Second-order differential invariants of the rotation group O(n) and of its extensions: E(n), P(1,n), G(1,n)

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Functional bases of second-order differential invariants of the Euclid, Poincaré, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to describe new classes of nonlinear many-dimensional invariant equations.
19 pages; some misprints of the journal article are corrected

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