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| [[Image:Pierre Francois Verhulst.jpg|thumb|250px|right|Pierre Francois Verhulst]] | | I woke up the other day and [http://www.bing.com/search?q=realized+-&form=MSNNWS&mkt=en-us&pq=realized+- realized -] I've been single for some time at the moment and following much intimidation from pals I now find myself registered for on line dating. They assured me that there are plenty of pleasant, normal and interesting individuals to meet up, therefore the pitch is gone by here!<br>My family and friends are awe-inspiring and spending time with them [http://lukebryantickets.sgs-suparco.org luke bryan concert dates 2014] at bar gigs or meals is obviously a must. I haven't ever been in to night clubs as [http://www.Squidoo.com/search/results?q=I+realize I realize] that you can do not have a good dialog with all the sound. In addition, I got 2 unquestionably cheeky and very cute puppies that are invariably enthusiastic to meet up fresh people.<br>I make an effort to maintain as toned as possible coming to the fitness center several-times a week. I appreciate my athletics and [http://www.ffpjp24.org luke bryan stage setup] strive to perform or see as numerous a possible. Being winter I will frequently at Hawthorn fits. Note: If you would contemplated shopping a sport I really do not mind, I've noticed the carnage of fumbling suits [http://www.cinemaudiosociety.org book luke bryan] at stocktake sales.<br><br>Also visit my page; [http://lukebryantickets.asiapak.net luke bryan concert dates 2014] |
| '''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: | |
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| :<math> \frac{dN}{dt} = r N \left(1 - \frac {N}{K} \right)</math>
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| 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.
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| The logistic equation can be integrated exactly, and has solution
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| :<math> N(t) = \frac{K}{1+ C K e^{-rt}} </math> | |
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| 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,
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| :<math> \frac{1}{N(t)} = \frac{1-e^{-rt}}{K}+ \frac{e^{-rt}}{N(0)}. </math>
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| 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.
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| 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.
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| ==See also==
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| *[[Population dynamics]]
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| *[[Logistic map]]
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| *[[Logistic function]]
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| *[[Logistic distribution]]
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| ==Works==
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| * {{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 |
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| url = http://books.google.com/?id=8GsEAAAAYAAJ&q=
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| | accessdate = 2013-02-18}}
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| * {{cite book
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| | title = Traité élémentaire des fonctions elliptiques : ouvrage destiné à faire suite aux traités élémentaires de calcul intégral
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| | publisher = Hayez
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| | first = Pierre-François
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| | last = Verhulst
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| | year = 1841
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| | place = Bruxelles
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| | url= http://books.google.com/?id=WS8LAAAAYAAJ&printsec=frontcover
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| | isbn =
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| | accessdate = 2013-02-18
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| }}
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| * {{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}}
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| * {{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}}
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| ==External links==
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| * {{MacTutor Biography|id=Verhulst}}
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| {{Authority control|VIAF=66616324}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME =Verhulst, Pierre Francois
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = mathematician
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| | DATE OF BIRTH = 28 October 1804
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| | PLACE OF BIRTH = Brussels, Belgium
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| | DATE OF DEATH = 15 February 1849
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| | PLACE OF DEATH = Brussels, Belgium
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| }}{{dmy|date=January 2011}}
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| {{DEFAULTSORT:Verhulst, Pierre Francois}}
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| [[Category:1804 births]]
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| [[Category:1849 deaths]]
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| [[Category:Belgian mathematicians]]
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| [[Category:19th-century writers]]
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