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Pierre François Verhulst
Pierre François Verhulst (28 October 1804, Brussels – 15 February 1849, Brussels) was a Belgian mathematician and a doctor in number theory from the University of Ghent in 1825. He is best known for the logistic growth model. Logistic equation Verhulst developed the logistic function in a series of three papers between 1838 and 1847, based on research on modeling population growth that he conducted in the mid 1830s, under the guidance of Adolphe Quetelet; see for details. Verhulst published in the equation: : \frac = rN - \alpha N^2 where ''N''(''t'') represents number of individuals at time ''t'', ''r'' the intrinsic growth rate, and ''\alpha'' is the density-dependent crowding effect (also known as intraspecific competition). In this equation, the population equilibrium (sometimes referred to as the carrying capacity, ''K''), N^*, is : N^* = \frac . In he named the solution the logistic curve. Later, Raymond Pearl and Lowell Reed popularized the equation, but w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Francois Verhulst
Pierre is a masculine given name. It is a French form of the name Peter. Pierre originally meant "rock" or "stone" in French (derived from the Greek word πέτρος (''petros'') meaning "stone, rock", via Latin "petra"). It is a translation of Aramaic כיפא (''Kefa),'' the nickname Jesus gave to apostle Simon Bar-Jona, referred in English as Saint Peter. Pierre is also found as a surname. People with the given name * Abbé Pierre, Henri Marie Joseph Grouès (1912–2007), French Catholic priest who founded the Emmaus Movement * Monsieur Pierre, Pierre Jean Philippe Zurcher-Margolle (c. 1890–1963), French ballroom dancer and dance teacher * Pierre (footballer), Lucas Pierre Santos Oliveira (born 1982), Brazilian footballer * Pierre, Baron of Beauvau (c. 1380–1453) * Pierre, Duke of Penthièvre (1845–1919) * Pierre, marquis de Fayet (died 1737), French naval commander and Governor General of Saint-Domingue * Prince Pierre, Duke of Valentinois (1895–1964), father ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is : \left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is defined to be :H = \frac = \frac = \left(\frac\right)^. The third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals. From the following formula: :H = \frac. it is more apparent that the harmonic mean is related to the arithmetic and geometric means. It is the reciprocal dual of the arithmetic mean for positive inputs: :1/H(1/x_1 \ldots 1/x_n) = A(x_1 \ldots x_n) The harmonic mean is a Schur-con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1849 Deaths
Events January–March * January 1 – France begins issue of the Ceres series, the nation's first postage stamps. * January 5 – Hungarian Revolution of 1848: The Austrian army, led by Alfred I, Prince of Windisch-Grätz, enters in the Hungarian capitals, Buda and Pest. The Hungarian government and parliament flee to Debrecen. * January 8 – Hungarian Revolution of 1848: Romanian armed groups massacre 600 unarmed Hungarian civilians, at Nagyenyed.Hungarian HistoryJanuary 8, 1849 And the Genocide of the Hungarians of Nagyenyed/ref> * January 13 ** Second Anglo-Sikh War – Battle of Tooele: British forces retreat from the Sikhs. ** The Colony of Vancouver Island is established. * January 21 ** General elections are held in the Papal States. ** Hungarian Revolution of 1848: Battle of Nagyszeben – The Hungarian army in Transylvania, led by Josef Bem, is defeated by the Austrians, led by Anton Puchner. * January 23 – Elizabeth Blackwell is awarded her M.D. by the Medi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1804 Births
Eighteen or 18 may refer to: * 18 (number), the natural number following 17 and preceding 19 * one of the years 18 BC, AD 18, 1918, 2018 Film, television and entertainment * ''18'' (film), a 1993 Taiwanese experimental film based on the short story ''God's Dice'' * ''Eighteen'' (film), a 2005 Canadian dramatic feature film * 18 (British Board of Film Classification), a film rating in the United Kingdom, also used in Ireland by the Irish Film Classification Office * 18 (''Dragon Ball''), a character in the ''Dragon Ball'' franchise * "Eighteen", a 2006 episode of the animated television series ''12 oz. Mouse'' Music Albums * ''18'' (Moby album), 2002 * ''18'' (Nana Kitade album), 2005 * '' 18...'', 2009 debut album by G.E.M. Songs * "18" (5 Seconds of Summer song), from their 2014 eponymous debut album * "18" (One Direction song), from their 2014 studio album ''Four'' * "18", by Anarbor from their 2013 studio album '' Burnout'' * "I'm Eighteen", by Alice Cooper common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Distribution
Logistic may refer to: Mathematics * Logistic function, a sigmoid function used in many fields ** Logistic map, a recurrence relation that sometimes exhibits chaos ** Logistic regression, a statistical model using the logistic function ** Logit, the inverse of the logistic function ** Logistic distribution, the derivative of the logistic function, a continuous probability distribution, used in probability theory and statistics * Mathematical logic, subfield of mathematics exploring the applications of formal logic to mathematics Other uses * Logistics, the management of resources and their distributions ** Logistic engineering, the scientific study of logistics ** Military logistics Military logistics is the discipline of planning and carrying out the movement, supply, and maintenance of military forces. In its most comprehensive sense, it is those aspects or military operations that deal with: * Design, development, acqui ..., the study of logistics at the service of milita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Map
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. Mathematically, the logistic map is written where is a number between zero and one, that represents the ratio of existing population to the maximum possible population. This nonlinear difference equation is intended to capture two effects: * ''reproduction'' where the population will increase at a rate proportional to the current population when the population size is small. * ''starvation'' (density-dependent mortality) where the growth rate will decrease at a rate proportional to the value obtained by taking the theoretical "carrying capacity" of the environment l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Dynamics
Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. History Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years,Malthus, Thomas Robert. An Essay on the Principle of Population: Library of Economics although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model. According to Malthus, assuming that the conditions (the environment) remain constant ('' ceteris paribus''), a population will grow (or decline) exponentially. This principle provided the basis for the subsequent predictive theories, such as the demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic model. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable at the growth rate , as time goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x_t = x_0(1+r)^t where is the value of at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R/K Selection Theory
In ecology, ''r''/''K'' selection theory relates to the selection of combinations of traits in an organism that trade off between quantity and quality of offspring. The focus on either an increased quantity of offspring at the expense of individual parental investment of ''r''-strategists, or on a reduced quantity of offspring with a corresponding increased parental investment of ''K''-strategists, varies widely, seemingly to promote success in particular environments. The concepts of quantity or quality offspring are sometimes referred to as "cheap" or "expensive", a comment on the expendable nature of the offspring and parental commitment made. The stability of the environment can predict if many expendable offspring are made or if fewer offspring of higher quality would lead to higher reproductive success. An unstable environment would encourage the parent to make many offspring, because the likelihood of all (or the majority) of them surviving to adulthood is slim. In contrast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beverton–Holt Model
The Beverton–Holt model is a classic discrete-time population model which gives the expected number ''n'' ''t''+1 (or density) of individuals in generation ''t'' + 1 as a function of the number of individuals in the previous generation, : n_ = \frac. Here ''R''0 is interpreted as the proliferation rate per generation and ''K'' = (''R''0 − 1) ''M'' is the carrying capacity of the environment. The Beverton–Holt model was introduced in the context of fisheries by Beverton & Holt (1957). Subsequent work has derived the model under other assumptions such as contest competition (Brännström & Sumpter 2005), within-year resource limited competition (Geritz & Kisdi 2004) or even as the outcome of a source-sink Malthusian patches linked by density-dependent dispersal (Bravo de la Parra et al. 2013). The Beverton–Holt model can be generalized to include scramble competition (see the Ricker model, the Hassell model and the Maynard S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Map
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst. Mathematically, the logistic map is written where is a number between zero and one, that represents the ratio of existing population to the maximum possible population. This nonlinear difference equation is intended to capture two effects: * ''reproduction'' where the population will increase at a rate proportional to the current population when the population size is small. * ''starvation'' (density-dependent mortality) where the growth rate will decrease at a rate proportional to the value obtained by taking the theoretical "carrying capacity" of the environment l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lowell Reed
Lowell Jacob Reed (January 8, 1886 – April 29, 1966) was 7th president of the Johns Hopkins University in Baltimore, Maryland. He was born in Berlin, New Hampshire, the son of Jason Reed, a millwright and farmer, and Louella Coffin Reed. Education and career He had a long career as a research scientist in biostatistics and public health administration at Hopkins, where he was previously dean and director of the School of Public Health and later was vice president in charge of medical activities. He was an Invited Speaker at the ICM in 1924 in Toronto. In 1927 he was elected as a Fellow of the American Statistical Association. As a researcher, he developed a well known statistical technique for estimating the ED-50, and his work with epidemiologist Wade Hampton Frost on the Reed–Frost epidemic models also remains well known. He died in Berlin, New Hampshire, in 1966. Lowell Reed attended the University of Maine, graduating in 1907 with a degree in electrical engineering. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
