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Eighteen days of MERLIN data and 42 hours of A-array VLA data at 1.4 GHz have been combined to image a 10-arcmin field centred on the Hubble Deep and Flanking Fields (HDF and HFF). A complete sample of 92 radio sources with 1.4-GHz flux densities above 40 microJy has been imaged using MERLIN+VLA. The images are amongst the most sensitive yet made at 1.4 GHz, with rms noise levels of 3.3 microJy/beam in the 0.2-arcsec images. Virtually all the sources are resolved, with angular sizes in the range 0.2 to 3 arcsec. No additional sources were detected down to 23 microJy in the central 3 arcmin, indicating that sources fainter than 40 microJy are heavily resolved with MERLIN and must have typical angular sizes greater than 0.5 arcsec. Compact radio sources were used to align the optical data to the ICRF, to <50 mas in the HDF. We find a statistical association of very faint (2 microJy and above) radio sources with optically bright HDF galaxies down to about 23 mag. Of the 92 radio sources above 40 microJy, about 85 percent are identified with galaxies brighter than about I = 25 mag; the remaining 15 percent are associated with optically faint systems. We identify several very red, optically faint systems including the the strongest sub-mm source in the HDF, HDF850.1. 72 percent of the radio sources are starburst or AGN-type systems; the remainder are unclassified. The proportion of starburst systems increases with decreasing flux density; below 100 microJy 70 percent of the sources are starburst-type systems in the redshift range 0.3 -- 1.3. Chandra detections are associated with 55 of the 92 radio sources but their X-ray flux densities do not appear to be correlated with the radio flux densities or morphologies.
A four-dimensional statistical description of electromagnetic radiation is developed and applied to the analysis of radio pulsar polarization. The new formalism provides an elementary statistical explanation of the modal broadening phenomenon in sing
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