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In the Gaia era, the membership analysis and parameter determination of open clusters (OCs) are more accurate. We performed a census of OCs classical Cepheids based on Gaia Early Data Release 3 (EDR3) and obtained a sample of 33 OC Cepheids fulfilling the constraints of the spatial position, proper motion, parallax and evolution state. 13 of 33 OC Cepheids are newly discovered. Among them, CM Sct is the first first-crossing Cepheids with direct evidence of evolution. DP Vel is likely a fourth- or fifth-crossing Cepheids. Based on independent distances from OCs, W_1-band period-luminosity relation of Cepheids is determined with a 3.5% accuracy: <MW1> = -(3.274 +- 0.090) log P - (-2.567 +- 0.080). The Gaia-band period-Wesenheit relation agrees well with Ripepi et al. (2019). A direct period-age relation for fundamental Cepheids are also determined based on OCs age, that is log t = -(0.638 +- 0.063) log P + (8.569 +- 0.057).
Context: The $chi^{1}$ Fornacis cluster (Alessi 13) is one of a few open clusters of its age and distance in the Solar neighbourhood that ought to benefit from more attention as it can serve as a cornerstone for numerous future studies related to sta
Classical double-mode pulsators (RR Lyrae stars and delta Cepheids) are important for their simultaneous pulsation in low-order radial modes. This enables us to put stringent constraints on their physical parameters. We use 30 bright galactic doubl
Context. Open clusters are very good tracers of the evolution of the Galactic disc. Thanks to Gaia, their kinematics can be investigated with an unprecedented precision and accuracy. Aims. The distribution of open clusters in the 6D phase space is re
Classical Cepheids in open clusters are key ingredients for stellar population studies and the characterization of variable stars, as they are tracers of young and massive populations and of recent star formation episodes. Cluster Cepheids are of par
We independently determine the zero-point offset of the Gaia early Data Release-3 (EDR3) parallaxes based on $sim 110,000$ W Ursae Majoris (EW)-type eclipsing binary systems. EWs cover almost the entire sky and are characterized by a relatively compl