The articles in this collection present new results in analysis, combinatorics, probability, theory of functions, and partial differential equations. The material presented in the book will be of interest to a broad range of specialists. In several papers, the authors study the classical solvability of the Cauchy-Dirichlet problem for a class of parabolic systems, the solvability of the Dirichlet problem for the quasilinear second order parabolic systems, estimates for solutions of uniformly elliptic systems, and generalizations of the embedding theorems. In other papers, the authors describe a new method for the computation of correlation dimension, present generalizations of the fast Fourier transform method for wavelet expansions, and study the spectrum of two-dimensional periodic magnetic Schrodinger operator.