This article is concerned with geometric integrators which are linearization-preserving, i.e. numerical integrators which preserve the exact linearization at every fixed point of an arbitrary system of ODEs. For a canonical Hamiltonian system, we propose a new symplectic and self-adjoint B-series method which is also linearization-preserving. In a similar fashion, we show that it is possible to...

In this Letter, we analyze the structure of linearization operators of the Korteweg–de Vries (KdV) hierarchy equations expanded around single-soliton solutions. We uncover the remarkable property that these linearization operators can be factored into the integro-differential operator which generates this hierarchy and the linearization operator of the KdV equation. An important consequence of ...

We present partial-tree linearization, a generalized word ordering (i.e. ordering a set of input words into a grammatical and fluent sentence) task for text-to-text applications. Recent studies of word ordering can be categorized into either abstract word ordering (no input syntax except for POS) or tree linearization (input words are associated with a full unordered syntax tree). Partial-tree ...

This research deals to introduce a new method for generalizing the well-famed Quantitative Feedback Theory (QFT) in granting robustness of Feedback linearization on nonlinear systems. In this new scheme, first applying feedback linearization, with selecting operating points in domain of system parameter's variations, nonlinear systems replaced with linear systems, then robust controller is desi...

The problem of multi-objective robust feedback linearization controller design of nonlinear system with parametric uncertainties is solved in this paper. The main objective of this paper is to propose an optimal technique to design a robust feedback linearization controller with multi-objective genetic algorithm. A nonlinear system is considered as a benchmark and feedback linearization control...

This paper introduces a wavelet-based linearization method to estimate the single-degree-of-freedom (SDOF) nonlinear system response based on the traditional equivalent linearization technique. The mechanism by which the signal is decomposed and reconstructed using the wavelet transform is investigated. Since the wavelet analysis can capture temporal variations in the time and frequency content...

This paper is concerned with a formal linearization problem for a general class of nonlinear time-varying dynamic systems. To a given system, a linearization function is made up of Chebyshev polynomials about its state variables. The nonlinear time-varying system is transformed into a linear time-varying system in terms of the linearization function using Chebyshev interpolation to state variab...

The paper aims to shed light on how serial order is computed in the human mind/brain, focusing on the nature of linearization in language. Linearization is here understood as the mapping of hierarchical syntactic structures onto linear strings. We take as our point of departure the now well-established need to subdivide Broca's region into different areas, and claim that these brain areas play ...

In this paper an efficient unconditionally stable numerical scheme is proposed for solving one dimensional quasi linear Burgers’ equation. The proposed scheme comprises of semi discretization via method of lines for the space variable and backward differentiation formula of order two (BDF2) for the time variable. The method of lines reduces the quasi linear partial differential equation in to n...

We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semi-strong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semi-strong limit the localized activator pulses interact strongly through the slowly varying inhibitor. The interaction is not tail-tail as in the weak interaction limit, and the pulse amplitudes and speed...