In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (...

We contrast two approaches to calculating trans-Planckian corrections to the inflationary perturbation spectrum: the New Physics Hypersurface [NPH] model, in which modes are normalized when their physical wavelength first exceeds a critical value, and the Boundary Effective Field Theory [BEFT] approach, where the initial conditions for all modes are set at the same time, and modified by higher ...

Actor–critic style two-time-scale algorithms are one of the most popular methods in reinforcement learning, and have seen great empirical success. However, their performance is not completely understood theoretically. In this article, we characterize global convergence an online natural actor–c...

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics slow and fast subsystems. Machine learning techniques are utilized approximate both Specifically, recurrent neural network (RNN) feedforward (FNN) predict state vectors, respectively. Moreover, investigate generalization error bounds for these machi...