• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.973-1008
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• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.408-413
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• 2001

The structural optimization is carried out in the continuous design space or discrete design space. Methods for discrete variables such as genetic algorithms are extremely expensive in computational cost. In this research, an iterative optimization algorithm using orthogonal arrays is developed for design in discrete space. An orthogonal array is selected on a discrete design space and levels are selected from candidate values. Matrix experiments with the orthogonal array are conducted. New results of matrix experiments are obtained with penalty functions for constraints. A new design is determined from analysis of means(ANOM). An orthogonal array is defined around the new values and matrix experiments are conducted. The final optimum design is found from iterative process. The suggested algorithm has been applied to various problems such as truss and frame type structures. The results are compared with those from a genetic algorithm and discussed.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.181-199
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• 2017

In this paper we consider the orthogonal polynomials with weights ${\omega}_{\alpha}(x)=x^{\alpha}{\exp}(-x^3+tx)$ and $W_{\alpha}(x)={\mid}x{\mid}^{2{\alpha}+1}{\exp}(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.82-89
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• 1995

In the present paper, a method of nearly orthogonal grid generation in an arbitrary simply-connected 3D domain will be presented. The method is a new direct and non-iterative scheme based on the concept of the decomposition of the global orthogonal transformation into consecutive mapping of a conformal mapping and an auxiliary orthogonal mapping, which was suggested by King and Leal [4]. In our numerical scheme. Kang and Leal's method is extended from 2D problems to 3D problems while the advantage of the non-iterative algorithm is maintained. The essence of the present mapping method is that an iterative scheme can be avoided by introducing a preliminary step. This preliminary step corresponds to a conformal map and is based on the boundary element method(BEM). This scheme is applied to generate several nearly-orthogonal grid systems which are orthogonal at boundaries.

• Journal of computational fluids engineering
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• v.5 no.1
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• pp.14-21
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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 an 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 peformed 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 Power Electronics
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• v.17 no.5
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• pp.1160-1172
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• 2017

A novel space vector modulation strategy in the non-orthogonal three-dimensional coordinate system for multi-level three-phase four-wire inverters is proposed in this paper. This new non-orthogonal three-dimensional space vector modulation converts original trigonometric functions in the orthogonal three-dimensional space coordinate into simple algebraic operations, which greatly reduces the algorithm complexity of three-dimensional space vector modulation and preserves the independent control of the zero-sequence component. Experimental results have verified the correctness and effectiveness of the proposed three-dimensional space vector modulation in the new non-orthogonal three-dimensional coordinate system.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.8
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• pp.891-897
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• 2003

In this paper, a circular orthogonal polarizer is newly fabricated and used in a differential detector to reduce the optical noise in a wireless optical interconnection. The orthogonal polarizer is composed of two semicircular polarizers whose transmission axes are orthogonal each other, The orthogonal polarizer is driven by a motor and matched to the signal polarization in order to reduce the optical noise interference. The noise power was reduced by about 20 dB using a differential detector with the orthogonal polarizer.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07a
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• pp.490-492
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• 2005

본 논문에서는 별도의 충돌 방지 메커니즘이 필요 없는 orthogonal code를 태그 ID로 부여함으로써 태그 인식을 간단하게 하는 메커니즘에 대해 설명한다. 첫 번째 적용 메커니즘으로 Local환경에서 Orthogonal code가 적용될 수 있는 여러 가지 응용 분야를 제안하고 두 번째로 Orthogonal code를 기존 ID 체계의 일부분으로 사용하여 anti-collision algorithm의 효율을 높이는 방법을 제시한다. 마지막으로 orthogonal code ID의 개수가 많아짐에 따라 code bit수가 길어지는 문제를 해결하기 위하여 code를 블록화 하여 사용 bit를 줄이는 메커니즘을 제시한다.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1147-1170
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• 2022

In this paper, we introduce a new class of mappings called the generalized orthogonal F-Suzuki contraction for a family of multivalued mappings in the setup of orthogonal b-metric spaces. We established the existence of some common fixed point results without using any commutativity condition for this new class of mappings in orthogonal b-metric spaces. Moreover, we illustrate and support these common fixed point results with example. The results obtained in this work generalize and extend some recent and classical related results in the existing literature.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.279-290
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• 2024

In this study, tubular surfaces were introduced according to the modified orthogonal frame defined at the points where the torsion is different from zero in the 3-dimensional Euclidean space. First, the relations between the Frenet frame and the modified orthogonal frame with torsion are given. Then, the singularity, Gaussian curvature, mean curvature and basic forms of the tubular surface given according to the modified orthogonal frame with torsion were calculated. In addition, the conditions for the parameter curves of the tubular surface to be geodesic, asymptotic and line of curvature were examined. Finally, tubular surface examples based on both the Frenet frame and the modified orthogonal frame with torsion were given to support the study.