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We are concerned with the stability of a 1-D coupled Rayleigh beam-string transmission system. We obtain the polynomial decay rate t - 1 or the exponential decay rate for the given transmission system whether the frictional damping is only effective in the beam part or the string part, respectively. This paper generalizes the recent result in [Y.-F. Li, Z.-J. Han and G.-Q. Xu, Explicit decay rate for coupled string-beam system with localized frictional damping, Appl. Math. Lett. 78 2018, 51–58]. The main ingredient of the proof is some careful analysis for the Rayleigh beam and string transmission system. [ABSTRACT FROM AUTHOR]

Let f : ℝ n → ℝ {f\colon\mathbb{R}^{n}\rightarrow\mathbb{R}} be a polynomial and 𝒵 ⁢ (f) {\mathcal{Z}(f)} its zero set. In this paper, in terms of the so-called Newton polyhedron of f, we present a necessary criterion and a sufficient condition for the compactness of 𝒵 ⁢ (f) {\mathcal{Z}(f)}. From this we derive necessary and sufficient criteria for the stable compactness of 𝒵 ⁢ (f) {\mathcal{Z}(f)}. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new class of generalized Hermite-Legendre polynomials of 2-variables and consequently a new class of Tricomi, Bessel and Hermite polynomials and their generalizations starting from suitable generating functions. The theory of Bessel, Legendre, Hermite and of the associated generating functions and their generalizations is reformulated within the framework of a series rearrangement formalism by using different analytical means on their respective generating functions. [ABSTRACT FROM AUTHOR]

A classical theorem due to Eneström and Kakeya gives some bounds for the moduli of the zeros of polynomials having a monotone sequence of non-negative (real) coefficients. Nowadays, one can find several modifications and generalizations of this result in the literature. The main subject of the paper is a study of links of coefficients which occur in some of these general results with a view to the recurrence relations fulfilled by systems of orthogonal polynomials on the unit circle. In particular, we discuss the question, if the relevant links are consistent with the recurrence relations or not. This leads to some new insight into the analyzed classes of polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we present our recent results on the so-called complex structures in algebras in the context relevant to the following four problems which, at first glance, have nothing in common: (i) solubility of polynomial equations in non-associative algebras, (ii) topological/geometric properties of quadratic maps, (iii) existence of bounded solutions to quadratic differential systems, and (iv) ellipticity of the Dirac equation. The unsolved problems related to (i)-(iv) are formulated as well. [ABSTRACT FROM AUTHOR]