• Communications for Statistical Applications and Methods
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• 제5권3호
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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.

• 품질경영학회지
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• 제32권4호
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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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• 제34권1호
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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.

• 응용통계연구
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• 제23권1호
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• pp.167-178
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• 2010

직교성은 실험계획에서 중요한 개념이다. 실험계획에서 실험점의 개수보다 인자의 개수가 많은 상황에서 우리는 초포화계획을 사용한다. 이러한 초포화계획은 직교성을 만족하지 못하게 되는 데 얼마나 직교성을 만족하는 지를 평가하는 데 우리는 주로 수치적인 측도들을 사용한다. 우리는 초포화계획의 직교성의 정도를 평가하는 방법으로서 그래픽방법을 사용할 수 있다.

• 품질경영학회지
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• 제36권3호
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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.

• 충청수학회지
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• 제24권4호
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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.

• 한국정밀공학회지
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• 제15권12호
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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.

• 대한수학회논문집
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• 제33권2호
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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.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2022년도 춘계학술대회
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• pp.86-88
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• 2022

LoRa 통신 프로토콜은 근 10년간 사물인터넷 네트워크를 위한 유망 기술로 평가받고 있다. 이론적으로, 처프 대역 확산 프로토콜을 사용하여 장거리 통신에 강인하고 하나의 물리 채널에 서로 직교하는 여러 논리채널을 제공할 수 있으며 중첩 성형의 망구조로 공간 다양성을 활용할 수 있는 것이 대표적 이유이다. 최근의 몇몇 연구들은 이러한 특징 중 논리 채널 사이의 불완전한 실질적인 준직교성을 지적한다. 그러나 직교하는 논리 채널을 형성하는 것은 확산 인자와 대역폭 두 가지 설정 인자임에도 불구하고 대부분의 연구는 확산 인자만을 요소로 직교성을 평가한다. 본 연구에서는 두 설정 인자를 모두 고려하여 논리 채널 사이의 준 직교성을 정리한다. 또한, 이에 따른 논리 채널 사이의 간섭으로 인해 변화하는 통신 품질을 정리한다.

• Korean Journal of Mathematics
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• 제22권2호
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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.