• 대한수학회논문집
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• 제20권4호
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• pp.765-774
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• 2005

The orthogonality of polynomials plays an important role in many areas and in many cases only finite orthogonalities are used. Concerning this fact we find characterizations of a finite orthogonal polynomial system satisfying a second order differential equation and then give several examples.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 봄 학술발표회논문집
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• pp.195-204
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• 2000

The finite element analysis (FEA) is widely used in modern structural dynamics because the performance of structure can be predicted in early stage. However, due to the difficulty in determination of various uncertain parameters, it is not easy to obtain a reliable finite element model. To overcome these difficulties, a updating program of FE model is developed by consisting of pretest, correlation and update. In correlation, it calculates modal assurance criteria, cross orthogonality, mixed orthogonality and coordinate modal assurance criteria. For the model updating, the continuum sensitivity analysis and design optimization tool(DOT) are used. The SENSUP program is developed for model updating giving physical parameter sensitivity. The developed program is applied to practical examples such as the BLDC spindle motor of HDD, and upper housing of induction motor. And the sensor placement for the square plate is compared using several methods.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.1633-1640
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• 2000

The finite element analysis (FEA) is widely used in modem structural dynamics because the performance of structure can be predicted in early stage. However, due to the difficult in determination of various uncertain parameters, it is not be easy to obtain a reliable finite element model. To overcome these difficulties, updating program of FE model is developed by consisting of pretest, correlation and updating. In correlation, it calculates modal assurance criteria, cross orthogonality, mixed orthogonality and coordinate modal assurance criteria. For the model updating, the continuum sensitivity analysis and design optimization tool (DOT) are used. The SENSUP program is developed for model updating to obtain physical parameter sensitivity. The developed program is applied to practical examples such as the base plate of HDD, BLDC spindle motor, and upper housing of induction motor. And the sensor placement for the square plate is compared using several methods.

• Computers and Concrete
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• 제26권5호
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• pp.421-427
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• 2020

In this study, the two-dimensional generalized finite integral transform(FIT) approach was extended for new accurate thermal buckling analysis of fully clamped orthotropic thin plates. Clamped-clamped beam functions, which can automatically satisfy boundary conditions of the plate and orthogonality as an integral kernel to construct generalized integral transform pairs, are adopted. Through performing the transformation, the governing thermal buckling equation can be directly changed into solving linear algebraic equations, which reduces the complexity of the encountered mathematical problems and provides a more efficient solution. The obtained analytical thermal buckling solutions, including critical temperatures and mode shapes, match well with the finite element method (FEM) results, which verifies the precision and validity of the employed approach.

• 대한수학회보
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• 제54권2호
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• pp.497-505
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• 2017

The rank over a finite field of the adjacency matrix of a directed strongly regular graph is studied, with some applications to the construction of linear codes. Three techniques are used: code orthogonality, adjacency matrix determinant, and adjacency matrix spectrum.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.63-71
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• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.

• 대한수학회논문집
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• 제31권3호
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• pp.549-565
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• 2016

A Hilbert space operator $T{\in}{\mathfrak{B}}(\mathfrak{H})$ is said to be n-*-paranormal, $T{\in}C(n)$ for short, if ${\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}$ for all $x{\in}{\mathfrak{H}}$. We proved some properties of class C(n) and we proved an asymmetric Putnam-Fuglede theorem for n-*-paranormal. Also, we study some invariants of Weyl type theorems. Moreover, we will prove that a class n-* paranormal operator is finite and it remains invariant under compact perturbation and some orthogonality results will be given.

• 한국전자파학회논문지
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• 제9권5호
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• pp.621-629
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• 1998

본 논문에서는 유한요소법을 사용하여 불균일 손실터널내의 전자파 전파특성을 해석하고 있다. 해석 방법으로서는 무손실 도파관내에 유전체를 삽입시킨 도파관 필터의 해석방법을 확장하여 손실터널내의 전자파 전파문제를 해석하고 있다. 수치해석의 결과, 손실터널내에서 일어나는 전자파의 감쇠는 손실벽면의 매질정수와 폭에 따라 크게 영향올 받는다는 것올 알 수 있었다. 또한, 모드간의 직교생으로부터 기본모드와 고차모드를 분리하여 고차모드의 발생정도와 모드에 따른 전따특성도 검토하고 있다. 해석결과의 타당성올 확인하기 위해 제작된 손실터널의 전파특성의 실험결과를 이론치와도 비교 검토하고 있다.

• 대한조선학회논문집
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• 제36권1호
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• pp.70-81
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• 1999

선체주위의 점성유동을 계산하기 위해서는 수치계산을 위한 3차원 공간 격자계가 필요하다. 본 논문에서는 타원형 미분 방정식인 Poisson 방정식의 해를 이용하여 3차원 공간 격자계를 구성하는 방법을 개발하였다. 2차원에서 사용되던 Sorenson방법을 3차원으로 확장하여 격자계의 분포 및 교차 각도를 지정하는 함수를 정의하게 하였다. 미분방정식의 해는 weighting function scheme과 modified strongly implicit procedure를 사용하여 구하였고, 3차원 내부 격자계와 경계면과의 매끄러운 연결을 위해 trans-finite interpolation을 이용하였다. 적용예로서 컨테이너 운반선과 대형 유조선 주위의 난류유동 계산을 위한 공간 격자계를 보였다.

• 한국생산제조학회지
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• 제18권4호
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• pp.337-347
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• 2009

Generally, finite element models used in structural analysis have some uncertainties of the geometric dimensions, applied loads and boundary conditions, as well as in material properties due to the manufacturability of aluminum intensive body. Therefore, it is very important to refine or update a finite element model by correlating it with dynamic and static tests. The structural optimization problems of automotive body are considered for mechanical structures with initial stiffness due to preloading and in operation condition or manufacturing. As the mean compliance and deflection under preloading are chosen as the objective function and constraints, their sensitivities must be derived. The optimization problem is iteratively solved by a sequential convex approximation method in the commercial software. The design variables are corrected by the strain energy scale factor in the element levels. This paper presents an updated method based on the sensitivities of structural responses and the residual error vectors between experimental and simulation models.