Heterodyne receivers register the sky signal on either a circular polarization basis (where it is split into left-hand and right-hand circular polarization) or a linear polarization basis (where it is split into horizontal and vertical linear polariz
ation). We study the problem of interferometric observations performed with telescopes that observe on different polarization bases, hence producing visibilities that we call mixed basis (i.e., linear in one telescope and circular in the other). We present novel algorithms for the proper calibration and treatment of such interferometric observations and test our algorithms with both simulations and real data. The use of our algorithms will be important for the optimum calibration of forthcoming observations with the Atacama Large mm/submm Array (ALMA) in very-long-baseline interferometry (VLBI) mode. Our algorithms will also allow us to optimally calibrate future VLBI observations at very high data rates (i.e., wide bandwidths), where linear-polarization feeds will be preferable at some stations, to overcome the polarimetric limitations due to the use of quarter-wave plates.
We give a number of examples of isospectral pairs of plane domains, and a particularly simple method of proving isospectrality. One of our examples is a pair of domains that are not only isospectral but homophonic: Each domain has a distinguished poi
nt such that corresponding normalized Dirichlet eigenfunctions take equal values at the distinguished points. This shows that one really cant hear the shape of a drum.
We describe examples motivated by the work of Serre and Abhyankar.
We strengthen The Free Will Theorem [1] in several ways, by replacing the axiom FIN by a weaker axiom MIN, and also by allowing the particles responses to depend on past half-spaces rather than on on past light cones. This change allows us to directl
y apply our theorem to relativistic theories of the GRW type.
