Coarse equivalence and topological couplings of locally compact groups
M. Gromov has shown that any two finitely generated groups $$\Gamma $$Γ and $$\Lambda $$Λ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions $$\Gamma \curvearrowright X \curvearrowleft \Lambda $$Γ↷X↶Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups.
Metrics in locally compact groups
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High-Speed Infrared Radiometers*
The paper describes high-speed infrared radiometers utilizing thermistor infrared detectors. Instruments with 4- and 8-in. diam Cassegrain mirror optics are described. The method of operation and the calibration of these radiometers is discussed.The radiometers are uniformly sensitive from 0.7 to 35 μ. They have a response time of 16 msec and a sensitivity of the order of 10−10 w/cm−2 corresponding to a blackbody temperature differential of 0.01°C.The radiometers are used for quantitative measurements of infrared radiation and remote temperature determinations.