• 한국분말재료학회지
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• 제10권5호
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• pp.318-324
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• 2003

The nano-scale crystallite sizes of uranium oxide powders in simulated spent fuel were measured by the neutron diffraction line broadening method in order to analyze the sintering behavior of the dry process fuel. The mixed $UO_2$ and fission product powders were dry-milled in an attritor for 30, 60, and 120 min. The diffraction patterns of the powders were obtained by using the high resolution powder diffractometer in the HANARO research reactor. Diffraction line broadening due to crystallite size was measured using various techniques such as the Stokes' deconvolution, profile fitting methods using Cauchy function, Gaussian function, and Voigt function, and the Warren-Averbach method. The non-uniform strain, stacking fault and twin probability were measured using the information from the diffraction pattern. The realistic crystallite size could be obtained after separation of the contribution from the non-uniform strain, stacking fault and twin.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.455-466
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• 2021

Coupled fixed point results have attracted much attention among the researchers in recent times specially in the field of fuzzy metric spaces. In this paper we established a coupled fixed point result for weakly compatible mappings in G-fuzzy metric spaces. We have deduced a corollary to our main theorem. Our result also supported by examples.

• East Asian mathematical journal
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• 제25권2호
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• pp.221-227
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• 2009

In this paper, we introduce the generalized H$\ddot{o}$lder space with a majorant function and prove the H$\ddot{o}$lder regularity for solutions of the Cauchy-Riemann equation in the generalized Holder spaces on a bounded convex domain in $\mathbb{C}^2$.

• 대한전기학회논문지
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• 제34권5호
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• pp.173-178
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• 1985

The control of a linear system with random coefficients is discussed here. The cost function is of a quadratic form and the random coefficients are assumed to be completely observable by the controller. Stochastic Process involved in the problem by the controller. Stochastic Process involved in the problem formulation is presented to be the unique strong solution to the corresponding stochastic differential equations. Condition for the optimal control is represented through the existence of solution to a Cauchy problem for the given nonlinear partial differential equation. The optimal control is shown to be a linear function of the states and a nonlinear function of random parameters.

• 한국통신학회논문지
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• 제18권1호
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• pp.143-149
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• 1993

An approach is presented for efficient numerical integration of the Sormnerfeld type integrals pertinent to the microstrip surface Green's function arising in the problem of an electric current point source on an infinite planar grounded dielectric substrate. This approach, valid for both lossless and lossy dielectric substrates, is based on the deformation of the integration contour via a coordinate transformation and Cauchy's residue theory, and identifies clearly the effects of surface waves. I ts useful application is in a rigorous moment method analysis of micros trip antenna arrays and microstrip guided wave structures. The efficiency and the usefulness of the present approach are emphasized through some numerical calculations of the impedance matrix elements with associated CPU times.

• 대한수학회지
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• 제45권2호
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• pp.455-466
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• 2008

Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.

• 비파괴검사학회지
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• 제31권6호
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• pp.665-670
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• 2011

In this paper, a new approach to detect surface cracks from a noisy thermal image in the infrared thermography is presented using an holomorphic characteristic of temperature field in a thin plate under steady-state thermal condition. The holomorphic function for 2-D heat flow field in the plate was derived from Cauchy Riemann conditions to define a contour integral that varies according to the existence and strength of a singularity in the domain of integration. The contour integral at each point of thermal image eliminated the temperature variation due to heat conduction and suppressed the noise, so that its image emphasized and highlighted the singularity such as crack. This feature of holomorphic function was also investigated numerically using a simple thermal field in the thin plate satisfying the Laplace equation. The simulation results showed that the integral image selected and detected the crack embedded artificially in the plate very well in a noisy environment.

• 충청수학회지
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• 제26권1호
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• pp.231-242
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• 2013

In this work, we deal with $q$-Genocchi numbers and polynomials. We derive not only new but also interesting properties of the $q$-Genocchi numbers and polynomials. Also, we give Cauchy-type integral formula of the $q$-Genocchi polynomials and derive distribution formula for the $q$-Genocchi polynomials. In the final part, we introduce a definition of $q$-Zeta-type function which is interpolation function of the $q$-Genocchi polynomials at negative integers which we express in the present paper.

• Journal of Mechanical Science and Technology
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• 제18권8호
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• pp.1375-1387
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• 2004

A solution is given for the elastodynamic problem of a crack perpendicular to the graded interfacial zone in bonded materials under the action of anti plane shear impact. The interfacial zone is modeled as a nonhomogeneous interlayer with the power-law variations of its shear modulus and mass density between the two dissimilar, homogeneous half-planes. Laplace and Fourier integral transforms are employed to reduce the transient problem to the solution of a Cauchy-type singular integral equation in the Laplace transform domain. Via the numerical inversion of the Laplace transforms, the values of the dynamic stress intensity factors are obtained as a function of time. As a result, the influences of material and geometric parameters of the bonded media on the overshoot characteristics of the dynamic stress intensities are discussed. A comparison is also made with the corresponding elastostatic solutions, addressing the inertia effect on the dynamic load transfer to the crack tips for various combinations of the physical properties.

• Structural Engineering and Mechanics
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• 제64권1호
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• pp.71-79
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• 2017

In this study, interaction of several interface cracks located between a functionally graded material (FGM) layer and an elastic layer under anti-plane deformation based on the distributed dislocation technique (DDT) is analyzed. The variation of the shear modulus of the functionally graded coating is modeled by an exponential and linear function along the thickness of the layer. The complex Fourier transform is applied to governing equation to derive a system of singular integral equations with Cauchy type kernel. These equations are solved by a numerical method to obtain the stress intensity factors (SIFs) at the crack tips. The effects of non-homogeneity parameters for exponentially and linearly form of shear modulus, the thickness of the layers and the length of crack on the SIFs for several interface cracks are investigated. The results reveal that the magnitude of SIFs decrease with increasing of FG parameter and thickness of FGM layer. The values of SIFs for FGM layer with exponential form is less than the linear form.