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Journal articles on the topic 'Perturbation methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Hinch, E. J., and Edward G. Harris. "Perturbation Methods." American Journal of Physics 60, no. 11 (1992): 1052–53. http://dx.doi.org/10.1119/1.16992.

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2

Heinrichs, Wilhelm. "Spectral methods for singular perturbation problems." Applications of Mathematics 39, no. 3 (1994): 161–88. http://dx.doi.org/10.21136/am.1994.134251.

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3

Cha, Philip D., and Austin Shin. "Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems." Shock and Vibration 2018 (October 17, 2018): 1–25. http://dx.doi.org/10.1155/2018/8609138.

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Dynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed. In this paper, three different methods based on the eigenvalue perturbation theory are introduced to analyze the effects of modifications without performing a potentially time-consuming and costly reanalysis. They will be referred to as the straightforward perturbation method, the incremental perturbation method, and the triple product method. In the straightforward perturbation

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4

Riley, N. "Perturbation methods, 1992." Journal of Fluids and Structures 6, no. 4 (1992): 523–24. http://dx.doi.org/10.1016/0889-9746(92)90029-3.

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5

Huang, Wei, Lei Zhang, Zizhou Wang, and Yan Wang. "GapMatch: Bridging Instance and Model Perturbations for Enhanced Semi-Supervised Medical Image Segmentation." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 16 (2025): 17458–66. https://doi.org/10.1609/aaai.v39i16.33919.

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Medical image segmentation provides detailed understanding and aids in diagnosis, treatment planning, and monitoring of diseases. Due to the high cost of acquiring labeled data in the field of medical image analysis, semi-supervised segmentation methods have garnered increasing attention. Benefiting from their simplicity and effectiveness, consistency regularization-based methods have emerged as a significant research focus by utilizing perturbations. However, existing methods typically consider perturbation strategies from only a single perspective: either instance perturbation or model pertu

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6

Duan, Jiale, Linyao Qiu, Guangjun He, Ling Zhao, Zhenshi Zhang, and Haifeng Li. "A Region-Adaptive Local Perturbation-Based Method for Generating Adversarial Examples in Synthetic Aperture Radar Object Detection." Remote Sensing 16, no. 6 (2024): 997. http://dx.doi.org/10.3390/rs16060997.

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In synthetic aperture radar (SAR) imaging, intelligent object detection methods are facing significant challenges in terms of model robustness and application security, which are posed by adversarial examples. The existing adversarial example generation methods for SAR object detection can be divided into two main types: global perturbation attacks and local perturbation attacks. Due to the dynamic changes and irregular spatial distribution of SAR coherent speckle backgrounds, the attack effectiveness of global perturbation attacks is significantly reduced by coherent speckle. In contrast, by

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7

Li, Mengyang, Fengguang Su, Ou Wu, and Ji Zhang. "Logit Perturbation." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 2 (2022): 1359–66. http://dx.doi.org/10.1609/aaai.v36i2.20024.

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Features, logits, and labels are the three primary data when a sample passes through a deep neural network. Feature perturbation and label perturbation receive increasing attention in recent years. They have been proven to be useful in various deep learning approaches. For example, (adversarial) feature perturbation can improve the robustness or even generalization capability of learned models. However, limited studies have explicitly explored for the perturbation of logit vectors. This work discusses several existing methods related to logit perturbation. Based on a unified viewpoint between

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8

Kuić, Domagoj, Alemka Knapp, and Diana Šaponja-Milutinović. "Finite Time Path Field Theory Perturbative Methods for Local Quantum Spin Chain Quenches." Universe 10, no. 10 (2024): 384. http://dx.doi.org/10.3390/universe10100384.

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We discuss local magnetic field quenches using perturbative methods of finite time path field theory (FTPFT) in the following spin chains: Ising and XY in a transverse magnetic field. Their common characteristics are: (i) they are integrable via mapping to a second quantized noninteracting fermion problem; and (ii) when the ground state is nondegenerate (true for finite chains except in special cases), it can be represented as a vacuum of Bogoliubov fermions. By switching on a local magnetic field perturbation at finite time, the problem becomes nonintegrable and must be approached via numeric

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9

Murdock, James. "Book Review: Perturbation methods." Bulletin of the American Mathematical Society 28, no. 2 (1993): 418–22. http://dx.doi.org/10.1090/s0273-0979-1993-00378-1.

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10

Chacon, Monique Revoredo, and Michael C. Zerner. "Perturbation-variational methods revisited." International Journal of Quantum Chemistry 47, no. 2 (1993): 103–18. http://dx.doi.org/10.1002/qua.560470202.

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11

PANI, PAOLO. "ADVANCED METHODS IN BLACK-HOLE PERTURBATION THEORY." International Journal of Modern Physics A 28, no. 22n23 (2013): 1340018. http://dx.doi.org/10.1142/s0217751x13400186.

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Black-hole perturbation theory is a useful tool to investigate issues in astrophysics, high-energy physics, and fundamental problems in gravity. It is often complementary to fully-fledged nonlinear evolutions and instrumental to interpret some results of numerical simulations. Several modern applications require advanced tools to investigate the linear dynamics of generic small perturbations around stationary black holes. Here, we present an overview of these applications and introduce extensions of the standard semianalytical methods to construct and solve the linearized field equations in cu

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12

Zhang, Hanbin, Min Chen, and Shuiyong Fan. "Study on the Construction of Initial Condition Perturbations for the Regional Ensemble Prediction System of North China." Atmosphere 10, no. 2 (2019): 87. http://dx.doi.org/10.3390/atmos10020087.

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The regional ensemble prediction system (REPS) of North China is currently under development at the Institute of Urban Meteorology, China Meteorological Administration, with initial condition perturbations provided by global ensemble dynamical downscaling. To improve the performance of the REPS, a comparison of two initial condition perturbation methods is conducted in this paper: (i) Breeding, which was specifically designed for the REPS, and (ii) Dynamical downscaling. Consecutive tests were implemented to evaluate the performances of both methods in the operational REPS environment. The per

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13

KODAMA, HIDEO, and MISAO SASAKI. "EVOLUTION OF ISOCURVATURE PERTURBATIONS I: PHOTON-BARYON UNIVERSE." International Journal of Modern Physics A 01, no. 01 (1986): 265–301. http://dx.doi.org/10.1142/s0217751x86000137.

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The isocurvature perturbation in the photon-baryon universe is comprehensively studied by analytic methods in the framework of the gauge-invariant perturbation theory. In particular the evolutionary behavior of the isocurvature perturbation and its influence on the anisotropy in the cosmic microwave background are examined in detail. The results are compared with those for the adiabatic perturbation and some peculiar features of the isocurvature perturbation are pointed out and their origin is clarified. Besides these studies the ambiguities associated with the definition of non-adiabatic pert

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14

Pakdemirli, M., and H. Boyaci. "Comparison of direct-perturbation methods with discretization-perturbation methods for non-linear vibrations." Journal of Sound and Vibration 186, no. 5 (1995): 837–45. http://dx.doi.org/10.1006/jsvi.1995.0491.

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15

Taylor, Zoe, Gregory S. Walsh, Hannah Hawkins, Mario Inacio, and Patrick Esser. "Perturbations during Gait: A Systematic Review of Methodologies and Outcomes." Sensors 22, no. 15 (2022): 5927. http://dx.doi.org/10.3390/s22155927.

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Background: Despite extensive literature regarding laboratory-based balance perturbations, there is no up-to-date systematic review of methods. This systematic review aimed to assess current perturbation methods and outcome variables used to report participant biomechanical responses during walking. Methods: Web of Science, CINAHL, and PubMed online databases were searched, for records from 2015, the last search was on 30th of May 2022. Studies were included where participants were 18+ years, with or without clinical conditions, conducted in non-hospital settings. Reviews were excluded. Partic

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16

Pratt, S., R. Zeng, Z. Yuan, and J. Keller. "Comparison of methods for the determination of KLaO2 for respirometric measurements." Water Science and Technology 50, no. 11 (2004): 153–61. http://dx.doi.org/10.2166/wst.2004.0683.

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The mass transfer coefficient for oxygen in water (KLaO2) is an important parameter for respirometric studies. But determination of KLaO2 in process conditions is not straightforward. In this paper, two distinct procedures for determining KLaO2 in process conditions are outlined and tested. The off-gas method relies on a gas mass balance over a bioreactor while the non-steady state methods rely on analysing DO recovery after perturbation. Various means for inducing perturbation are tested and compared. KLaO2 values for a bioreactor are determined by the listed methods. It was found that the of

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17

Mendonça, Antônio Marcos, and JoséPaulo Bonatti. "Experiments with EOF-Based Perturbation Methods and Their Impact on the CPTEC/INPE Ensemble Prediction System." Monthly Weather Review 137, no. 4 (2009): 1438–59. http://dx.doi.org/10.1175/2008mwr2581.1.

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Abstract The impact of modifications of the perturbation method based on empirical orthogonal functions (EOFs) used operationally upon the ensemble prediction system (EPS) at the Center for Weather Prediction and Climate Studies/National Institute for Space Research (CPTEC/INPE) is evaluated. The main changes proposed in this study are to apply the EOF method to perturb the midlatitudes, apply additional perturbations to the surface pressure (P) and specific humidity (Q) fields, and compute regional perturbations over South America. The impact of these modifications in the characteristics of t

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18

Vinter, R. B. "PERTURBATION METHODS IN OPTIMAL CONTROL." Bulletin of the London Mathematical Society 23, no. 6 (1991): 616–17. http://dx.doi.org/10.1112/blms/23.6.616.

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19

Ganapol, B. D. "Perturbation Methods in Heat Transfer." Nuclear Technology 73, no. 2 (1986): 252. http://dx.doi.org/10.13182/nt86-a33790.

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20

Shivamoggi,, BK, and J. Awrejcewicz,. "Perturbation Methods for Differential Equations." Applied Mechanics Reviews 56, no. 6 (2003): B77—B78. http://dx.doi.org/10.1115/1.1623750.

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21

Nayfeh, Ali H. "Numerical-perturbation methods in mechanics." Computers & Structures 30, no. 1-2 (1988): 185–204. http://dx.doi.org/10.1016/0045-7949(88)90226-x.

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22

Gorbunov, M. E. "Perturbation methods in geometric optics." Radiophysics and Quantum Electronics 38, no. 7 (1995): 438–43. http://dx.doi.org/10.1007/bf01060459.

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23

Miller, D., B. J. T. Morgan, M. S. Ridout, P. D. Carey, and P. Rothery. "Methods for exact perturbation analysis." Methods in Ecology and Evolution 2, no. 3 (2010): 283–88. http://dx.doi.org/10.1111/j.2041-210x.2010.00074.x.

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24

Baikov, V. A., R. K. Gazizov, and N. Kh Ibragimov. "Perturbation methods in group analysis." Journal of Soviet Mathematics 55, no. 1 (1991): 1450–90. http://dx.doi.org/10.1007/bf01097534.

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25

Eichhorn, R. "Perturbation methods in heat transfer." International Journal of Heat and Fluid Flow 6, no. 2 (1985): 121. http://dx.doi.org/10.1016/0142-727x(85)90046-3.

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26

MISHRA, R. K., and NAVYA JAIN. "Stability Analysis in Cosmological Models Using Perturbative Methods in f(R,T) Theory." Romanian Journal of Physics 69, no. 9-10 (2024): 113. https://doi.org/10.59277/romjphys.2024.69.113.

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This study examines the stability of cosmological models through perturbation theory, focusing on different formulations of the deceleration parameter (DP). By analysing the eigenvalues of perturbations, we identify key insights into the models’ long-term dynamics and stability. The results reveal the presence of stable and marginally stable modes, indicating how perturbations evolve and dissipate over cosmic time. These findings provide a deeper understanding of cosmic evolution, the formation of large-scale structures, and the behaviour of perturbations, offering significant contributions to

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27

Nandhini, K., and M. Sumathi. "New and Modified Homotopy Perturbation Methods for Addressing Burger’s Non-linear Equation." Indian Journal Of Science And Technology 17, no. 38 (2024): 4019–29. http://dx.doi.org/10.17485/ijst/v17i38.2029.

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Objectives: The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. Methods: New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader range of problems. Findings: The solution for two-dimensional coupled

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28

Chander, Harish, Sachini N. K. Kodithuwakku Arachchige, Christopher M. Hill, et al. "Virtual-Reality-Induced Visual Perturbations Impact Postural Control System Behavior." Behavioral Sciences 9, no. 11 (2019): 113. http://dx.doi.org/10.3390/bs9110113.

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Background: Virtual reality (VR) is becoming a widespread tool in rehabilitation, especially for postural stability. However, the impact of using VR in a “moving wall paradigm” (visual perturbation), specifically without and with anticipation of the perturbation, is unknown. Methods: Nineteen healthy subjects performed three trials of static balance testing on a force plate under three different conditions: baseline (no perturbation), unexpected VR perturbation, and expected VR perturbation. The statistical analysis consisted of a 1 × 3 repeated-measures ANOVA to test for differences in the ce

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29

DOUGLAS, JIM, and SEONGJAI KIM. "IMPROVED ACCURACY FOR LOCALLY ONE-DIMENSIONAL METHODS FOR PARABOLIC EQUATIONS." Mathematical Models and Methods in Applied Sciences 11, no. 09 (2001): 1563–79. http://dx.doi.org/10.1142/s0218202501001471.

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Classical alternating direction (AD) and fractional step (FS) methods for parabolic equations, based on some standard implicit time-stepping procedure such as Crank–Nicolson, can have errors associated with the AD or FS perturbations that are much larger than the errors associated with the underlying time-stepping procedure. We show that minor modifications in the AD and FS procedures can virtually eliminate the perturbation errors at an additional computational cost that is less than 10% of the cost of the original AD or FS method. Moreover, after these modifications, the AD and FS procedures

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30

Ferreira, Rafael N., Nuno Ferrete Ribeiro, Joana Figueiredo, and Cristina P. Santos. "Provoking Artificial Slips and Trips towards Perturbation-Based Balance Training: A Narrative Review." Sensors 22, no. 23 (2022): 9254. http://dx.doi.org/10.3390/s22239254.

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Humans’ balance recovery responses to gait perturbations are negatively impacted with ageing. Slip and trip events, the main causes preceding falls during walking, are likely to produce severe injuries in older adults. While traditional exercise-based interventions produce inconsistent results in reducing patients’ fall rates, perturbation-based balance training (PBT) emerges as a promising task-specific solution towards fall prevention. PBT improves patients’ reactive stability and fall-resisting skills through the delivery of unexpected balance perturbations. The adopted perturbation conditi

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31

He, Bangyan, Jian Liu, Yiming Li, et al. "Generating Transferable 3D Adversarial Point Cloud via Random Perturbation Factorization." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 1 (2023): 764–72. http://dx.doi.org/10.1609/aaai.v37i1.25154.

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Recent studies have demonstrated that existing deep neural networks (DNNs) on 3D point clouds are vulnerable to adversarial examples, especially under the white-box settings where the adversaries have access to model parameters. However, adversarial 3D point clouds generated by existing white-box methods have limited transferability across different DNN architectures. They have only minor threats in real-world scenarios under the black-box settings where the adversaries can only query the deployed victim model. In this paper, we revisit the transferability of adversarial 3D point clouds. We ob

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32

Johnson, Aaron, Xuguang Wang, Ming Xue, et al. "Multiscale Characteristics and Evolution of Perturbations for Warm Season Convection-Allowing Precipitation Forecasts: Dependence on Background Flow and Method of Perturbation." Monthly Weather Review 142, no. 3 (2014): 1053–73. http://dx.doi.org/10.1175/mwr-d-13-00204.1.

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Abstract Multiscale convection-allowing precipitation forecast perturbations are examined for two forecasts and systematically over 34 forecasts out to 30-h lead time using Haar Wavelet decomposition. Two small-scale initial condition (IC) perturbation methods are compared to the larger-scale IC and physics perturbations in an experimental convection-allowing ensemble. For a precipitation forecast driven primarily by a synoptic-scale baroclinic disturbance, small-scale IC perturbations resulted in little precipitation forecast perturbation energy on medium and large scales, compared to larger-

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33

HE, JI-HUAN. "SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS." International Journal of Modern Physics B 20, no. 10 (2006): 1141–99. http://dx.doi.org/10.1142/s0217979206033796.

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This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are e

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34

Munjal, Manish, Amit Grewal, and Harsh Yadav. "Optical Fibre Sensors and Methods." Journal of Advance Research in Electrical & Electronics Engineering (ISSN: 2208-2395) 1, no. 2 (2014): 17–19. http://dx.doi.org/10.53555/nneee.v1i2.260.

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This research paper is about a multi-mode fibre optic sensor for optically sensing a physical perturbation including a multi- mode optical fibre segment which accepts coherent monochromatic radiation from a suitable source. As the radiation is propagated in the fibre, the various modes form a complex interference pattern which changes in response to a physical perturbation of the fibre. A detector provides an output signal to a signal processor which analyzes the signal as a function of the change in intensity to provide an information signal functionally related to the perturbation.

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35

Johnson, Aaron, and Xuguang Wang. "A Study of Multiscale Initial Condition Perturbation Methods for Convection-Permitting Ensemble Forecasts." Monthly Weather Review 144, no. 7 (2016): 2579–604. http://dx.doi.org/10.1175/mwr-d-16-0056.1.

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Abstract The impacts of multiscale flow-dependent initial condition (IC) perturbations for storm-scale ensemble forecasts of midlatitude convection are investigated using perfect-model observing system simulation experiments. Several diverse cases are used to quantitatively and qualitatively understand the impacts of different IC perturbations on ensemble forecast skill. Scale dependence of the results is assessed by evaluating 2-h storm-scale reflectivity forecasts separately from hourly accumulated mesoscale precipitation forecasts. Forecasts are initialized with different IC ensembles, incl

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36

K, Nandhini, and Sumathi M. "New and Modified Homotopy Perturbation Methods for Addressing Burger's Non-linear Equation." Indian Journal of Science and Technology 17, no. 38 (2024): 4019–29. https://doi.org/10.17485/IJST/v17i38.2029.

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Abstract <strong>Objectives:</strong> The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. <strong>Methods:</strong> New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader

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37

Ganji, D. D., and A. Rajabi. "Assessment of homotopy–perturbation and perturbation methods in heat radiation equations." International Communications in Heat and Mass Transfer 33, no. 3 (2006): 391–400. http://dx.doi.org/10.1016/j.icheatmasstransfer.2005.11.001.

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38

HISLOP, PETER D., and SHU NAKAMURA. "STARK HAMILTONIAN WITH UNBOUNDED RANDOM POTENTIALS." Reviews in Mathematical Physics 02, no. 04 (1990): 479–94. http://dx.doi.org/10.1142/s0129055x90000156.

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Spectral properties of one-dimensional Schrödinger operators with unbounded potentials are studied. The main example is the Stark Hamiltonian with unbounded Anderson-type random perturbations. In this case, it is shown that if the perturbation is o(x) then the spectrum is the real line and absolutely continuous except for eigenvalues with no accumulation points. If the perturbation is larger than O(x), then the Hamiltonian has no absolutely continuous spectrum. The methods of proof involve the Mourre estimate and trace-class perturbation theory as recently used by Simon and Spencer.

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39

Che, Lei, Chengcong Wu, and Yan Hou. "Large Language Model Text Adversarial Defense Method Based on Disturbance Detection and Error Correction." Electronics 14, no. 11 (2025): 2267. https://doi.org/10.3390/electronics14112267.

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This study aims to effectively defend against complex and diverse adversarial attacks, enhance adversarial defense performance in the field of textual adversarial examples, and address existing issues in current defense methods such as models’ inability to accurately detect perturbations and perform effective error correction. To this end, we propose a Large Language Model Adversarial Defense (LLMAD) method based on perturbation detection and correction. The LLMAD framework consists of two modules: a perturbation detection module and a perturbation correction module. The detection module combi

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40

Xie, Yi, Zhuohang Li, Cong Shi, Jian Liu, Yingying Chen, and Bo Yuan. "Enabling Fast and Universal Audio Adversarial Attack Using Generative Model." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 16 (2021): 14129–37. http://dx.doi.org/10.1609/aaai.v35i16.17663.

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Recently, the vulnerability of deep neural network (DNN)-based audio systems to adversarial attacks has obtained increasing attention. However, the existing audio adversarial attacks allow the adversary to possess the entire user's audio input as well as granting sufficient time budget to generate the adversarial perturbations. These idealized assumptions, however, make the existing audio adversarial attacks mostly impossible to be launched in a timely fashion in practice (e.g., playing unnoticeable adversarial perturbations along with user's streaming input). To overcome these limitations, in

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41

Karandikar, Mandar, Cristiano Porciani, and Oliver Hahn. "Testing the assumptions of the Effective Field Theory of Large-Scale Structure." Journal of Cosmology and Astroparticle Physics 2024, no. 01 (2024): 051. http://dx.doi.org/10.1088/1475-7516/2024/01/051.

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Abstract The Effective Field Theory of Large-Scale Structure (EFTofLSS) attempts to amend some of the shortcomings of the traditional perturbative methods used in cosmology. It models the evolution of long-wavelength perturbations above a cutoff scale without the need for a detailed description of the short-wavelength ones. Short-scale physics is encoded in the coefficients of a series of operators composed of the long-wavelength fields, and ordered in a systematic expansion. As applied in the literature, the EFTofLSS corrects a summary statistic (such as the power spectrum) calculated from st

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42

Ousmane, Samba Coulibaly. "IDENTIFICATION THE HEAT SOURCE DEPENDENT ON A SPATIAL VARIABLE, REGULARIZATION AND CONTROL OF NOISE LEVEL IN CASE PERTURBATION BY SPECTRAL TRUNCATION AND KRYLOV METHODS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 6, no. 9 (2017): 240–48. https://doi.org/10.5281/zenodo.886668.

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This paper deals with regularization and noise level control of source depending only on the spatial variable in the heat equation. In this problem, the Krylov method is employed to get the regularization solution and control noise level in case perturbation. Various numerical tests are given to verify the efficiency of the proposed method and until what point the method resist at the perturbations.

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43

Sun, Da Wei. "Perturbation Analysis of Diffeomorphisms in Contact Dynamical System." Advanced Materials Research 529 (June 2012): 264–67. http://dx.doi.org/10.4028/www.scientific.net/amr.529.264.

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This paper studies the perturbations of strictly contact diffeomorphisms in contact dynamical system. By constructing new lifting methods for contact system and using some perturbation techniques in Hamiltonian mechanics, this paper proves that there exists an arbitrary small perturbations such that the corresponding function of the strictly contact isotopy does not equal to a constant at any time.

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44

Itô, Masayuki. "A remark on singular perturbation methods." Hiroshima Mathematical Journal 14, no. 3 (1985): 619–29. http://dx.doi.org/10.32917/hmj/1206132941.

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45

Otanez, Paul G., and Mark E. Campbell. "Detection Methods for Mode Perturbation Signatures." IEEE Transactions on Automatic Control 57, no. 11 (2012): 2923–28. http://dx.doi.org/10.1109/tac.2012.2195932.

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46

Goodson, D. Z., and D. R. Herschbach. "Summation methods for dimensional perturbation theory." Physical Review A 46, no. 9 (1992): 5428–36. http://dx.doi.org/10.1103/physreva.46.5428.

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47

Killingbeck, J. P., and G. Jolicard. "Perturbation methods for the matrix eigenproblem." Journal of Physics A: Mathematical and General 25, no. 23 (1992): 6455–59. http://dx.doi.org/10.1088/0305-4470/25/23/037.

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48

Cross, M. "Perturbation Methods for Scientists and Engineers." Applied Mathematical Modelling 16, no. 8 (1992): 446. http://dx.doi.org/10.1016/0307-904x(92)90080-m.

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49

Buldaev, A. S. "Perturbation methods in optimal control problems." Ecological Modelling 216, no. 2 (2008): 157–59. http://dx.doi.org/10.1016/j.ecolmodel.2008.03.030.

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50

Hongxing, Li. "Fuzzy clustering methods based on perturbation." Fuzzy Sets and Systems 33, no. 3 (1989): 291–302. http://dx.doi.org/10.1016/0165-0114(89)90119-x.

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