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For any topological group $G$ the dual object $\widehat{G}$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\widehat{G}$ is discrete. In an earlier paper we proved that $\widehat{G}$ is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when $G$ is an almost metrizable precompact group.

In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation $u_t-A{u}_{xx}-Bu=0$, where $B$ is an arbitrary square complex matrix and $A$ ia s matrix such that the real part of the eigenvalues of the matrix $\frac{1}{2}(A+A^H)$ is positive. Given an admissible error $\epsilon$ and a finite domain $G$, and analytic-numerical solution whose error is uniformly upper bounded by $\epsilon$ in $G$, is constructed.