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In mathematics, a rate is the quotient of two quantities in different units of measurement, often represented as a fraction. [1] If the divisor (or fraction denominator) in the rate is equal to one expressed as a single unit, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the dividend (the fraction numerator) of the rate expresses ...
Rate function. In mathematics — specifically, in large deviations theory — a rate function is a function used to quantify the probabilities of rare events. Such functions are used to formulate large deviation principles. A large deviation principle quantifies the asymptotic probability of rare events for a sequence of probabilities.
Convergence definitions. Suppose that the sequence converges to the number . The sequence is said to converge with order to , and with a rate of convergence[ 3] of , if. (Definition 1) for some positive constant if , and if . [ 4][ 5] It is not necessary, however, that be an integer.
Rate equation. In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only ...
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. [1] 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 ...
For example, let f(x) = 6x 4 − 2x 3 + 5, and suppose we wish to simplify this function, using O notation, to describe its growth rate as x approaches infinity. This function is the sum of three terms: 6x 4, −2x 3, and 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of x ...
describes the relationship between x, y and h, for a right triangle. Differentiating both sides of this equation with respect to time, t, yields. Step 3: When solved for the wanted rate of change, dy / dt, gives us. Step 4 & 5: Using the variables from step 1 gives us: Solving for y using the Pythagorean Theorem gives:
Sample-rate conversion, sampling-frequency conversion or resampling is the process of changing the sampling rate or sampling frequency of a discrete signal to obtain a new discrete representation of the underlying continuous signal. [ 1] Application areas include image scaling [ 2] and audio/visual systems, where different sampling rates may be ...