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 On a class of random perturbations of the hierarchical LaplacianA. D. Bendikov, A. A. Grigor'yan, S. A. Molchanov, G. P. Samorodnitsky 3 Calculus of variations in the large, existence of trajectories in a domain with boundary, and Whitney's inverted pendulum problemS. V. Bolotin, V. V. Kozlov 39 Inequalities for harmonic measures with respect to non-overlapping domainsV. N. Dubinin 47 Multi-colour dynamical tilings of tori into bounded remainder setsV. G. Zhuravlev 65 Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev typeM. O. Korpusov 103 Dualizing coverings of the planeVik. S. Kulikov 163 The $K(\pi,1)$-property for smooth marked curves over finite fieldsPh. Lebacque, A. Schmidt 193 Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groupsN. S. Romanovskiy 201 Periodic solutions of the quasilinear equation of forced beam vibrations with homogeneous boundary conditionsI. A. Rudakov 215 Browder functions and theorems on fixed points and coincidencesT. N. Fomenko 239