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The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s(t), is the real-valued function: = {()}, where arg is the complex argument function. The instantaneous frequency is the temporal rate of change of the instantaneous phase.
In mathematics, a rate is the quotient of two quantities, 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 the corresponding rate of change ...
Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. [1] The short rate, r t {\displaystyle r_{t}\,} , then, is the ( continuously compounded , annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time t {\displaystyle t} .
If this instantaneous return is received continuously for one period, then the initial value P t-1 will grow to = during that period. See also continuous compounding . Since this analysis did not adjust for the effects of inflation on the purchasing power of P t , RS and RC are referred to as nominal rates of return .
In probability theory, a transition-rate matrix (also known as a Q-matrix, [1] intensity matrix, [2] or infinitesimal generator matrix [3]) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states.
(M) and (F) are additive instantaneous rates that sum up to (Z), the instantaneous total mortality coefficient; that is, Z=M+F. [2] These rates are usually calculated on an annual basis. Estimates of fish mortality rates are often included in mathematical yield models to predict yield levels obtained under various exploitation scenarios.
Rate of change may refer to: Rate of change (mathematics) , either average rate of change or instantaneous rate of change Instantaneous rate of change , rate of change at a given instant in time
For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ. For any non-zero time τ the growth rate is given by the dimensionless positive number b. Thus the law of exponential growth can be written in different but mathematically equivalent forms, by using a different base.