The paper investigates an approach to find out an objective integer in a large integer interval. It first puts forward an approach to subdivide a large integer interval into small ones that are available for the Monte Carlo randomized search algorithm, then selects a small interval by the Monte Carlo algorithm and applies a deterministic search algorithm on the selected one. In order to make the search in an expected computing time, the paper proposes certain regulations to set an initial length for the small interval and to update it in accordance with the expectation of the time complexity. Mathematical foundations for setting-up the initial value and updating it to an acceptable value are presented and proved in detail and a parallel computing strategy is introduced to realized it. Except for the availability in integer factorization, the approach is also applicable in big data searches.
The C and CO reduction proportional fraction was studied in this work to evaluate consumption of the reducer accurately. Based on two-step reaction mechanism (TSRM) theory, a phase equilibrium calculation model (PECM) was established. As three typical kinds of reducers, C, CO, and CH 4 were introduced to the calculation. Reduction of C is the main reaction for the C reducer. Co-reduction of C and CO happens for the CO reducer. As a decomposition product of CH 4 , H 2 plays an important role of reduction, as half of the copper slag is reduced by H 2 . Effects of temperature, reducer addition ratio, and Ca/Si ratio on the indirect reduction index (IDR) and reduction reaction proportional fraction are discussed. With an increase of C and CH 4 reducer addition ratio, the reduction degree of C was strengthened. With addition of CaO, the CO reduction reaction and CH 4 cracking reaction were all promoted. The accuracy of the calculated results was verified by a temperature-programmed direct reduction experiment. As a renewable reducer, biochar was introduced in verified experiments.
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