• 대한수학회논문집
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• 제20권4호
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• pp.765-774
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• 2005

The orthogonality of polynomials plays an important role in many areas and in many cases only finite orthogonalities are used. Concerning this fact we find characterizations of a finite orthogonal polynomial system satisfying a second order differential equation and then give several examples.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 하계종합학술대회논문집
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• pp.211-214
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• 1998

A detection filter assigns a specific direction to the response with respect to each fault, by which it can detect the occurrence of the several faults. The separability of a detection filter can be determined by the orthogonality among these directions. In this paper, we define the separability of a detection filter as the orthogonality of the directions in output space, and present it mathematically by using conditions number. An algorithm to determine the optimal sensor gain to maximize separability is proposed and applied to the PWR nuclear reactor model.

• 대한전자공학회논문지
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• 제24권1호
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• pp.159-166
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• 1987

A new family of sinusoidal orthogoal trnasform is introduced. For a derivation, a parametric sinusoidal matrix whose transform might be implemented by a suitable FFT algorithm is modeled basically on the analogy of well-known sinusoidal transform such as DCT,SCT, etc., and its orthogonality condition is calculated. The parameters satisfying orthogonality condition are determined, in a sense, by particular solution after trial and error. However more than then transform matrices not yet known are obtained. It is also shown that these transforms can be computed by a DFT. of an image.

• East Asian mathematical journal
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• 제31권5호
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• pp.627-634
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• 2015

In this paper, we investigate the following orthogonally additive-quadratic functional equation f(2x + y) - f(x + 2y) - f(x + y) - f(y - x) - f(x) + f(y) + f(2y) = 0. and prove the generalized Hyers-Ulam stability for it in orthogonality spaces by using the fixed point method.

• 대한수학회보
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• 제45권3호
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• pp.601-606
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• 2008

The purpose of this paper is to introduce and discuss the concept of ${\omega}$-Chebyshev subspaces in Banach spaces. The concept of quasi Chebyshev in Banach space is defined. We show that ${\omega}$-Chebyshevity of subspaces are a new class in approximation theory. In this paper, also we consider orthogonality in normed spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.343-357
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• 2015

Using the fixed point method, we prove the Hyers-Ulam stability of lin- ear mappings in Banach modules over a unital C*-algebra and in non-Archimedean Banach modules over a unital C*-algebra associated with the orthogonally Cauchy- Jensen additive functional equation.

• Structural Engineering and Mechanics
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• 제6권2호
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• pp.229-243
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• 1998

In this study, a theoretical method to analyze the vibration of a T-type Timoshenko frame is proposed. The effects of axial inertia, rotatory inertia and shear deformation of each branch are considered. The orthogonality of any two distinct sets of mode shape functions is also demonstrated. Vibration of the frame due to moving loads is studied by the method and the response characteristics of the frame are investigated. Furthermore, the effect of column length on the response of the frame is also studied.

• 대한수학회논문집
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• 제36권2호
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• pp.299-312
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• 2021

The main aim of this paper is to introduce and study the generalized Laguerre polynomials and prove that these polynomials are characterized by the generalized hypergeometric function. Also we investigate some properties and formulas for these polynomials such as explicit representations, generating functions, recurrence relations, differential equation, Rodrigues formula, and orthogonality.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권2호
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• pp.189-199
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• 2022

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

• 한국정밀공학회지
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• 제24권9호
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• pp.68-75
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• 2007

The pitch and orthogonality of two-dimensional (2D) gratings have been measured by using a metrological atomic force microscope (MAFM) and measurement uncertainty has been analyzed. Gratings are typical standard artifacts for the calibration of precision microscopes. Since the magnification and orthogonality in two perpendicular axes of microscopes can be calibrated simultaneously using 2D gratings, it is important to certify the pitch and orthogonality of 2D gratings accurately for nano-metrology using precision microscopes. In the measurement of 2D gratings, the MAFM can be used effectively for its nanometric resolution and uncertainty, but a new measurement scheme was required to overcome some limitations of current MAFM such as nonnegligible thermal drift and slow scan speed. Two kinds of 2D gratings, each with the nominal pitch of 300 nm and 1000 nm, were measured using line scans for the pitch measurement of each direction. The expanded uncertainties (k = 2) of measured pitch values were less than 0.2 nm and 0.4 nm for each specimen, and those of measured orthogonality were less than 0.09 degree and 0.05 degree respectively. The experimental results measured using the MAFM and optical diffractometer were coincident with each other within the expanded uncertainty of the MAFM. As a future work, we also proposed another scheme for the measurements of 2D gratings to increase the accuracy of calculated peak positions.