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Sufficient conditions for the existence and asymptotic stability of the invariant sets of an impulsive system of differential equations defined in the direct product of a torus and an Euclidean space are obtained.

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In the paper we present conditions for uniform convergence with probability one of wavelet expansions of ϕ-sub-Gaussian (in particular, Gaussian) random processes defined on the space R.It is shown that upon certain conditions for the bases of wavelets the wavelet expansions of stationary almost sure continuous Gaussian processes and wavelet expansions of fractional Brownian motion converge uniformly with probability one on any finite interval.

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