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The article discusses the matrices of the form A(n)(1), A(n)(m), A(N)(m), whose inverses are: tridiagonal matrix A(n)(-1) (n - dimension of the A(N)(-m) matrix), banded matrix A(n)(-m) (m is the half-width band of the matrix) or block-tridiagonal matrix A(N)(-m) (N = n x m - full dimension of the block matrix; m - the dimension of the blocks) and their relationships with the covariance matrices of measurements with ordinary (simple) Markov Random Processes (MRP), multiconnected MRP and vector MRP, respectively. Such covariance matrices frequently occur in the problems of optimal filtering, ext ...More
In this work, we apply the method of integral transformation to prove uniqueness theorems for the new class of Fredholm linear integral equations of the first kind in the axis.
The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem with an oscillating initial condition. The presence of a rapidly oscillating function in the initial condition has led to the appearance of a boundary layer function in the solution, which has the rapidly oscillating character of the change. In addition, it is shown that the asymptotics of the solution contains exponential, parabolic boundary layer functions and their products describing the angular boundary layers. Continuing the ideas of works [1, 3] a complete regularize ...More
In this paper, it is established a characterization of T-normal coverings by means of approximation of the Cech complete paracompacta, which are the perfect preimages of complete metric spaces of weight