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Various Properties of Sturmian Words [PDF]
, 2005 This overview paper is devoted to Sturmian words. The first part summarizes different characterizations of Sturmian words. Besides the well known theorem of Hedlund and Morse it also includes recent results on the characterization of Sturmian words using
P. Baláži, Baláži, P.
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Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients
Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 We investigate a type of the Sturm‐Liouville difference equations with almost periodic coefficients. We prove that there exists a constant, which is the borderline between the oscillation and the nonoscillation of these equations. We compute this oscillation constant explicitly.
Petr Hasil +2 more
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On Constants in Nonoscillation Criteria for Half‐Linear Differential Equations
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 We study the half‐linear differential equation (r(t)Φ(x′)) ′ + c(t)Φ(x) = 0, where Φ(x) = |x|p−2x, p > 1. Using the modified Riccati technique, we derive new nonoscillation criteria for this equation. The results are closely related to the classical Hille‐Nehari criteria and allow to replace the fixed constants in known nonoscillation criteria by a ...
Simona Fišnarová +2 more
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Weyl‐Titchmarsh Theory for Time Scale Symplectic Systems on Half Line
Abstract and Applied Analysis, Volume 2011, Issue 1, 2011., 2011 We develop the Weyl‐Titchmarsh theory for time scale symplectic systems. We introduce the M(λ)‐function, study its properties, construct the corresponding Weyl disk and Weyl circle, and establish their geometric structure including the formulas for their center and matrix radii. Similar properties are then derived for the limiting Weyl disk. We discuss
Roman Šimon Hilscher +2 more
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International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We obtain the asymptotic distribution of the nonprincipal eigenvalues associated with the singular problem x″ + λq(t)x = 0 on an infinite interval [a, +∞). Similar to the regular eigenvalue problem on compact intervals, we can prove a Weyl‐type expansion of the eigenvalue counting function, and we derive the asymptotic behavior of the eigenvalues.
Juan Pablo Pinasco
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Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 285-294, 2004., 2004 We present basic methods of oscillation theory of symplectic difference systems (SDSs). A particular attention is devoted to the variational principle and to the transformation method. Hyperbolic Prüfer transformation for SDSs is established.
Ondřej Došlý
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On certain comparison theorems for half‐linear dynamic equations on time scales
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 551-565, 2004., 2004 We obtain comparison theorems for the second‐order half‐linear dynamic equation [r(t)Φ(yΔ)]Δ+p(t)Φ(yσ)=0, where Φ(x) = |x|α−1sgn x with α > 1. In particular, it is shown that the nonoscillation of the previous dynamic equation is preserved if we multiply the coefficient p(t) by a suitable function q(t) and lower the exponent α in the nonlinearity Φ ...
Pavel Řehák
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Substitutions and their Generalisations
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and potentials.
Neil Mañibo
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On polynomials of Sheffer type arising from a Cauchy problem
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 33, Page 2119-2137, 2003., 2003 A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials ...
D. G. Meredith
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Sturmian theorems for systems of differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 1, Page 177-184, 1980., 1979 Two Sturmian theorems are established for second order linear nonhomogeneous systems of two differential equations with the use of a maximum principle. The results also hold for homogeneous systems. For illustration, an example is given.
C. Y. Chan
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