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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Each monomer "borrows" functions from other nearby components, effectively increasing its basis set and improving the calculation of derived properties such as energy. [3] If the total energy is minimised as a function of the system geometry, the short-range energies from the mixed basis sets must be compared with the long-range energies from ...
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Chemical reactions: The rates of certain types of chemical reactions depend on the concentration of one or another reactant. Reactions whose rate depends only on the concentration of one reactant (known as first-order reactions) consequently follow exponential decay. For instance, many enzyme-catalyzed reactions behave this way.
To apply a Q test for bad data, arrange the data in order of increasing values and calculate Q as defined: Q = gap range {\displaystyle Q={\frac {\text{gap}}{\text{range}}}} Where gap is the absolute difference between the outlier in question and the closest number to it.
Standard addition involves adding known amounts of analyte to an unknown sample, a process known as spiking.By increasing the number of spikes, the analyst can extrapolate for the analyte concentration in the unknown that has not been spiked. [2]
Best rational approximants for π (green circle), e (blue diamond), ϕ (pink oblong), (√3)/2 (grey hexagon), 1/√2 (red octagon) and 1/√3 (orange triangle) calculated from their continued fraction expansions, plotted as slopes y/x with errors from their true values (black dashes)
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.