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Acknowledgments This analysis relies crucially on Super-Kamiokande data. The author acknowledges the extensive help and cooperation of the Super-Kamiokande collaboration as well as the Kamioka Mining and Smelting Company. S. S. National Science Foundation. Appendix: Fitting Method To estimate and limit oscillation parameters, a \2 describing the shape of the SK zenith spectrum is extended to take into account the measured neutrino interaction rates by various experiments. " (due to hep neutrinos) in energy bin i and zenith-angle bin z are calculated.