• 대한수학회논문집
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• 제11권1호
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• pp.175-190
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• 1996

In this paper we establish the existence of the conditional Feynman integral of certain functions which are not in the Banach algebra S of functions on Wiener space which are a kind of stochastic Fourier transform of complex Borel measures on $L^2[a, b]$. This result is used to provide the fundamental solution for the Schr$\ddot{o}$dinger equation for the forced harmonic potential.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.139-153
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• 2021

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

• East Asian mathematical journal
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• 제17권1호
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• pp.33-45
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• 2001

In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.249-267
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• 2023

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.443-461
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• 2023

In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

• 대한수학회지
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• 제38권3호
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• pp.657-667
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• 2001

We propose a statistical interpolation approximate solution for a nonlinear stochastic integral equation of a stock price process. The proposed method has the order O(h$^2$) of local error under the weaker conditions of $\mu$ and $\sigma$ than those of Milstein' scheme.

• 한국표면공학회지
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• 제17권4호
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• pp.99-105
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• 1984

Integral coloring of aluminum and its alloy with the elecrolytic solution of sulfosallicylic acid and sodium hydroxide was investigated in this study. Addition of hydrogen peroxide and potassium permanganate accelerated the anodizing speed and deepened the color of anodized film. Electron microscopic study was also performed on the surface and cross section.

• 대한수학회논문집
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• 제36권3호
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• pp.485-494
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• 2021

In this article, we prove the existence of a solution to some classes of integral equations of generalized convolution type generated by the Kontorovich-Lebedev (K) transform, the Laplace (𝓛) transform and the Fourier (F) transform in some appropriate function spaces and represent it in a closed form.

• 한국전자파학회논문지
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• 제16권10호
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• pp.982-988
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• 2005

본 논문에서는 모드 변환기나 필터, 매칭 구조가 모두 연결되어 있는 개구면 안테나의 특성을 예측을 위해 급전 부분에 전이 구조가 붙어 있는 원형 개구면 안테나의 해석적인 산란 해를 제시한다. 개구면의 모양이 원형이기 때문에 길이가 짧고 반지름이 다른 원형 도파관이 연결되어 있는 구조로 모델링하여 안테나를 해석했다. 안테나의 해석에서 급전 도파관과 개구면 사이의 영역은 일반화된 산란 행렬을 이용하여 전기장과 자기장을 나타냈고, 개구면에서 복사되는 전기장과 자기장은 적분 변환을 이용하여 나타내어 전체 구조를 해석했다. 여기서 필요한 산란 행렬과 적분 변환은 모두 해석적으로 계산 가능하고, 엄밀한 해이므로 안테나의 반사 특성, 복사 특성 등을 정확하게 예측 가능하다.

• Structural Engineering and Mechanics
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• 제64권4호
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• pp.487-494
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• 2017

The present paper deals with a theoretical study of delamination fracture in the Crack Lap Shear (CLS) functionally graded beam configuration. The basic purpose is to analyze the fracture with taking into account the material non-linearity. The mechanical behavior of CLS was described by using a non-linear stress-strain relation. It was assumed that the material is functionally graded along the beam height. The fracture was analyzed by applying the J-integral approach. The curvature and neutral axis coordinate of CLS beam were derived in order to solve analytically the J-integral. The non-linear solution of J-integral obtained was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, crack location along the beam height and material non-linearity on fracture behavior were evaluated. The J-integral non-linear solution derived is very suitable for parametric studies of longitudinal fracture in the CLS beam. The results obtained can be used to optimize the functionally graded beam structure with respect to the fracture performance. The analytical approach developed in the present paper contributes for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.