The analysis of causes of destruction of main gas pipelines for the last two decades is carried out. It is shown that the share of accidents because of corrosion cracking energized increases. The conclusion is drawn that inspection and repair of emergency sites has to become a paramount task. It will allow to reach considerable decrease in accident rate. At the same time the extent of emergency sites of gas pipelines with a diameter of 1420 mm is about 1700 km, 1220 mm – 1000 km; 1020 mm – 400 km that, generally, makes 2.3% of the total extent of gas pipelines of the corresponding diameters (1020-1420 mm).

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N. Minculete has introduced the divisor-of-order-r function τ (r) and the sum-of-divisors-of-order-r function σ (r) . We investigate the asymptotic behaviour of n≤x τ (r) (n) and n≤x σ (r) (n) and improve known estimates.

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