• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.881-893
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• 1997

E. M. Silvia introduced the class $S^\lambda_\alpha$ of $\alpha$-spirallike functions f(z) satisfying the condition $$ (A) Re[(e^{i\lambda} - \alpha) \frac{zf'(z)}{f(z)} + \alpha \frac{(zf'(z))'}{f'(z)}] > 0, $$ where $\alpha \geq 0, $\mid$\lambda$\mid$ < \frac{\pi}{2}$ and $$\mid$z$\mid$ < 1$. We will generalize Silvia class of functions by formally replacing f(z) in the denominator of (A) by a spirallike function g(z). We denote the new class of functions by $Y(\alpha,\lambda)$. In this note we obtain some results for the class $Y(\alpha,\lambda)$ including integral representation formula, relations between our class $Y(\alpha,\lambda)$ and Ziegler class $Z_\lambda$, the radius of convexity problem, a few coefficient estimates and a covering theorem for the class $Y(\alpha,\lambda)$.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.177-190
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• 2015

Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let $C_{rc}(X,E)$ be the Banach space of all continuous functions $f:X{\rightarrow}E$ such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear operators $T:C_{rc}(X,E){\rightarrow}F$. We characterize continuous operators from $C_{rc}(X,E)$, provided with the strict topologies ${\beta}_z(X,E)$ ($z={\sigma},{\tau}$) to F, in terms of their representing operator-valued measures.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.9
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• pp.1244-1249
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• 1995

Wavelet transform technique is applied to two important electromagnetic problems:1) to analyze the frequency-domain radar echo from finite-size targets and 2) to the integral solution of two- dimensional electromagnetic scattering problems. Since the frequency- domain radar echo consists of both small-scale natural resonances and large-scale scattering center information, the multiresolution property of the wavelet transform is well suited for analyzing such ulti-scale signals. Wavelet analysis examples of backscattered data from an open- ended waveguide cavity are presented. The different scattering mechanisms are clearly resolved in the wavelet-domain representation. In the wavelet transform domain, the moment method impedance matrix becomes sparse and sparse matrix algorithms can be utilized to solve the resulting matrix equationl. Using the fast wavelet transform in conjunction with the conjugate gradient method, we present the time performance for the solution of a dihedral corner reflector. The total computational time is found to be reduced.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.7-16
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• 2018

The main objective of this paper is to demonstrate how one can obtain very quickly so far unknown Laplace transforms of rather general cases of the generalized hypergeometric function $_3F_3$ by employing generalizations of classical summation theorems for the series $_3F_2$ available in the literature. Several new as well known results obtained earlier by Kim et al. follow special cases of main findings.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.63-77
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• 2005

The Dirichlet-Neumann problem for the dissipative Helmholtz equation in a connected plane region bounded by closed curves and containing cuts is studied. The Neumann condition is given on the closed curves, while the Dirichlet condition is specified on the cuts. The existence of a classical solution is proved by potential theory. The integral representation of the unique classical solution is obtained. The problem is reduced to the Fredholm equation of the second kind and index zero, which is uniquely solvable. Our results hold for both interior and exterior domains.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.7
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• pp.1110-1114
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• 2001

The discrete wavelet concept in the k-domain is applied to efficiently represent Green function of integral equations. Application of discrete wavelet concept to Green function in the k-domain can be implemented equivalently by using spatial domain variable-sized windows. The proposed method consists of constant Q-filtering, changing the center of coordinates, and transforming spatially filtered Green functions into those in the k-domain. A mathematical expression of Green function based on the discrete wavelet concept is derived and its characteristics are discussed.

• Structural Engineering and Mechanics
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• v.57 no.1
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• pp.65-89
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• 2016

This paper presents the development of methodologies using Extended Finite Element Method (XFEM) for cracked unstiffened and concentric stiffened panels subjected to constant amplitude tensile fatigue loading. XFEM formulations such as level set representation of crack, element stiffness matrix formulation and numerical integration are presented and implemented in MATLAB software. Stiffeners of the stiffened panels are modelled using truss elements such that nodes of the panel and nodes of the stiffener coincide. Stress Intensity Factor (SIF) is computed from the solutions of XFEM using domain form of interaction integral. Paris's crack growth law is used to compute the number of fatigue cycles up to failure. Numerical investigations are carried out to model the crack growth, estimate the remaining life and generate damage tolerant curves. From the studies, it is observed that (i) there is a considerable increase in fatigue life of stiffened panels compared to unstiffened panels and (ii) as the external applied stress is decreasing number of fatigue life cycles taken by the component is increasing.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.523-534
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• 2010

In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.3
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• pp.397-400
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• 1986

In this paper, the orthogonal properties of the eigenmodes of optical resonators which have phase conjugate mirrors at both ends are derived. The modes which propagate in resonators are descdribed by the Huygens integral. Then, the eigeneuqation which is needed in order to prove the orthogonality of the eigenmodes of the resonator is obtained from this representation. When the kernel being a part of the eigenequation is Hermitian as in conventional resonators and in optical resonator with only one phase conjugate mirror, one can show that the eigenmodes have essentially biorthogonal relations, which are satisfied the set of modes propagating in one direcdtion around the resonator and the adjoint set of modes propagating in the reversed direction.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.549-560
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• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.