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The Born cross sections of the processes $e^+e^- \rightarrow \omega\pi^{0}$and $e^+e^- \rightarrow \omega\eta$ are measured at center-of-mass energiesbetween 3.773 and 4.701 GeV using a total integrated luminosity of 22.7fb$^{-1}$ collected with the BESIII detector operating at the BEPCII collider.A simple $s^{-n}$ dependence for the continuum process can describe themeasured Born cross sections. No significant contributions from the$\psi(4160)$, $Y(4230)$, $Y(4360)$, $\psi(4415)$, $Y(4660)$ resonances arefound, which indicates relative small branching fractions for these resonancesinto the $\omega\pi^{0}$ and $\omega\eta$ final states.

Cross section measurements of the processes $e^+e^- \rightarrow  \omega\pi^{0}$ and $\omega\eta$ at center-of-mass energies between 3.773 and  4.701 GeV