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  2. Proportionality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Proportionality_(mathematics)

    With inverse proportion, an increase in one variable is associated with a decrease in the other. For instance, in travel, a constant speed dictates a direct proportion between distance and time travelled; in contrast, for a given distance (the constant), the time of travel is inversely proportional to speed: s × t = d.

  3. Direct method in the calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Direct_method_in_the...

    In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given functional, [1] introduced by Stanisław Zaremba and David Hilbert around 1900. The method relies on methods of functional analysis and topology. As well as being used to prove the existence of ...

  4. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]

  5. Proportion (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Proportion_(mathematics)

    A proportion is a mathematical statement expressing equality of two ratios. [1] [2]: =: a and d are called extremes, b and c are called means. Proportion can be written as =, where ratios are expressed as fractions.

  6. Coefficient of determination - Wikipedia

    en.wikipedia.org/wiki/Coefficient_of_determination

    Ordinary least squares regression of Okun's law.Since the regression line does not miss any of the points by very much, the R 2 of the regression is relatively high.. In statistics, the coefficient of determination, denoted R 2 or r 2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).

  7. Exponential growth - Wikipedia

    en.wikipedia.org/wiki/Exponential_growth

    The differential equation is solved by direct integration: = = = ⁡ =. so that () =. In the above differential equation, if k < 0 , then the quantity experiences exponential decay . For a nonlinear variation of this growth model see logistic function .

  8. Total variation distance of probability measures - Wikipedia

    en.wikipedia.org/wiki/Total_variation_distance...

    The total variation distance (or half the norm) arises as the optimal transportation cost, when the cost function is (,) =, that is, ‖ ‖ = (,) = {(): =, =} = ⁡ [], where the expectation is taken with respect to the probability measure on the space where (,) lives, and the infimum is taken over all such with marginals and , respectively.

  9. Total variation - Wikipedia

    en.wikipedia.org/wiki/Total_variation

    In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x ...

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