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Van Genuchten–Gupta Model
The Van Genuchten–Gupta model is an inverted S-curve applicable to crop yield and soil salinity relations.M. Th. van Genuchten and S.K. Gupta, 1993. USDA-ARS, U.S. Salinity Laboratory 4500 Glenwood Drive, Riverside, California, USA, 92501. ''A reassessment of the Crop Tolerance Response Function.'' Journal of the Indian Society of Soil Science, Vol. 41, No. 4, pp 730–737. It is named after Martinus Theodore van Genuchten and Satyandra K. Gupta's work from the 1990s. Equation The mathematical expression is: : Y = \frac where ''Y'' is the yield, ''Y''m is the maximum yield of the model, ''C'' is salt concentration of the soil, ''C''50 is the ''C'' value at 50% yield, and ''P'' is an exponent to be found by optimization and maximizing the model's goodness of fit to the data. In the figure: ''Y''m = 3.1, ''C''50 = 12.4, ''P'' = 3.75 Alternative one As an alternative, the '' logistic S-function'' can be used. The mathematical expression is: : Y^ = \frac where: : Y^ = \fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmoid Function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: :S(x) = \frac = \frac=1-S(-x). Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as an alias for the logistic function. Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and hype ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crop Yield
In agriculture, the yield is a measurement of the amount of a crop grown, or product such as wool, meat or milk produced, per unit area of land. The seed ratio is another way of calculating yields. Innovations, such as the use of fertilizer, the creation of better farming tools, new methods of farming and improved crop varieties, have improved yields. The higher the yield and more intensive use of the farmland, the higher the productivity and profitability of a farm; this increases the well-being of farming families. Surplus crops beyond the needs of subsistence agriculture can be sold or bartered. The more grain or fodder a farmer can produce, the more draft animals such as horses and oxen could be supported and harnessed for labour and production of manure. Increased crop yields also means fewer hands are needed on farm, freeing them for industry and commerce. This, in turn, led to the formation and growth of cities, which then translated into an increased demand for foodstuff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soil Salinity
Soil salinity is the salt content in the soil; the process of increasing the salt content is known as salinization. Salts occur naturally within soils and water. Salination can be caused by natural processes such as mineral weathering or by the gradual withdrawal of an ocean. It can also come about through artificial processes such as irrigation and road salt. Natural occurrence Salts are a natural component in soils and water. The ions responsible for salination are: Na+, K+, Ca2+, Mg2+ and Cl−. Over long periods of time, as soil minerals weather and release salts, these salts are flushed or leached out of the soil by drainage water in areas with sufficient precipitation. In addition to mineral weathering, salts are also deposited via dust and precipitation. Salts may accumulate in dry regions, leading to naturally saline soils. This is the case, for example, in large parts of Australia. Human practices can increase the salinity of soils by the addition of salts in i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martinus Theodore Van Genuchten
Martinus may refer to: * Martin (magister militum per Armeniam), 6th-century Byzantine/East Roman general * Martinus (son of Heraclius), 7th-century Byzantine/East Roman co-emperor * Martinus of Arles, doctor of theology, priest, and author on demonology and witches * Saint Martinus or Saint Martin of Tours * Martinus College, a secondary school in the Netherlands * VV Martinus, a Dutch volleyball club People with the name * Derek Martinus (1931–2014), British television and theatre director * Flavius Martinus, ''vicarius'' (governor) of the Roman provinces of Britain * Martinus Beijerinck, Dutch microbiologist * Martinus von Biberach (died 1498), theologian from Heilbronn, Germany * Martinus Bosselaar, Dutch football (soccer) player * Martinus Brandal, Norwegian engineer and businessman * Martinus Dom, first abbot of the Trappist Abbey of Westmalle * Martinus Fabri, Dutch composer of the late 14th century * Martinus Gosia, scholar and Italian jurist, one of the Four Doctors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Genugten-Gupta Model
A van is a type of road vehicle used for transporting goods or people. Depending on the type of van, it can be bigger or smaller than a pickup truck and SUV, and bigger than a common car. There is some varying in the scope of the word across the different English-speaking countries. The smallest vans, microvans, are used for transporting either goods or people in tiny quantities. Mini MPVs, compact MPVs, and MPVs are all small vans usually used for transporting people in small quantities. Larger vans with passenger seats are used for institutional purposes, such as transporting students. Larger vans with only front seats are often used for business purposes, to carry goods and equipment. Specially-equipped vans are used by television stations as mobile studios. Postal services and courier companies use large step vans to deliver packages. Word origin and usage Van meaning a type of vehicle arose as a contraction of the word caravan. The earliest records of a van as a vehicle i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goodness Of Fit
The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test). In the analysis of variance, one of the components into which the variance is partitioned may be a lack-of-fit sum of squares. Fit of distributions In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: * Bayesian information criterion *Kolmogorov–Smirnov test *Cramér–von Mises criterion *Anderson–Darling test * Shapiro–Wilk test *Chi-squared test *Akaike informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-curve Model
S curve or S-curve may refer to: * S-curve (art), an "S"-shaped curve which serves a wide variety of compositional purposes * S-curve (math), a characteristic "S"-shaped curve of a Sigmoid function * S-curve corset, an Edwardian corset style * S-Curve Records, a record company label * Reverse curve In civil engineering, a reverse curve (or "S" curve) is a section of the horizontal alignment of a highway or railroad route in which a curve to the left or right is followed immediately by a curve in the opposite direction. On highways in the ..., or "S" curve, in civil engineering See also * * Recurve (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Function
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +\infty and approaching zero as x approaches -\infty. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I. The standard logistic function, where L=1,k=1,x_0=0, is sometimes simply called ''the sigmoid''. It is also sometimes called the ''expit'', being the inverse of the logit. History The logistic function was introduced in a series of three papers by Pierre François Verhulst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Regression
Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system where the unit cell is in the shape of a cube * Cubic function, a polynomial function of degree three * Cubic equation, a polynomial equation (reducible to ''ax''3 + ''bx''2 + ''cx'' + ''d'' = 0) * Cubic form, a homogeneous polynomial of degree 3 * Cubic graph (mathematics - graph theory), a graph where all vertices have degree 3 * Cubic plane curve (mathematics), a plane algebraic curve ''C'' defined by a cubic equation * Cubic reciprocity (mathematics - number theory), a theorem analogous to quadratic reciprocity * Cubic surface, an algebraic surface in three-dimensional space * Cubic zirconia, in geology, a mineral that is widely synthesized for use as a diamond simulacra * CUBIC, a histology method Computing * Cubic IDE, a modular deve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Regression
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable ''x'' and the dependent variable ''y'' is modelled as an ''n''th degree polynomial in ''x''. Polynomial regression fits a nonlinear relationship between the value of ''x'' and the corresponding conditional mean of ''y'', denoted E(''y'' , ''x''). Although ''polynomial regression'' fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(''y'' , ''x'') is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression. The explanatory (independent) variables resulting from the polynomial expansion of the "baseline" variables are known as higher-degree terms. Such variables are also used in classification settings. History Polynomial regression models are usu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
