Results 271 to 280 of about 2,121,946 (336)

A reduction principle for singular perturbation problems

Applied Mathematics and Computation, 1999
Consider singularly perturbed systems of the type \[ \begin{multlined} f(x^{(m)}, x^{(m-1)}, \dots ,x,y^{(n)}, y^{(n-1)}, \dots ,y)=0,\\ y^{(r)} + \varepsilon g(y^{(p)} ,\dots ,y,x^{(q)}, \dots ,x) + h(y^{(r-1)}, \dots ,y,x^{(s)} ,\dots ,x)=0,\end{multlined} \tag{*} \] with \(p >r, q>s\).
Lee, K.H., Ong, E.H.
exaly   +3 more sources

Perturbation expansion of variational principles at arbitrary order

Physical Review A, 1995
When perturbation theory is applied to a quantity for which a variational principle holds (eigenenergies of Hamiltonians, Hartree-Fock or density-functional-theory energy, etc.), different variational perturbation theorems can be derived. A general demonstration of the existence of variational principles for an even order of perturbation, when ...
Gonze, Xavier
openaire   +3 more sources

The hierarchical principle in perturbation theory

Il Nuovo Cimento A Series 10, 1966
The hierarchical principle is discussed in perturbation theory in the light of the fact that Cutkosky integrals can have lower-order singularities corresponding to contracting out complete closed loops. It is shown that a strict hierarchical principle can be defined for Feynman integrals in theα-representation but that due to a hitherto overlooked ...
P. V. Landshoff, D. I. Olive, J. C. Polkinghorne   +2 more
openaire   +2 more sources

The use of the variational principle in molecular perturbation theory

Journal of Chemical Physics, 1985
We have shown how the Variational Principle can be used to optimize the choice of the expansion functional and the reference state potential in molecular perturbation theory. The method was applied to a Stockmayer and to a Lennard-Jones diatomic fluid.
Saul Goldman
exaly   +2 more sources

Application of the variational principle to perturbation theory

American Journal of Physics, 1994
In this note I discuss briefly a rather unusual example of the use of the variational principle, which perhaps is interesting for someone who studies or teaches quantum mechanics.
exaly   +2 more sources

Optical soliton perturbation with Kudryashov's equation by semi–inverse variational principle

Physics Letters, Section A: General, Atomic and Solid State Physics, 2020
The semi–inverse variational principle retrieved bright 1–soliton solution to the perturbed Kudryashov's equation. The perturbation terms appear with maximum intensity and additionally higher order dispersion effects are included.
Anjan Biswas, Mir Asma, Padmaja Guggilla   +2 more
exaly   +2 more sources

Optical soliton perturbation in a log-law medium with full nonlinearity by He's semi-inverse variational principle

Inverse Problems in Science and Engineering, 2012
Anjan Biswas, Daniela Milović
exaly   +2 more sources

State Estimation Algorithm for Nonlinear System with Unknown Parameter Based on Minimum Perturbation Principle

Cybersecurity and Cyberforensics Conference, 2022
For the state estimation problem of nonlinear systems with unknown parameters, based on the principle of minimum perturbation, the state equation with unknown parameters and both the state equation and measurement equation with unknown parameters are ...
Kai Zhao, Han Yu, Yang Zhou, Yuanyuan Li, Chao Lu, Lu Xiao   +5 more
exaly   +2 more sources

Separation principle of delay perturbed singular systems

IMA Journal of Mathematical Control and Information, 2023
Abstract In this paper, we establish a separation principle for a class of time-varying delay perturbed singular systems. Furthermore, we propose a singular observer to estimate the system states. Based on the Lyapunov–Krasovskii functionals, the practical stability of the proposed singular observer is achieved. These results are applied
Khawla Ben Mrad, Ines Ellouze
openaire   +1 more source

Hierarchical Sliding-Mode Surface-Based Adaptive Actor–Critic Optimal Control for Switched Nonlinear Systems With Unknown Perturbation

IEEE Transactions on Neural Networks and Learning Systems, 2022
This article studies the hierarchical sliding-mode surface (HSMS)-based adaptive optimal control problem for a class of switched continuous-time (CT) nonlinear systems with unknown perturbation under an actor–critic (AC) neural networks (NNs ...
Haoyan Zhang, Xudong Zhao, Huanqing Wang, Guangdeng Zong, Ning Xu   +4 more
semanticscholar   +1 more source