• Communications of the Korean Mathematical Society
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• v.20 no.4
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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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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• v.26 no.5
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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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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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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• v.55 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.9 no.5
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• pp.621-629
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• 1998

Propagation characteristics of electromagnetic waves in lossy tunnels are analysed using Finite Element Method with edge basis function. According to the analysis lossy dielectric wall on the tunnel highly affects the characteristics of the waves in the tunnel. Also higer modes are separated using mode orthogonality principle, and the propagation characteristics of higer modes are investigated. To verity the numerical results, miniatures of the tunnels are constructed and measurements of the waves are accomplished.

• Journal of the Society of Naval Architects of Korea
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• v.36 no.1
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• pp.70-81
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• 1999

To predict the viscous boundary layers and wakes around a ship, the CFD techniques are commonly used. For the efficient application of CFD tools to practical hull farms, a 3-D field grid generating system is developed. The present grid generating system utilizes the solution of Poisson equation. Sorenson's method developed for 2-D is extended into 3-D to provide the forcing functions controling grid interval and orthogonality on hull surface, etc. The weighting function scheme is used for the discretization of the Poisson equation and the linear equations are solved by using MSIP salver. The trans-finite interpolation is also employed to assure the smooth transition into boundary surface grids. To rove the applicability, the field grid systems around a container ship and a VLCC with bow and stem bulb are illustrated, and the procedures for generating 3-D field grid system are explained.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.18 no.4
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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.