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Summary  

New results for the eigenvalue ratios of vibrating strings are presented partially in connection with previous results concerning Schrdinger operators.

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Abstract  

Given a graph G with characteristic polynomial ϕ(t), we consider the ML-decomposition ϕ(t) = q 1(t)q 2(t)2 ... q m(t)m, where each q i(t) is an integral polynomial and the roots of ϕ(t) with multiplicity j are exactly the roots of q j(t). We give an algorithm to construct the polynomials q i(t) and describe some relations of their coefficients with other combinatorial invariants of G. In particular, we get new bounds for the energy E(G) =
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop \sum \limits_{i = 1}^n$$ \end{document}
i| of G, where λ1, λ2, ..., λn are the eigenvalues of G (with multiplicity). Most of the results are proved for the more general situation of a Hermitian matrix whose characteristic polynomial has integral coefficients.
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47 – 50 . [19] Wu , J. 2009 Power sums of Hecke eigenvalues and application Acta Arith. 137 333

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- 100 . [14] Shen , C. L. and Shieh , C. T. , Some properties of the first eigenvalue of the Laplace operator on the spherical band in S2

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. [8] Fulton , C. T. 1977 Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions Proc. R. Soc. Edinburgh A77

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Abstract  

We establish several comparison results on the eigenvalue gap for vibrating strings with symmetric single-well densities or symmetric double-well densities.

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Studia Scientiarum Mathematicarum Hungarica
Authors: Carlos M. da Fonseca, Victor Kowalenko, and László Losonczi

-Capizzano , S. . , Eigenvalues and eigenvectors of banded Toeplitz matrices and the related symbols , Numer. Linear Algebra Appl. , 25 ( 2018 ), e2137 . [9] Elsner , L. and Redheffer , R. M. , Remarks on band matrices , Numer. Math. , 10 ( 1967

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This paper presents a numerical investigation of rectangular 2D waveguide problems. Thereby, the resulting Helmholtz equation is approximated by different finite elements techniques. Both homogeneous and heterogeneous material parameters are considered.

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