• 천문학논총
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• 제26권2호
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• pp.55-70
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• 2011

Cosmological linear perturbation theory has fundamental importance in securing the current cosmological paradigm by connecting theories with observations. Here we present an explanation of the method used in relativistic cosmological perturbation theory and show the derivation of basic perturbation equations.

• 천문학회보
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• 제42권2호
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• pp.55.3-55.3
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• 2017

We present the preliminary result of our Lagrangian perturbation theory for the large-scale structure formation, in the presence of the cold dark matter (CDM) and the baryonic fluid. In the linear order, two mutually independent pseudo-particles can describe the evolution of density fluctuations and the accuracy of the calculation is better than the 4-mode (growing, decaying, streaming, compensated) Eulerian linear perturbation theory. In the $2^{nd}$ order, the separability of pseudo-particles is not as straightforward as in the linear order, and the related difficulty in developing the $2^{nd}$ order theory will also be presented.

• 천문학회지
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• 제29권spc1호
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• pp.17-18
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• 1996

COBE's results on the anisotropy of the cosmic microwave background radiation (CMBR) is discussed. Some ambiguities in the linear GI cosmic perturbation theory are clarified. The problem of the last scattering surface and the deficiencies of the linear cosmic perturbation theory are mentioned. The possible ways to overcome the theoretical difficulties are discussed also.

• Structural Engineering and Mechanics
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• 제55권2호
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• pp.281-298
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• 2015

In this study, nonlinear transverse vibrations of tensioned Euler-Bernoulli nanobeams are studied. The nonlinear equations of motion including stretching of the neutral axis and axial tension are derived using nonlocal beam theory. Forcing and damping effects are included in the equations. Equation of motion is made dimensionless via dimensionless parameters. A perturbation technique, the multiple scale methods is employed for solving the nonlinear problem. Approximate solutions are applied for the equations of motion. Natural frequencies of the nanobeams for the linear problem are found from the first equation of the perturbation series. From nonlinear term of the perturbation series appear as corrections to the linear problem. The effects of the various axial tension parameters and different nonlocal parameters as well as effects of different boundary conditions on the vibrations are determined. Nonlinear frequencies are estimated; amplitude-phase modulation figures are presented for simple-simple and clamped-clamped cases.

• 천문학논총
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• 제18권1호
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• pp.1-9
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• 2003

In the framework of linear perturbation theory and linear approximation of spacetime anisotropy, we investigated the formulae for the CMBR temperature anisotropy and fluctuation spectrum which have their origin in the primordial tensor perturbations of the perturbed Bianchi type I universe model. The resulting formulae were compared with those of the flat Friedmann model.

• 대한전자공학회논문지
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• 제19권2호
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• pp.1-6
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• 1982

본 논문에서는 런덤파라미터를 포함하는 선형 시스템의 실제 해석에 perturbation 이론의 응용을 보이고 있다. 시스템의 출력의 통계치가 시스템의 파라미터와 입력의 통계치들에 의해 (perturb된 선형 연산자 방정식에 의해) 구해졌고, perturb된 state 변환 매트릭스도 유도되었다. 간단한 일차, 이차 선형 시스템 모델을 가지고, 정확한 해와 perturbation 결과사이의 정확도가 비교되어 졌고 perturbation series의 수렴도도 조사되어 졌다.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.1-16
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• 2006

The classical perturbation theory is extended to the weighted Kronecker product linear systems $W(A{\bigotimes}B)W\chi=h$. Upper bounds are derived for the normwise condition number.

• 한국소음진동공학회논문집
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• 제23권8호
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• pp.734-741
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• 2013

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.191-203
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• 2011

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.