• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.04a
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• pp.172-179
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• 2001

비감쇠 혹은 비비례감쇠 시스템의 고유치를 구하기 위한 대부분의 방법들은 저차의 몇 개의 모드만을 사용하여 동적응답을 구하는 경우 누락된 고유치의 존재여부를 검사하기 위해 잘 알려진 Sturm 수열 성질(Sturm sequence property)을 이용한다. 반면 감쇠시스템 즉, 지반-구조물의 진동제어 시스템, 복합재료 구조물과 같은 경우에는 저차 몇 개의 모드만을 사용할 경우 누락 고유치를 검사할 수 있는 효율적인 기법이 아직 확립되지 않은 상태이다. 본 논문에서는 Gleyse의 정리를 이용하여 감쇠스템의 누락된 고유치를 검사하는 기법을 제안하고 이 방법의 효용성을 수치예제를 통하여 검증하였다.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.407-414
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• 2020

In this article, a second-order Sturm-Liouville problem with impulsive effects and involving the one-dimensional p-Laplacian is considered. The existence of at least three weak solutions via variational methods and critical point theory is obtained.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.499-506
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• 2013

The half-inverse spectral problem for an impulsive Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm-Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if $q(x)$ is prescribed on (0, ${\frac{\pi}{2}}$), then only one spectrum is sufficient to determine $q(x)$ on the interval (0, ${\pi}$) for this problem.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.34-41
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• 2001

Most of the eigenvalue analysis methods for the undamped or proportionally damped systems use the well-known Sturm sequence property to check the missed eigenvalues when only a set of the lowest modes is to be used for large structures. However, in the case of the non-proportionally damped systems such as the soil-structure interaction system, the structural control system and the composite structures, no counterpart of the Sturm sequence property for undamped systems has been developed yet. Hence, when some important modes are missed for those systems, it may leads to poor results in dynamic analysis. In this paper, a technique for calculating the number of eigenvalues inside the open disk of arbitrary radius for the eigenproblem with the damping matrix is proposed by applying Chen's algorithm and Gleyse's theorem. To verify the applicability of the proposed method, two numerical examples are considered.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.365-383
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• 2001

We consider path integrals, more precisely projective systems of Fresnel distributions, associated with Sturm-Liouville boundary value problems.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.17-34
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• 2006

Inverse coefficient identification problems associated with the fourth-order Sturm-Liouville operator in the steady state Euler-Bernoulli beam equation are investigated. Unlike previous studies in which spectral data are used as additional information, in this paper only boundary information is used, hence non-destructive tests can be employed in practical applications.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.823-826
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• 2010

Let p be a prime. We generalized Sturm's bound to a group ${\Gamma}_{0}^{+}(p)$ of which the genus is zero.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1109-1118
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• 2009

In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.679-686
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• 2010

This paper is concerned with the following fourth-order four-point Sturm-Liouville boundary value problem $u^{(4)}(t)=f(t,\;u(t),\;u^{\prime\prime}(t))$, $0\;{\leq}\;t\;{\leq}1$, ${\alpha}u(0)-{\beta}u^{\prime}(0)={\gamma}u(1)+{\delta}u^{\prime}(1)=0$, $au^{\prime\prime}(\xi_1)-bu^{\prime\prime\prime}(\xi_1)=cu^{\prime\prime}(\xi_2)+du^{\prime\prime\prime}(\xi_2)=0$. Some sufficient conditions are obtained for the existence of at least one positive solution to the above boundary value problem by using the well-known Guo-Krasnoselskii fixed point theorem.

• Journal for History of Mathematics
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• v.29 no.2
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• pp.103-143
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• 2016

We study the topics of the lectures in Analysis in 19th century at Ecole Polytechnique of France through the lists of the contents of the Cours d'Analyse by Cauchy, Sturm and Jordan, respectively and also we show how they stated the definitions of functions, continuity and limits in their Cours d'Analyse. Through this, we see that in 19th century, in France, analysis included differential and integral calculus, differential equations, variations and applications of these to differential geometry, and it was far from today's mathematical analysis.