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Group Theory in Statistical Signal Processing and Control
Published in Harish Parthasarathy, Advanced Probability and Statistics: Applications to Physics and Engineering, 2023
Now gβ,α∑k=−qpgβ+kα is the representation space of the irreducible repre-sentation ρα of sl(2,ℂ) = span{H̄α, X±α} and consequently, its highest weight (β+pα)H̄α) and lowest weight (β-qα)H̄α>) are integers and hence <β−qα,α>=−<β+pα,α> or equivalently, a(β,α)=β(H¯α)=2<β,α>/<α,α>=p+qis a non-negative integer.
The re-evaluation of seismic hazard for the Paks NPP, Hungary
Published in Edmund Booth, Seismic Design Practice into the Next Century, 1998
The slip rate assuming a waning subsidence rate was given the highest weight, slightly higher than that derived from the last 5 million years, as it is likely to be a better representation of the current tectonic regime. The highest slip rate was given the lowest weight since this was based on the maximum rate which could have occurred rather than an observed displacement.
Risk assessment and implementation of deformation disaster for operation tunnel based on entropy weight-grey relational analysis
Published in Geomatics, Natural Hazards and Risk, 2022
Yingchao Wang, Wen Jiang, Mitian Wang, Yuanhai Li
The difference between the EWM and GRA is, EWM pays more attention to the change of data, that is, each monitoring point of the shield tunnel lining structure represents an assessment unit, each assessment unit will fluctuate in the same monitoring period. The greater the degree of fluctuation or confusion, the more unstable the assessment unit, thus the greater the weight of data. The total weight can be obtained by summing the weights of each evaluation unit of each group of data, that is, the total weight of the group of data. The results by using EWM are shown in Table 6. It can be seen that the Group 3 has the highest weight, and the Group 1 has the lowest weight. According to the criterion of EWM, the data of Group 3 are the most unfavorable deformation data in the monitoring period.
A composite energy resilience performance indicator for Bangladesh
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2022
Farzana Sharmin, Shobhakar Dhakal
Contrary to the perception of the key stakeholders, the PCA findings suggest that the resilience of the energy system of Bangladesh is more critically dependent on a set of affordability, sustainability, and availability issues compared to the qualitative aspects covering institutional effectiveness, corruption, and regulatory quality. As such, the group containing indicators GDP per capita, per capita generation, import diversification, reserves in months, investment in energy sector, self-sufficiency, energy intensity, and CO2 emission reduction has the highest weight, while the qualitative dimension is found to have the least weight among the groups. Nonetheless, these indicators are critical for the energy system resilience of the country. The findings have significant policy implications as it implies the energy strategies for supporting economic development aspiration of the country should consider affordability, sustainability, and availability issues along with the institutional and governance quality. As such, a holistic or systematic approach to ensure energy system resilience would be critical.
Model-Based Dynamic Categorization of Alarm Trip Points for Manufacturing Process Disruption Minimization
Published in International Journal of Computer Integrated Manufacturing, 2021
Zubair Ahmad Khan, Khalid Khan, Muhammad Tahir Khan, Javaid Iqbal, Shahbaz Khan
Most of the matrix F elements would be zero, except for one in the instant case, representing the weight of the faulty tag, i.e. tag 2 of workstation 1. Each column in matrix F represents the normalized MTTR values of all the faulty tags in a given workstation. If there are two or more than two faulty tags in the same workstation, then the tag with the highest MTTR value or weight is considered. Therefore, to find out the faulty tag with the highest weight, a column-wise maximum operation is performed on the matrix resulting in the vector where the element of the vector fmax is determined using the column-wise maximum operation given in Eq. 9.