• Honam Mathematical Journal
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• v.24 no.1
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• pp.103-108
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• 2002

Applications of a column-reduced orthogonal rational matrix function to McMillan degrees and Wiener-Hopf factorizations are considered.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.21-31
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• 2010

A latin square of order n is an $n{\times}n$ array with entries from a set of n numbers arrange in such a way that each number occurs exactly once in each row and exactly once in each column. Two latin squares of the same order are orthogonal latin square if the two latin squares are superimposed, then the $n^2$ cells contain each pair consisting of a number from the first square and a number from the second. In Europe, Orthogonal Latin squares are the mathematical concepts attributed to Euler. However, an Euler square of order nine was already in existence prior to Euler in Korea. It appeared in the monograph Koo-Soo-Ryak written by Choi Seok-Jeong(1646-1715). He construct a magic square by using two orthogonal latin squares for the first time in the world. In this paper, we explain Choi' s orthogonal latin squares and the history of the Orthogonal Latin squares.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.669-672
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• 2008

In this paper, we propose a constant-amplitude multi-rode trans-bi-orthogonal modulation scheme by introducing a simple constant-amplitude coding scheme with redundant bits and trans-code, which if a modified orthogonal modulation scheme. Generally speaking, the orthogonal modulation scheme is not appropriate for the high speed data transmission applications because of bad bandwidth efficiency. Therefore, we use the multi-rode trans-bi-orthogonal modulation with trans-code for high bandwidth efficiency. Moreover, redundant bits are used for constant-amplitude-coding. Finally, we compare the performance of the proposed scheme with the orthogonal modulation and constant-amplitude multi-code trans-orthogonal modulation by using the computer simulation.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.47-54
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• 1994

We present a generating function and three semi-orthogonal relations for a class of hypergeometric functions. We employ semi-orthogonal relations to generate a theory concerning finite series expansions involving our hypergeometric functions.

• ETRI Journal
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• v.30 no.1
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• pp.161-163
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• 2008

An M-ary bi-orthogonal modulation scheme for ultra-wideband (UWB) systems capable of narrowband interference (NBI) suppression is proposed in this letter. We utilize a set of bi-orthogonal pulse series to achieve NBI suppression. Through analysis and simulation, we verify that the proposed scheme can suppress NBIs effectively.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.837-842
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• 2008

Students taking linear model courses have difficulty in determining which parametric functions are estimable when the design matrix of a linear model is rank deficient. In this note a special form of estimable functions is presented with a linear combination of some orthogonal estimable functions. Here, the orthogonality means the least squares estimators of the estimable functions are uncorrelated and have the same variance. The number of the orthogonal estimable functions composing the special form is equal to the rank of the design matrix. The orthogonal estimable functions can be easily obtained through the singular value decomposition of the design matrix.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.489-507
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• 1999

We investigate the asymptotic behavior of the extreme zeros of orthogonal polynomials with respect to a positive measure d$\alpha$(x) in terms of the three term recurrence coefficients. We then show that the asymptotic behavior of extreme zeros of orthogonal polynomials with respect to g(x)d$\alpha$(x) is the same as that of extreme zeros of orthogonal polynomials with respect to d$\alpha$(x) when g(x) is a polynomial with all zeros in a certain interval determined by d$\alpha$(x). several illustrating examples are also given.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.581-588
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• 2007

We reconsider the classical orthogonal polynomials which are solutions to a second order differential equation of the form $$l_2(x)y'(x)+l_1(x)y'(x)={\lambda}_ny(x)$$. We investigate two characterization theorems of F. Marcellan et all and K.H.Kwon et al. which gave necessary and sufficient conditions on $l_1(x)\;and\;l_2(x)$ for the above differential equation to have orthogonal polynomial solutions. The purpose of this paper is to give a proof that each result in their papers respectively is equivalent.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1557-1566
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• 2006

We present a procedure for the application of global orthogonal polynomial into an atmospheric re-entry maneuvering problem. This trajectory optimization is imbedded in a family of canonically parameterized optimal control problem. The optimal control problem is transcribed to nonlinear programming via global orthogonal polynomial and is solved a sparse nonlinear optimization algorithm. We analyze the optimal trajectories with respect to the performance of re-entry maneuver.

• Journal of the Korean Statistical Society
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• v.32 no.3
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• pp.225-233
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• 2003

In this paper we make use of the parity check matrices of the codes based on inverting construction $Y_1$ to construct a number of new asymmetric orthogonal arrays with higher strength and higher number of levels using the method of construction of asymmetric orthogonal arrays given by Suen et al. (2001).