This is a completely revised and updated translation of the Russian original work Numerical Metho(Js for Solving lll-Posed Problems, Nauka, Moscow © 1990 Translation by R.A.M. Hoksbergen All Rights Reserved

We observe a signal for the doubly charmed baryon Xi(+)(cc) in the charged decay mode Xi(+)(cc)-->Lambda(+)(c)K-pi(+) in data from SELEX, the charm hadroproduction experiment at Fermilab. We observe an excess of 15.9 events over an expected background of 6.1+/-0.5 events, a statistical significance of 6.3sigma. The observed mass of this state is 3519+/-1 MeV/c(2). The Gaussian mass width of this state is 3 MeV/c(2), consistent with resolution; its lifetime is less than 33 fs at 90% confidence.

We observe a signal for the doubly charmed baryon Ξ + cc in the decay mode Ξ + cc → pD + K − to complement the previous reported decay Ξ + cc → Λ + c K − π + in data from SELEX, the charm hadroproduction experiment at Fermilab. In this new decay mode we observe an excess of 5.62 events over a combinatoric background estimated by event mixing to be 1.38 ± 0.13 events. The mixed background has Gaussian statistics, giving a signal significance of 4.8σ. The Poisson probability that a background fluctuation can produce the apparent signal is less than 6.4 × 10 −4. The observed mass of this state is 3518 ± 3 MeV/c 2 , consistent with the published result. Averaging the two results gives a mass of 3518.7 ± 1.7 MeV/c 2. The observation of this new weak decay mode confirms the previous SELEX suggestion that this state is a double charm baryon. The relative branching ratio for these two modes is 0.36 ± 0.21.

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