• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• 대한수학회지
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• 제39권3호
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• pp.351-361
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• 2002

We extend the Holder-McCarthy inequality for a positive and an arbitrary operator, respectively. The powers of each inequality are given and the improved Reid's inequality by Halmos is generalized. We also give the bound of the Holder-McCarthy inequality by recursion.

• Kyungpook Mathematical Journal
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• 제50권1호
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• pp.15-35
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• 2010

By strengthening dichotomy condition and weakening decay conditions, we show that a four term 2n-th order differential operator with unbounded coefficients is nonlimit-point. Using stringent conditions we show that the deficiency index of this operator is determined by the behaviour of the coefficients themselves. Similarly, we prove the absence of singular continuous spectrum and that the absolutely continuous spectrum has multiplicity two.

• 대한수학회지
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• 제16권1호
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• pp.9-16
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• 1979

• 대한수학회보
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• 제43권2호
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• pp.389-393
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• 2006

In this paper it is shown that the spectrum ${\sigma}$ is continuous at every p-hyponormal operator when restricted to the set of essentially p-hyponormal operators and moreover ${\sigma}$ is continuous when restricted to the set of compact perturbations of p-hyponormal operators whose spectral pictures have no holes associated with the index zero.

• 대한수학회지
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• 제34권2호
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• pp.483-500
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• 1997

We investigate the geometric properties reflected by the spectra of the Jacobi operator of a harmonic map when the target manifold is a Riemannian product manifold or a Kaehlerian product manifold. And also we study the spectral characterization of Riemannian sumersions when the target manifold is $S^n \times S^n$ or $CP^n \times CP^n$.

• 대한수학회지
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• 제54권4호
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• pp.1175-1187
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• 2017

The spectral problem $$-y^{{\prime}{\prime}}+q(x)y={\lambda}y,\;0 < x < 1, \atop y(0)cos{\beta}=y^{\prime}(0)sin{\beta},\;0{\leq}{\beta}<{\pi};\;{\frac{y^{\prime}(1)}{y(1)}}=h({\lambda})$$ is considered, where ${\lambda}$ is a spectral parameter, q(x) is real-valued continuous function on [0, 1] and $$h({\lambda})=a{\lambda}+b-\sum\limits_{k=1}^{N}{\frac{b_k}{{\lambda}-c_k}},$$ with the real coefficients and $a{\geq}0$, $b_k$ > 0, $c_1$ < $c_2$ < ${\cdots}$ < $c_N$, $N{\geq}0$. The sharpened asymptotic formulae for eigenvalues and eigenfunctions of above-mentioned spectral problem are obtained and the uniform convergence of the spectral expansions of the continuous functions in terms of eigenfunctions are presented.

• 항공우주시스템공학회지
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• 제14권3호
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• pp.17-23
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• 2020

본 연구는 Chebyshev collocation operator를 지배 방정식의 시간 미분항에 적용하여 비정상 유동해석을 해석할 수 있는 기법을 개발한 논문이다. 시간적분으로 유속항은 내재적으로 처리하였으며 시간 미분항은 Chebyshev collocation operator을 적용하여 원천항 형태로 외재적으로 처리하여 부분 내재적 시간적분법을 적용하였다. 본 연구의 방법을 검증하기 위해 1차원 비정상 burgers 방정식과 2차원 진동하는 airfoil에 적용하였으며 기존의 비정상 유동 주파수 해석기법과 시험 결과를 비교하여 나타내었다. Chebyshev collocation operator는 주기적인 문제와 비주기적인 문제에 대해서 시간 미분항을 처리할 수 있으므로 추후 비주기적인 문제에 적용할 예정이다.

• Structural Engineering and Mechanics
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• 제39권5호
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• pp.669-682
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• 2011

A Chebyshev spectral method (CSM) for the dynamic analysis of non-uniform Timoshenko beams under various boundary conditions and concentrated masses at their ends is proposed. The matrix-based Chebyshev spectral approach was used to construct the spectral differentiation matrix of the governing differential operator and its boundary conditions. A matrix condensation approach is crucially presented to impose boundary conditions involving the homogeneous Cauchy conditions and boundary conditions containing eigenvalues. By taking advantage of the standard powerful algorithms for solving matrix eigenvalue and generalized eigenvalue problems that are embodied in the MATLAB commands, chebfun and eigs, the modal parameters of non-uniform Timoshenko beams under various boundary conditions can be obtained from the eigensolutions of the corresponding linear differential operators. Some numerical examples are presented to compare the results herein with those obtained elsewhere, and to illustrate the accuracy and effectiveness of this method.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.27-47
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• 2012

It has become apparent from the recent work by Choi et al. [3] on the nonlinear beam deflection problem, that analysis of the integral operator $\mathcal{K}$ arising from the beam deflection equation on linear elastic foundation is important. Motivated by this observation, we perform investigations on the eigenstructure of the linear integral operator $\mathcal{K}_l$ which is a restriction of $\mathcal{K}$ on the finite interval [$-l,l$]. We derive a linear fourth-order boundary value problem which is a necessary and sufficient condition for being an eigenfunction of $\mathcal{K}_l$. Using this equivalent condition, we show that all the nontrivial eigenvalues of $\mathcal{K}l$ are in the interval (0, 1/$k$), where $k$ is the spring constant of the given elastic foundation. This implies that, as a linear operator from $L^2[-l,l]$ to $L^2[-l,l]$, $\mathcal{K}_l$ is positive and contractive in dimension-free context.