• 대한수학회논문집
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• 제37권1호
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• pp.75-89
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• 2022

In this paper, we prove new fixed point theorems for single-valued and multi-valued weakly Picard operators in complete metric spaces and give several examples. As applications, we give several results to Fredholm integral equation.

• Nuclear Engineering and Technology
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• 제16권2호
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• pp.89-96
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• 1984

현재 서울대학교 원자핵공학과에서 제작중인 SNUT-79 토카막 장치에서의 고온 플라즈마의 구속을 위해서 순인장력 D형 곡선을 가진 토로이달 자장 코일을 수치 해석적 방법으로 설계하였다. 16개의 D형 토로이달 코일 뭉치는 플라즈마가 없는 경우 자장의 세기가 3T가 되도록 설계하였다. 토로이달 리플은 플라즈마영역에서 평균 토로이달 자장의 4%이하이다. 6개로 된 평형 코일의 위치와 전류 값을 Fredholm 제1종 적분 방정식을 선형 방정식으로 변환하여 얻었다. 평형 자장의 곡률도는 플라즈마 루프의 수직 수평 방향의 변위에 대한 안정화 조건을 만족시켰다.

• 대한수학회논문집
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• 제13권3호
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• pp.481-487
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• 1998

Let (equation omitted) denote the closure of the set (equation omitted) of dominant operators in the norm topology. We show that the Weyl spectrum of an operator T $\in$ (equation omitted) satisfies the spectral mapping theorem for analytic functions, which is an extension of [5, Theorem 1]. Also we show that an operator approximately equivalent to an operator of class (equation omitted) is of class (equation omitted).

• Journal of Mechanical Science and Technology
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• 제14권8호
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• pp.845-850
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• 2000

We consider the problem of determining the singular stresses and electric fields in a piezoelectric ceramic strip containing a Griffith crack under in-plane normal loading within the framework of linear piezoelectricity. The potential theory method and Fourier transforms are used to reduce the problem to the solution of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the field intensity factors are obtained, and the influences of the electric fields for PZT-6B piezoelectric ceramic are discussed.

• 대한기계학회논문집
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• 제5권2호
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• pp.82-87
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• 1981

이 논문에서는 타원형의 크랙을 포함하는 유한한 두께을 가진 isotropic탄성체의 삼차원응력해석을 다루었다. 크랙은 평판의 면에 나란하고 그 중립면에 위치하며 일정한 인장력이 평판의 면에 작용하고 있다. 문제를 해석하기 위하여 이중 Fourier 적분변환을 사용하여 응력해석이 제 일종 Fredholm 적분 방정식의 해로 될 수 있음을 보였다. 두 극한의 경우 즉(i) 평판의 두께가 무한한 경우와 (ii) 타원이 원으로 reduce 되는 경우에 기존의 해와 일치됨을 보였다. 적분 방정식의 해 빛 응력해석은 제 이장에서 다루기로 한다.

• 대한기계학회논문집
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• 제5권3호
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• pp.217-222
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• 1981

The stress analysis of two-orthotropic layer, adhesively bonded structures is considered. An orthotropic plate has a through-crack of finite length and is adhesively bounded by a sound orthotropic plate. The problem is resuced to a pair of Fredholm integral equations ofthe second kind. Using a numerical integration scheme to evaluate the intgrals, The integral equations are reduced to a system of algebraic equations. By solving these equations some numerical results for stress intensity factors are presented for various crack lengths.

• 대한수학회논문집
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• 제21권1호
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• pp.53-64
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• 2006

In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.

• 대한수학회논문집
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• 제11권3호
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• pp.657-663
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• 1996

In this paper we give some conditions under which the Weyl spectrum of an operator satisfies the spectral mapping theorem for analytic functions. Also we show that Weyl's theorem holds for p(T) where T is an operator of M-power class (N) and p is a polynomial on a neighborhood of $\sigam(T)$. Finally we answer an old question of Oberai.

• 대한수학회지
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• 제46권3호
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• pp.463-473
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• 2009

Two $C^1$-mappings, whose domain is a connected compact $C^1$-Banach manifold modelled over a Banach space X over $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$ and whose range is a Banach space Y over $\mathbb{K}$, are introduced. Sufficient conditions are given to assert they share only a value. The proof of the result, which is based upon continuation methods, is constructive.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.17-30
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• 2020

In this paper, we firstly introduce the class of C^*-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.