• Communications for Statistical Applications and Methods
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• 제15권4호
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• pp.483-496
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• 2008

This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.623-641
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• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.45-60
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• 2002

Some error estimates in terms of the p-norms of the fourth derivative for the remainder in a perturbed trapezoid formula are given. Applications for the expectation of a random variable and the Hermite-Hadamard divergence in Information Theory are also pointed out.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.813-829
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• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• 전산구조공학
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• 제7권3호
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• pp.115-122
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• 1994

불확정 구조계획의 선형 고유치 문제는 재료정수나 경게조건 및 외부하중 등에 결정론적으로 사용할 수 없는 확률량을 포함하고 있다. 변동량을 내포한 고유치 문제의 해석은 기대치에 대한 지배 방정식과 변동량 결정방정식을 고려해야 한다. 비선형성이 심한 구조계를 선형화할 대 일차 및 이차 변동값을 반영함으로 고유치의 정도를 향상시킬 수 있다. 매개변수에 불확정성을 포함한 고유치 문제는 최적설계 정식화에서 변동된 값을 고료해 줌으로 신뢰성 있는 설계가 된다. 최적설계 알고리즘 중에는 목적함수와 제한 조건식의 설계 민감도를 요한다. 이차 기울기에 근거를 둔 최적설계 수행시에 변동량에 고려하여 제한식으로 설정하고, 설계 민감도를 구할 수 있는 방법을 제시하였다.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.233-242
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• 2011

We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

• 대한기계학회논문집
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• 제15권6호
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• pp.2015-2025
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• 1991

본 연구에서는 무거운 부하중량(payload)을 운반하는 평행구동기구(parallel drive mechanism)를 가진 2 자유도 수직 로봇 조작기의 마지막 링크를 고속화 및 작업 영역의 확대를 위해 경량의 길이가 긴 링크로 구성하고, 동적 해석 및 제어를 위해 이 를 수직면상에서 회전하는 첨단질량을 가진 Euler-Bernoulli 외팔보로 모델링하였다. Hamilton의 원리를 적용하여 계의 지배방정식을 구하였으며 이를 조작기의 최종 자세 (configuration)에 대한 교란변수들(periturbed variables)을 도입하여 이산시간계 상 태방정식으로 표시하였다. 계의 상태방정식에 대해 디지탈 최적제어 및 최적관측기 이론을 적용하여, 유연한 조작기의 위치 및 진동제어를 병해하여 수행하는 제어기를 설계하였으며, 제어기의 효율성 및 적용성을 검토하기 위하여 수치해석 및 실험을 행 하였고 이들 결과를 비교, 검토하였다.

• 대한수학회지
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• 제60권2호
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• pp.465-477
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• 2023

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2004년도 제5회 압연심포지엄 신 시장 개척을 위한 압연기술
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• pp.359-367
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• 2004

In this research on-line model for the prediction of the effective strain distribution in strip on finishing mill process is presented. To describe the effective strain distribution in strip, three guide points and a distribution fitting variable are used. On-line models to get these points and fitting variable non-dimensionalization method and least square method were used with FEM simulation results. The model is developed using strip only FEM simulation as reference sets and compared with roll coupled FEM simulation results as perturbed sets. The on-line model to describe effective strain distribution shows good agreement with coupled FEM analysis results.