• Title, Summary, Keyword: orthogonality

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An Approximate Parameter Orthogonality

  • Kwan Jeh Lee
    • 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.

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Graphical Methods for Evaluating the Degree of the Orthogonality of Nearly Orthogonal Arrays (근사직교배열의 직교성의 정도를 평가하기 위한 그레픽방법)

  • Jang Dae-Heung
    • Journal of the 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.

General Orthogonality for Orthogonal Polynomials

  • Sun, Hosung
    • 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.

Graphical Methods for Evaluating Supersaturated Designs (초포화계획을 평가하기 위한 그래픽방법)

  • Kim, Youn-Gil;Jang, Dae-Heung
    • 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.

Mutual Information as a Criterion for Evaluating the Degree of the Orthogonality of Nearly Orthogonal Arrays (근사직교배열의 직교성을 평가하기 위한 측도로서의 상호정보)

  • Jang, Dae-Heung
    • Journal of the 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.

NORMALIZED DUALITY MAPPING AND GENERALIZED BEST APPROXIMATIONS

  • Park, Sung Ho;Rhee, Hyang Joo
    • 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.

ORTHOGONALITY IN FINSLER C*-MODULES

  • Amyari, Maryam;Hassanniah, Reyhaneh
    • 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.

Orthogonality Measurement of Square Plane Mirrors for Laser Interferometry (레이저 간섭계의 직각 평면거울에 대한 직각도 오차 측정)

  • 김태호;김승우
    • 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.

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COMBINATORIAL INTERPRETATIONS OF THE ORTHOGONALITY RELATIONS FOR SPIN CHARACTERS OF $\tilde{S}n$

  • Lee, Jaejin
    • 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.