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The extrema of the probabilities of the transitions $\nu_{\mu} (\nu_e) \to\nu_e (\nu_{\mu;\tau})$, $\nu_{2} \to \nu_e$, etc. of neutrinos passing througha medium consisting of i) two layers of different constant densities or ii)three layers of constant density, of which the first and the third areidentical but differ in density from the second (e.g., mantle-core-mantle inthe Earth), are analyzed. We show that in addition to the MSW and neutrinooscillation length resonance (NOLR) local maxima previously discussed, thereexist new resonance-like absolute maxima of interference nature. The lattercorrespond to a new effect of total neutrino conversion. The conditions forexistence of the new maxima are fulfilled, in particular, for theEarth-core-crossing solar and atmospheric neutrinos. We prove that the NOLR andthe new resonance-like enhancement are caused by a maximal constructiveinterference between the amplitudes of the neutrino transitions in thedifferent density layers. The strong resonance-like enhancement of thetransitions in the Earth of the Earth-core-crossing solar and atmosphericneutrinos is due to the new effect of total neutrino conversion.Comment: 43 pages, latex, 17 (12 colored) figures, 6 tables; results and  conclusions unchanged, typos corrected, 8 colored figures prepared for the  1999 publication but not included in it, illustrating the Earth mantle-core  resonance enhancement of the $\nu_{\mu} (\nu_e) \to \nu_e (\nu_{\mu})$,  $\bar{\nu}_{\mu} \to \bar{\nu}_s$, $\nu_e \to \nu_s$, etc. transitions, adde

Enhancing mechanisms of neutrino transitions in a medium of nonperiodic constant-density layers and in the Earth