• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.313-325
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• 2021

In this paper, we provide a characterization of upper semi-Fredholm operators via the relative demicompactness concept. The obtained results are used to investigate the stability of various essential spectra of closed linear operators under perturbations belonging to classes involving demicompact, as well as, relative demicompact operators.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.365-375
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• 2015

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our analysis is based on the theory of a strongly continuous semigroup of operators and the Banach fixed point theorem.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.853-869
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• 2018

We give a new characterization of Browder's theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [9] and [25] become stable under commuting Riesz perturbations.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.681-698
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• 2016

In this paper, we investigate relative essential spectra of $2{\times}2$ block operator matrix using the Fredholm perturbation theory. Furthermore, an example for two-group transport equations is presented to illustrate the validity of the main results.

• Composites Research
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• v.15 no.4
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• pp.37-42
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• 2002

We consider the problem of determining the singular stresses and electric fields in a functionally graded piezoelectric ceramic strip containing a Griffith eccentric crack under anti-plane shear loading with the theory of linear piezoelectricity. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the stress intensity factor and the energy release rate are obtained.

• Composites Research
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• v.16 no.5
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• pp.21-27
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• 2003

Using the theory of linear piezoelectricity, the dynamic response of a central crack in a functionally graded piezoelectric ceramic under anti-plane shear impact is analyzed. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. By using the Laplace and Fourier transform, the problem is reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. Numerical values on the dynamic stress intensity factors are presented to show the dependence of the gradient of material properties and electric loading.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.513-526
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• 2010

In this paper, the theory of n-ary hypergroups and some applications of hyperalgebras (Fredholm-Voltra integral, copula) are studied. We define some new concepts of topological hyperdynamical systems, universal hyperdynamical systems and immersed universal hyperalgebra. Also, we present some results in this respect.

• Journal of Mechanical Science and Technology
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• v.14 no.8
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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.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.275-296
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• 2007

We study the self-duality operator on conic 4-manifolds. The self-duality operator can be identified as a regular singular operator in the sense of $Br\"{u}ning$ and Seeley, based on which we construct its parametrizations and closed extensions. We also compute the indexes.