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Quantitative comparison of explainable AI methods for interpreting deep learning-based classification of 3D gait kinematics. [PDF]
Lan Z +4 more
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Optogenetic control of a GEF of RhoA uncovers a signaling switch from retraction to protrusion. [PDF]
de Seze J +3 more
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Uniform asymptotic expansions of solutions of the Mathieu equation and the modified Mathieu equation
Journal of Soviet Mathematics, 1979By the method of the model equation, uniform asymptotic expansions of the Floquet solutions of the Mathieu equation and two linearly independent solutions of the modified Mathieu equation are obtained for any real values of the separation parameter contained in these equations.
N S Grigor'Eva, Grigor'Eva N S
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Applications of the Mathieu equation
American Journal of Physics, 1996The properties of the Mathieu equation are reviewed in order to discuss some of the applications that have appeared in recent years. Those mentioned are: vibrations in an elliptic drum, the inverted pendulum, the radio frequency quadrupole, frequency modulation, stability of a floating body, alternating gradient focusing, the Paul trap for charged ...
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Transition Curves for the Quasi-Periodic Mathieu Equation
SIAM Journal on Applied Mathematics, 1998The quasi-periodic Mathieu equation \[ \ddot\psi+ \bigl[\delta+ \varepsilon(\cos t+\cos\omega t)\bigr]\psi=0 \] is investigated for small \(\varepsilon\) and irrational \(\omega\). The aim is to obtain a stability diagram in the \(\delta f\)-\(\omega\) plane (for fixed \(\varepsilon)\) for which all solutions are bounded.
Richard H Rand
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Variational method and Mathieu equation
Journal of Mathematical Physics, 1978A variational method is developed to study the linear and nonlinear Mathieu equations. For the linear Mathieu equation, various modes of the Mathieu functions, the characteristic curves, and the stability regions are found, which agree with the established results. The variational method is then applied to the nonlinear Mathieu equation.
D Y Hsieh, Hsieh D Y
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