• Communications for Statistical Applications and Methods
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• 제21권4호
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• pp.327-334
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• 2014

Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• 호남수학학술지
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• 제41권1호
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• pp.1-17
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• 2019

The aim of this paper is to establish certain integrals involving product of the Aleph function with exponential function and multi Gauss's hypergeometric function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, twelve corollaries are also recorded here as special case of our main results.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.487-503
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• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• 한국전자파학회논문지
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• 제14권7호
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• pp.769-776
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• 2003

본 논문은 경계적분법과 세그멘테이션 기법을 이용하여 광대역 주파수 및 광 조향각 범위에서 빔조향이 가능한 마이크로스트립 로트만 렌즈의 해석 및 설계를 제안하고 있다. 렌즈 각 포트간의 모든 상호결합과 다중반사 및 선로간 불연속 특성이 해석에 포함되었다. 등간격 포트 설계를 통해 광조향각 범위에서 배열포트의 출력 리플을 억제하는 구조를 구현하였다. 12 입력 12 출력의 각 포트에 지수함수 테이퍼를 적용하여 임피던스 정합 및 포트간 상호결합을 해석하고 최적화하였다. 제작된 렌즈는 측정결과 6~18 GHz의 광대역 주파수 범위와 $\pm$53$^{\circ}$의 조향각 범위에 대해 $\pm$1.8 dB 이하의 삽입손실 편차와 1$^{\circ}$이하의 조향 정확도를 가지며, 해석결과 와도 잘 일치함을 확인하였다.

• 공업화학
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• 제17권3호
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• pp.296-302
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• 2006

산소농도에 따른 폐폴리우레탄의 열적 산화분해에 관한 속도론적 연구를 $10{\sim}50^{\circ}C/min$ 사이의 여러 가열속도에서 비등온 질량감소 기술을 이용하여 수행하였다. 폐폴리우레탄의 열적 산화분해를 묘사하기 위하여 Arrhenius식에 근거한 미분법과 적분법을 이용하여 산소농도에 대한 영향을 고려할 수 있는 속도론 모델을 제시하였으며 활성화 에너지 및 반응차수 그리고 pre-exponential 인자와 같은 속도 상수들에 대한 정보를 얻기 위하여 본 연구에서 제시한 속도론 해석 방법을 이용하여 질량감소 곡선 및 그 미분값을 해석하였다. 본 연구로부터 산소농도에 대한 반응차수는 모두 음의 값을 나타내었으며 활성화 에너지는 산소농도가 증가함에 따라 감소함을 확인할 수 있었다. 또한 단일 가열속도에서의 실험값을 이용하는 적분법의 경우 가열속도에 따라 반응속도 상수의 값이 변화함을 알 수 있었다. 따라서 여러 가열속도에서의 실험값을 이용하는 미분법이 폐폴리우레탄의 열적 산화분해 반응을 보다 효율적으로 나타내고 있는 것으로 판단된다.

• 지구물리와물리탐사
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• 제21권1호
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• pp.1-7
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• 2018

전기탐사 2차원 모델링에서는 다수의 파수영역 전위를 계산하고 이를 푸리에 역변환하여 공간영역 전위를 계산한다. 푸리에 역변환은 여러 개의 서로 다른 파수에서의 파수영역 전위를 사용하여 수치적으로 얻어진다. 적분의 정확도를 향상시키기 위하여 파수의 크기에 따라 적분 구간을 지수 근사와 대수 근사 구간으로 분할하는 방법이 널리 사용되고 있다. 푸리에 역변환에는 크게 구간 적분법과 가우스 적분법이 사용되고 있다. 그러나 이들 방법은 송수신 간격을 고려하지 못하므로 송수신 간격에 따른 오차를 피할 수 없다. 특히 송수신 간격이 매우 작거나 클 경우 오차가 급격하게 증가하는 문제점을 가지고 있다. 이 연구에서는 송수신 간격을 고려하여 가우스 좌표값 및 가중값을 적용하는 새로운 수치 적분법을 개발하였다. 반무한 공간에 대한 수치 실험 결과, 개발된 수치 적분법은 송수신 간격에 관계없이 0.4% 이하의 정밀도를 나타내었다.

• Geomechanics and Engineering
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• 제21권3호
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• pp.279-288
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• 2020

The permeation grouting is a commonly used technique to improve the engineering geology condition of the soft ground. It is of great significance to predict the permeation range of the grout so as to ensure the effects of grouting. This paper conducts a theoretical analysis of jet-grouting effects in ground improvement and rotary grouting pile installation by utilizing deformation-permeation coupled poroelastic solutions based on Biot's theory and Laplace-Fourier integral transform technique. The exponential function and the intermittent trigonometric function are chosen to represent time-dependent grouting pressure usually encountered in ground improvement and rotary grouting pile installation process, respectively. The results, including the radial displacement, the hoop stress, the excess pore fluid pressure, the radial discharge, and the permeation radius of grout, are presented for different grouting time, radial positions and grouting lengths. Parametric study is conducted to explore the effects of variation of the exponent in the exponential grouting pressure-time relationship on grouting-induced responses. It is expected that the proposed solutions can be used to estimate the permeation range of grouting in ground improvement and rotary grouting pile installation.

• Structural Engineering and Mechanics
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• 제76권1호
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• pp.115-127
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• 2020

This study presents an analytical approach to investigate the thermodynamic behavior of functionally graded beam resting on elastic foundations. The formulation is based on a refined deformation theory taking into consideration the stretching effect and the type of elastic foundation. The displacement field used in the present refined theory contains undetermined integral forms and involves only three unknowns to derive. The mechanical characteristics of the beam are assumed to be varied across the thickness according to a simple exponential law distribution. The beam is supposed simply supported and therefore the Navier solution is used to derive analytical solution. Verification examples demonstrate that the developed theory is very accurate in describing the response of FG beams subjected to thermodynamic loading. Numerical results are carried out to show the effects of the thermodynamic loading on the response of FG beams resting on elastic foundation.

• Structural Engineering and Mechanics
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• 제76권3호
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• pp.325-336
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• 2020

In this study, the continuous and discontinuous contact problems of functionally graded (FG) layer resting on a rigid foundation were considered. The top of the FG layer was loaded by a distributed load. It was assumed that the shear modulus and the density of the layer varied according to exponential functions along the depth whereas the the Poisson ratio remained constant. The problem first was solved analytically and the results were verified with the ones obtained from finite element (FE) solution. In analytical solution, the stress and displacement components for FG layer were obtained by the help of Fourier integral transform. Critical load expression and integral equation for continuous and discontinuous contact, respectively, using corresponding boundary conditions in each case. The finite element solution of the problem was carried out using ANSYS software program. In continuous contact case, initial separation distance and contact stresses along the contact surface between the FG layer and the rigid foundation were examined. Separation distances and contact stresses were obtained in case of discontinuous contact. The effect of material properties and loading were investigated using both analytical and FE solutions. It was shown that obtained results were compatible with each other.