• 충청수학회지
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• 제20권4호
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• pp.465-476
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• 2007

The aim of this paper is to investigate the stability problem bounded by function for the generalized sine functional equations as follow: $f(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2\\g(x)g(y)=f(\frac{x+y}{2})^2-f(\frac{x+{\sigma}y}{2})^2$. As a consequence, we have generalized the superstability of the sine type functional equations.

• 한국측량학회지
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• 제37권3호
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• pp.189-198
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• 2019

사진측량에서 단사진의 후방교회법은 이미 알고 있는 카메라의 내부표정요소, 지상좌표, 사진좌표를 이용하여 촬영당시 카메라의 위치와 자세에 해당하는 외부표정요소를 결정하는 방법이다. 본 연구에서는 코사인 법칙과 선형식기반의 3차원 좌표변환식을 이용하여 카메라의 외부표정요소를 결정할 수 있는 단사진의 공간후방교회법 알고리즘을 제안하였다. 제안한 알고리즘은 먼저 렌즈왜곡이 보정된 정규좌표를 코사인 법칙을 이용하여 지상좌표와 이에 대응되는 정규좌표간의 축척을 계산하였다. 그리고 나서 축척을 고려한 정규좌표와 지상좌표를 이용하는 선형방정식 기반의 3차원 좌표변환식을 적용하여 외부표정요소를 결정하였다. 제안한 알고리즘은 비선형방정식으로 편미분이 필요하나 지상좌표의 조합 중 가장 긴 거리를 구하여 각 지상좌표에 나누는 방법을 이용하여 초기값에 민감하지 않은 장점이 있었다. 또한, 세 점을 이용하여도 외부표정요소를 결정할 수 있기 때문에 기준점의 기하학적 배치에 안정적인 장점이 있었다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.387-398
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• 2021

In this paper, we will find solutions and investigate the superstability bounded by constant for the p-radical functional equations as follows: $f\(\sqrt[p]{\frac{x^p+y^p}{2}}\)^2-f\(\sqrt[p]{\frac{x^p-y^p}{2}}\)^2=\;\{(i)\;f(x)f(y),\\(ii)\;g(x)f(y),\\(iii)\;f(x)g(y),\\(iv)\;g(x)g(y).$ with respect to the sine functional equation, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebra.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.1455-1460
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• 2000

When a tube is oscillated at a resonant frequency, acoustic variables such as density, velocity, and pressure undergo very large perturbation, often described as nonlinear oscillation. In order to analyze these phenomena, nonlinear governing equation has been drived and solved numerically. Numerical simulations were accomplished to study the effect of the tube shape on the maximum pressure we can obtain. The tubes of cylindrical, conical, and cosine-shape, which have same volume and length, were investigated. Results show that the resonant frequency and patterns of pressure waves strongly depend on not only the tube shape but also the amplitude of driving acceleration. The degree of non-linearity of wave patterns was also measured by the newly defined nonlinear energy ratio of the pressure signals. It was found that the 1/2 cosine-shape tube is more suitable to induce high compression ratio than other shapes.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2002년도 학술대회지
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• pp.209-212
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• 2002

Since Berkhoff proposed the mild-slope equation in 1972, it has widely been used for calculation of shallow water wave transformation. Recently, it was extended to give an extended mild-slope equation, which includes the bottom slope squared term and bottom curvature term so as to be capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. In the present study, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize . The computational domain was discretized with proper finite elements, while the radiation condition at infinity was treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model was verified through example analyses of two-dimensional wave reflection and transmission. .

• 대한수학회보
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• 제46권2호
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• pp.235-243
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• 2009

In this paper we will investigate the superstability of the generalized d'Alembert type functional equations ${\sum}^m_{i=1}f(x+{{\sigma}^i}(y))$ = kg(x)f(y) and ${\sum}^m_{i=1}f(x+{{\sigma}^i}(y))$ = kf(x)g(y).

• Smart Structures and Systems
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• 제25권2호
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• pp.219-228
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• 2020

This work presents a modified continuum model to explore and investigate static and vibration behaviors of perforated piezoelectric NEMS structure. The perforated nanostructure is modeled as a thin perforated nanobeam element with Euler-Bernoulli kinematic assumptions. A size scale effect is considered by included a nonlocal constitutive equation of Eringen in differential form. Modifications of geometrical parameters of perforated nanobeams are presented in simplified forms. To satisfy the Maxwell's equation, the distribution of electric potential for the piezoelectric nanobeam model is assumed to be varied as a combination of a cosine and linear functions. Hamilton's principle is exploited to develop mathematical governing equations. Modified numerical finite model is adopted to solve the equation of motion and equilibrium equation. The proposed model is validated with previous respectable work. Numerical investigations are presented to illustrate effects of the number of perforated holes, perforation size, nonlocal parameter, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric nanobeams.

• 한국정보통신학회논문지
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• 제27권1호
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• pp.47-53
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• 2023

X-Ray, CT, MRI, 스캐너 등과 같은 장치는 영상 획득 과정 중 여러 원인으로 인해 S&P 잡음을 생성할 수 있다. 영상에 나타난 S&P 잡음은 영상의 품질을 저하시키기 때문에, 영상처리 과정에 잡음제거 기술을 필수적으로 사용해야 한다. S&P 잡음 제거에 관한 연구는 이미 다양한 방법이 제안되었으나, 이들 모두 잡음 밀도가 큰 환경에서는 잔여 잡음을 생성하는 문제점이 있었다. 따라서 본 논문은 영상의 grayscale 값을 새로운 축으로 설정하여 3차원의 평면 방정식을 기반으로 필터링하는 알고리즘을 제안하였다. 제안한 알고리즘은 로컬마스크를 세분화하여 가장 근접한 3개의 비잡음 화소를 유효 화소로 설계하여, 복수의 화소를 가진 영역에 대해 코사인 유사도를 적용하였다. 또한, 입력한 화소가 평면을 이룰 수 없는 경우에도 예외 화소로 분류하여 잔여 잡음 없이 우수한 복원을 이루었다.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
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• pp.38-40
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• 2007

In this paper, we propose a novel architecture, which is based on DCT (Discrete Cosine Transform), for ME (Motion Estimation) and MC (Motion Compensation). The traditional algorithms of ME and MC based on DCT did not suffer the advantage of the coarseness of the 2-dimensional DCT (2-D DCT) coefficients to reduce the operational time. Therefore, we derive a recursion equation for transform-domain ME and MC and design the structure by using highly regular, parallel, and pipeline processing elements. The main difference with others is removing the IDCT block by using to transform domain. Therefore, the performance of our algorithm is more efficient in practical image processing such as DVR (Digital Video Recorder) system. We present the simulation result which is compare with the spatial domain methods. it shows reducing the calculation cost. compression ratio. and peak signal to noise ratio (PSNR).