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oai:arar.sci.am:439336 2026-08-27T12:22:15Z dLibraDigitalLibrary dLibraDigitalLibrary:Articles

0. To identify the cause of the discrepancies, regardless of the specific form of the Pearson distribution, a numerical inverse Laplace transform was applied using modern algorithms. The inverse function m1(t)/m1(0), where m1(t) is the frequency of the first flare, was in this case represented and approximated by its purely observational realization n1(t)/n(t), where n1(t) is the number of stars that have survived exactly one flare by time t, and n(t) is the cumulative number of flares. This approach does not require knowledge of Ntot and provides the most reliable of the available cross-checks for reconstruction using the inverse Laplace transform. The nature of these discrepancies reveals the structure of the underlying distribution: a smooth density curve with a peak shifted towards values of ν ∼ 2 × 10−3 d−1, with a long tail in the region of high ν values.]]>