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The wave field and dispersion equations are found for a porous layer surrounded by two elastic half-spaces. The porous layer is described by the effective model of a medium in which elastic and fluid layers alternate. To investigate the normal waves, all real roots of dispersion equations are determined and their movements as the wave number increases are investigated. As a result, the dispersion curves of all normal waves are constructed and the dependence of normal waves on the parameters of the porous layer and elastic half-spaces is analyzed. Bibliography: 6 titles.

Let a function f(x) ∈ C(r)[a,b], r ≥ 0, and take values that have different signs at the endpoints of the interval [a,b]. In the article, we propose effective methods for calculating real roots of the equation f(x)=0 on the given interval [a,b]. We substantiate this method and make a comparison between this method and the chord and Newton methods.

New algebraic criteria of absolute stability are obtained on the basis of a polynomial form of the frequency condition for absolute stability (Popov inequality). The analysis of the inequality is reduced to an analysis of the local properties of polynomials and a rational function on the negative real semiaxis. As a result, the stability criteria do not require the plotting of any sort of curves and can be expressed on the basis of algorithms of the Routh–Hurwitz type and calculations of the negative real roots of polynomials.

The article is concerned with the problem of estimating the stability margins for a system with a single negative feedback loop from the distribution of real roots of polynomials characterizing the frequency hodographs of the forward loop.