he possibilities of improving sorting time parameters through preprocessing by stochastic sorting were investigated. The hypothesis that two-component stochastic + classical sorting outperforms classic one-component sorting in terms of time efficiency was experimentally confirmed. Sorting with different computational complexity is accepted as classical sorting algorithms: shaker sort- ing with computational complexity O(n2), insertions O(n2), Shell O(n·(log n)2) ... O(n3/2), fast with optimization of ending sequences O(n·log n). The greatest effect is obtained when performing comparisons using stochastic sorting in the amount of 160 percent of the array’s size. Indicators of the efficiency of the exchange of two elements, as well as series of exchanges, are introduced. This allowed to determine the highest efficiency of stochastic sorting (as the first component of two-component sorting), when one element for comparison is chosen from the first part of the array and the other from the second. For algorithms with a computational complexity of O(n2) the improvement in time efficiency reached 70–80 percent. However, for Shell sort and quick sort, the stochas- tic presort has no positive effect, but instead increases the total sorting time, which is apparently due to the initial high efficiency of these sorting methods. The hypothesis that three-component sorting fast + stochastic + insertions would increase sorting time efficiency was not confirmed. However, during the experiment, the recommended size of the array was determined, at which point the two-component quick + insertion sort must be switched to the second component – insertion sorting. The optimal length of the ending sequences is between 60 and 80 elements. Given that algorithm time efficiency is affected by computer architecture, operat- ing system, software development and execution environment, data types, data sizes, and their values, time efficiency indicators should be specified in each specific case.
The purpose of the work is to determine rational schemes for their production by analyzing the technological and design parameters of a number of broadband mills that roll hot-rolled strips less than 2,0 mm thick. It is shown that at present there is a constant increase in the production of extremely thin hot-rolled strips (0,8-1,5 mm thick), which can be used instead of more expensive (by $ 20-30 per ton) cold-rolled strips. The development of the production of hot-rolled strips of such a thickness is limited by a number of problems, in particular, the low temperature of the end of rolling (760-820 °C), which leads to a significant decrease in the ductility of the rolled stock; limiting the rolling filling speed, which does not allow increasing the temperature of the end of rolling the complexity of controlling the cross-sectional profile and flatness of the strips. Using mathematical modeling, it was found that the strip thickness and rolling speed have the greatest influence on the temperature of the end of rolling. The thickness and temperature of the rolls at the entrance to the finishing group of stands have a lesser effect. A decrease in the number of stands in the finishing group increases the temperature of the end of rolling at a constant thickness of the rolls, but when the thickness of the rolls changes in accordance with the number of stands, the effect is significantly reduced. The most favorable technological parameters for the production of extra-thin hot-rolled strips are provided by casting and rolling units, which are characterized, in comparison with broad-strip mills, as a rule, by a greater thickness and temperature of the rolls (or continuously cast slabs) and a smaller number of stands. An increase in the thickness of billets (slabs) requires an increase in the permissible values of the energy-power parameters of rolling, as well as the use of special solutions that will ensure minimal heat loss by the rolls before entering the finishing group of stands. Calculations show that, based on the reliable maximum refueling speed of hotrolled strips (10-11.5 m / s) achieved in the industry, the minimum thickness of strips with high plastic characteristics is: for broad-strip mills - 1.9-2.0 mm; for casting and rolling units, depending on their type - 1.3-1.6 mm.
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