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Monotonically Computable Real Numbers
, 2001
"... A real number x is called kmonotonically computable (kmc), for constant k> 0, if there is a computable sequence (xn)n∈N of rational numbers which converges to x such that the convergence is kmonotonic in the sense that k · x−xn  ≥ x−xm  for any m> n and x is monotonically computable (m ..."
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A real number x is called kmonotonically computable (kmc), for constant k> 0, if there is a computable sequence (xn)n∈N of rational numbers which converges to x such that the convergence is kmonotonic in the sense that k · x−xn  ≥ x−xm  for any m> n and x is monotonically computable (mc) if it is kmc for some k> 0. x is weakly computable if there is a computable sequence (xs)s∈N of rational numbers converging to x such that the sum s∈N xs − xs+1  is finite. In this paper we show that all mc real numbers are weakly computable but the converse fails. Furthermore, we show also an infinite hierarchy of mc real numbers.
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"... The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsem ..."
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The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this
PRELIMINARY STUDIES OF THE INFLUENCE OF FORCES AND KINETICS ON INTERFACIAL COLLOIDAL ASSEMBLY Approved as to style and content by:
, 2004
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www.hydrolearthsystsci.net/10/309/2006/ © Author(s) 2006. This work is licensed under a Creative Commons License.
"... Vectors of subsurface stormflow in a layered hillslope during runoff initiation ..."
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Vectors of subsurface stormflow in a layered hillslope during runoff initiation
The a...
, 2013
"... The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation University Transportation Centers Program, in the interest of ..."
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The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof. This report does not necessarily reflect the official
Improving the Resolution of NonInvasive Time Domain
"... Non Invasive Time Domain Reflectometry (TDR) may be used to estimate the volumetric moisture content, θv, with depth for a variety of sample materials. The forward physical model is couched in terms of a moments method where integration is performed over a discretised sample space to estimate the me ..."
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Non Invasive Time Domain Reflectometry (TDR) may be used to estimate the volumetric moisture content, θv, with depth for a variety of sample materials. The forward physical model is couched in terms of a moments method where integration is performed over a discretised sample space to estimate the measured propagation time, tp down a pair of parallel transmission lines. We show that inverse solution to this, which recovers relative permittivity and thus θv, is greatly facilitated by a simplification of the system geometry via, 1) realistically modeling the prior density of the sample, 2) using this prior with the inherent system symmetry to reduce the number of required discretisation cells, and 3) determining a physically meaningful reduction operator to allow a coarse discretisation mesh to be used. The observational equation is expressed in the Bayesian paradigm with the most accurate and robust solution obtained using the Conditional Mean of the posterior distribution constructed via a Monte Carlo method. Results of simulation show that the method is capable of providing accurate estimates of the moisture density profile down to a depth of 100 mm with an error < 4%. Further, the reduction in the number of discretised cells required to accurately estimate these profiles means that the inversion procedure is quick enough to enable the real time application of the equipment, a fundamental requirement in the development.
and IV: Continued Field Testing and Refinement of Novel
, 2013
"... Water and Ice Sensor Systems on Bridge Decks ..."
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"... www.hydrolearthsystsci.net/19/1125/2015/ doi:10.5194/hess1911252015 © Author(s) 2015. CC Attribution 3.0 License. Quantitative highresolution observations of soil water dynamics in a complicated architecture using timelapse groundpenetrating radar ..."
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www.hydrolearthsystsci.net/19/1125/2015/ doi:10.5194/hess1911252015 © Author(s) 2015. CC Attribution 3.0 License. Quantitative highresolution observations of soil water dynamics in a complicated architecture using timelapse groundpenetrating radar