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Abstract SX Phoenicis (SXP) variables are short-period pulsating stars that exhibit a period–luminosity (PL) relation. We derived thegri-band PL and extinction-free period–Wesenheit (PW) relations, as well as the period-color and reddening-free period-Q-index relations for 47 SXP stars located in 21 globular clusters, using the optical light curves taken from Zwicky Transient Facility. These empirical relations were derived for the first time in thegrifilters except for theg-band PL relation. We used ourgi-band PL and PW relations to derive a distance modulus to Crater II dwarf spheroidal which hosts one SXP variable. Assuming that the fundamental and first-overtone pulsation mode for the SXP variable in Crater II, we found distance moduli of 20.03 ± 0.23 mag and 20.37 ± 0.24 mag, respectively, using the PW relation, where the latter is in excellent agreement with independent RR Lyrae based distance to Crater II dwarf galaxy.
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Maps with No a Priori Bounds
Abstract The modulus of a polynomial-like (PL) map is an important invariant that controls distortion of the straightening map and, hence, geometry of the corresponding PL Julia set. Lower bounds on the modulus, calledcomplex a priori bounds, are known in a great variety of contexts. For any rational function we complement this by an upper bound for moduli of PL maps in the satellite case that dependsonly on the relative period and the degree of the PL map.This rules out a priori bounds in the satellite case with unbounded relative periods. We also apply our tools to obtain lower bounds for hyperbolic lengths of geodesics in the infinitely renormalizable case, and to show that moduli of annuli must converge to 0 for a sequence of arbitrary renormalizations, under several conditions all of which are shown to be necessary.
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- Award ID(s):
- 2349942
- PAR ID:
- 10593957
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 406
- Issue:
- 6
- ISSN:
- 0010-3616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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