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| 1 | Cosmological Bianchi-I type model in the (n + 1)-dimensional gravitational theory with several forms is considered. When electric non-composite brane ansatz is adopted the Wheeler-DeWitt (WDW) equation for the model, written in the conformally-covariant form, is analyzed. Under certain restrictions asymptotic solutions to WDW equation near the singularity are found which reduce the problem to the so-called quantum billiard on the (n − 1)-dimensional Lobachevsky space H^n−1. Keywords: cosmological billiards, branes, Wheeler-DeWitt equation | 1370 | ||||