formulasearchengine - User contributions [en]

Biclustering

2014-12-15T01:33:03Z

50.0.90.168: /* Development */ grammar fix

Hello! I'm Turkish female :D. I really love Billiards! Have a look at my blog; [http://galeria.Asiscrapki.com.pl/displayimage.php?pid=30& FIFA 15 coin hack]

Box plot

2014-12-12T09:12:43Z

50.0.90.168: style

Roberto is the name 1 love to be known with although it can not the name on my birth certificate. My [http://Search.About.com/?q=friends friends] say it's not wonderful for me but the thing that I love doing is definitely to drive but Concerning been taking on unique things lately. South Carolina is where my brand new home is. I used as a way to be [http://Www.Dict.cc/englisch-deutsch/unemployed.html unemployed] but at this time I am a cashier but the promotion never comes. I've been working on individual website for some point in time now. Check it out here: http://prometeu.net 

my page ... [http://prometeu.net clash of clans unlimited gems hack]

Noncommutative topology

2014-08-23T06:05:40Z

50.0.193.12: Matilde Marcolli link

51 yrs old Boat Designer and Repairer Rusty Hyslop from Milton, really likes guitar, property developers in singapore and church/church activities. Is encouraged how huge the world is after going to Maya Site of Copan. Also visit my weblog - [http://drive.ilovetheory.com/content/singapore-property-itemizing-0 property developers in singapore list]

Field with one element

2014-08-23T05:50:45Z

50.0.193.12: Add some links

== New Balance Shoes Usa Gasprijzen kan Skyhigh deze dagen ==

Gasprijzen kan Skyhigh deze dagen, en het openbaar vervoer staat altijd het risico van te laat of slecht functioneert. Je hoeft alleen maar geld om het te starten, de perfecte locatie, Constructieve wat [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=70 New Balance Shoes Usa] je hoeft te isit onthouden is erg lastig! Veel van degenen die beweren dat cannabis moeten worden gekweekt illegaal lichaam en geest, een verschil van marihuana beleid landelijk.. Deze app stelt u [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=53 New Balance Sale Nl] in staat om alle gegevens die je nodig [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=84 New Balance Sale] zou hebben bij de opsomming van een onroerend goed in Amerika op te nemen. Het was ongeveer 8 jaar voordat iemand anders begon een vergelijkbare site op dit gebied .. "Dat God in ons woont, dat deze organen zijn niet de onze." Ik weet niet zeker wat te schijnsel van dit, anders dan misschien wat ik zei over het vorige citaat ik gaf. We zullen een reële marktwaarde te betalen en het bedrijf toelaten om te blijven doen [http://www.gasgaugedirect.com/descriptions/library/pear.asp?a=89 New Balance Heren] wat zij heeft gedaan.. Ik zou denken dat onze kinderen verdienen niets minder .. Het kan geen kwaad, en alleen maar helpen. Brigham vertelde de kinderen dat ze niet betrokken was, dan eiste ze in de auto, zodat zij ze naar Dr kon brengen Dit is een grote onder ogen behandeling. Dus het is makkelijk te krijgen in AAU, maar hun klassen zijn echte college kunstlessen, dus je moet bereid zijn om het werk te doen, zoals op elk kunstacademie.. Ik ervan overtuigd dat een enorme bron van verwijzingen wacht op hen met Facebook strategisch op te zetten fan pagina's die zijn verbonden door eerdere klanten, zelfs als dat betekent dat het betalen van hen om het toe te voegen aan hun profiel. Nog steeds proberen om te zien als meer informatie als je kunt aan die boom.. Smajdor heeft geschreven over en betrokken geweest bij een aantal projecten te bespreken en het bevorderen van toekomstige reproductieve technologieën, zoals het gebruik van kunstmatige gameten. Zoals ik staarde uit het raam van de bus, ik kon niet helpen, maar vraag me af hoe er kon een vlinder heiligdom en natuurgebied op slechts een paar uur afstand ... St George is een cijfer dat veel van de wereld rond kan verzamelen in een geest van eenheid, vieren samen. De volgende logische stap in de evolutie van de Gilder Technology Report (door Gilder Publishing, LLC gepubliceerd in samenwerking met Forbes Inc, 19962007), de Gilder telecosmos Forum, is een online community waar honderden investeerders, ondernemers, ingenieurs en geld managers, waaronder George Gilder, Charlie Burger, en voormalig GTR analisten en redacteurs, verzamelen dagelijks om beleggingsadvies en debat technologie, beleggen, economie, politiek en financiën te delen..<ul>

<li>[http://www.qwol.com.cn/thread-27415-1-1.shtml http://www.qwol.com.cn/thread-27415-1-1.shtml]</li>

<li>[http://www.phyll.com.cn/forum.php?mod=viewthread&tid=199448&fromuid=19496 http://www.phyll.com.cn/forum.php?mod=viewthread&tid=199448&fromuid=19496]</li>

<li>[http://yesbet.org/forum.php?mod=viewthread&tid=494386 http://yesbet.org/forum.php?mod=viewthread&tid=494386]</li>

<li>[http://website.242000.com/news/html/?24248.html http://website.242000.com/news/html/?24248.html]</li>

<li>[http://www.observatoiredesreligions.fr/spip.php?article11 http://www.observatoiredesreligions.fr/spip.php?article11]</li>

</ul>

== New Balance Belgie ondanks een partnership met Microsoft ==

Ik ben op zoek op het hosten van een kleine website met enkele familiefoto's op. In de algemene wedstrijd (inclu. Om ervoor te zorgen [http://newbalancebelgie.presdetilff.be/ New Balance Belgie] dat we doen het best mogelijke werk wat we kunnen, ik ben enthousiast om zoveel mogelijk feedback te. Van plan om [http://poloralphlaurengent.presdetilff.be/ Polo Ralph Lauren Antwerpen] te lezen lezen nu ik heb het gelezen. Deze Licentieovereenkomst doet geen afbreuk aan de wettelijke rechten van enige partij die als een consumer.10. Ik probeerde mijn SQUIDOO pagina gebruiken om bij mij en mijn boeken te tonen. Hit het podium op 1:00. De collectie, die Jones 'populair Green Apple, Root Beer en StrawberryLime smaken omvat wordt verkocht als een sixpack dat een van elke fles gemaakt, waaronder exclamatory juweeltjes zoals bevat: "Nation eist Tax Dollars Only Be Wasted op Materiaal Dat is geweldig", "War op String Mag niet te winnen zijn, zegt Kat generaal "en het onheilspellende" Werk Vriend ongeluk Becomes Real Friend "... Deze fysieke onvolkomenheden don overstuur iedereen die hen heeft, natuurlijk. Yahoo sleept nog steeds Google op grote schaal in de online zoekmarkt, ondanks een partnership met Microsoft (MSFT, Fortune 500) .. In geschroefd nieuws. Of The World "TV Newswire NBC. Daarnaast kunnen anderen geplaatst vraag beantwoorden als u niet [http://nikebelgium.presdetilff.be/ Nike Brussel] beschikbaar bent. Dus im niet precies een appel hater als dat is wat je denken. Ik denk dat het de juiste beslissing. Stoops en zijn assistenten kunnen worden uitgeschakeld om South Bend en OU kunt kijken naar de toekomst en krijgt de nieuwe coach die we nodig hebben .. [http://nikeairmaxdames.ecf3c2000.nl/ Nike Air Max 1 Dames] Of u wilt de gebeurtenis te beschrijven als discontinue verandering, radicale innovatie, verstoring van het systeem, of een andere even indrukwekkende combinatie die titel van een bestseller boek voor het bedrijfsleven kan helpen, het was een ongeluk of een dwaasheid. Als u extra informatie te vinden, ga terug naar de pagina previos en kies een andere bedrijfsvermelding.. Ibuprofen wordt gemetaboliseerd door de lever ook .. En de Lumix lenzen, vooral de 20mm zijn geweldig. Hij was op weg naar het Caribisch gebied, wanhopig feestelijk in zijn rode vakantie overhemd, versierd met figuren van tropische vogels. Natuurlijk maken webben terug in 99, dat is ongeveer alles wat je echt nodig om een te maken voor. Nieuwbouw Phoenix Arizona is gewoon iets dat past bij uw smaak en de status .. Wat is belangrijker dan de openbare veiligheid? Hier is een foto van de bluffs in 1932. Deze persoon kan mensen helpen hun prijzen te verlagen op vliegtickets, hotels en autoverhuurbedrijven, door ze allemaal in een enkele transactie. Hij bevestigde dat op 6 maart bracht hij zeven hourson de Spaanse kant van de grens controle van de paspoorten.<ul>

<li>[http://arcade168.com/activity/p/180374/ http://arcade168.com/activity/p/180374/]</li>

<li>[http://www.jvbbs.com/forum.php?mod=viewthread&tid=357124&fromuid=36719 http://www.jvbbs.com/forum.php?mod=viewthread&tid=357124&fromuid=36719]</li>

<li>[http://elec.newroomschat.com/spip.php?article30/ http://elec.newroomschat.com/spip.php?article30/]</li>

<li>[http://www.yqxysd.com/forum.php?mod=viewthread&tid=69944&fromuid=6352 http://www.yqxysd.com/forum.php?mod=viewthread&tid=69944&fromuid=6352]</li>

<li>[http://0563d.com/forum.php?mod=viewthread&tid=104281 http://0563d.com/forum.php?mod=viewthread&tid=104281]</li>

</ul>

== Timberland Schoenen Zie gerelateerde ==

Het was niet leuk .. Irving en Dick Shawn respectievelijk. Alle eer gaat naar de Staat van Utah. Wanneer uw kind tekenen van om het potje te gebruiken, moet hij of zij worden geleid naar de badkamer en aangemoedigd om te zitten op het potje stoel. En een of andere manier, ik moet deze tijd zinvol te maken. In plaats daarvan, de vragen meer omringen hoe hij zal slagen in de dekking op de NFL-niveau en vooral zo als een inside linebacker.. Het zal een tijdje duren om schoon te maken "Hier zijn enkele tips voor het maken van dat uw terrein te herstellen wanneer de zon terugkeert:. 1 Het is evident Ms Dus is het logisch dat de media nu zal wenden tot een verhaal van" is 3D printen alle dat zijn gebarsten te zijn? 'Brand uw eigen papieren tijger.. Ground vlas maaltijd, 2 kopjes water, 3 eetlepels. Het is als het vergelijken van katholieken protestanten. Laat ze niet zuigen het plezier van uw ervaring in sociale netwerken. Wedden dat u een aantal bizarre dingen hebben gezien op Craigslist. Als het gaat om een ouder, kan ik je vertellen dat ik niet veel anders dan iemand anders. Hij vond het Verdrag van Versailles vernederende, met name de demilitarisering van het Rijnland en de bepaling dat Duitsland de verantwoordelijkheid voor het starten van de oorlog te accepteren ... (Zie gerelateerde: "opslag, biobrandstoffen Lead $ 156 Miljoen in Energy Research Grants."). U wilt maken het zo makkelijk mogelijk voor mensen om de inhoud die ze zoeken op uw site .. Nog voordat het kind begrijpt de betekenis van deze woorden leert zij ze zijn belangrijk, omdat mama en papa gebruiken ze veel te vinden en ze hebben zulke aardige uitdrukkingen op hun gezichten als ze zeggen deze woorden.. 11 gevallen hebben vaak het rapport van de september Als u wilt gaan naar Birmingham, moet je betalen. "Passagiers zeiden dat ze werden gestuurd uit het vliegtuig om pinautomaten in Wenen om geld in te zamelen. Wat we hopen is [http://timberlandbelgie.presdetilff.be/ Timberland Schoenen] dat we aangehaald zou uiteindelijk vinden een omgeving die niet alleen bewoonbaar maar heeft ook de juiste chemie om de organische dat we denken dat moet er zijn behouden.. Het kopen van een volledig seizoen van een show kunt u terug van $ 20 tot $ 50, net als een gewone DVD box set .. De kamer mag niet te koud zijn en je [http://mbtschoenen.ecf3c2000.nl/ Mbt Schoenen] kunt dragen zwaarder pyjama als dat nodig is. Als u niet meer wilt weten, ga door .. 4. De super [http://louisvuittonbelgie.presdetilff.be/ Louis Vuitton Antwerpen] zachte materiaal voelt aan [http://nikerosherundames.ecf3c2000.nl/ Nike Roshe Run Dames] als zijde en wraps je benen als een tweede huid. Donker vlees bevat bijna twee keer zoveel vet als wit vlees ..<ul>

<li>[http://cosplaysavannah.com/activity/p/282163/ http://cosplaysavannah.com/activity/p/282163/]</li>

<li>[http://pppppirn.com/news/html/?283898.html http://pppppirn.com/news/html/?283898.html]</li>

<li>[http://enseignement-lsf.com/spip.php?article64#forum18663805 http://enseignement-lsf.com/spip.php?article64#forum18663805]</li>

<li>[http://metransparent.nfrance.com/~k1001/spip.php?article5808&lang=ar&id_forum=6858/ http://metransparent.nfrance.com/~k1001/spip.php?article5808&lang=ar&id_forum=6858/]</li>

<li>[http://www.joinspire.com/node/73#comment-319626 http://www.joinspire.com/node/73#comment-319626]</li>

</ul>

== Michael Kors Handtassen volgens Wes Henson ==

Cursussen zijn volledig webbased waardoor meerdere mogelijkheden tot interactie met docenten en klasgenoten .. Ik dacht dat het was leuk met het kind drager zoals bij de zuigelingenvoeding vervoerders kunt u gemakkelijk de drager en klik deze in een wandelwagen of gewoon de baby te dragen aan . Als gevolg van mijn geest moet compenseren en doorgaan. Nu Wat moet ik doen De "verdedigbaar Swag" How to Realistisch Schat uw markt PotentialThere is een fundamentele fout in het denkproces van de vele ondernemers die er in het midden van het bouwen van hun bedrijf en op zoek naar angel of venture capitalist investering: simpel gezegd, hun . Ik ben opgevoed door ouders die geloofden dat elke burger een plicht had om op te komen voor rechtvaardigheid en een betere wereld. Willy herinnert zich een peuter, zitten rond een vuur en luisteren naar zijn vader spelen de fluit. Hij zei Takota had ook botten gebroken en bloeden op de hersenen. Tarieven voor inschrijfgelden variëren van $ 0 $ 225 en maandelijkse kosten over het algemeen variëren van $ 30 $ 49 per persoon. Het beschrijven van zijn werk, zegt hij, naar [http://michaelkorsbelgie.presdetilff.be/ Michael Kors Handtassen] de einden der aarde, en dan gaan we onder water. Giet suiker mengsel in zes 1 cup capaciteit, ovenschaaltjes. Dit is te wijten aan de vooruitgang van ijsvissen technologieën. Maar het fundamentele probleem is dat noch kunnen ze samen wonen, zeer vreedzaam noch kunnen zij gelukkig blijven zonder elkaar.. Zoals elke buurtbewoner u contact opneemt met zal u verzekeren met trots en opluchting, de drug oorlogen zijn geschiedenis, niet een huidige realiteit. Staten hadden verplichte wetten die nodig zijn artsen om gevallen van verdachte kindermisbruik rapporteren uitgevaardigd. Wat mij opvalt aan dit hele berichten is dat je meer bezorgd over je "recht" om uw kind meer dan je bent over het verliezen van de voogdij over uw kind een pak [http://vibramschoenen.ecf3c2000.nl/ Vibram Nederland] slaag. En dat is het punt, volgens Wes Henson, predikant bij de Walnut Street Baptist Church in het zuiden van Illinois stad Carbondale.. 125 ml (1/2 kopje) buttermilkGrease de zijkant en bodem van een diepe 23cm [http://newbalancebelgie.presdetilff.be/ New Balance Brugge] of 24cm diameter (binnenkant van de bovenste meting) ronde taartvorm. Maar het is wat er gebeurt als de lichten uitgaan dat de munt echt interessant maakt. B) flirtende en onbetrouwbaar. Maar president Bill Clinton was meer geneigd om last-minute wijzigingen aan zijn proza te maken, en hij was een meester in [http://mbtschoenen.ecf3c2000.nl/ Mbt Schoenen] improvisatie was, volgens die dicht bij hem .. Bijvoorbeeld, als u rijdt 200.000 bezoeken voor uw merk, je kon de organische besparingen showcase door het presenteren van organisch verkeer gem. (Con Ed is met behulp van $ 136.000.000 in de federale stimulans geld voor dat doel.) Zou niet alleen nieuwe technologie energie systemen beter bestand zijn tegen stormen, maar het zou ook hen efficiënter en beter in staat om energie te integreren uit hernieuwbare bronnen, zoals het maken .<ul>

<li>[http://jz.791.com/news/html/?548619.html http://jz.791.com/news/html/?548619.html]</li>

<li>[http://www.k2220.com/#?胁??????????/read.php?tid=6668 http://www.k2220.com/#?胁??????????/read.php?tid=6668]</li>

<li>[http://www.gha-systemprofile.de/index.php?site=gallery&picID=71 http://www.gha-systemprofile.de/index.php?site=gallery&picID=71]</li>

<li>[http://www.dailyqr.com/blog_entry.php?user=1187874&blogentry_id=18080005 http://www.dailyqr.com/blog_entry.php?user=1187874&blogentry_id=18080005]</li>

<li>[http://ciarcr.org/spip.php?article310/ http://ciarcr.org/spip.php?article310/]</li>

</ul>

Turbulence

2014-02-03T08:10:18Z

50.0.121.102: /* Further reading */ add McDonough lecture notes

The '''heat index''' ('''HI''') or '''humiture''' or '''humidex''' (not to be confused with the [[humidex|Canadian humidex]]) is an index that combines [[air]] [[temperature]] and [[relative humidity]] in an attempt to determine the human-perceived equivalent temperature—how hot it feels. The result is also known as the "felt air temperature" or "[[apparent temperature]]". For example, when the temperature is {{j|90 °F}} {{j|(32 °C)}} with very high humidity, the heat index can be about {{j|105 °F (41 °C).}}

The human body normally cools itself by [[perspiration]], or sweating. [[Heat]] is removed from the body by [[evaporation]] of that sweat. However, relative humidity reduces the evaporation rate because the higher vapor content of the surrounding air does not allow the maximum amount of evaporation from the body to occur. This results in a lower rate of heat removal from the body, hence the sensation of being overheated. This effect is subjective; its measurement has been based on subjective descriptions of how hot subjects feel for a given temperature and humidity. This results in a heat index that relates one combination of temperature and humidity to another one at higher temperature and lower humidity.

== History ==
The heat index was developed in 1978 by [[George Winterling]] as the "humiture" and was adopted by the USA's [[National Weather Service]] a year later.<ref>[http://www.news4jax.com/news/19262258/detail.html George Winterling: A Lifelong Passion For Weather] [[WJXT]], April 23, 2009</ref> It is derived from work carried out by Robert G. Steadman.<ref name=SteadmanI>The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science, R. G. Steadman, Journal of Applied Meteorology, July 1979, Vol 18 No7, pp861-873 {{doi|10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2}} [http://journals.ametsoc.org/doi/pdf/10.1175/1520-0450%281979%29018%3C0861%3ATAOSPI%3E2.0.CO%3B2]</ref><ref>The Assessment of Sultriness. Part II: Effects of Wind, Extra Radiation and Barometric Pressure on Apparent Temperature Journal of Applied Meteorology, R. G. Steadman, July 1979, Vol 18 No7, pp874-885</ref> Like the [[wind chill]] index, the heat index contains assumptions about the human body mass and height, clothing, amount of physical activity, thickness of blood, sunlight and ultraviolet radiation exposure, and the wind speed. Significant deviations from these will result in heat index values which do not accurately reflect the perceived temperature.<ref>[http://www.slate.com/id/2123486/fr/rss/ How do they figure the heat index? - By Daniel Engber - Slate Magazine]</ref>

In [[Canada]], the similar [[humidex]] is used in place of the heat index. While both the humidex and the heat index are calculated using dew point, the humidex uses a dew point of {{convert|45|°F|°C}} as a base, whereas the heat index uses a dew point base of {{convert|57|°F|°C}}. Further, the heat index uses heat balance equations which account for many variables other than vapor pressure, which is used exclusively in the humidex calculation. A joint committee formed by the United States and Canada to resolve differences has since been disbanded.

The heat index is defined so as to equal the actual air temperature when the [[partial pressure]] of [[water vapor]] is equal to a baseline value of 1.6 [[Pascal (unit)|kPa]]. At [[standard atmospheric pressure]] (101.325 kPa), this baseline corresponds to a [[dew point]] of {{j|14 °C}} {{j|(57 °F)}} and a [[mixing ratio]] of 0.01 (10 g of water vapor per kilogram of dry air).<ref name=SteadmanI/> This corresponds to an air temperature of {{j|25 °C}} {{j|(77 °F)}} and relative humidity of 50% in the sea-level [[psychrometric chart]].

At high temperatures, the level of ''relative'' humidity needed to make the heat index higher, than the actual temperature, is lower than at cooler temperatures. For example, at approximately {{j|27 °C}} {{j|(80 °F)}}, the heat index will agree with the actual temperature if the relative humidity is 45%, but at about {{j|43 °C (110 °F),}} any relative-humidity reading above 17% will make the heat index higher than {{j|43 °C}}.

The formula described is considered valid only if the actual temperature is above {{j|27 °C}} {{j|(80 °F)}}, dew point temperatures greater than {{j|12 °C (54 °F),}} and relative humidities higher than 40%.<ref>[http://www.campbellsci.com/documents/technical-papers/heatindx.pdf Heat Index Campbell Scientific Inc.] (PDF file), CampbellSci.com.</ref> The heat index and humidex figures are based on temperature measurements taken in the shade and not the sun, so extra care must be taken while in the sun. The heat index also does not factor in the effects of wind, which lowers the apparent temperature.

Sometimes the heat index and the [[wind chill]] are denoted collectively by the single term "apparent temperature", "relative outdoor temperature", or "feels like".

==Meteorological considerations==

Outdoors in open conditions, as the relative humidity increases, first haze and ultimately a thicker cloud cover develops, reducing the amount of direct sunlight reaching the surface. Thus, there is an inverse relationship between maximum potential temperature and maximum potential relative humidity. Because of this factor, it was once believed that the highest heat index reading actually attainable anywhere on Earth is approximately {{convert|71|°C|°F|abbr=on}}. However, in [[Dhahran]], [[Saudi Arabia]] on July 8, 2003, the [[dew point]] was {{convert|35|°C|°F|abbr=on}} while the temperature was {{convert|42|°C|°F|abbr=on}}, resulting in a heat index of {{convert|78|°C|°F|abbr=on}}. This is comparable to the temperatures that are recommended to kill bacteria in many meat products, and it is common in a [[sauna]]. High heat-index values also indicate that intense thunderstorms are approaching, depending on the intensity of the cold front, causing more violent storms.<ref>
{{cite book
| last = Burt | first = Christopher C.
| authorlink =
| title = Extreme Weather: A Guide & Record Book
| url = http://books.google.com/books?id=NuP7ATq9nWgC&dq=extreme+weather+a+guide+%26+record+book&printsec=frontcover#PPA28,M1
| publisher = W. W. Norton & Company
| year = 2004 | pages = 28
| doi =
| isbn = 0-393-32658-6 }}</ref>

==Table of Heat Index values==
This table is from the U.S. [[National Oceanic and Atmospheric Administration]].
{{HeatTable}}

To find the Heat Index temperature, look at the Heat Index chart above. For example, if the air temperature is 96°F and the relative humidity is 65%, the heat index—how hot it feels—is 121°F.

This table is an approximation of the Heat Index, using the formula and first set of constants below, converted to Celsius.
{{HeatTableC}}

==Effects of the heat index (shade values)==
{| class="wikitable"
|-
! Celsius || Fahrenheit || Notes
|-
| 27–32 °C || 80–90 °F
| Caution: fatigue is possible with prolonged exposure and activity. Continuing activity could result in [[heat cramp]]s.
|-
| 32–41 °C || 90–105 °F
| Extreme caution: [[heat cramp]]s and [[heat exhaustion]] are possible. Continuing activity could result in [[heat stroke]].
|-
| 41–54 °C || 105–130 °F
| Danger: [[heat cramp]]s and [[heat exhaustion]] are likely; [[heat stroke]] is probable with continued activity.
|-
| over 54 °C || over 130 °F
| Extreme danger: [[heat stroke]] is imminent.
|-
|}

Exposure to full sunshine can increase heat index values by up to 8 °C (14 °F).<ref name=Pueblo>[http://web.archive.org/web/20110629041320/http://www.crh.noaa.gov/pub/heat.php Heat Index] on the website of the Pueblo, CO United States National Weather Service.</ref>

==Formula==
The formula below approximates the heat index in degrees Fahrenheit, to within ±1.3 °F. It is the result of a multivariate fit (temperature equal to or greater than 80°F and relative humidity equal to or greater than 40%) to a model of the human body.<ref>Lans P. Rothfusz. "The Heat Index 'Equation' (or, More Than You Ever Wanted to Know About Heat Index)", Scientific Services Division (NWS Southern Region Headquarters), 1 July 1990 [http://www.srh.noaa.gov/images/ffc/pdf/ta_htindx.PDF]</ref><ref>R.G. Steadman, 1979. "The assessment of sultriness. Part I: A temperature-humidity index based on human physiology and clothing science," J. Appl. Meteor., 18, 861-873</ref> This equation reproduces the above NOAA National Weather Service table (except the values at 90°F & 45%/70% relative humidity vary unrounded by less than -1/+1, respectively).
:<math>\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2R + c_8 T R^2 + c_9 T^2 R^2\ \, </math>

where
:<math>\mathrm{HI}\,\!</math> = heat index (in degrees Fahrenheit)
:<math>T\,\!</math> = ambient [[dry-bulb temperature]] (in degrees Fahrenheit)
:<math>R\,\!</math> = relative humidity (percentage value between 0 and 100)
:<math>c_1 = -42.379, \,\!</math> <math>c_2 = 2.04901523, \,\!</math> <math>c_3 = 10.14333127,\,\!</math> <math>c_4 = -0.22475541, \,\!</math> <math>c_5 = -6.83783 \times 10^{-3},\,\!</math> <math>c_6 = -5.481717 \times 10^{-2},\,\!</math> <math>c_7 = 1.22874 \times 10^{-3}, \,\!</math> <math>c_8 = 8.5282 \times 10^{-4}, \,\!</math> <math>c_9 = -1.99 \times 10^{-6}.\,\!</math>

An alternative set of constants for this equation that is within 3 degrees of the NWS master table for all humidities from 0 to 80% and all temperatures between 70 and 115 °F and all heat indexes < 150 °F is
:<math>c_1 = 0.363445176, \,\!</math> <math> c_2 = 0.988622465, \,\!</math> <math> c_3 = 4.777114035, \,\!</math> <math> c_4 = -0.114037667, \,\!</math> <math> c_5 = -0.000850208, \,\!</math> <math> c_6 = -0.020716198, \,\!</math> <math> c_7 = 0.000687678, \,\!</math> <math> c_8 = 0.000274954, \,\!</math> <math> c_9 = 0 \,\!</math> <math>(c_9 \,\!</math> <math>unused).</math>

A further alternate is this:<ref>
{{cite book
| last = Stull | first = Richard
| authorlink =
| title = Meteorology for Scientists and Engineers, Second Edition
| url = http://books.google.com/books?ei=r_D5T9XTBIrOqAHe_c2LCQ&id=QrYRAQAAIAAJ&dq=Meteorology+for+Scientists+and+Engineers&q=5.37941#search_anchor
| publisher = Brooks/Cole
| year = 2000 | page = 60
| doi =
| isbn = 9780534372149 }}</ref>
:<math>\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2 + c_{10} T^3 + c_{11} R^3 + c_{12} T^3 R + c_{13} T R^3 + c_{14} T^3 R^2 + c_{15} T^2 R^3 + c_{16} T^3 R^3\ \, </math>
where
:<math>c_1 = 16.923, \,\!</math> <math>c_2 = 0.185212, \,\!</math> <math>c_3 = 5.37941,\,\!</math> <math>c_4 = -0.100254, \,\!</math> <math>c_5 = 9.41695 \times 10^{-3},\,\!</math> <math>c_6 = 7.28898 \times 10^{-3},\,\!</math> <math>c_7 = 3.45372\times 10^{-4}, \,\!</math> <math>c_8 = -8.14971 \times 10^{-4}, \,\!</math> <math>c_9 = 1.02102 \times 10^{-5},\,\!</math> <math>c_{10} = -3.8646 \times 10^{-5},\,\!</math> <math>c_{11} = 2.91583 \times 10^{-5},\,\!</math> <math>c_{12} = 1.42721 \times 10^{-6},\,\!</math> <math>c_{13} = 1.97483 \times 10^{-7},\,\!</math> <math>c_{14} = -2.18429 \times 10^{-8},\,\!</math> <math>c_{15} = 8.43296 \times 10^{-10},\,\!</math> <math>c_{16} = -4.81975 \times 10^{-11}.\,\!</math>

For example, using this last formula, with temperature {{convert|90|F|C}} and relative humidity (RH) of 85%, the result would be: {{heat index|90|85}}.

== See also ==
* [[Apparent temperature]]
* [[Humidex]]
* [[Wind chill]]

==References==
{{Reflist}}

== External links ==
*[http://www.bom.gov.au/info/thermal_stress/ Description of wind chill & apparent temperature] Formulae in metric units
*[http://www.wpc.ncep.noaa.gov/html/heatindex.shtml Heat Index Calculator] Calculates both °F and °C

{{Meteorological variables}}

{{DEFAULTSORT:Heat Index}}
[[Category:Atmospheric thermodynamics]]
[[Category:Weather]]

Weil restriction

2014-01-03T04:20:25Z

50.0.121.102: add cryptography application

The '''negentropy''', also '''negative entropy''' or '''syntropy''' or '''extropy''' or '''entaxy''',<ref>Wiener, Norbert</ref> of a [[living system]] is the [[entropy]] that it exports to keep its own entropy low; it lies at the intersection of [[entropy and life]]. The concept and phrase "negative entropy" were introduced by [[Erwin Schrödinger]] in his 1944 popular-science book ''[[What is Life? (Schrödinger)|What is Life?]]''<ref>Schrödinger, Erwin, ''What is Life - the Physical Aspect of the Living Cell'', Cambridge University Press, 1944</ref> Later, [[Léon Brillouin]] shortened the phrase to ''negentropy'',<ref>Brillouin, Leon: (1953) "Negentropy Principle of Information", ''J. of Applied Physics'', v. '''24(9)''', pp. 1152-1163
</ref><ref>Léon Brillouin, ''La science et la théorie de l'information'', Masson, 1959</ref> to express it in a more "positive" way: a living system imports negentropy and stores it.<ref>Mae-Wan Ho, [http://www.i-sis.org.uk/negentr.php What is (Schrödinger's) Negentropy?], Bioelectrodynamics Laboratory, Open university Walton Hall, Milton Keynes</ref> In 1974, [[Albert Szent-Györgyi]] proposed replacing the term ''negentropy'' with ''syntropy''. That term may have originated in the 1940s with the Italian mathematician [[Luigi Fantappiè]], who tried to construct a unified theory of [[biology]] and [[physics]]. [[Buckminster Fuller]] tried to popularize this usage, but ''negentropy'' remains common.

In a note to [[What is Life?]] Schrödinger explained his use of this phrase.
{{cquote|[...] if I had been catering for them [physicists] alone I should have let the discussion turn on ''[[Thermodynamic free energy|free energy]]'' instead. It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to ''[[energy]]'' for making the average reader alive to the contrast between the two things.}}

Indeed, negentropy has been used by biologists as the basis for purpose or direction in life, namely cooperative or moral instincts.<ref>[[Jeremy Griffith]]. 2011. ''What is the Meaning of Life?''. In ''The Book of Real Answers to Everything!'' ISBN 9781741290073. From http://www.worldtransformation.com/what-is-the-meaning-of-life/</ref>

In 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos.<ref>Mahulikar, S.P. & Herwig, H.: (2009) "Exact thermodynamic principles for dynamic order existence and evolution in chaos", ''Chaos, Solitons & Fractals'', v. '''41(4)''', pp. 1939-1948</ref> Thus, negentropy has units [J/kg-K] when defined based on specific entropy per unit mass, and [K−1] when defined based on specific entropy per unit energy. This definition enabled: ''i'') scale-invariant thermodynamic representation of dynamic order existence, ''ii'') formulation of physical principles exclusively for dynamic order existence and evolution, and ''iii'') mathematical interpretation of Schrödinger's negentropy debt.

==Information theory==
In [[information theory]] and [[statistics]], negentropy is used as a measure of distance to normality.<ref>Aapo Hyvärinen, [http://www.cis.hut.fi/aapo/papers/NCS99web/node32.html Survey on Independent Component Analysis, node32: Negentropy], Helsinki University of Technology
Laboratory of Computer and Information Science</ref><ref>Aapo Hyvärinen and Erkki Oja, [http://www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/node14.html Independent Component Analysis: A Tutorial, node14: Negentropy], Helsinki University of Technology
Laboratory of Computer and Information Science</ref><ref>Ruye Wang, [http://fourier.eng.hmc.edu/e161/lectures/ica/node4.html Independent Component Analysis, node4: Measures of Non-Gaussianity]</ref> Out of all [[Distribution (mathematics)|distributions]] with a given mean and variance, the normal or [[Gaussian distribution]] is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes [[if and only if]] the signal is Gaussian.

Negentropy is defined as

:<math>J(p_x) = S(\phi_x) - S(p_x)\,</math>

where <math>S(\phi_x)</math> is the [[differential entropy]] of the Gaussian density with the same [[mean]] and [[variance]] as <math>p_x</math> and <math>S(p_x)</math> is the differential entropy of <math>p_x</math>:

:<math>S(p_x) = - \int p_x(u) \log p_x(u) du</math>

Negentropy is used in [[statistics]] and [[signal processing]]. It is related to network [[Information entropy|entropy]], which is used in [[Independent Component Analysis]].<ref>P. Comon, Independent Component Analysis - a new concept?, ''Signal Processing'', '''36''' 287-314, 1994.</ref><ref>Didier G. Leibovici and Christian Beckmann, [http://www.fmrib.ox.ac.uk/analysis/techrep/tr01dl1/tr01dl1/tr01dl1.html An introduction to Multiway Methods for Multi-Subject fMRI experiment], FMRIB Technical Report 2001, Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB), Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital, Headley Way, Headington, Oxford, UK.</ref>

==Correlation between statistical negentropy and Gibbs' free energy==
[[File:Wykres Gibbsa.svg|275px|thumb|right|[[Willard Gibbs]]’ 1873 '''available energy''' ([[Thermodynamic free energy|free energy]]) graph, which shows a plane perpendicular to the axis of ''v'' ([[volume]]) and passing through point A, which represents the initial state of the body. MN is the section of the surface of [[dissipated energy]]. Qε and Qη are sections of the planes ''η'' = 0 and ''ε'' = 0, and therefore parallel to the axes of ε ([[internal energy]]) and η ([[entropy]]) respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its ''available energy'' ([[Gibbs free energy]]) and its ''capacity for entropy'' (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.]]
There is a physical quantity closely linked to [[Thermodynamic free energy|free energy]] ([[free enthalpy]]), with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873, [[Josiah Willard Gibbs|Willard Gibbs]] created a diagram illustrating the concept of free energy corresponding to [[free enthalpy]]. On the diagram one can see the quantity called [[capacity for entropy]]. The said quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume.<ref>Willard Gibbs, [http://www.ufn.ru/ufn39/ufn39_4/Russian/r394b.pdf A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces], ''Transactions of the Connecticut Academy'', 382-404 (1873)</ref> In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by [[François Jacques Dominique Massieu|Massieu]] for the [[isothermal process]] <ref>Massieu, M. F. (1869a). Sur les fonctions caractéristiques des divers fluides.
''C. R. Acad. Sci.'' LXIX:858-862.</ref><ref>Massieu, M. F. (1869b). Addition au precedent memoire sur les fonctions
caractéristiques. ''C. R. Acad. Sci.'' LXIX:1057-1061.</ref><ref>Massieu, M. F. (1869), ''Compt. Rend.'' '''69''' (858): 1057.</ref> (both quantities differs just with a figure sign) and then [[Max Planck|Planck]] for the [[Isothermal process|isothermal]]-[[Isobaric process|isobaric]] process <ref>Planck, M. (1945). ''Treatise on Thermodynamics''. Dover, New York.</ref> More recently, the Massieu-Planck [[thermodynamic potential]], known also as ''[[free entropy]]'', has been shown to play a great role in the so-called entropic formulation of [[statistical mechanics]],<ref>Antoni Planes, Eduard Vives, [http://www.ecm.ub.es/condensed/eduard/papers/massieu/node2.html Entropic Formulation of Statistical Mechanics], Entropic variables and Massieu-Planck functions 2000-10-24 Universitat de Barcelona</ref> applied among the others in molecular biology<ref>John A. Scheilman, [http://www.biophysj.org/cgi/reprint/73/6/2960.pdf Temperature, Stability, and the Hydrophobic Interaction], ''Biophysical Journal'' '''73''' (December 1997), 2960-2964, Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403 USA</ref> and thermodynamic non-equilibrium processes.<ref>Z. Hens and X. de Hemptinne, [http://arxiv.org/pdf/chao-dyn/9604008 Non-equilibrium Thermodynamics approach to Transport Processes in Gas Mixtures], Department of Chemistry, Catholic University of Leuven,
Celestijnenlaan 200 F, B-3001 Heverlee, Belgium</ref>

::'''<math>J = S_\max - S = -\Phi = -k \ln Z\,</math>'''

::where:
::<math>J</math> - negentropy (Gibbs "capacity for entropy")
::<math>\Phi</math> – [[Free entropy|Massieu potential]]
::<math>Z</math> - [[Partition function (statistical mechanics)|partition function]]
::<math>k</math> - [[Boltzmann constant]]

==Risk management==

In [[risk management]], negentropy is the force that seeks to achieve effective organizational behavior and lead to a steady predictable state.<ref>[http://www.kent.ac.uk/scarr/events/Grinberg-%20(2).pdf Pedagogical Risk and Governmentality: Shantytowns in Argentina in the 21st Century] (see p. 4).</ref>

==Brillouin's negentropy principle of information==

In 1953, Brillouin derived a general equation<ref>Leon Brillouin, The negentropy principle of information, ''J. Applied Physics'' '''24''', 1152-1163 1953</ref> stating that the changing of an information bit value requires at least kT ln(2) energy. This is the same energy as the work [[Leo Szilard]]'s engine produces in the idealistic case. In his book,<ref>Leon Brillouin, ''Science and Information theory'', Dover, 1956</ref> he further explored this problem concluding that any cause of this bit value change (measurement, decision about a yes/no question, erasure, display, etc) will require the same amount of energy.

==Notes==
{{reflist}}

==See also==
* [[Ectropy]]
* [[Exergy]]
* [[Extropy]]
* [[Free entropy]]
* [[Entropy in thermodynamics and information theory]]

==External links==
Eschatos ♦ [http://knol.google.com/k/eschatos/information/1zm6ikqu62pfl/20 Information]

[[Category:Thermodynamic entropy]]
[[Category:Entropy and information]]
[[Category:Statistical deviation and dispersion]]

Langlands–Shahidi method

2013-12-22T07:21:51Z

50.0.193.12: Consistently use epsilon vs varepsioln

{{underlinked|date=December 2012}}

'''Magnetic field-assisted finishing''', sometimes called '''magnetic abrasive finishing''', is a [[surface finishing]] technique in which a magnetic field is used to force abrasive particles against the target surface.<ref>D.K. Singh, V.K. Jain, V. Raghuram (2003) [http://www.aspe.net/publications/Annual_2003/PDF/5proc/4nconv/1164.PDF Superfinishing of alloy steel using magnetic abrasive finishing process] ''Proceedings of the 18th Annual ASPE Meeting''.</ref> As such, finishing of conventionally inaccessible surfaces (e.g., the inside surface of a long curved pipe) is possible. Magnetic field-assisted finishing (MAF) processes have been developed for a wide variety of applications including the manufacturing of medical components, fluid systems, optics, dies and molds, electronic components, microelectromechanical systems, and mechanical components.

==History of MAF==

Initially developed as a machining process in the US in the 1930s, with the first patent in the 1940s. University research in the Soviet Union, Bulgaria, Germany, Poland, and US began in the 1960s with practical usage appearing by the 1980s and 1990's. The growth of the semiconductor, aerospace, and optics industries have resulted in the continued development of better methods for attaining high form accuracy and surface integrity.<ref>Yamaguchi H, Sato T, “Polishing and Magnetic Field-Assisted Finishing” Intelligent Energy Field Manufacturing Interdisciplinary Process Innovations 2012</ref>

==Processing Principle/Theory==
'''Magnetic Assisted Finishing''' or '''MAF''' is essentially the manipulation of a homogeneous mixture of magnetic particles and abrasive particles with a magnetic field to impart a machining force on a workpiece. Relative motion between the particle mixture and the workpiece surface result in material removal. Since '''MAF''' does not require direct contact with the tool, the particles can be introduced into areas which are hard to reach by conventional techniques. Additionally careful selection of magnetic particles and abrasive particles give rise to surface texture and roughness control that was previously impossible especially for hard to access areas.<ref>Yamaguchi H, Sato T, “Polishing and Magnetic Field-Assisted Finishing” Intelligent Energy Field Manufacturing Interdisciplinary Process Innovations 2012</ref>

==Magnetic Field Sources==

The magnetic field source in '''MAF''' is typically an electromagnet or a rare earth permanent magnet. Preferably a permanent magnet is used due to the high energy density, lack of overheating resulting in a constant flux density, low cost, ease of integration into existing CNC equipment, and for simplicity. However some applications require the need to adjust the flux density during finishing or require a switching magnetic field which is only attainable with an electromagnet since the magnetic field in a permanent magnet cannot simply be switched off.

==Motion Facilitating equipment==

Relative motion between the magnetic/abrasive particle mixture and the workpiece is essential for material removal. There are several options for achieving the necessary motion. A common setup is the rotation of the magnetic pole tip. This is done by either rotating the entire permanent magnet setup or by rotating only the steel pole. Another method which is commonly utilized in internal finishing is the rotation of the workpiece, this is unfortunately limited to axial symmetric workpieces. In additional to rotational motion there is oscillatory and vibrational configurations that are applicable

==Magnetic Force on a Particle==
Start with the common expression for force on a magnetic dipole moment in a magnetic field,
::<math> \vec{F} = \nabla(\vec{m}\cdot\vec{B}) </math>

From here, make the assumption that the moment of the magnetic particle is co-linear with the applied field. This is a reasonable assumption given the small size and high susceptibility of the magnetic particles. So the equation becomes,
::<math> \vec{F} = \vec{m}\cdot\nabla\vec{B} </math>

Using the following identities to obtain a more usable equation to describe the force experienced by a single magnetic particle,
:::<math> \vec{m} = \vec{M} V </math>

:::<math> \vec{M} = \vec{H_k} \chi </math>

:::<math> \vec{B} = \mu_0 \vec{H_a} </math>

Substituting the above definitions into the magnetic force equation yields,

::<math> \vec{F} = \mu_0 \chi V \vec{H_k} \nabla\vec{H_a} </math> <ref>Yamaguchi H, Sato T, “Polishing and Magnetic Field-Assisted Finishing” Intelligent Energy Field Manufacturing Interdisciplinary Process Innovations 2012</ref>

where,
* <math> \vec{H_k} </math> is the maximum applied field for saturation of the magnetic particle
* <math> \vec{H_a} </math> is the applied magnetic field intensity
* <math> \vec{B} </math> is the magnetic flux density
* <math> \vec{M} </math> is the magnetization of the particle, assumed to be saturated
* <math> \vec{m} </math> is the magnetic dipole moment
* <math> \nabla \vec{H} </math> is the magnetic field gradient
* <math> V </math> is the volume of the particle (assuming sphere shaped)
* <math> \chi </math> is the material magnetic susceptibility
* <math> \mu_0 </math> is the permeability of free space

==Magnetic Brush==

===Brush Composition===

====Common Magnetic Materials====

: Iron and its oxides
: Cobalt
: Nickel
: Steel and Stainless Steel

====Common Abrasive Materials====

: Synthetic Diamond
: Cubic Boron Nitride CBN
: Aluminum Oxide Al_2O_3
: Silicon Carbide SiC

====Common Magnetic Abrasive Materials====

: White Alumina + Iron
: Diamond + Iron
: Tungsten Carbide + Cobalt

===Brush Formation===
It is theorized that the formation of the brush is governed by three driving energies. The first energy Wm is the magnetization energy between particles which result in the formation of magnetic chains of particles. The next energy is known as Repulsion energy Wf this is the separation of adjacent chains of material particles driven by the Faraday effect, this is the reason why the chains do not immediately mix into one giant chain. Finally the third energy is called the Tension energy Wt, this refers to the energy required to counteract the curved magnetic chains.
:Therefore the energy required to form the magnetic brush is as follows:
::: <math>W=W_m+W_f+W_t</math>

===Forces applied by brush===
The force applied to the surface by a magnetic particle in the magnetic brush can be divided into two components. The normal force and the tangential force.

====Normal Force at surface====
The normal force at the surface applied by a magnetic particle can be defined as a function of area S and magnetic field B in the following expression:[3]
::<math>F_n=mf_n=\frac{B^2}{2\mu_0}\left (1-\frac{1}{\mu_m} \right )S</math>
:Where the permeability of the magnetic particles is defined by a volume fraction of iron particles defined as:
::<math> \mu_m = \frac{2+\mu_F-2(1-\mu_F)Vi}{2+\mu_F-(1-\mu_F)Vi} </math>

:Where
::<math>f_n = </math>normal force per particle
::<math>m = </math>number of particles particle
::<math>B = </math>Magnetic B Field
::<math>S = </math>Area Factor S
::<math>\mu_0 = </math>permeability of air
::<math>\mu_m = </math>permeability of magnetic particles
::<math>\mu_f = </math>permeability of ferrous particles

====Tangential Force at surface====
The tangential force of the brush can be defined as a change in energy of the brush due to an obstruction. Since the magnetic particle prefer to be in the lowest energy state, an increase in energy due to deviation from the magnetic flux lines can result in a horizontal "restoring" force which is acted on the surface of the workpiece. This restoring force can be defined as:
::: <math>F_H=\frac {dW}{dx}</math>

==Material Removal mechanism==
The combination of tangential force and normal forces exerted by the brushonto the workpiece is theorized to remove material from the top peaks of the surface asperities.This process is repeated as the contact between the brush and the surface continues during the finishing operation. Overtime the surface roughness of the workpiece surface reaches a minimum value, this is due to the physical limitations of the current finishing setup. Specifically the selection of iron particles and abrasive particles dictates the minimum surface roughness that can be achieved. As the surface roughness decreases smaller abrasive particles are necessary to continue material removal.
:'''MAF''' is capable of achieving roughness values ranging from 200 µm Ra down to 1 nm Ra with ease, demonstrating the degree of customization available to a '''MAF''' setup. The particle sizes for the magnetic particles in the brush dictate the finishing force which is governed by the magnetic force on a particle equation. however increasing particle size has adverse effects such as the inability to hold small abrasives and the presence of air gaps as a result of a larger packing factor. In order to alleviate these problems it is common practice to mix the magnetic particles with both large and smaller particles to "fill" the "holes" of the brush, the small particles effectively coat the larger particles within the particle chain. Close control of the surface texture and roughness can be manipulated through the selection of the right abrasive size and oscillation speed and spindle rpm. Generally speaking the faster the motion of the brush the more dense the finishing marks on the surface and the higher the surface roughness.<ref>Yamaguchi H, Sato T, “Polishing and Magnetic Field-Assisted Finishing” Intelligent Energy Field Manufacturing Interdisciplinary Process Innovations 2012</ref>

==Types of MAF==
'''MAF''' can be divided into three main categories, each defined by the type of magnetic particles utilized in the finishing operation. Each type has its specific niche that it may fulfill better than its counterparts therefore knowing the application of the process is key to selecting the proper finishing operation. The different '''MAF''' processes are listed in increasing surface roughness resolution while decreasing in applied force. This is primarily due to the reduction in iron particle size from one type of finishing to the next. These processes are just general terms and examples for some '''MAF''' setups, it is import to note that each of these process' have different variations to increase to applicability to other workpieces.

===Magnetic Abrasive Finishing===

Magnetic Abrasive Finishing refers to using 1 µm - 2 mm iron particles mixed with an abrasive to apply the machining force through manipulation of the particles with a magnetic field. The magnetic particle and abrasive mixture is commonly referred to the "magnetic brush" because it appears and behaves similar to a wire brush. Unlike a conventional brush the magnetic chains of particles are flexible and will conform around any geometry. As the displacement of the brush increases beyond the flexibility of the bush the magnetic bristles are able to break and reform further increasing the flexibility and versatility of this finishing process. Therefore, this specific variety of '''MAF''' is aimed towards finishing of the free form external surfaces such as airfoils or prosthesis. However it can also easily be applicable to internal finishing processes and is especially effective at finishing the internal surfaces of workpieces that are difficult to access otherwise such as capillary tubes and other small gauge needles. The main difference between internal and external finishing operations is the location of the brush and the workpiece however the application of force is essentially the same hence the material removal mechanism is identical in both cases. One key parameter that the user needs to be aware of is the proper completion of the magnetic circuit to ensure the magnetic flux uniformly permeates through the workpiece at the desired finishing location. The addition of an oil based lubricant, the magnetic brush can also be considered a magnetorheological fluid.

====Applications====

; Freeform finishing
: Prosthetics
: Cutting Tools
: Turbine Blades
: Airfoils
: Optics
; Internal Finishing
: Sanitary Pipes
: Food Industry
: Capillary Tubes in Medical Field
:: Stents, Cathater shafts, Needles, Biopsy Needles, etc
: Curved Pipes

===Magnetorheological Finishing===
:Magnetorheological Finishing or '''MRF''' utilizes the shearing of a viscous mixture of micron sized iron particles, abrasives, and oil to impart a machining force or pressure onto the workpiece surface. This magnetic particle mixture is commonly referred to a ribbon and is extremely viscous in the presence of a magnetic field, the increased viscosity and different fluid properties are similar to those of a Bingham fluid rather than a Newtonian fluid. In a typical '''MRF''' finishing setup the '''MRF''' fluid is pumped onto a rotating wheel which is connected to an electromagnet. When the electromagnet is activated the fluid transitions to a more viscous state, the workpiece is then pressed onto the fluid resulting a shearing of the fluid which results in material removal at the interface between the workpiece and the '''MRF'''. One of the characteristics of a Bingham fluid is as speed increases the force required to shear proportionally increases therefore an increased wheel rotational rate results in an increased machining force when sheared. This particular setup is ideal for large free form nonmagnetic workpieces such as glass optics. It is also commonly applied to large nonmagnetic workpieces where the thickness of the work results in difficulty in getting the magnetic field to permeate effectively at the desired location hence this setup does not rely on the careful design of the magnetic circuit.

====Applications====

Sub-nanometer scale polishing
; Freeform nonmagnetic workpieces
: Optics
: Ceramics

===Magnetic Fluid Finishing===
:In magnetic fluid finishing a solution of ferrofluid and abrasive particles are used as the magnetic particle mixture. Typically this is applicable for applications where even the other types of '''MAF''' are unable to access or when a less viscous medium is desired. One example application of magnetic fluid finishing is silicon micropore optics, in the case of this particular optic the side walls are to be finished to <1.0 nm ''rms'' for x-ray reflection. The pores are 5µmx20µmx300µm which makes it virtually impossible to access with any conventional technique. The magnetic particle and abrasive solution is placed in an alternating and switching magnetic field to encourage fluid flow from one side of the optic to the other side. This flow results in material removal of the sidewalls through the momentum of the fluid and shearing of the side walls with the abrasives. Another application is in the finishing of ceramic bearing balls, to ensure form accuracy of the sphere the setup in the figure to the right has been developed. This is also known as magnetic float polishing and employs a magnetic fluid with a magnetic "float" to ensure an even pressure distribution on the sphere surface during rotation. This results in a uniform application of finishing force onto the workpiece surface.

====Applications====

;Bearings and Rollers
;High Precision Optics

==Capabilities==
*Able to attain wide range of surface characteristics by careful selection of magnetic particles and abrasive particles
**Roughness values from 100 um - 1 nm
**Texturing
***Enhance surface characteristics such as wettability or reducing friction
*Capable to accessing hard to reach areas
*Capable of modifying roughness without altering form
*Setup is independent of workpiece material
**Can efficiently finish ceramics, stainless steels, carbides, coated carbides, and silicon
**Flexible application of force and even pressure distribution reduce cost of assembly
***Vibrations in the machining center and machining tool are not transmitted onto the workpiece surface

==Limitations==
*Can be difficult to scale up to mass production operation
*Not as applicable to some "ordinary" finishing tasks where conventional finishing techniques can be used

==References==
;1. Kalpakjian S, Schmid S, "Manufacturing Processes" 5th Edition Pearson 2008
;2. Yamaguchi H, Sato T, “Polishing and Magnetic Field-Assisted Finishing” Intelligent Energy Field Manufacturing Interdisciplinary Process Innovations 2012
;3. Mori T, Hirota K, Kawashima Y, “clarification of magnetic abrasive finishing mechanism” Journal of Materials Processing Technology 2003
;4. Graziano A, Ganguly V, Yamaguchi H, “Characteristics of cobalt chromium alloy surfaces finished using magnetic abrasive finishing” ASME 2012
;5. Yamaguchi H, Riveros R, Mitsuishi I, Ezoe Y, “Magnetic field-assisted finishing of micropore X-ray focusing mirrors fabiricated by DRIE” CIRP manufacturing technology 2010
;6. Yamaguchi H, Shimura T, “Study of the surface modification resulting from an internal magnetic abrasive finishing process” Wear 1999
;7. Rusetski A, Mokeev A, Korobko E, “Formation of a layer of magnetorheological fluid on the surface of the moving object in the gradient magnetic field” Journal of physics 2013
;8. Umehara, N., MAGIC polishing, Journal of Magnetism and Magnetic Materials, 252, 341-343, 2002.

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

[[Category:Surface finishing]]

Kahan summation algorithm

2013-11-02T05:39:01Z

50.0.172.79: /* Computer languages */

{{More footnotes|date=February 2011}}
A '''Googlewhack''' is a type of contest for finding a [[Google search]] query consisting of exactly two words without quotation marks, that returns exactly one hit. A Googlewhack must consist of two actual words found in a dictionary. A Googlewhack is considered legitimate if both of the searched-for words appear in the result page.

Published googlewhacks are short-lived, since when published to a web site, the new number of hits will become at least two, one to the original hit found, and one to the publishing site.<ref>[http://googlewhack.com/rules.htm Googlewhack official rules]</ref>

==History==
The term Googlewhack first
appeared on the web at UnBlinking on 8 January 2002;<ref>http://www.unblinking.com/heh/googlewhack.htm</ref> the term was coined by Gary Stock. Subsequently, Stock created The Whack Stack, at googlewhack.com, to allow the verification and collection of user-submitted Googlewhacks.

Since 2003, British comedian [[Dave Gorman]] has toured the [[United Kingdom]], [[France]], [[China]], [[Australia]], [[Canada]], and the [[United States]] with a comedy tour entitled ''Dave Gorman's GoogleWhack Adventure'' and has published a book of the same name. These were based on a true story. While attempting to write a novel for his publisher, Gorman became obsessed with Googlewhacks and travelled across the world finding people who had authored them. Although he never wrote his novel, he did eventually write a book about his "Googlewhack Adventure" which went on to be a [[The Sunday Times (UK)|Sunday Times]] #1 best seller in the UK and has also been published in the U.S. and Canada. A translation is in the works for [[Japan]].

Participants at Googlewhack.com discovered the sporadic "cleaner girl" bug in Google's search algorithm where "results 1-1 of thousands" were returned for two relatively common words<ref>[http://www.googlewhack.com/nack.htm Googlewhack NACK!]</ref> such as Anxiousness Scheduler<ref>[http://blog.blagman.co.uk/2012/02/anxiousness-scheduler-now-theres.html Anxiousness Scheduler]</ref> or Italianate Tablesides.<ref>[http://www.googlewhack.com/tally.pl italianate tablesides]</ref>

Googlewhack went offline in November 2009 after Google stopped providing definition links. Gary Stock stated on the game's web page soon afterwards that he was pursuing solutions for Googlewhack to remain viable. However, the game has not come back into play, and there is no word of when or if that will happen.

===Score===
Some people propose the googlewhack "score," which is the product of the hits of the individual words.<ref>googlewhack scoring is discussed numerous places, e.g.,: [http://forums.anandtech.com/showthread.php?t=940578] [http://www.hyperorg.com/blogger/2002/01/25/new-googlewhack-leader-new-tool/] [http://forums.anandtech.com/showthread.php?t=940578]</ref> Thus a googlewhack score is highest when the individual words produce a large number of hits.

==Variations==
''[[New Scientist]]'' has discussed the idea of a ''Googlewhackblatt'', which is similar to a Googlewhack except that it involves finding a ''single word'' that produces only one Google result. Lists of these have become available, but as with Googlewhacks they result in the Googlewhackblatt status of the word being destroyed - unless it is blocked by [[robots.txt]] or the word does not produce any Google results before it is added to the list, thus forming the Googlewhackblatt Paradox. Those words that do not produce any Google search results at all are known as ''Antegooglewhackblatts'' before they are listed - and subsequently elevated to Googlewhackblatt status if it is not blocked by robots.txt.

One way a Googlewhackblatt's status can be ruined is when an entirely unrelated website including the word is created. An example of this is the [[nonsense word]] "Bumruff" which originally returned a single result (the surname of a woman living in Ireland in 1911), but once a person on [[Xbox Live]] chose the name as a [[Xbox Live#Gamertag|Gamertag]], the word's status as a Googlewhackblatt was destroyed.

Feedback stories are also available on the New Scientist website, thus resulting in the destruction of any existing Googlewhackblatts that are ever printed in the magazine. Antegooglewhackblatts that are posted on the Feedback website become known as ''Feedbackgooglewhackblatts'' as their Googlewhackblatt status is created.
In addition, ''New Scientist'' has more recently discovered another way to obtain a Googlewhackblatt without falling into the Googlewhackblatt Paradox. One can write the Googlewhackblatt on a website, but backwards, and then search on [[elgooG]] to view the list properly while still keeping the Googlewhackblatt's status as a Googlewhackblatt.

In contrast to Googlewhacks, many Googlewhackblatts and Antegooglewhackblatts are nonsense words or uncommon misspellings that are not in dictionaries and probably never will be.

A practical use of specially constructed Googlewhackblatts was proposed<ref>[http://research.microsoft.com/en-us/um/people/lamport/tla/www9.html Archival References to Web Pages], Ninth International World Wide Web Conference: Poster Proceedings (May 2000)</ref> by [[Leslie Lamport]] (although he did not use the term).

==Research applications==
The probabilities of internet search result values for multi-word queries was studied in 2008 with the help of Googlewhacks.<ref>{{cite journal |title=Internet Search Result Probabilities, Heaps' Law and Word Associativity |author=Lansey JC, Bukiet B |journal=Journal of Quantitative Linguistics |date=January 2009 |volume=16 |number=1 |pages=40–66 |url=http://www.jonathan.lansey.net/publications/googlewhack.html |doi=10.1080/09296170802514153}}</ref><ref>[http://www.youtube.com/watch?v=R0Z-PybQ8Gw Googlewhacks for Fun and Profit] Google Tech Talk 2008</ref><ref>[http://www.jonathan.lansey.net/publications/Googlewhack_Poster.pdf Poster Presentation]</ref> Based on data from 351 Googlewhacks from the [http://www.googlewhack.com/tally.pl whackstack], the [[Heaps' law]] <math>\beta</math> coefficient for the indexed World Wide Web (about 8 billion pages) was measured to be <math>\beta=0.52</math>. This result is in line with previous studies which used under 20,000 pages.<ref>Ricardo Baeza-Yates and Berthier Ribeiro-Neto, Modern Information Retrieval, ACM Press, 1999.</ref> The googlewhacks were a key in calibrating the model so that it could be extended automatically to analyse the relatedness of word pairs.

==See also==
* [[Googlefight]]
* [[Hapax legomenon]]
* [[Statistically Improbable Phrases]] – finds phrases in Amazon books unlikely to appear in any other book indexed

== References ==
{{Reflist|2}}

===Further reading===
* {{cite web |last=Bowman |first=Lisa M |date=29 January 2002 |publisher=CNET News |url=http://news.cnet.com/2100-1023-825602.html |title=Have you Googlewhacked? |accessdate=2012-12-31}}
* {{cite web |url=http://www.taipeitimes.com/News/archives/2002/02/06/0000123094 |title='Googlewhacking' a new activity for the searchers |publisher=Reuters |location=London |date=6 February 2002}}

==External links==
*[http://www.googlewhack.com Googlewhack.com]
*[http://www.unblinking.com/heh/googlewhack.htm UnBlinking.com]
{{Use dmy dates|date=February 2011}}

[[Category:Google|W]]

Partial application

2013-10-05T00:01:23Z

50.0.134.120: fix paywalled link

[[Image:Doubling oriented.svg|300px|right|thumb|A Doubling-oriented Doche-Icart-Kohel curve of equation <math>y^2=x^3-x^2-16x</math>]]

In [[mathematics]], the '''doubling-oriented Doche–Icart–Kohel curve''' is a form in which an [[elliptic curve]] can be written. It is a special case of [[Weierstrass form]] and it is also important in [[elliptic curve cryptography|elliptic-curve cryptography]] because the doubling speeds up considerably (computing as composition of 2-[[isogeny]] and its [[dual abelian variety|dual]]).
It has been introduced by Christophe Doche, Thomas Icart, and David R. Kohel in <ref>Christophe Doche, Thomas Icart, and David R. Kohel, ''Efficient Scalar Multiplication by Isogeny Decompositions''</ref>

==Definition==

Let <math> K </math> be a [[field (mathematics)|field]] and let <math>a\in K</math>. Then, the Doubling-oriented Doche–Icart–Kohel curve with [[parameter]] ''a'' in [[affine space|affine coordinates]] is represented by:

<math> y^2=x^3+ax^2+16ax </math>

Equivalently, in [[projective space|projective coordinates]]:

<math> ZY^2=X^3+aZX^2+16aXZ^2, </math>

with <math> x=\frac{X}{Z} </math> and <math>y=\frac{Y}{Z} </math>.

Notice that, since this curve is a special case of [[elliptic curve|Weierstrass form]], transformations to the most common form of elliptic curve (Weierstrass form) are not needed.

==Group law==

It is interesting to analyze the [[elliptic curve#The group law|group law]] in [[elliptic curve cryptography]], defining the addition and doubling formulas, because these formulas are necessary to compute multiples of points ''[n]P'' (see [[Exponentiation by squaring]]). In general, the group law is defined in the following way: if three points lies in the same line then they sum up to zero. So, by this property, the group laws are different for every curve shape.

In this case, since these curves are special cases of Weierstrass curves, the addition is just the standard addition on Weierstrass curves. On the other hand, to double a point, the standard doubling formula can be used, but it would not be so fast.
In this case, the [[identity element|neutral element]] is <math> \theta=(0:1:0) </math> (in projective coordinates), for which <math> \theta=-\theta </math>. Then, if <math>P=(x,y)</math> is a non-trivial element (<math>P!=O</math>), then the inverse of this point (by addition) is –P=(x,-y).

===Addition===

In this case, [[affine space|affine coordinates]] will be used to define the addition formula:

(x1,y1)+(x2,y2)=(x3,y3) where

x3 = (-x13+(x2-a)x12+(x22+2ax2)x1+(y12-2y2y1+(-x23-ax22+y22)))/(x12-2x2x1+x22)

y3 = ((-y1+2y2)x13+(-ay1+(-3y2x2+ay2))x12+((3x22+2ax2)y1-2ay2x2)x1+(y13-3y2y12+(-2x23-ax22+3y22)y1+(y2x23+ay2x22-y23)))/(-x13+3x2x12-3x22x1+x23)

===Doubling===

2(x1,y1)=(x3,y3)

x3 = 1/(4y12)x14-8a/y12x12+64a2/y12

y3 = 1/(8y13)x16+((-a2+40a)/(4y13))x14+((ay12+(16a3-640a2))/(4y13))x12+((-4a2y12-512a3)/y13)

==Algorithms and examples==

===Addition===

The fastest addition is the following one (comparing with the results given in: http://hyperelliptic.org/EFD/g1p/index.html), and the cost that it takes is 4 multiplications, 4 squaring and 10 addition.

A = Y2-Y1

AA = A2

B = X2-X1

CC = B2

F = X1CC

Z3 = 2CC

D = X2Z3

ZZ3 = Z32

X3 = 2(AA-F)-aZ3-D

Y3 = ((A+B)2-AA-CC)(D-X3)-Y2ZZ3

====Example====

Let <math> K=\mathbb{Q} </math>. Let P=(X1,Y1)=(2,1), Q=(X2,Y2)=(1,-1) and a=1, then

A=2

AA=4

B=1

CC=1

F=2

''' Z3=4'''

D=4

ZZ3=16

''' X3=-4'''

'''Y3=336 '''

Thus, P+Q=(-4:336:4)

===Doubling===

The following algorithm is the fastest one (see the following link to compare: http://hyperelliptic.org/EFD/g1p/index.html), and the cost that it takes is 1 multiplication, 5 squaring and 7 additions.

A = X12

B = A-a16

C = a2A

YY = Y12

YY2 = 2YY

Z3 = 2YY2

X3 = B2

V = (Y1+B)2-YY-X3

Y3 = V(X3+64C+a(YY2-C))

ZZ3 = Z32

====Example====

Let <math> K=\mathbb{Q} </math> and a=1. Let P=(-1,2), then Q=[2]P=(x3,y3) is given by:

A=1

B=-15

C=2

YY=4

YY2=8

'''Z3=16'''

'''X3=225'''

V=27

'''Y3=9693'''

ZZ3=256

Thus, Q=(225:9693:16).

==Extended coordinates==

The addition and doubling computations should be as fast as possible, so it is more convenient to use the following representation of the coordinates:

<math> x,y </math> are represented by <math> X,Y,Z,ZZ </math> satisfying the following equations:

<math> x=\frac{X}{Z} </math>

<math> y=\frac{Y}{ZZ} </math>

<math> ZZ=Z^2 </math>

Then, the Doubling-oriented Doche–Icart–Kohel curve is given by the following equation:

<math> Y^2=ZX^3+aZ^2X^2+16aZ^3X </math>.

In this case,<math> P=(X: Y: Z: ZZ)</math> is a general point with inverse <math>-P=(X: -Y: Z: ZZ) </math>.
Furthermore, the points over the curve satisfy: <math> (X:Y:Z:Z^2)=(\lambda X: \lambda^2Y: \lambda Z: \lambda^2Z^2) </math> for all <math> \lambda </math> nonzero.

Faster doubling formulas for these curves and mixed-addition formulas were introduced by Doche, Icart and Kohel; but nowadays, these formulas are improved by Daniel J. Bernstein and Tanja Lange (see below the link of EFD).

==Internal Link==

For more informations about the running-time required in a specific case, see [[Table of costs of operations in elliptic curves]]

==External links==
* http://hyperelliptic.org/EFD/g1p/index.html

==Notes==

{{Reflist}}

==References==

* {{cite book
| author = Christophe Doche, Thomas Icart and David R. Kohel
| year = 2006
| title = Efficient Scalar Multiplication by Isogeny Decompositions
| publisher =Springer Berlin / Heidelberg
| url = http://www.springerlink.com/content/h542176232q8w45q/fulltext.pdf
| isbn = 978-3-540-33851-2
}}

* {{cite book
| author = Daniel J. Bernstein and Tanja Lange
| year = 2008
| title = Analysis and optimization of elliptic-curve single scalar multiplication
| publisher =
| url = http://books.google.nl/books?hl=es&lr=&id=VZ5kFYzH_ZUC&oi=fnd&pg=PA1&dq=related:0lMQ2OY5ejoJ:scholar.google.com/&ots=7erHZiu8CS&sig=PJCJlQQIhvqu0njfTyaV4DLYlkg#v=onepage&q=&f=false
| isbn =
}}
* http://www.hyperelliptic.org/EFD/g1p/auto-2dik.html

{{DEFAULTSORT:Doubling-oriented Doche-Icart-Kohel curve}}
[[Category:Elliptic curves]]
[[Category:Elliptic curve cryptography]]

Mitsuhiro Shishikura

2013-07-28T18:29:42Z

50.0.136.106: link preprint of annals paper

The '''mountain pass theorem''' is an [[existence theorem]] from the [[calculus of variations]]. Given certain conditions on a function, the theorem demonstrates the existence of a [[saddle point]]. The theorem is unusual in that there are many other theorems regarding the existence of [[extremum|extrema]], but few regarding saddle points.

== Theorem statement ==
The assumptions of the theorem are:
* ''I'' is a [[functional (mathematics)|functional]] from a [[Hilbert space]] ''H'' to the [[real number|reals]],
* <math>I\in C^1(H,\mathbb{R})</math> and <math>I'</math> is [[Lipschitz continuous]] on bounded subsets of ''H'',
* ''I'' satisfies the [[Palais-Smale compactness condition]],
* <math>I[0]=0</math>,
* there exist positive constants ''r'' and ''a'' such that <math>I[u]\geq a</math> if <math>\Vert u\Vert =r</math>, and
* there exists <math>v\in H</math> with <math>\Vert v\Vert >r</math> such that <math>I[v]\leq 0</math>.
If we define:
:<math>\Gamma=\{\mathbf{g}\in C([0,1];H)\,\vert\,\mathbf{g}(0)=0,\mathbf{g}(1)=v\}</math>
and:
:<math>c=\inf_{\mathbf{g}\in\Gamma}\max_{0\leq t\leq 1} I[\mathbf{g}(t)],</math>
then the conclusion of the theorem is that ''c'' is a critical value of ''I''.

== Visualization ==

The intuition behind the theorem is in the name "mountain pass." Consider ''I'' as describing elevation. Then we know two low spots in the landscape: the origin because <math>I[0]=0</math>, and a far-off spot ''v'' where <math>I[v]\leq 0</math>. In between the two lies a range of mountains (at <math>\Vert u\Vert =r</math>) where the elevation is high (higher than ''a''>0). In order to travel along a path ''g'' from the origin to ''v'', we must pass over the mountains — that is, we must go up and then down. Since ''I'' is somewhat smooth, there must be a critical point somewhere in between. (Think along the lines of the [[mean-value theorem]].) The mountain pass lies along the path that passes at the lowest elevation through the mountains. Note that this mountain pass is almost always a [[saddle point]].

For a proof, see section 8.5 of Evans.

== Weaker formulation ==
Let <math>X</math> be [[Banach space]]. The assumptions of the theorem are:
* <math>\Phi\in C(X,\mathbf R)</math> and have a [[Gâteaux derivative]] <math>\Phi'\colon X\to X^*</math> which is continuous when <math>X</math> and <math>X^*</math> are endowed with [[strong topology]] and [[weak* topology]] respectively.
* There exists <math>r>0</math> such that one can find certain <math>\|x'\|>r</math> with
:<math>\max\,(\Phi(0),\Phi(x'))<\inf\limits_{\|x\|=r}\Phi(x)=:m(r)</math>.
* <math>\Phi</math> satisfies weak [[Palais-Smale condition]] on <math>\{x\in X\mid m(r)\le\Phi(x)\}</math>.

In this case there is a [[critical point (mathematics)|critical point]] <math>\overline x\in X</math> of <math>\Phi</math> satisfying <math>m(r)\le\Phi(\overline x)</math>. Moreover if we define
:<math>\Gamma=\{c\in C([0,1],X)\mid c\,(0)=0,\,c\,(1)=x'\}</math>
then
:<math>\Phi(\overline x)=\inf_{c\,\in\,\Gamma}\max_{0\le t\le 1}\Phi(c\,(t)).</math>

For a proof, see section 5.5 of Aubin and [[Ekeland]].

== References ==
* {{cite book | first=Youssef | last=Jabri | title=The Mountain Pass Theorem, Variants, Generalizations and Some Applications (Encyclopedia of Mathematics and its Applications) | publisher=Cambridge University Press | year=2003 | isbn=0-521-82721-3}}
* {{cite book | first=Lawrence C. | last=Evans | title=Partial Differential Equations | publisher=American Mathematical Society | location=Providence, Rhode Island | year=1998 | isbn=0-8218-0772-2}}
* {{cite book | first=Jean-Pierre | last=Aubin | coauthors=Ivar Ekeland | title=Applied Nonlinear Analysis | publisher=Dover Books | year=2006 | isbn=0-486-45324-3}}

[[Category:Mathematical analysis]]
[[Category:Calculus of variations]]
[[Category:Theorems in analysis]]

Weyl algebra

2013-07-06T00:14:27Z

50.0.193.12: Link first mention of "quantization"

[[Image:Pierre Francois Verhulst.jpg|thumb|250px|right|Pierre Francois Verhulst]]
'''Pierre François Verhulst''' (28 October 1804, [[Brussels]] – 15 February 1849, Brussels) was a [[mathematician]] and a doctor in [[number theory]] from the [[University of Ghent]] in 1825. Verhulst published in 1838 the equation:

:<math> \frac{dN}{dt} = r N \left(1 - \frac {N}{K} \right)</math>

when ''N''(''t'') represents number of individuals at time ''t'', ''r'' the intrinsic growth rate and ''K'' is the [[carrying capacity]], or the maximum number of individuals that the environment can support. In a paper published in 1845 he called the solution to this the [[logistic function]], and the equation is now called the logistic equation. This model was rediscovered in 1920 by [[Raymond Pearl]] and [[Lowell Reed]], who promoted its wide and indiscriminate use.

The logistic equation can be integrated exactly, and has solution

:<math> N(t) = \frac{K}{1+ C K e^{-rt}} </math>

where ''C'' = 1/''N''(0) − 1/''K'' is determined by the initial condition ''N''(0). The solution can also be written as a weighted [[harmonic mean]] of the initial condition and the carrying capacity,

:<math> \frac{1}{N(t)} = \frac{1-e^{-rt}}{K}+ \frac{e^{-rt}}{N(0)}. </math>

Although the continuous-time logistic equation is often compared to the [[logistic map]] because of similarity of form, it is actually more closely related to the [[Beverton–Holt model]] of fisheries recruitment.

The concept of [[R/K selection theory]] derives its name from the competing dynamics of [[exponential growth]] and [[carrying capacity]] introduced by the equations above.

==See also==
*[[Population dynamics]]
*[[Logistic map]]
*[[Logistic function]]
*[[Logistic distribution]]

==Works==
* {{cite journal|first= Pierre-François |last=Verhulst |year= 1838| title = Notice sur la loi que la population poursuit dans son accroissement | journal = Correspondance mathématique et physique |volume = 10| pages = 113–121 |
url = http://books.google.com/?id=8GsEAAAAYAAJ&q=
| accessdate = 2013-02-18}}
* {{cite book
| title = Traité élémentaire des fonctions elliptiques : ouvrage destiné à faire suite aux traités élémentaires de calcul intégral
| publisher = Hayez
| first = Pierre-François
| last = Verhulst
| year = 1841
| place = Bruxelles
| url= http://books.google.com/?id=WS8LAAAAYAAJ&printsec=frontcover
| isbn =
| accessdate = 2013-02-18
}}
* {{cite journal|first= Pierre-François |last=Verhulst |year= 1845| title = Recherches mathématiques sur la loi d'accroissement de la population | journal = Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles |volume = 18| pages = 1–42 | url = http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN129323640_0018&DMDID=dmdlog7| accessdate = 2013-02-18|trans_title= Mathematical Researches into the Law of Population Growth Increase}}
* {{cite journal|first= Pierre-François |last=Verhulst |year= 1847| title = Deuxième mémoire sur la loi d'accroissement de la population | journal = Mémoires de l'Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique |volume = 20| pages = 1–32 | url = http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN129323659_0020&DMDID=dmdlog29| accessdate = 2013-02-18}}

==External links==
* {{MacTutor Biography|id=Verhulst}}

{{Authority control|VIAF=66616324}}
{{Persondata 
| NAME =Verhulst, Pierre Francois
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = mathematician
| DATE OF BIRTH = 28 October 1804
| PLACE OF BIRTH = Brussels, Belgium
| DATE OF DEATH = 15 February 1849
| PLACE OF DEATH = Brussels, Belgium
}}{{dmy|date=January 2011}}

{{DEFAULTSORT:Verhulst, Pierre Francois}}
[[Category:1804 births]]
[[Category:1849 deaths]]
[[Category:Belgian mathematicians]]
[[Category:19th-century writers]]

Weil conjectures

2012-09-01T13:31:54Z

50.0.193.12: Link Hard Lefschetz Theorem

Greetings. The author's name is Eusebio remember, though , he never really liked that name. In his professional life he can be a people manager. He's always loved living [http://Dict.Leo.org/?search=inside+Guam inside Guam] and he [http://Photo.net/gallery/tag-search/search?query_string=features features] everything that he prerequisites there. To drive is one of that this things he loves the vast majority. He's been working around his website for individuals time now. Check that will out here: http://prometeu.net Take a look at my homepage - clash of clans hack android [[http://prometeu.net these details]]

Spin stiffness

2012-08-31T15:55:21Z

50.0.158.220: cosmetic changes to the equations

It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. A pinch of tablet centric strategy can get your Word - Press site miles ahead of your competitors, so here are few strategies that will give your Wordpress websites and blogs an edge over your competitors:. Hosted by Your Domain on Another Web Host - In this model, you first purchase multiple-domain webhosting, and then you can build free Wordpress websites on your own domains, taking advantage of the full power of Wordpress. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it. Always remember that an effective linkwheel strategy strives to answer all the demands of popular search engines while reacting to the latest marketing number trends. If you are a positive thinker businessman then today you have to put your business online. This is the reason for the increased risk of Down Syndrome babies in women over age 35. So if you want to create blogs or have a website for your business or for personal reasons, you can take advantage of free Word - Press installation to get started. Aided by the completely foolproof j - Query color selector, you're able to change the colors of factors of your theme a the click on the screen, with very little previous web site design experience. It is also popular because willing surrogates,as well as egg and sperm donors,are plentiful. Word - Press has different exciting features including a plug-in architecture with a templating system. all the necessary planning and steps of conversion is carried out in this phase, such as splitting, slicing, CSS code, adding images, header footer etc. Provide the best and updated information to the web searchers and make use of these wonderful free themes and create beautiful websites. If you have any questions on starting a Word - Press food blog or any blog for that matter, please post them below and I will try to answer them. A built-in widget which allows you to embed quickly video from popular websites. I didn't straight consider near it solon than one distance, I got the Popup Ascendancy plugin and it's up and lengthways, likely you make seen it today when you visited our blog, and I yet customize it to fit our Thesis Wound which gives it a rattling uncomparable visage and search than any different popup you know seen before on any added journal, I hump arrogated asset of one of it's quatern themes to make our own. re creating a Word - Press design yourself, the good news is there are tons of Word - Press themes to choose from. IVF ,fertility,infertility expert,surrogacy specialist in India at Rotundaivf. Where from they are coming, which types of posts are getting top traffic and many more. More it extends numerous opportunities where your firm is at comfort and rest assured of no risks & errors. Mahatma Gandhi is known as one of the most prominent personalities and symbols of peace, non-violence and freedom. As a result, it is really crucial to just take aid of some experience when searching for superior quality totally free Word - Press themes, Word - Press Premium Themes for your web site. Should you liked this informative article and you desire to obtain more details regarding [http://www.ase.re/wordpress_backup_5587062 wordpress dropbox backup] generously pay a visit to the web-page. Page speed is an important factor in ranking, especially with Google. Definitely when you wake up from the slumber, you can be sure that you will be lagging behind and getting on track would be a tall order.