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BeamCraft: Deep Reinforcement Learning-DrivenMulti-Objective Beamforming for ISAC
Dao DN, Miao Y.
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Lyapunov Function Constructions for Slowly Time-Varying Systems
Proceedings of the 45th IEEE Conference on Decision and Control, 2006We provide general methods for explicitly constructing strict Lyapunov functions for general nonlinear slowly time-varying non-autonomous systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable.
Mazenc, Frédéric, Malisoff, Michael
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Limiting reiteration for real interpolation with slowly varying functions
Mathematische Nachrichten, 2004AbstractWe present reiteration formulae with limiting values θ = 0 and θ = 1 for a real interpolation method involving slowly varying functions. Applications to the Lorentz–Karamata spaces, the Fourier transform and the Riesz potential are given. In particular, our results yield improvements of limiting Sobolev‐type embeddings due to Trudinger, Hansson,
Gogatishvili, A. (Amiran) +2 more
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Slowly varying linear functional differential equations
IEEE Transactions on Automatic Control, 1972Several authors have studied the stability behavior of slowly varying linear systems of ordinary differential equations. These studies have yielded a sufficient condition for uniform exponential stability. In this work this result is extended to slowly varying linear functional differential equations.
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Slowly varying function method applied to quartz crystal oscillator transient calculation
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 1998By using an approach based on the full nonlinear Barkhausen criterion, it is possible to describe oscillator behavior under the form of a nonlinear characteristic polynomial whose coefficients are functions of the circuit components and of the oscillation amplitude.
Brendel, R. +4 more
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A FAST-MANIFOLD APPROACH TO MELNIKOV FUNCTIONS FOR SLOWLY VARYING OSCILLATORS
International Journal of Bifurcation and Chaos, 1996A new approach to obtaining the Melnikov function for homoclinic orbits in slowly varying oscillators is proposed. The present method applies the usual two-dimensional Melnikov analysis to the “fast” dynamics of the system which lie on an invariant manifold. It is shown that the resultant Melnikov function is the same as that obtained in the usual way
Chen, Shyh-Leh, Shaw, Steven W.
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Journal of Mathematical Analysis and Applications, 2021
In this paper, the authors contribute to the qualitative theory of linear differential equations of second-order in the form \[ [r(t)x'(t)]'+s(t)x(t)=0, \] where \(r > 0\), \(s\) are continuous functions. In the first section, some background information on the subject of this article is provided.
Petr Hasil, Michal Veselý
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In this paper, the authors contribute to the qualitative theory of linear differential equations of second-order in the form \[ [r(t)x'(t)]'+s(t)x(t)=0, \] where \(r > 0\), \(s\) are continuous functions. In the first section, some background information on the subject of this article is provided.
Petr Hasil, Michal Veselý
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Slowly varying, linear, neutral, functional, differential equations†
International Journal of Control, 1973Abstract For a slowly varying, linear, neutral, functional, differential equation, a sufficient condition is derived which ensures uniform exponential stability.
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Perturbation methods and the Melnikov functions for slowly varying oscillators
Chaos, Solitons & Fractals, 2005A new approach based on the Lindstedt-Poincaré method is proposed to obtain the Melnikov function for homoclinic orbits in slowly varying oscillators. The goal of the authors is to show that without dealing explicitly with the complicated geometry related to the three-dimensional distance measured in a Poincaré section, the same Melnikov function can ...
Lakrad, Faouzi, Charafi, Moulay Mustapha
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