/2009/jan/02/japan-population Japan sees biggest population fall]</ref> The United Nations Population Division expects world population to peak at over 10 billion at the end of the 21st century but Sanjeev Sanyal has argued that global fertility will fall below replacement rates in the 2020s and that world population will peak below 9 billion by 2050 followed by a long decline.<ref>[http://www.project-syndicate.org/commentary/the-end-of-population-growth]</ref>

==Growth by country==
According to [[United Nations]] population statistics, the world population grew by 30%, or 1.6 billion people, between 1990 and 2010.<ref name="UN">[http://esa.un.org/unpd/wpp/unpp/Panel_profiles.htm World Population Prospects, the 2010 Revision]</ref> In number of people the increase was highest in [[India]] 350 million and [[China]] 196 million. Population growth was among highest in the [[United Arab Emirates]] (315%) and [[Qatar]] (271%).<ref name="UN" />

{| class="wikitable sortable"
|+ Growth rates of the world's most populous countries
|-
!Rank
!Country
!Population 2010
!Population 1990
!Growth (%) 1990–2010
|-
|
| {{noflag}} World
| align="right"|6,895,889,000
| align="right"|5,306,425,000
| align="right"|30.0%
|-
| 1
| {{flag|China}}
| align="right"|1,341,335,000
| align="right"|1,145,195,000
| align="right"|17.1%
|-
| 2
| {{flag|India}}
| align="right"|1,224,614,000
| align="right"|873,785,000
| align="right"|40.2%
|-
| 3
| {{flag|United States}}
| align="right"|310,384,000
| align="right"|253,339,000
| align="right"|22.5%
|-
| 4
| {{flag|Indonesia}}
| align="right"|239,871,000
| align="right"|184,346,000
| align="right"|30.1%
|-
| 5
| {{flag|Brazil}}
| align="right"|194,946,000
| align="right"|149,650,000
| align="right"|30.3%
|-
| 6
| {{flag|Pakistan}}
| align="right"|173,593,000
| align="right"|111,845,000
| align="right"|55.3%
|-
| 7
| {{flag|Nigeria}}
| align="right"|158,423,000
| align="right"|97,552,000
| align="right"|62.4%
|-
| 8
| {{flag|Bangladesh}}
| align="right"|148,692,000
| align="right"|105,256,000
| align="right"|41.3%
|-
| 9
| {{flag|Russia}}
| align="right"|142,958,000
| align="right"|148,244,000
| align="right"|-3.6%
|-
| 10
| {{flag|Japan}}
| align="right"|128,057,000
| align="right"|122,251,000
| align="right"|4.7%
|-
|}

===1960s to 2010 table of population growth===
{| class="wikitable" style="float: right; clear:right; margin-left: 10px"
! colspan="2" align=center style="background-color: #cfb;" | Population growth 1990–2008 (%)<ref name=IEAco-2011>[http://www.iea.org/co2highlights/co2Highlights.XLS CO2 Emissions from Fuel Combustion] Population 1971–2008 IEA</ref>
|-----
| align="left" | [[Africa]] || align="right"| 55%
|-----
| align="left" | [[Middle East]] || align="right"| 51%
|-----
| align="left" | [[Asia]] || align="right"| 35%
|-----
| align="left" | [[Latin America]] || align="right"| 30%
|-----
| align="left" | [[OECD]] [[North America]] || align="right"| 24%
|-----
| align="left" | OECD [[Europe]] || align="right"| 9%
|-----
| align="left" | OECD [[Pacific]] || align="right"| 8%
|-----
| align="left" | [[Former Soviet Union]] || align="right"| −1%
|-----
| align="left" | Non-OECD Europe || align="right"| −11%
|-
|}

Many of the world's countries, including many in [[Sub-Saharan Africa]], the [[Middle East]], [[South Asia]] and [[South East Asia]], have seen a sharp rise in population since the end of the [[Cold War]]. The fear is that high population numbers are putting further strain on natural resources, food supplies, fuel supplies, employment, housing, etc. in some the less fortunate countries. For example, the population of [[Chad]] has ultimately grown from 6,279,921 in 1993 to 10,329,208 in 2009,<ref name="cia"/> further straining its resources. [[Vietnam]], [[Mexico]], [[Nigeria]], [[Egypt]], [[Ethiopia]], and the [[Democratic Republic of the Congo|DRC]] are witnessing a similar growth in population.

The situation was most acute in northern, western and central Africa. Refugees from places like the [[Sudan]] have helped further strain the resources of neighbouring states like Chad and Egypt. The nation is also host to roughly 255,000 [[refugee]]s from Sudan's [[Darfur]] region, and about 77,000 refugees from the [[Central African Republic]], while approximately 188,000 Chadians have been displaced by their own civil war and famines, have either fled to either the Sudan, the Niger, or more recently, [[Libya]].

{| class="wikitable sortable"
|-
! Example nation !! 1st Population total.!! 2nd Population total.!! 3rd Population total.!!4th Population total.!!5th Population total.!!Life expectancy in years. !!Total population growth from 1st Pop. Total to 5th Pop. Total.
|-
|[[Eritrea]]* || N/A* ||N/A*|| 3,437,000(1994)<ref name="collins student atlas"/> ||4,298,269 (2002) || 5,673,520 (2008)<ref>
url=http://www.un.org/esa/population/publications/wpp2008/wpp2008_text_tables.pdf</ref>||61 (2008)<ref name="ReferenceB">'Modern School Atlas (96th edition)', ISBN 978-1-84907-013-3.</ref>||2,236,520 (since independence)
|-
| [[Ethiopia]]* ||23,457,000(1967)*<ref name="ReferenceOxford Atlas">The British Oxford economic atlas of the World 4th edition, ISBN 0-19-894107-2</ref>||50,974,000(1990)* <ref name="ReferenceC">The British Collins Atlas of the World, the 1993 edition, ISBN 0-00-448038-4</ref> || 54,939,000(1994) <ref name="collins student atlas">The British ''Collins Longman Student Atlas'', the 1996 and in 1998 publications, ISBN 978-0-00-448879-0 for the 1998 edition, ISBN 0-00-448365-0 for the 1996 edition</ref> || 67,673,031(2003) ||79,221,000(2008)<ref name="csa.gov.et">[http://www.csa.gov.et/surveys/National%20statistics/national%20statistics%202007/Population.pdf Ethiopia Central Statistics Office -- Population Projection for mid-2008]</ref>|| 55(2008)<ref name="ReferenceB"/>|| 55,764,000
|-
| [[Sudan]]**||14,355,000(1967)**<ref name="ReferenceOxford Atlas"/> ||25,204,000(1990)** <ref name="ReferenceC"/> || 27,361,000 (1994)**<ref name="collins student atlas"/> || 38,114,160 (2003)** || 42,272,000(2008)**<ref>{{cite journal | url=http://www.un.org/esa/population/publications/wpp2008/wpp2008_text_tables.pdf | title=World Population Prospects, Table A.1| version=2008 revision | format=PDF | publisher=United Nations | author=Department of Economic and Social Affairs}}</ref>||50(2008)**<ref name="ReferenceB"/>|| 27,917,000
|-
| [[Chad]] ||3,410,000(1967)<ref name="ReferenceOxford Atlas"/> ||5,679,000(1990) <ref name="ReferenceC"/> || 6,183,000 (1994)<ref name="collins student atlas"/> ||9,253,493(2003) ||10,329,208 (2009)<ref name="cia"/>||47(2008)<ref name="ReferenceB"/>|| 6,919,205
|-
| [[Niger]]||3,546,000(1967)<ref name="ReferenceOxford Atlas"/>||7,732,000(1990) <ref name="ReferenceC"/> || 8,846,000(1994)<ref name="collins student atlas"/> || 10,790,352 (2001) || 15,306,252 (2009)<ref>{{cite web |author=Central Intelligence Agency |authorlink=CIA |publisher=[[The World Factbook]]|title=Niger |url=https://www.cia.gov/library/publications/the-world-factbook/geos/ng.html |year=2009|accessdate=January 10, 2010}}</ref>||44 (2008)<ref name="ReferenceB"/>|| 11,760,252
|-
|[[Nigeria]]||61,450,000(1967)<ref name="ReferenceOxford Atlas"/>||88,500,000(1990) <ref name="ReferenceC"/> ||108,467,000 (1994)<ref name="collins student atlas"/> ||129,934,911 (2002)||158,259,000 (2008)<ref name="Department of Economic and Social Affairs Population Division 2009">{{cite journal | url=http://www.un.org/esa/population/publications/wpp2008/wpp2008_text_tables.pdf | title=World Population Prospects, Table A.1| version=2008 revision | format=PDF | publisher=United Nations | author=Department of Economic and Social Affairs Population Division | year=2009 | accessdate= 2009-03-12}}</ref>||47(2008)<ref name="ReferenceB"/>|| 96,809,000
|-
|[[Mali]]||4,745,000(1967)<ref name="ReferenceOxford Atlas"/>||8,156,000(1990),<ref name="ReferenceC"/> ||10,462,000(1994)<ref name="collins student atlas"/>||11,340,480(2002)||14,517,176(2010).<ref name=census>{{cite web|url=http://instat.gov.ml/voir_actu.aspx?lactu=44 |title=Mali preliminary 2009 census|publisher=Institut National de la Statistique|accessdate=January 12, 2010}}</ref>||50(2008)<ref name="ReferenceB"/>|| 9,772,176
|-
| [[Mauritania]] ||1,050,000(1967)<ref name="ReferenceOxford Atlas"/> ||2,025,000(1990) <ref name="ReferenceC"/> || 2,211,000 (1994)<ref name="collins student atlas"/> ||2,667,859 (2003) ||3,291,000 (2009)<ref name="cia"/>||54(2008)<ref name="ReferenceB"/>|| 2,241,000
|-
| [[Senegal]]||3,607,000(1967)<ref name="ReferenceOxford Atlas"/>||7,327,000(1990) <ref name="ReferenceC"/> ||8,102,000 (1994) <ref name="collins student atlas"/> ||9,967,215(2002)||13,711,597 (2009)<ref>{{cite web |author=Central Intelligence Agency |authorlink=CIA |publisher=[[The World Factbook]]|title=Senegal |url=https://www.cia.gov/library/publications/the-world-factbook/geos/sg.html |year=2009|accessdate=January 10, 2010}}</ref>||57(2008)<ref name="ReferenceB"/>|| 10,104,597
|-
|[[Gambia]]||343,000(1967)<ref name="ReferenceOxford Atlas"/>||861,000(1990) <ref name="ReferenceC"/> ||1,081,000 (1994)<ref name="collins student atlas"/> ||1,367,124 (2000)||1,705,000(2008)<ref name="Department of Economic and Social Affairs Population Division 2009"/>||55(2008)<ref name="ReferenceB"/>|| 1,362,000
|-
| [[Algeria]] || 11,833,126 (1966)<ref name="ReferenceOxford Atlas"/>|| 25,012,000 (1990) <ref name="ReferenceC"/> || 27,325,000 (1994) <ref name="collins student atlas"/> || 32,818,500 (2003) ||34,895,000<ref name="csa.gov.et"/><ref name=unpop>{{cite journal | url=http://www.un.org/esa/population/publications/wpp2010/wpp2010_text_tables.pdf | title=World Population Prospects, Table A.1| version=2008 revision | format=PDF | publisher=United Nations | author=Department of Economic and Social Affairs Population Division | year=2010 | accessdate= 2009-03-12}}{{Dead link|date=October 2010|bot=H3llBot}}</ref>(2008)|| 74 (2008)<ref name="ReferenceB"/>|| 23,061,874
|-
| [[The DRC]]/Zaire|| 16,353,000(1967)<ref name="ReferenceOxford Atlas"/>|| 35,562,000 (1990) <ref name="ReferenceC"/> || 42,552,000 (1994) <ref name="collins student atlas"/> || 55,225,478 (2003) || 70,916,439 (2008) <ref name="csa.gov.et"/><ref name="cia.govx">[https://www.cia.gov/library/publications/the-world-factbook/geos/cg.html The World Factbook- Congo, Democratic Republic of the.] Central Intelligence Agency.</ref>|| 54(2008)<ref name="ReferenceB"/>|| 54,563,439
|-
| [[Egypt]] || 30,083,419 (1966)<ref name="ReferenceOxford Atlas"/>|| 53,153,000 (1990) <ref name="ReferenceC"/> || 58,326,000 (1994) <ref name="collins student atlas"/> || 70,712,345 (2003) || 79,089,650 <ref name=popclock/><ref name=popclock>{{cite web|url=http://www.msrintranet.capmas.gov.eg/pls/fdl/tst12e?action=&lname= |title=Central Agency for Population Mobilisation and Statistics — Population Clock (July 2008) |publisher=Msrintranet.capmas.gov.eg |date= |accessdate=2010-08-25}}</ref> (2008) <ref name="csa.gov.et"/>|| 72 (2008)<ref name="ReferenceB"/>|| 49,006,231
|-
| [[Réunion]] (French colony)||418,000 (1967)<ref name="ReferenceOxford Atlas"/>|| N/A (1990) <ref name="ReferenceC"/> ||N/A (1994)<ref name="collins student atlas"/> || 720,934 (2003)|| 827,000 (2009) <ref name=unpop>{{cite journal | url=http://www.un.org/esa/population/publications/wpp2008/wpp2008_text_tables.pdf | title=World Population Prospects, Table A.1| version=2008 revision | format=PDF | publisher=United Nations | author=Department of Economic and Social Affairs
Population Division | year=2009 | accessdate= 2009-03-12}}</ref>||N/A (2008)<ref name="ReferenceB"/>|| 409,000
|-
| The [[Falkland Islands]] (UK Territory)||2,500(1967)<ref name="ReferenceOxford Atlas"/>|| N/A (1990) <ref name="ReferenceC"/> || N/A (1994)<ref name="collins student atlas"/> || 2,967 (2003) || 3,140(2010)<ref name=cia>{{cite web
|url = https://www.cia.gov/library/publications/the-world-factbook/geos/fk.html
|title = Falkland Islands (Islas Malvinas)
|publisher=The World Factbook
|publisher=CIA
|accessdate = 5 March 2010}}</ref>
|| N/A (2008)<ref name="ReferenceB"/>|| 640
|-
| [[Chile]]||8,935,500(1967)<ref name="ReferenceOxford Atlas"/>||13,173,000 (1990) <ref name="ReferenceC"/> || 13,994,000(1994)<ref name="collins student atlas"/> || 15,116,435 (2002) || 17,224,200 (2011) ||77 (2008)<ref name="ReferenceB"/>|| 8,288,700
|-
| [[Colombia]]||19,191,000(1967)<ref name="ReferenceOxford Atlas"/>|| 32,987,000(1990) <ref name="ReferenceC"/> || 34,520,000(1994)<ref name="collins student atlas"/> || 41,088,227 (2002) || 45,925,397(2010)<ref name="DANE clock">{{cite web|url=http://www.dane.gov.co/reloj/reloj_animado.php |title=Departamento Administrativo Nacional de Estadística |publisher=Dane.gov.co |date= |accessdate=2010-08-22}}</ref> ||73 (2008)<ref name="ReferenceB"/>|| 26,734,397
|-
| [[Brazil]]||85,655,000(1967)<ref name="ReferenceOxford Atlas"/>||150,368,000 (1990) <ref name="ReferenceC"/> ||153,725,000 (1994)<ref name="collins student atlas"/> || 174,468,575 (2000) || 190,732,694(2010) <ref>IBGE. [http://www.ibge.gov.br/home/presidencia/noticias/noticia_visualiza.php?id_noticia=1766&id_pagina=1 Censo 2010: população do Brasil é de 190.732.694 pessoas].</ref>|| 72(2008)<ref name="ReferenceB"/>|| 105,077,694
|-
| [[Mexico]]||45,671,000(1967)<ref name="ReferenceOxford Atlas"/>|| 86,154,000(1990) <ref name="ReferenceC"/> || 93,008,000(1994)<ref name="collins student atlas"/> || 103,400,165 (2000)||112,322,757(2010)<ref name="INEGI 2010 Census Statistics">{{cite web|url=http://www.inegi.org.mx/inegi/contenidos/espanol/prensa/comunicados/rpcpyv10.asp |title=INEGI 2010 Census Statistics|publisher=inegi.org.mx |accessdate=2010-11-25}}</ref>||76(2008)<ref name="ReferenceB"/>|| 66,651,757
|-
| [[Fiji]] ||476,727 (1966)<ref name="ReferenceOxford Atlas"/>|| 765,000(1990) <ref name="ReferenceC"/> ||771,000 (1994)<ref name="collins student atlas"/> || 844,330 (2001) || 849,000<ref name="unpop"/> (2010)||70 (2008)<ref name="ReferenceB"/>|| 372,273
|-
| [[Nauru]]||6,050(1966)<ref name="ReferenceOxford Atlas"/>||10,000(1990) <ref name="ReferenceC"/> ||N/A (1994)<ref name="collins student atlas"/> ||12,329 (2002)||9,322 (2011)<ref name=CIA>{{cite web|author=Central Intelligence Agency |authorlink=Central Intelligence Agency |publisher=[[The World Factbook]]|title=Nauru |url=https://www.cia.gov/library/publications/the-world-factbook/geos/nr.html |year=2011|accessdate=12 February 2011}}</ref>||N/A (2008)<ref name="ReferenceB"/>|| 3,272
|-
| [[Jamaican]] ||1,876,000 (1967)<ref name="ReferenceOxford Atlas"/>|| 2,420,000 (1990) <ref name="ReferenceC"/> || 2,429,000 (1994)<ref name="collins student atlas"/> || 2,695,867 (2003)|| 2,847,232<ref>https://www.cia.gov/library/publications/the-world-factbook/geos/jm.html</ref>(2010)||74 (2008)<ref name="ReferenceB"/>|| 971,232
|-
| [[Australia]] ||11,540,764 (1964)<ref name="ReferenceOxford Atlas"/>|| 17,086,000 (1990) <ref name="ReferenceC"/> || 17,843,000 (1994)<ref name="collins student atlas"/> || 19,546,792 (2003)||{{formatnum:{{#expr: 22579660 + (86400 / 97) * {{Age in days|2011|4|12}} round 0}}}}<ref>{{cite web|url=http://www.abs.gov.au/ausstats/abs@.nsf/94713ad445ff1425ca25682000192af2/1647509ef7e25faaca2568a900154b63?OpenDocument|title=Population clock|work=[[Australian Bureau of Statistics]] website|publisher=Commonwealth of Australia|accessdate=12 April 2011}} The population estimate shown is automatically calculated daily at 00:00 UTC and is based on data obtained from the population clock on the date shown in the citation.</ref> (2010)||82 (2008)<ref name="ReferenceB"/>|| 11,066,508
|-
| [[Albania]] ||1,965,500(1964)<ref name="ReferenceOxford Atlas"/>|| 3,250,000 (1990) <ref name="ReferenceC"/> || 3,414,000 (1994)<ref name="collins student atlas"/> || 3,510,484 (2002) ||2,986,952 (July 2010 est.)<ref name=cia/><ref>[http://www.google.com/publicdata/explore?ds=n4ff2muj8bh2a_&ctype=l&strail=false&nselm=h&met_y=POP&hl=en&dl=en#ctype=l&strail=false&nselm=h&met_y=POP&fdim_y=scenario:1&scale_y=lin&ind_y=false&rdim=world&idim=country:AL&hl=en&dl=en Population Forecast to 2060 by International Futures hosted by Google Public Data Explorer]</ref> (2010)||78 (2008)<ref name="ReferenceB"/>|| 1,021,452
|-
| [[Poland]]||31,944,000(1967)<ref name="ReferenceOxford Atlas"/>||38,180,000 (1990) <ref name="ReferenceC"/> ||38,554,000 (1994)<ref name="collins student atlas"/> || 38,626,349 (2001)||38,192,000(2010)<ref>{{cite web|url=http://wiadomosci.wp.pl/kat,1347,title,Wzrasta-liczba-ludnosci-Polski,wid,12502858,wiadomosc.html |title=Wzrasta liczba ludności Polski - Wiadomości - WP.PL |publisher=Wiadomosci.wp.pl |date=2010-07-23 |accessdate=2010-07-27}}</ref> ||75 (2008)<ref name="ReferenceB"/>|| 6,248,000
|-
| [[Hungary]]||10,212,000(1967)<ref name="ReferenceOxford Atlas"/>||10,553,000 (1990) <ref name="ReferenceC"/> ||10,261,000 (1994)<ref name="collins student atlas"/> || 10,106,017 (2002)||9,979,000(2010)<ref name="KSH">[http://portal.ksh.hu/pls/ksh/docs/hun/xstadat/xstadat_evkozi/e_wdsd001a.html Hungarian Central Statistical Office]. Retrieved 25 July 2010.</ref>|| 73 (2008)<ref name="ReferenceB"/>|| -142,000
|-
| [[Bulgaria]]||8,226,564(1965)<ref name="ReferenceOxford Atlas"/>||8,980,000 (1990) <ref name="ReferenceC"/> ||8,443,000 (1994)<ref name="collins student atlas"/> ||7,707,495(2000)||7,351,234 (2011)<ref>http://www.nsi.bg/EPDOCS/Census2011pr.pdf</ref> ||73 (2008)<ref name="ReferenceB"/>|| -875,330
|-
| [[UK]] || 55,068,000 (1966)<ref name="ReferenceOxford Atlas"/>|| 57,411,000 (1990) <ref name="ReferenceC"/> || 58,091,000 (1994) <ref name="collins student atlas"/> ||58,789,194 (2002)|| 62,008,048 (2010)<ref>{{cite web |url= http://epp.eurostat.ec.europa.eu/tgm/table.do?tab=table&language=en&pcode=tps00001&tableSelection=1&footnotes=yes&labeling=labels&plugin=1 |title=Total population at 1 January |publisher=Eurostat |date =11 March 2011 |accessdate =29 April 2011}}</ref>||79(2008)<ref name="ReferenceB"/>|| 7,020,048
|-
| [[Ireland]]/Éire ||2,884,002(1966)<ref name="ReferenceOxford Atlas"/>|| 3,503,000(1990) <ref name="ReferenceC"/> || 3,571,000 (1994)<ref name="collins student atlas"/> ||3,840,838 (2000)|| 4,470,700 <ref name="europa1">{{cite web|url=http://www.cso.ie/releasespublications/documents/population/current/popmig.pdf |title=CSO – Population and Migration Estimates April 2010 |format=PDF |date=September 2010 |accessdate=21 September 2010}}</ref> (2010)||78 (2008)<ref name="ReferenceB"/>|| 1,586,698
|-
| The [[PRC]]/China||720,000,000(1967)<ref name="ReferenceOxford Atlas"/>|| 1,139,060,000(1990) <ref name="ReferenceC"/> ||1,208,841,000 (1994)<ref name="collins student atlas"/> || 1,286,975,468 (2004)|| 1,339,724,852(2010)<ref name="Census2010">[http://www.stats.gov.cn/english/newsandcomingevents/t20110428_402722244.htm Communiqué of the National Bureau of Statistics of People's Republic of China on Major Figures of the 2010 Population Census]</ref>||73 (2008)<ref name="ReferenceB"/>|| 619,724,852
|-
| [[Japan]]*** ||98,274,961(1965)<ref name="ReferenceOxford Atlas"/>||123,537,000(1990) <ref name="ReferenceC"/> ||124,961,000 (1994)<ref name="collins student atlas"/> ||127,333,002 (2002)||127,420,000 (2010)<ref>[http://www.stat.go.jp/english/data/jinsui/tsuki/index.htm Official Japan Statistics Bureau estimate]</ref>||82(2008)<ref name="ReferenceB"/>|| 28,123,865
|-
| [[Ryukyu Islands]] (Once occupied by the US)*** ||934,176(1965)<ref name="ReferenceOxford Atlas"/>||—||—||—||—||—||—
|-
| [[India]]#||511,115,000 (1967)<ref name="ReferenceOxford Atlas"/>||843,931,000 (1990) <ref name="ReferenceC"/> ||918,570,000 (1994)<ref name="collins student atlas"/> ||1,028,610,328 (2001) || 1,210,193,422(2011)<ref name="pop">{{cite web|url=http://www.censusindia.gov.in/2011-prov-results/indiaatglance.html|title=Provisional Population Totals - Census 2011|work=|publisher=Indian Census Bureau 2011|accessdate=2011-03-29}}</ref> ||69 (2008)<ref name="ReferenceB"/>|| 699,078,422
|-
|}

;Notes
:<nowiki>*</nowiki> [[Eritrea]] left [[Ethiopia]] in 1991.
:<nowiki>**</nowiki> Split into the nations of [[Sudan]] and [[Southern Sudan]] during 2011.
:<nowiki>***</nowiki> Merged in 1972.
:<nowiki>#</nowiki> Merged in 1975.

==Into the future==
{{main|Projections of population growth}}

According to UN's 2010 revision to its population projections, world population will peak at 10.1bn in 2100 compared to 7bn in 2011.<ref>http://esa.un.org/wpp/Documentation/publications.htm</ref> However, some experts dispute the UN's forecast and have argued that birthrates will fall below replacement rate in the 2020s. According to these forecasters, population growth will be only sustained till the 2040s by rising longevity but will peak below 9bn by 2050.<ref>http://www.project-syndicate.org/commentary/the-end-of-population-growth</ref>

==See also==
{{col-begin}}
{{col-break}}
*[[Baby boom]]
*[[Biological exponential growth]]
*[[Compound annual growth rate]]
*[[Demographic momentum]]
*[[Demographic transition]]
*[[Density dependence]]
*[[Doubling time]]
*[[Exponential growth]]
{{col-break}}
*[[List of countries by population growth rate]]
*[[List of sovereign states and dependent territories by fertility rate]]
*[[Logistic function]] - concept related to logistic model
*[[Natalism]] and [[Antinatalism]]
*[[Population bottleneck]]
*[[Rank mobility index]]
*[[Ronald Fisher]] - who referred to the population growth rate as the ''Malthusian Parameter''
{{col-end}}

==References==
{{reflist|30em}}

==External links==
*[http://esa.un.org/unpd/wpp/index.html World Population Prospects, the 2010 Revision], Website of the United Nations Population Division
*[http://esa.un.org/unpd/ppp/index.html Probabilistic Population Projections, 2nd Revision], Website of the United Nations Population Division
*[http://www.populationpress.org/publication/index.html 2008 Essays on Population Growth] Blue Planet United — Population Press
*[http://www.census.gov/ipc/www/idb/worldpopinfo.php World population growth and trends 1950-2050] US Census
*[http://www.acunu.org/millennium/sof2006.html UN University annual "State of the Future" report, including updates on Millennium Project goals including balancing global population growth & resources]
*[http://news.bbc.co.uk/1/hi/sci/tech/6219922.stm BBC News - Birth rate 'harms poverty goals'] - 08/12/06
*[http://www.carbon-projects.co.uk/earth_clock.htm Visual representation of global population and other statistics]
*Tsirel, S. V. 2004. [http://www.mmsed.narod.ru/articles/artTsirel.ps On the Possible Reasons for the Hyperexponential Growth of the Earth Population]. ''Mathematical Modeling of Social and Economic Dynamics'' / Ed. by M. G. Dmitriev and A. P. Petrov, pp. 367–9. Moscow: Russian State Social University, 2004.
*{{cite web|url=http://www.gapminder.org/videos/what-stops-population-growth/|title=What stops population growth?|last=Rosling|first=Hans|date=25 January 2009|work=Gapminder|accessdate=2009-07-06}}

{{Population}}

[[Category:Demography]]
[[Category:Ecological metrics]]
[[Category:Environmental issues with population]]
[[Category:Population ecology]]

Louis Poinsot

2013-12-31T23:38:56Z

87.115.214.146:

{{lowercase|title=sRGB}}
[[Image:Cie Chart with sRGB gamut by spigget.png|250px|right|thumb|CIE 1931 xy [[chromaticity diagram]] showing the [[gamut]] of the sRGB color space and location of the primaries. The D65 [[white point]] is shown in the center. The Planckian locus is shown with color temperatures labeled in [[kelvin]]. The outer curved boundary is the spectral (or monochromatic) locus, with wavelengths shown in nanometers (labeled in blue). Note that the colors in this displayed file are being specified using sRGB. Areas outside the triangle cannot be accurately colored because they are out of the gamut of sRGB therefore they have been interpreted. Also note how the D65 label is not an ideal 6500-kelvin [[blackbody]] because it is based on atmospheric filtered daylight.]]

[[Image:SRGB gamma.svg|thumb|250px|right|Plot of the sRGB intensities versus sRGB numerical values (red), and this function's slope in log-log space (blue) which is the effective gamma at each point. Below a compressed value of 0.04045 or a linear intensity of 0.00313, the curve is linear so the gamma is 1. Behind the red curve is a dashed black curve showing an exact gamma = 2.2 power law.]]

'''sRGB''' is a standard [[RGB color space]] created cooperatively by [[Hewlett-Packard|HP]] and [[Microsoft]] in 1996 for use on monitors, printers and the [[Internet]].

sRGB uses the [[Rec. 709|ITU-R BT.709]] primaries, the same as are used in studio monitors and [[HDTV]],<ref>{{cite book | title = Digital Video and HDTV: Algorithms and Interfaces | author = Charles A. Poynton | publisher = Morgan Kaufmann | year = 2003 | isbn = 1-55860-792-7 | url = http://books.google.com/books?id=ra1lcAwgvq4C&pg=RA1-PA239&dq=rec+709+smpte }}</ref> and a transfer function ([[gamma correction|gamma curve]]) typical of [[Cathode ray tube|CRTs]]. This specification allowed sRGB to be directly displayed on typical CRT monitors of the time, a factor which greatly aided its acceptance.

Unlike most other [[RGB color space]]s, the sRGB [[Gamma correction|gamma]] cannot be expressed as a single numerical value. The overall gamma is approximately 2.2, consisting of a linear (gamma 1.0) section near black, and a non-linear section elsewhere involving a 2.4 exponent and a gamma (slope of log output versus log input) changing from 1.0 through about 2.3.

==Background==

The sRGB color space has been endorsed by the [[World Wide Web Consortium|W3C]], [[Exif]], [[Intel]], [[Pantone]], [[Corel]], and many other industry players. It is used in proprietary and open [[graphics file format]]s, such as [[Scalable Vector Graphics|SVG]].

The sRGB color space is well specified and is designed to match typical home and office viewing conditions, rather than the darker environment typically used for commercial color matching.

Much software is now designed with the assumption that an 8-bit-per-channel image file placed unchanged onto an 8-bit-per-channel display will appear much as the sRGB specification recommends. [[LCD]]s, [[Digital photography|digital cameras]], printers, and scanners all follow the sRGB standard. Devices which do not naturally follow sRGB (like older CRT monitors did) include compensating circuitry or software so that, in the end, they also obey this standard. For this reason, one can generally assume, in the absence of embedded profiles or any other information, that any 8-bit-per-channel image file or any 8-bit-per-channel image [[Application programming interface|API]] or device interface can be treated as being in the sRGB color space. However, when the correct displaying of an RGB color space is needed, [[color management]] usually must be employed.

==The sRGB gamut==

sRGB defines the chromaticities of the red, green, and blue [[primary color|primaries]], the colors where one of the three channels is nonzero and the other two are zero. The [[gamut]] of chromaticities that can be represented in sRGB is the [[color triangle]] defined by these primaries. As with any [[RGB color space]], for non-negative values of R, G, and B it is not possible to represent colors outside this triangle, which is well inside the range of colors visible to a human.

{| class="wikitable" align="left"
|-
! [[CIE 1931 color space#The CIE xy chromaticity diagram|Chromaticity]]
! Red
! Green
! Blue
! White point
|-
| ''x''
| 0.6400
| 0.3000
| 0.1500
| 0.3127
|-
| ''y''
| 0.3300
| 0.6000
| 0.0600
| 0.3290
|-
| ''Y''
| 0.2126
| 0.7153
| 0.0721
| 1.0000
|}

[[Image:srgbnonlinearity.png|frame|right|104px|On an sRGB display, each solid bar should look as bright as the surrounding striped dither. (Note: must be viewed at original, 100% size)]]

sRGB also defines a nonlinear transformation between the intensity of these primaries and the actual number stored. The curve is similar to the gamma response of a CRT display. It is more important to replicate this curve than the primaries to get correct display of an sRGB image. This nonlinear conversion means that sRGB is a reasonably efficient use of the values in an integer-based image file to display human-discernible light levels.

sRGB is sometimes avoided by high-end print publishing professionals because its color gamut is not big enough, especially in the blue-green colors, to include all the colors that can be reproduced in [[CMYK]] printing.

== Specification of the transformation ==
===The forward transformation (CIE xyY or CIE XYZ to sRGB)===
The first step in the calculation of sRGB tristimulus values from the [[CIE 1931 color space|CIE XYZ]] tristimulus values is a linear transformation, which may be carried out by a matrix multiplication. The numerical values below match those in the official sRGB specification (IEC 61966-2-1:1999) and differ slightly from those in a publication by sRGB's creators.<ref name=orig_pub>{{cite web | url = http://www.w3.org/Graphics/Color/sRGB  | title = A Standard Default Color Space for the Internet – sRGB, Version 1.10 | author = Michael Stokes, Matthew Anderson, Srinivasan Chandrasekar, Ricardo Motta | date = November 5, 1996}}</ref> Note that these linear values are ''not'' the final result.

:<math>
\begin{bmatrix}
R_\mathrm{linear}\\G_\mathrm{linear}\\B_\mathrm{linear}\end{bmatrix}=
\begin{bmatrix}
3.2406&-1.5372&-0.4986\\
-0.9689&1.8758&0.0415\\
0.0557&-0.2040&1.0570
\end{bmatrix}
\begin{bmatrix}
X \\
Y \\
Z \end{bmatrix}
</math>

Note also, that if the [[CIE xyY]] color space values are given (where ''x'', ''y'' are the chromaticity coordinates and ''Y'' is the [[luminance]]), they must first be transformed to CIE XYZ tristimulus values by:

:<math>X = Y x / y,\,</math>
:<math>Z = Y (1- x - y)/y\,</math>

The intermediate parameters <math>R_\mathrm{linear}</math>, <math>G_\mathrm{linear}</math> and <math>B_\mathrm{linear}</math> for in-gamut colors are defined to be in the range [0,1], which means that the initial ''X'', ''Y'', and ''Z'' values need to be similarly scaled (if you start with XYZ values going to 100 or so, divide them by 100 first, or apply the matrix and then scale by a constant factor to the [0,1] range). The linear RGB values are usually clipped to that range, with display white represented as (1,1,1); the corresponding original XYZ values are such that white is [[CIE Standard Illuminant D65|D65]] with unit luminance (''X'',''Y'',''Z'' = 0.9505, 1.0000, 1.0890). Calculations assume the 2° [[standard colorimetric observer]].<ref name=orig_pub/>

sRGB was designed to reflect a typical real-world monitor with a gamma of 2.2, and the following formula transforms the linear values into sRGB. Let <math>C_\mathrm{linear}</math> be <math>R_\mathrm{linear}</math>, <math>G_\mathrm{linear}</math>, or <math>B_\mathrm{linear}</math>, and <math>C_\mathrm{srgb}</math> be <math>R_\mathrm{srgb}</math>, <math>G_\mathrm{srgb}</math> or <math>B_\mathrm{srgb}</math>:

:<math>C_\mathrm{srgb}=\begin{cases}
12.92C_\mathrm{linear}, & C_\mathrm{linear} \le 0.0031308\\
(1+a)C_\mathrm{linear}^{1/2.4}-a, & C_\mathrm{linear} > 0.0031308
\end{cases}
</math>
*where <math>a = 0.055</math>
These gamma-corrected values are in the range 0 to 1. If values in the range 0 to 255 are required, e.g. for video display or 8-bit graphics, the usual technique is to multiply by 255 and round to an integer.

===The reverse transformation===
Again the sRGB component values <math>R_\mathrm{srgb}</math>, <math>G_\mathrm{srgb}</math>, <math>B_\mathrm{srgb}</math> are in the range 0 to 1. (A range of 0 to 255 can simply be divided by 255).
:<math>C_\mathrm{linear}=
\begin{cases}\frac{C_\mathrm{srgb}}{12.92}, & C_\mathrm{srgb}\le0.04045\\
\left(\frac{C_\mathrm{srgb}+a}{1+a}\right)^{2.4}, & C_\mathrm{srgb}>0.04045
\end{cases}
</math>

(where <math>C</math> is <math>R</math>, <math>G</math>, or <math>B</math>). Followed by a matrix multiplication of the linear values to get XYZ:

:<math>
\begin{bmatrix}
X\\Y\\Z\end{bmatrix}=
\begin{bmatrix}
0.4124&0.3576&0.1805\\
0.2126&0.7152&0.0722\\
0.0193&0.1192&0.9502
\end{bmatrix}
\begin{bmatrix}
R_\mathrm{linear}\\
G_\mathrm{linear}\\
B_\mathrm{linear}\end{bmatrix}
</math>

== Theory of the transformation ==

It is often casually stated that the [[gamma correction|decoding gamma]] for sRGB data is 2.2, yet the above transform shows an exponent of 2.4. This is because the net effect of the piecewise decomposition is necessarily a changing instantaneous gamma at each point in the range: it goes from gamma = 1 at zero to a gamma of 2.4 at maximum intensity with a median value being close to 2.2. The transformation was designed to approximate a gamma of about 2.2, but with a linear portion near zero to avoid having an infinite slope at ''K'' = 0, which can cause numerical problems. The continuity condition for the curve <math>C_\mathrm{linear}</math> which is defined above as a piecewise function of <math>C_\mathrm{srgb}</math>, is

:<math>\left(\frac{K_0+a}{1+a}\right)^\gamma=\frac{K_0}{\phi}.</math>

Solving with <math>\gamma = 2.4</math> and the standard value <math>\phi=12.92</math> yields two solutions, <math>K_0</math> ≈ <math>0.0381548</math> or <math>K_0</math> ≈ <math>0.0404482</math>. The IEC 61966-2-1 standard uses the rounded value <math>K_0=0.04045</math>. However, if we impose the condition that the slopes match as well then we must have

:<math>\gamma\left(\frac{K_0+a}{1+a}\right)^{\gamma-1}\left(\frac{1}{1+a}\right)=\frac{1}{\phi}.</math>

We now have two equations. If we take the two unknowns to be <math>K_0</math> and <math>\phi</math> then we can solve to give

:<math>K_0=\frac{a}{\gamma-1},\ \ \ \phi=\frac{(1+a)^\gamma(\gamma-1)^{\gamma-1}}{(a^{\gamma-1})(\gamma^\gamma)}.</math>

Substituting <math>a=0.055</math> and <math>\gamma=2.4</math> gives <math>K_0</math> ≈ <math>0.0392857</math> and <math>\phi</math> ≈ <math>12.9232102</math>, with the corresponding linear-domain threshold at <math>K_0 / \phi</math> ≈ <math>0.00303993</math>. These values, rounded to <math>K_0=0.03928</math>, <math>\phi=12.92321</math>, and <math>K_0/\phi=0.00304</math>, are sometimes used to describe sRGB conversion.<ref>{{cite book | title = Colour Engineering: Achieving Device Independent Colour | author = Phil Green and Lindsay W. MacDonald | publisher = John Wiley and Sons| url = http://books.google.com/books?id=tn09voxr6agC&pg=PA350&dq=srgb+0.03928+date:0-2002 | year = 2002 | isbn = 0-471-48688-4 }}</ref> Publications by sRGB's creators<ref name=orig_pub/> rounded to <math>K_0=0.03928</math> and <math>\phi=12.92</math>, resulting in a small discontinuity in the curve. Some authors adopted these values in spite of the discontinuity.<ref>{{cite book | title = Acquisition and Reproduction of Color Images: Colorimetric and Multispectral Approaches | author = Jon Y. Hardeberg | url = http://books.google.com/books?id=e2umTIdI2u4C&pg=PA40&dq=srgb+0.00304+date:0-2002 | publisher = Universal-Publishers.com | year = 2001 | isbn = 1-58112-135-0 }}</ref> For the standard, the rounded value <math>\phi=12.92</math> was kept and the <math>K_0</math> value was recomputed to make the resulting curve continuous, as described above, resulting in a slope discontinuity from 12.92 below the intersection to 12.70 above.

== Viewing environment ==

{| class="wikitable"
|-
! Parameter
! Value
|-
| Luminance level
| 80 cd/m2
|-
| Illuminant white point
| ''x'' = 0.3127, ''y'' = 0.3291 (D65)
|-
| Image surround reflectance
| 20% (~medium gray)
|-
| Encoding ambient illuminance level
| 64 lux
|-
| Encoding ambient white point
| ''x'' = 0.3457, ''y'' = 0.3585 (D50)
|-
| Encoding viewing flare
| 1.0%
|-
| Typical ambient illuminance level
| 200 lux
|-
| Typical ambient white point
| ''x'' = 0.3457, ''y'' = 0.3585 (D50)
|-
| Typical viewing flare
| 5.0%
|}
The sRGB specification assumes a dimly lit encoding (creation) environment with an ambient correlated color temperature (CCT) of 5000 K. It is interesting to note that this differs from the CCT of the illuminant (D65). Using D50 for both would have made the white point of most photographic paper appear excessively blue.<ref>{{cite book|url=http://books.google.com/books?id=jFl-3v9sSEUC&pg=PA121&lpg=PA121&dq=%22My+suggestion+is+to+calibrate+to+a+D65+white+point.%22|first=Andrew|last=Rodney|publisher=Focal Press|year=2005|isbn=978-0-240-80649-5|title=Color Management for Photographers|page=121|quote=[http://www.xrite.com/product_overview.aspx?ID=592&Action=Support&SupportID=3349 Why Calibrate Monitor to D65 When Light Booth is D50]}}</ref> The other parameters, such as the luminance level, are representative of a typical CRT monitor.

For optimal results, the [[International Color Consortium|ICC]] recommends using the encoding viewing environment (i.e., dim, diffuse lighting) rather than the less-stringent typical viewing environment.<ref name=orig_pub/>

==Usage==
{{Refimprove section|date=July 2010}}
Due to the standardization of sRGB on the Internet, on computers, and on printers, many low- to medium-end consumer [[digital camera]]s and [[Image scanner|scanners]] use sRGB as the [[Default (computer science)|default]] (or only available) working color space. As the sRGB gamut meets or exceeds the gamut of a low-end [[inkjet printer]], an sRGB image is often regarded as satisfactory for home use. However, consumer-level [[Charge-coupled device|CCDs]] are typically uncalibrated, meaning that even though the image is being labeled as sRGB, one can't conclude that the image is color-accurate sRGB.

If the color space of an image is unknown and it is an 8- to 16-bit image format, assuming it is in the sRGB color space is a safe choice. This allows a program to identify a color space for all images, which may be much easier and more reliable than trying to track the "unknown" color space. An [[ICC profile]] may be used; the ICC distributes three such profiles:<ref>[http://color.org/srgbprofiles.xalter sRGB profiles], ICC</ref> a profile conforming to version 4 of the ICC specification, which they recommend, and two profiles conforming to version 2, which is still commonly used.

Images intended for professional printing via a fully color-managed workflow, e.g. [[prepress]] output, sometimes use another color space such as [[Adobe RGB color space|Adobe RGB (1998)]], which allows for a wider gamut. If such images are to be used on the Internet they may be converted to sRGB using [[color management]] tools that are usually included with software that works in these other color spaces.

The two dominant programming interfaces for 3D graphics, [[OpenGL]] and [[Microsoft Direct3D|Direct3D]], have both incorporated half part support for the sRGB color space by using sRGB's gamma curve.
OpenGL supports the [[Texture mapping|textures]] with sRGB gamma encoded color components (first introduced with [http://www.opengl.org/registry/specs/EXT/texture_sRGB.txt EXT_texture_sRGB extension], added to the core in OpenGL 2.1) and rendering into sRGB gamma encoded [[framebuffer]]s (first introduced with [http://www.opengl.org/registry/specs/EXT/framebuffer_sRGB.txt EXT_framebuffer_sRGB extension], added to the core in OpenGL 3.0). Direct3D supports sRGB gamma textures and rendering into sRGB gamma surfaces starting with DirectX 9. Correct [[mipmap]]ping and [[interpolation]] of sRGB gamma textures has direct hardware support in texturing units of most modern [[GPU]]s (for example nVidia GeForce 8 performs conversion from 8-bit texture to linear values before interpolating those values), and do not have any performance penalty.<ref>GPU Gems 3, section 24.4.1, http://http.developer.nvidia.com/GPUGems3/gpugems3_ch24.html</ref>

==See also==
*[[RGB color space]]
*[[scRGB]]

==References==

<references/>

===Standards===

* IEC 61966-2-1:1999 is the official specification of sRGB. It provides viewing environment, encoding, and [[colorimetric]] details.
* Amendment A1:2003 to IEC 61966-2-1:1999 describes an analogous sYCC encoding for [[YCbCr]] color spaces, an extended-[[gamut]] RGB encoding, and a [[CIELAB]] transformation.
* sRGB on [http://www.color.org/chardata/rgb/srgb.xalter www.color.org]
* The fourth working draft of IEC 61966-2-1 is available online, but is not the complete standard. It can be downloaded from [http://www2.units.it/ipl/students_area/imm2/files/Colore1/sRGB.pdf www2.units.it].

==External links==
* [http://www.color.org/ International Color Consortium]
* [http://web.archive.org/web/20030124233043/http://www.srgb.com/ Archive copy of http://www.srgb.com], now unavailable, containing much information on the design, principles and use of sRGB
* [http://www.w3.org/Graphics/Color/sRGB A Standard Default Color Space for the Internet – sRGB] at [[World Wide Web Consortium|w3.org]]
* [http://oss.sgi.com/projects/ogl-sample/registry/EXT/texture_sRGB.txt OpenGL extension for sRGB gamma textures] at [[Silicon Graphics International|sgi.com]]
* [http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html Conversion matrices for RGB vs. XYZ conversion]
* [http://ninedegreesbelow.com/photography/srgb-profile-comparison.html Will the Real sRGB Profile Please Stand Up?]

{{Color space}}

[[Category:Color space]]
[[Category:Film and video technology]]

Stalagmometric method

2013-10-04T18:41:47Z

87.115.124.8: /* Stalagmometer */

{{Noref|date=August 2009}}
[[Image:Hesse normal form.png|thumb|Drawing of the normal and the distance calculated with the Hesse normal form]]
The '''Hesse normal form''' named after [[Otto Hesse]], is an equation used in [[analytic geometry]], and describes a line in <math>\mathbb{R}^2</math> or a plane in Euclidean space <math>\mathbb{R}^3</math> or a hyperplane in higher dimensions. It is primarily used for calculating distances, and is written in vector notation as

:<math>\vec r \cdot \vec n_0 - d = 0.\,</math>

This equation is satisfied by all points ''P'' described by the location vector <math>\vec r</math>, which lie precisely in the plane ''E'' (or in 2D, on the line ''g'').

The vector <math>\vec n_0</math> represents the unit normal vector of ''E'' or ''g'', that points from the origin of the coordinate system to the plane (or line, in 2D). The distance <math>d \ge 0</math> is the distance from the origin to the plane (or line). The dot <math>\cdot</math> indicates the scalar product or dot product.

== Derivation/Calculation from the normal form ==

Note: For simplicity, the following derivation discusses the 3D case. However, it is also applicable in 2D.

In the normal form,

:<math>(\vec r -\vec a)\cdot \vec n = 0\,</math>

a plane is given by a normal vector <math>\vec n</math> as well as an arbitrary position vector <math>\vec a</math> of a point <math>A \in E</math>. The direction of <math>\vec n</math> is chosen to satisfy the following inequality

:<math>\vec a\cdot \vec n \geq 0\,</math>

By dividing the normal vector <math>\vec n</math> by its [[Euclidean_vector#Length_of_a_vector|Magnitude]] <math>| \vec n |</math>, we obtain the unit (or normalized) normal vector

:<math>\vec n_0 = {{\vec n} \over {| \vec n |}}\,</math>

and the above equation can be rewritten as

:<math>(\vec r -\vec a)\cdot \vec n_0 = 0.\,</math>

Substituting

:<math>d = \vec a\cdot \vec n_0 \geq 0\,</math>

we obtain the Hesse normal form

:<math>\vec r \cdot \vec n_0 - d = 0.\,</math>

<center>[[File:Ebene Hessesche Normalform.PNG]]</center>

In this diagram, ''d'' is the distance from the origin. Because <math>\vec r \cdot \vec n_0 = d</math> holds for every point in the plane, it is also true at point ''Q'' (the point where the vector from the origin meets the plane E), with <math>\vec r = \vec r_s</math>, per the definition of the [[Scalar product]]

:<math>d = \vec r_s \cdot \vec n_0 = |\vec r_s| \cdot |\vec n_0| \cdot \cos(0^\circ) = |\vec r_s| \cdot 1 = |\vec r_s|.\,</math>

The magnitude <math>|\vec r_s|</math> of <math>{\vec r_s}</math> is the shortest distance from the origin to the plane.

[[Category:Analytic geometry]]

Roll's critique

2013-09-06T10:18:16Z

87.115.0.90:

'''Swap regret''' is a concept from [[game theory]]. It is a generalization of regret in a repeated, ''n''-decision game.

==Definition==
A player's ''swap-regret'' is defined to be the following:

: <math>\mbox{swap-regret}=
\sum_{i=1}^n \max_{j \leq n}\frac{1}{T}\sum_{t=1}^T x^t_i \cdot (p^t_j-p^t_i).\,</math>

Intuitively, it is how much a player could improve by switching each occurrence of decision ''i'' to the best decision ''j'' possible in hindsight. The swap regret is always nonnegative.

Swap regret is useful for computing [[correlated equilibrium|correlated equilibria]].

==References==
{{unreferenced|date=July 2008}}

[[Category:Game theory]]

{{gametheory-stub}}

Conditional quantum entropy

2012-10-06T08:38:35Z

87.115.64.73: typo S(A) changed to S(B)

{{refimprove|date=August 2012}}
A '''decagonal number''' is a [[figurate number]] that represents a [[decagon]]. The ''n''-th decagonal number is given by the formula
: <math>D_n = 4n^2 - 3n.</math>
The first few decagonal numbers are:
: [[0 (number)|0]], [[1 (number)|1]], [[10 (number)|10]], [[27 (number)|27]], [[52 (number)|52]], [[85 (number)|85]], [[126 (number)|126]], [[175 (number)|175]], 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, [[4000 (number)|4000]], 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326 {{OEIS|id=A001107}}

The ''n''-th decagonal number can also be calculated by adding the square of ''n'' to thrice the (''n''—1)-th [[pronic number]] or, to put it algebraically, as
: <math>D_n = n^2 + 3(n^2 - n).</math>

== Properties ==

* Decagonal numbers consistently alternate [[Even and odd numbers#Parity in mathematics|parity]].

[[Category:Figurate numbers]]

{{Classes of natural numbers |state=collapsed}}
{{num-stub}}