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The expressions: a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth are used as fixed phrases. The expression a zero-order approximation is also common. Cardinal numerals are occasionally used in expressions like an order-zero approximation, an order-one approximation, etc.
As an example of the first type, the reaction NO 2 + CO → NO + CO 2 is second-order in the reactant NO 2 and zero order in the reactant CO. The observed rate is given by v 0 = k [ NO 2 ] 2 , {\displaystyle v_{0}=k[{\ce {NO2}}]^{2},} and is independent of the concentration of CO.
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.
Zero-order process (statistics), a sequence of random variables, each independent of the previous ones; Zero order process (chemistry), a chemical reaction in which the rate of change of concentration is independent of the concentrations; Zeroth-order approximation, an approximation of a function by a constant; Zeroth-order logic, a form of ...
Under zero-based numbering, the initial element is sometimes termed the zeroth element, [1] rather than the first element; zeroth is a coined ordinal number corresponding to the number zero. In some cases, an object or value that does not (originally) belong to a given sequence, but which could be naturally placed before its initial element ...
In fact, however, the observed reaction rate is second-order in NO 2 and zero-order in CO, [5] with rate equation r = k[NO 2] 2. This suggests that the rate is determined by a step in which two NO 2 molecules react, with the CO molecule entering at another, faster, step. A possible mechanism in two elementary steps that explains the rate ...
First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an integrator. For FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled.
In probability theory and statistics, a zero-order process is a stochastic process in which each observation is independent of all previous observations. For example, a zero-order process in marketing would be one in which the brands purchased next do not depend on the brands purchased before, implying a fixed probability of purchase since it is zero order in regards to probability.