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Displaying similar documents to “Precise asymptotic behavior of solutions to damped simple pendulum equations.”

The phase of the Daubechies filters.

Djalil Kateb, Pierre Gilles Lemarié-Rieusset (1997)

Revista Matemática Iberoamericana

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We give the first term of the asymptotic development for the phase of the N-th (minimum-phased) Daubechies filter as N goes to +∞. We obtain this result through the description of the complex zeros of the associated polynomial of degree 2N+1.

Norm estimates of discrete Schrödinger operators

Ryszard Szwarc (1998)

Colloquium Mathematicae

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Harper’s operator is defined on 2 ( Z ) by H θ ξ ( n ) = ξ ( n + 1 ) + ξ ( n - 1 ) + 2 cos n θ ξ ( n ) , where θ [ 0 , π ] . We show that the norm of H θ is less than or equal to 2 2 for π / 2 θ π . This solves a conjecture stated in [1]. A general formula for estimating the norm of self-adjoint tridiagonal infinite matrices is also derived.

Inverse Trigonometric Functions Arcsec and Arccosec

Bing Xie, Xiquan Liang, Fuguo Ge (2008)

Formalized Mathematics

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This article describes definitions of inverse trigonometric functions arcsec and arccosec, as well as their main properties.MML identifier: SINCOS10, version: 7.8.10 4.100.1011