• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.606-611
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• 2007

Proper orthogonal decomposition (POD) is a method for extracting bases for modal decomposition from the ensemble of dynamic signals. Using the POD method, we analyzed the proper orthogonal modes (POMs) of AFM microcantilevers in dynamic mode operations such as Tapping Mode. The POMs and POVs (proper orthogonal values) were computed through MATLAB simulation for the 5-mode model of the microcantilever. We found that the POV portion of the higher POMs of the tapping microcanilever slightly increased in comparison with no tapping. This implies that the modal energy in the fundamental mode can be transferred to the higher modes during tapping.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1997-2000
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• 2005

In this work, the effects of orthogonal ribs on warpage of plastic structure through injection molding process were investigated. Three kinds of injection molds were prepared to perform injection molding experiments of orthogonal stiffened plastic plate. The warpage of each injection molded specimen was measured using 3D CMM. And plastic injection molding analysis with commercial code was performed for the presented model. Numerical results of injection molding analysis were compared with those of experiments. It was shown that orthogonal ribs have a significant effect on the warpage of the structure in both cases of experiment and numerical analysis.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.99-106
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• 2000

A method of two and three dimensional orthogonal grid generation with control of spacing by using the covariant Laplace equation is Presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries still maintaining good orthogonality in whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and au auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length, and orthogonal correction is performed in the auxiliary domain. It is concluded that the methodology can successfully generate well controlled orthogonal grids around bodies of 2 and 3 dimensional configurations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.109-119
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• 2000

It was shown that if Q is a fully indecomposable $n{\times}n$ orthogonal matrix then Q has at least 4n-4 nonzero entries in 1993. In this paper, we show that for each integer p with $4n-4{\leq}p{\leq}n^2$, there exist a fully indecomposable $n{\times}n$ orthogonal matrix with exactly p nonzero entries. Furthermore, we obtain a method of construction of a fully indecomposable $n{\times}n$ orthogonal matrix which has exactly 4n-4 nonzero entries. This is a part of the study in sparse matrices.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.175-190
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• 2010

One of the intractable problems in multiresolution structural analysis is the decoupling computation between scales, which can be realized by the operator-orthogonal wavelets based on the lifting scheme. The multiresolution finite element space is described and the formulation of multiresolution finite element models for structural problems is discussed. Various operator-orthogonal wavelets are constructed by the lifting scheme according to the operators of multiresolution finite element models. A dynamic multiresolution algorithm using operator-orthogonal wavelets is proposed to solve structural problems. Numerical examples demonstrate that the lifting scheme is a flexible and efficient tool to construct operator-orthogonal wavelets for multiresolution structural analysis with high convergence rate.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.2
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• pp.159-165
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• 2010

The Multi-code (Mc) modulation has been developed for high-speed data transmission over the wireless environments, but it suffers two critical problems due to the limited resource of Orthogonal Codes (OC) and high Peak-Average Power Ratio (PAPR). In this paper, we propose a novel modulation technique called AOCG [1] (Advanced Orthogonal Code Group)-OFDM (Orthogonal Frequency Division Multiplexing) to solve the above problems and obtain the variable high bit rates which can be controlled by the four parameters depending on the quality of services (QoS) required by users.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.7
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• pp.885-895
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• 2004

Generally, automatic design is carried out with computer simulation and the simulation models are established by investigating the correlations between the simulation and real experiments. Therefore, the experiment results are utilized as complimentary data although they are considered to be precise. Orthogonal arrays have been adopted for discrete design. A method is proposed to directly exploit the experiment results in the design process with orthogonal arrays. Experiments are allocated to some rows of an orthogonal array and computer simulations are allocated to the others. A rule for the allocation is found to keep the orthogonality. Error analysis of the design results is performed. Mathematical examples are made to verify the validity of the proposed method. Error models are defined with the examples and the design solutions from the examples are discussed.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.10a
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• pp.359-364
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• 1999

Due to rapid growth of die and mould industries, it is urgently required to maximize the productivity and the efficiency of machining. In recent years, owing to the development of new kinds of material, die and mould materials are much harder and it is more difficult to cut. In this study, the workpiece SKD11(HRC45) is cut with TiAlN coated tungsten-carbide cutting tools. To find the general characteristics of difficult-to-cut materials, orthogonal turning test is performed. Orthogonal cutting theory can be expanded to oblique cutting model. The oblique cutting process in the small cutting edge element has been analyzed as orthogonal cutting process in the plane containing the cutting velocity vector and chip-flow vector. Hence, with the orthogonal cutting data obtained from orthogonal turning test, the cutting forces can be analyzed through oblique cutting model. The simulation results have shown a fairy good agreement with the test results.

• Journal of Computing Science and Engineering
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• v.4 no.2
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• pp.97-109
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• 2010

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, which is to decompose a data matrix into a product of two factor matrices with all entries restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropriate to the clustering problems. In this paper, we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. The result of orthogonal NMF can be clearly interpreted for the clustering problems, and also the performance of clustering is usually better than that of the NMF. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1049-1070
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• 2004

We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ ＋ 2B($\chi$, y) $u_{{\chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($\chi$) $u_{{\chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.