• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.673-693
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• 2005

In this paper, we first find a necessary and sufficient condition for the existence of multiple orthogonal polynomials by the moments of a pair of measures $(d{\mu},\;dv)$ and then give representations for multiple orthogonal polynomials. We also prove four term recurrence relations for multiple orthogonal polynomials of type II and several interesting relations for multiple orthogonal polynomials are given. A generalized recurrence relation for multiple orthogonal polynomials of type I is found and then four term recurrence relations are obtained as a special case.

• Proceedings of the KIEE Conference
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• 1997.11a
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• pp.142-145
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• 1997

This paper presents an modified orthogonal neural network(MONN) based on orthogonal functions and applies the network to nonlinear system control. The accuracy of orthogonal neural network is essentially dependent on the choice of basic orthogonal functions. Modified orthogonal neural network is modified model of orthogonal neural network with input transformation to adapt its basic orthogonal functions. The results show that the modified orthogonal neural network has the excellent performance of approximating and controlling nonlinear systems and the input transformation make the ability of modified orthogoneural neural network better than one of orthogonal neural network.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.9A
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• pp.1322-1331
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• 2000

In this paper, we compare the performance of noncoherent DS-CDMA system where orthogonal code is used for identifying the user to reduce multiple access interference or for M-ary orthogonal signaling to improve the performance of demodulation. The effects of M-ary orthogonal signaling on the noncoherent demodulation is investigated and compared with one of coherent demodulation. The analysis results show that M-ary orthogonal signaling gives better performance than quasi-synchronous orthogonal scheme for a moderate number of users when the processing gain is 128 over AWGN channel. In addition, when the number of user is 41, M=64 orthogonal signaling has a similar performance to the quasi-synchronous orthogonal scheme at the BER of 10-2 when the time misalignment between channels is within 1/2 chip and M=256 orthogonal signaling always outperforms the quasi-synchronous orthogonal scheme. Start after striking space key 2 times.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.119-129
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• 1999

In [1], it was shown that for $n\geq 2$ the least number of nonzero entries in an $n\times n$ orthogonal matrix is not direct summable is 4n-4, and zero patterns of the $n\times n$ orthogonal matrices with exactly 4n-4 nonzero entries were determined. In this paper, we construct $n\times n$ orthogonal matrices with exactly 4n-r nonzero entries. furthermore, we determine m${\times}$n sparse row-orthogonal matrices.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.181-189
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• 2017

A method for recovering Chui-Lian's orthogonal symmetric/antisymmetric multiwavelets of order 2 from orthogonal two-direction wavelets of order 2 was proposed by Yang and Xie. In this paper we pursue the converse, that is, we propose a method for constructing orthogonal two-direction wavelets of order 2 from orthogonal symmetric/antisymmetric multiwavelets of order 2.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.116-127
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• 2014

This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.359-376
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• 2002

We give a new interpretation of Darboux transforms in the context of orthogonal polynomials and find conditions in or-der for any Darboux transform to yield a new set of orthogonal polynomials. We also discuss connections between Darboux trans-forms and factorization of linear differential operators which have orthogonal polynomial eigenfunctions.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.49-54
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• 2006

When using response surface designs, the experimental trials should be carried out in blocks in case of heterogeneity of conditions. When we use nearly orthogonal blocking, we need evaluate the degree of orthogonal blocking. Graphical methods for evaluating the degree of orthogonal blocking are suggested.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.669-675
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• 2006

When using response surface designs, the experimental trials should be carried out in blocks in case of heterogeneity of conditions. When we use nearly orthogonal blocking, we need evaluate the degree of orthogonal blocking. Graphical methods for evaluating the degree of orthogonal blocking are suggested.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.307-315
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• 2019

In this paper we construct orthogonal two-direction scaling function of order 3 and corresponding wavelet function. In this paper we propose a different approach using orthogonal symmetric/antisymmetric multiwavelets of order 3. An example for constructing orthogonal two-direction scaling function of order 3 and corresponding wavelet function is given.