• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.927-934
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• 1998

An approximate parameter orthogonality is defined, which is called an $\alpha$-approximate orthogonality The useful consequences of parameter orthogonality mentioned by Cox and Reid(1987) can be shared by an $\alpha$-approximate orthogonality. If $\alpha\geq1/2$, the consequences of orthogonality and $\alpha$-approximate orthogonality are asymptotically equivalent.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.220-228
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• 2004

The orthogonality is an important property in the experimental designs. When we use nearly orthogonal arrays, we need evaluate the degree of the orthogonality of given experimental designs. Graphical methods for evaluating the degree of the orthogonality of nearly orthogonal arrays are suggested.

• Bulletin of the Korean Chemical Society
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• v.34 no.1
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• pp.197-200
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• 2013

The bound state wave functions for all the known exactly solvable potentials can be expressed in terms of orthogonal polynomials because the polynomials always satisfy the boundary conditions with a proper weight function. The orthogonality of polynomials is of great importance because the orthogonality characterizes the wave functions and consequently the quantum system. Though the orthogonality of orthogonal polynomials has been known for hundred years, the known orthogonality is found to be inadequate for polynomials appearing in some exactly solvable potentials, for example, Ginocchio potential. For those potentials a more general orthogonality is defined and algebraically derived. It is found that the general orthogonality is valid with a certain constraint and the constraint is very useful in understanding the system.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.167-178
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• 2010

The orthogonality is an important property in the experimental designs. We usually use supersaturated designs in case of large factors and small runs. These supersaturated designs do not satisfy the orthogonality. Hence, we need the means for the evaluation of the degree of the orthogonality of given supersaturated designs. We usually use the numerical measures as the means for evaluating the degree of the orthogonality of given supersaturated designs. We can use the graphical methods for evaluating the degree of the orthogonality of given supersaturated designs.

• Journal of Korean Society for Quality Management
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• v.36 no.3
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• pp.13-21
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• 2008

The orthogonality is an important property in the experimental designs. When we use nearly orthogonal arrays(for example, supersaturated designs), we need evaluate the degree of the orthogonality of given nearly orthogonal arrays. We can use the mutual information as a new criterion for evaluating and testing the degree of the orthogonality of given nearly orthogonal arrays.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.849-862
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• 2011

In this paper, we introduce certain concepts which provide us with a perspective and insight into the generalization of orthogonality with the normalized duality mapping. The material of this paper will be mainly, but not only, used in developing algorithms for the best approximation problem in a Banach space.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.12
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• pp.169-179
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• 1998

Plane mirror type laser interferometers are popularly being used in many modern ultraprecision machines, as they can perform simultaneous measurements of multiple axis positions with nanometer resolution capabilities. One important issue in this application of laser interferometers is to provide a good level of alignment between the reflecting mirrors and the laser beams so that measurement errors due to undesirable coupling effects can be avoided in multiple axis measurements In this investigation, a thorough metrological analysis is given to develop an suitable mathematical model for a precision x-y stage in which the orthogonality misalignment between the reflecting mirrors significantly affects overall x-y mea-surement results. Then a noble calibration method is suggested in which two-dimensional displacement sensors of moire gratings of concentric circles are used to realize the reversal principle of orthogonality evaluation in situ. Finally, actual experimental results are discussed to verify that the suggested method can effectively calibrate the orthogonality error with an uncertainty of 0.2667 arcsec.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.561-569
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• 2018

In this paper, we introduce some notions of orthogonality in the setting of Finsler $C^*$-modules and investigate their relations with the Birkhoff-James orthogonality. Suppose that ($E,{\rho}$) and ($F,{\rho}^{\prime}$) are Finsler modules over $C^*$-algebras $\mathcal{A}$ and $\mathcal{B}$, respectively, and ${\varphi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a *-homomorphism. A map ${\Psi}:E{\rightarrow}F$ is said to be a ${\varphi}$-morphism of Finsler modules if ${\rho}^{\prime}({\Psi}(x))={\varphi}({\rho}(x))$ and ${\Psi}(ax)={\varphi}(a){\Psi}(x)$ for all $a{\in}{\mathcal{A}}$ and all $x{\in}E$. We show that each ${\varphi}$-morphism of Finsler $C^*$-modules preserves the Birkhoff-James orthogonality and conversely, each surjective linear map between Finsler $C^*$-modules preserving the Birkhoff-James orthogonality is a ${\varphi}$-morphism under certain conditions. In fact, we state a version of Wigner's theorem in the framework of Finsler $C^*$-modules.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2022.05a
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• pp.86-88
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• 2022

LoRa has been evaluated as a promising technology for Internet of things networks. Theoretically, the technology is robust for long-range communication by using chirp spreading spectrum, provides several orthogonal logical channels in a physical channel, exploits spatial reusability by introducing a star-of-stars topology. A part of recent studies indicates the quasi-orthogonality, or the imperfect orthogonality, between logical channels. The channel elements, however, are both spreading factor and bandwidth. Nevertheless, Most of the researches only treat the spreading factor. This study presents the quasi-orthogonality between all of the logical channels built by variations of the both factors. Furthermore, it shows the performance varied by the logical channel interference.

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.325-337
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• 2014

In 1911 Schur[6] derived degree and character formulas for projective representations of the symmetric groups remarkably similar to the corresponding formulas for ordinary representations. Morris[3] derived a recurrence for evaluation of spin characters and Stembridge[8] gave a combinatorial reformulation for Morris' recurrence. In this paper we give combinatorial interpretations for the orthogonality relations of spin characters based on Stembridge's combinatorial reformulation for Morris' rule.