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Mathematical Background
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
2.77 Definition (randomized complexity classes) The complexity class ZPP (“zero-sided probabilistic polynomial time”) is the set of all decision problems for which there is a randomized algorithm with 0-sided error which runs in expected polynomial time.The complexity class RP (“randomized polynomial time”) is the set of all decision problems for which there is a randomized algorithm with 1-sided error which runs in (worst-case) polynomial time.The complexity class BPP (“bounded error probabilistic polynomial time”) is the set of all decision problems for which there is a randomized algorithm with 2-sided error which runs in (worst-case) polynomial time.
An improved risk and reliability framework-based maintenance planning for food processing systems
Published in Quality Technology & Quantitative Management, 2023
Hamzeh Soltanali, Mehdi Khojastehpour, José Torres Farinha
This study addresses a framework of reliability modeling-based maintenance plans for the food processing industries. In the proposed framework, the potential failures were identified through the risk-based approaches such as the Failure Mode and Effect Analysis (FMEA) and Fault Tree Analysis (FTA) techniques and, the validity of the independent and identically distributed nature of the process was investigated by the trend and correlation tests. Besides, the capability of the RP, NHPP, HPP, and BPP models through the MLE method was examined to find the best-fit model of failure data. Finally, the failure rate and reliability functions were calculated, and their outcomes were carried out to recommend the maintenance intervals. The results of the proposed framework appointed that to achieve a high level of reliability, the main bottlenecks of the process should be considered as a priority. To suggest the maintenance intervals, the various levels of reliability focusing on the plant policy were conducted. Furthermore, due to the series configuration of equipment in the edible oil purification, the opportunistic maintenance intervals were undertaken to reduce the intervals times as much as possible. The proposed maintenance intervals could be useful for improving the availability and safety of critical equipment in edible oil industries. As a consequence, the results of the present study could be beneficial for other food and agro-industries to achieve sustainable production lines.
A comparative study of raw, acid-modified and EDTA-complexed Acacia auriculiformis biomass for the removal of hexavalent chromium
Published in Chemistry and Ecology, 2020
Tasrin Shahnaz, Chandi Patra, Vivek Sharma, N. Selvaraju
Unlike the previously mentioned two-parameter isotherm models Redlich–Peterson (R–P) isotherm model represents a three-parameter isotherm that conjugates and fixes the incorrectness of both the two-parameter isotherms, i.e. Langmuir and Freundlich isotherms. R–P isotherm can be represented asHere, ARP, BRP and g are constants. Values for ‘g’ vary from 0 to 1. If g = 1, then Redlich–Peterson model equation confirms the Langmuir isotherm [46].
Numerical modelling of open channel junctions using the Riemann problem approach
Published in Journal of Hydraulic Research, 2019
Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi
As a conclusion of these comparisons, in the Y-shaped confluence case, the RP approach appears to outperform the momentum-based models for both concordant and discordant bottom. Indeed, some reasonable doubt arises in terms of the extent to which such momentum-based models are generalizable, especially to cases that are not strictly similar to those of the original experiments. By contrast, the RP approach, which is based on general mechanical bases, performs well, mainly with respect to case-independence.