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 Best Linear Approximation Methods for Functions of Taikov Classes in the Hardy spaces $H_{q,\rho}$, $q\ge1$, $0<\rho\le1$S. B. Vakarchuk, V. I. Zabutnaya 323 Sequences of Composition Operators in Spaces of Functions of Bounded $\Phi$-VariationO. E. Galkin 330 On Independent and Stationary Subsystems of the Walsh System and Periodic Multiplicative SystemsV. F. Gaposhkin 342 Discreteness of the Spectrum of a Polar Differential Operation in the Space of Vector FunctionsM. G. Gimadislamov 351 Surface Basic Sets with Wildly Embedded Supporting SurfacesE. V. Zhuzhoma, V. S. Medvedev 356 Time Required to Unify All Particles in the Scheme of Equiprobable Allocation into a Sequence of Cell LayersA. M. Zubkov, O. K. Shibanov 373 Instability of Closed Invariant Sets of Semidynamical Systems. Method of Sign-Constant Lyapunov FunctionsB. S. Kalitin 382 Local and Global Estimates of the Solutions of the Cauchy Problem for Quasilinear Parabolic Equations with a Nonlinear Operator of Baouendi–Grushin TypeV. A. Markasheva, A. F. Tedeev 395 The Behavior of Solutions of Semilinear Elliptic Equations of Second Order of the Form $Lu=e^u$ in the Infinite CylinderA. V. Neklyudov 408 The Geometry of a Quasilinear System of Two Partial Differential Equations Containing the First and the Second Partial Derivatives of Two Functions in Two Independent VariablesL. N. Orlova 421 On the Error of Multidimensional Quadrature Formulas for Certain Classes of FunctionsM. A. Romanov 433 On the Well-Posedness of the Prediction-Control Problem for Certain Systems of EquationsA. V. Urazaeva, V. E. Fedorov 440 On Spectral Properties of the Discrete Schrödinger Operator with Pure Imaginary Finite PotentialM. M. Faddeev 451 The Inverse Scattering Problem for a Perturbed Difference Hill EquationAg. Kh. Khanmamedov 456 On Hermitian Nonnegative-Definite Solutions to Matrix EquationsX.-Q. Liu, J.-Y. Rong 470 Brief Communications Exact Constants in the Inequalities for Intermediate Derivatives in $n$-Dimensional SpaceA. A. Lunev 476 Letter to editor Letter to the EditorA. G. Losev, Yu. S. Fedorenko 480