Mathermatics

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Mathermatics

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    Control of String Vibrations by Displacement of One End with the Other End Fixed, Given the Deflection Form at an Intermediate Moment of Time
    (MDPI AG, 2022) Vanya Barseghyan ; Svetlana Solodusha
    We consider a boundary control problem for the equation of string vibration with given initial and final conditions, given the deflection form at an intermediate moment of time. The control is carried out by displacement of one end with the other end fixed. The problem is reduced to the problem of a distributed action control with zero boundary conditions. We propose a constructive approach to constructing a boundary control action by the separation of variables and methods of the theory of control of finite-dimensional systems. The approach is applied to given functions. A computational experiment was carried out with the construction of the corresponding graphs and their comparative analysis. They confirm the obtained results.
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    Statistical Estimation for Stationary Models with Tapered Data
    (Armenian Academy of Sciences, 2021) M. S. Ginovyan ; A. A. Sahakyan
    In this paper, we survey some recent results on parametric and nonparametric statistical estimation about the spectrum of stationary models with tapered data, as well as, a question concerning robustness of inferences, carried out on a linear stationary process contaminated by a small trend. We also discuss some questions concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fejer-type ´ singular integrals. These are the main tools for obtaining the corres ponding results, and also are of interest in themselves. The processes considered will be discrete- time and continuous-time Gaussian, linear or Levy-driven linear processes with memory.