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X-ray timing and spectrophotometry of accretion-powered neutron stars have been used to determine or constrain many of the intrinsic properties of these stars, including their masses, radii, magnetic fields, spin frequencies, and internal structure. These measurements have important implications for the evolution of ordinary and neutron stars in binary systems, the supernova process in massive stars, accretion-induced collapse of white dwarfs and neutron stars, and the properties of extremely dense matter. High-speed X-ray spectrophotometry has also revealed a variety of phenomena, such as pulse-frequency variations, QPOs, aperiodic X-ray variability, and systematic X-ray brightness and spectral changes that provide valuable information about the structure and dynamics of accretion flows, the interaction of such flows with the magnetic fields and surfaces of neutron stars, and hydrodynamics in the presence of intense radiation and very strong magnetic fields. The X-ray Timing Explorer will have a unique combination of large-area detectors, 2--200 keV energy response, all-sky monitors, microsecond time resolution, sophisticated onboard data processing, high telemetry rates, and unprecedented maneuverability and is expected to produce major advances in these areas of physics and astrophysics. Some of the possible advances will be described.
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