30 research outputs found

    Cornerstones of Sampling of Operator Theory

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    This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

    Mobility of Metal Tracers in Unsaturated Tuffs of Busted Butte, Nevada

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    A complex tracer mixture was injected continuously for over two years into a 10 m x 10 m x 7 m block of unsaturated tuff as part of the Busted Butte unsaturated-zone tracer test at Yucca Mountain. The test was designed to measure tracer transport within the Topopah Springs and Calico Hills tuffs, units that occur between the potential high-level nuclear waste repository at Yucca Mountain and the water table below. The mixture included nonreactive (Br, I, and fluorinated benzoic acids (FBAs)) and reactive tracers (Li, Ce, Sm, Ni, Co, and Mn). Bromide, I, FBAs, and Li were detected during the test on absorbent pads emplaced in a series of solute collection boreholes located beneath the injectors but the more strongly sorbing metals did not reach the collection boreholes during this period. To determine the distribution and mobility of these metals, tracer constituents were extracted from tuff samples collected during overcoring and mineback of the test block. Tracers were extracted from the tuff samples by leaching with a 5% nitric acid solution for metals and a bicarbonate-carbonate buffer for anions. Results from the overcore sample suite show that metals have migrated through the tuff in the region adjacent to and immediately below the tracer injectors. Consistent with laboratory sorption measurements and observed breakthrough in the collection boreholes, rock analyses showed that Li is the most mobile of the metals. Co and Ni behave similarly, traveling tens of cm from the injection sites, while Sm and Ce moved far less, possibly due to precipitation reactions in addition to sorption. Determination of Mn transport is complicated by high background concentrations in the tuff; additional background samples are currently being evaluated. As expected, the rock analyses show that the nonreactive tracers Br and FBAs have moved beyond the overcore region, corroborating results from collection boreholes

    The flight control system for the experimental aircraft programme (EAP) demonstrator aircraft

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    Published in: Active control systems - review, evaluation and projections, Conference Proceedings no. 384Copy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman
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