Discrete Laplace Cycles of Period Four

We study discrete conjugate nets whose Laplace sequence is of period four. Corresponding points of opposite nets in this cyclic sequence have equal osculating planes in different net directions, that is, they correspond in an asymptotic transformation. We show that this implies that the connecting lines of corresponding points form a discrete W-congruence. We derive some properties of discrete Laplace cycles of period four and describe two explicit methods for their construction

A Determination of the Hubble Constant Using Measurements of X-Ray Emission and the Sunyaev-Zeldovich Effect at Millimeter Wavelengths in the Cluster Abell 1835

We present a determination of the Hubble constant and central electron density in the cluster Abell 1835 (z = 0.2523) from measurements of X-ray emission and millimeter-wave observations of the Sunyaev-Zeldovich (S-Z) effect with the Sunyaev-Zeldovich Infrared Experiment (SuZIE) multifrequency array receiver. Abell 1835 is a well studied cluster in the X-ray with a large central cooling flow. Using a combination of data from ROSAT PSPC and HRI images and millimeter wave measurements we fit a King model to the emission from the ionized gas around Abell 1835 with θ0 = 022 ± 002 and β = 0.58 ± 0.02. Assuming the cluster gas to be isothermal with a temperature of 9.8 keV, we find a y-parameter of 4.9 ± 0.6 × 10-4 and a peculiar velocity of 500 ± 1000 km s-1 from measurements at three frequencies, 145, 221, and 279 GHz. Combining the S-Z measurements with X-ray data, we determine a value for the Hubble constant of H0 = 59 km s-1 Mpc-1 and a central electron density for Abell 1835 of ne0 = 5.64 × 10-2 cm-3 assuming a standard cosmology with Ωm = 1 and ΩΛ = 0. The error in the determination of the Hubble constant is dominated by the uncertainty in the temperature of the X-ray emitting cluster gas