Computable solution of fractional kinetic equations using Mathieu-type series
Advances in Difference Equations, 2019 The Mathieu series appeared in the study of elasticity of solid bodies in the work of Émile Leonard Mathieu. Since then numerous authors have studied various problems arising from the Mathieu series in several diverse ways.
Owais Khan +3 more
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Influence of Material Defects on the Dynamic Stability of the Bernoulli-Euler Beam [PDF]
Archives of Metallurgy and Materials, 2021 The paper presents the results of tests on dynamic stability of Bernoulli-Euler beam with damages. Damages (cracks) were modeled using three rotational springs.
W. Sochacki, S. Garus, J. Garus
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On a fine localization of the Mathieu azimuthal numbers by Cassini ovals
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 The study is devoted to numerical and analytical problems concerning generating periodic and antiperiodic solutions of the angular (circumferential) Mathieu equation obtained for the circumferential harmonics of an elliptic cylinder.
Yuri Nikolaevich Radayev +1 more
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Evolution of Cosmological Perturbation in Reheating Phase of the Universe [PDF]
, 1996 The evolution of the cosmological perturbation during the oscillatory stage of the scalar field is investigated. For the power law potential of the inflaton field, the evolution equation of the Mukhanov's gauge invariant variable is reduced to the ...
Nambu, Yasusada, Taruya, Atsushi
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The Double Points of Mathieu's Differential Equation [PDF]
Mathematics of Computation, 1969 Mathieu’s differential equation, y + ( a − 2 q cos 2 x ) y = 0 y + (a - 2q\cos 2x)y = 0 , admits of solutions of period π \pi or 2 π 2\pi for four countable sets of characteristic ...
Blanch, G., Clemm, D. S.
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Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions [PDF]
, 2000 Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space.
Abramowitz M +23 more
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On the singular spectrum of the Almost Mathieu operator. Arithmetics and Cantor spectra of integrable models [PDF]
, 1999 I review a recent progress towards solution of the Almost Mathieu equation (A.G. Abanov, J.C. Talstra, P.B. Wiegmann, Nucl. Phys. B 525, 571, 1998), known also as Harper's equation or Azbel-Hofstadter problem. The spectrum of this equation is known to be
Wiegmann, P. B.
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Numerical solution of fractional Mathieu equations by using block-pulse wavelets
Journal of Ocean Engineering and Science, 2019 In this paper, we introduce a method based on operational matrix of fractional order integration for the numerical solution of fractional Mathieu equation and then apply it in a number of cases.
P. Pirmohabbati +3 more
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Parametric amplification with a friction in heavy ion collisions [PDF]
, 2000 We study the effects of the expansion of the system and the friction on the parametric amplification of mesonic fields in high energy heavy ion collisions within the linear $\sigma$ model .
A. A. Anselm +19 more
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Approximate solutions to Mathieu's equation [PDF]
Physica E: Low-dimensional Systems and Nanostructures, 2018 9 pages, 7 ...
Wilkinson, Samuel A. +4 more
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