... short-range

Due to the power-law relation between flux density and frequency, the influence of the flux density variability on the spectral index decreases with increasing frequency interval.

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... relativity

 If $\vartheta$ is the angle enclosed by the line of sight and the direction of motion and if $\beta$ is the intrinsic velocity, one finds $\beta_{\rm app}=\frac{\beta~\sin\vartheta}{1-\beta~\cos\vartheta}$. The minimal intrinsic velocity $\beta_{\rm min}=\sqrt{(\beta_{\rm app}^2)/(1+\beta_{\rm app}^2)}$ implies an angle $\vartheta_{\rm min}$ fulfilling: $\cot(\vartheta_{\rm min})=\beta_{\rm app}$.

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... dominant

E.g. at the last epoch the extended components show flux densities of 20% of the central flux density.

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... factor

With the terms of footnote 2 it is $\delta = (\gamma~(1-\beta~\cos\vartheta))^{-1}$ with $\gamma=1/\sqrt{1-\beta^2}$.

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... estimate

If much more (spectral and multi-epoch) data are available as e.g. in the case of the quasar 3C 345, inhomogeneities in the particle number density can also be estimated. Lobanov & Zensus (1999) used more detailed analyzis to explain the observed flux density variations quantitatively with time of 3C 345.

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