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Furthermore, a global maximum (or minimum) either must be a local maximum (or minimum) in the interior of the domain, or must lie on the boundary of the domain. So a method of finding a global maximum (or minimum) is to look at all the local maxima (or minima) in the interior, and also look at the maxima (or minima) of the points on the ...
Shelford's law of tolerance is a principle developed by American zoologist Victor Ernest Shelford in 1911. It states that an organism's success is based on a complex set of conditions and that each organism has a certain minimum, maximum, and optimum environmental factor or combination of factors that determine success. [1]
A continuous function () on the closed interval [,] showing the absolute max (red) and the absolute min (blue).. In calculus, the extreme value theorem states that if a real-valued function is continuous on the closed and bounded interval [,], then must attain a maximum and a minimum, each at least once.
In a totally ordered set the maximal element and the greatest element coincide; and it is also called maximum; in the case of function values it is also called the absolute maximum, to avoid confusion with a local maximum. [1] The dual terms are minimum and absolute minimum. Together they are called the absolute extrema. Similar conclusions ...
Liebig's law has been extended to biological populations (and is commonly used in ecosystem modelling).For example, the growth of an organism such as a plant may be dependent on a number of different factors, such as sunlight or mineral nutrients (e.g., nitrate or phosphate).
The minimum and the maximum value are the first and last order statistics (often denoted X (1) and X (n) respectively, for a sample size of n). If the sample has outliers, they necessarily include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum need not ...
An absolute scale begins at a natural minimum, leaving only one direction in which to progress. An absolute scale can only be applied to measurements in which a true minimum is known to exist. Time , for example, which does not have a clearly known beginning, is measured on a relative scale, with an arbitrary zero-point such as the conventional ...
The maximum of a subset of a preordered set is an element of which is greater than or equal to any other element of , and the minimum of is again defined dually. In the particular case of a partially ordered set , while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements.