• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.627-639
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• 2013

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.

• Ocean Systems Engineering
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• v.13 no.2
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• pp.123-146
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• 2023

In this paper, Moore-Gibson-Thompson theory of thermoelasticity is considered to investigate the fundamental solution and vibration of plane wave in an isotropic photothermoelastic solid. The governing equations are made dimensionless for further investigation. The dimensionless equations are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature distribution and carrier density distribution). Fundamental solutions are constructed for the system of equations for steady oscillation. Also some preliminary properties of the solution are explored. In the second part, the vibration of plane waves are examined by expressing the governing equation for two dimensional case. It is found that for the non-trivial solution of the equation yield that there exist three longitudinal waves which advance with the distinct speed, and one transverse wave which is free from thermal and carrier density response. The impact of various models (i)Moore-Gibson-Thomson thermoelastic (MGTE)(2019), (ii) Lord and Shulman's (LS)(1967) , (iii) Green and Naghdi type-II(GN-II)(1993) and (iv) Green and Naghdi type-III(GN-III)(1992) on the attributes of waves i.e., phase velocity, attenuation coefficient, specific loss and penetration depth are elaborated by plotting various figures of physical quantities. Various particular cases of interest are also deduced from the present investigations. The results obtained can be used to delineate various semiconductor elements during the coupled thermal, plasma and elastic wave and also find the application in the material and engineering sciences.

• Carbon letters
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• v.14 no.2
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• pp.89-93
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• 2013

Size-sorted graphene nanoplatelets are highly desired for fundamental research and technological applications of graphene. Here we show a facile approach for fabricating size-sorted graphene oxide (GO) nanoplatelets by a simple centrifugal method using different dispersion solvents. We found that the small-sized GO nanoplatelets were more effectively separated when dispersed in water or dimethylformamide (DMF) than in an alkali aqueous solution. After several iterations of the centrifugation, the sizes of GO in the supernatant solution were mostly several micrometers. We found that the GO area was not strongly correlated with the C-O content of the GO dispersed in water. However, the size-sorted GO nanoplatelets in DMF showed different C-O content, since DMF can reduce GO nanoplatelets during exfoliation and centrifugation processes.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.8
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• pp.1382-1387
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• 2010

Recently, there has been a growing interest in the environmental conservation. Accordingly, problems related to the audible noise of transformers have became more frequent. Therefore, it is urgent to find a fundamental solution about the audible noises in the substations. This paper described a sort of fundamental solution to solve the noise problem. As a fundamental solution, we suggested the proper audible noise level of transformers through noise prediction in the substation construction phase. And we applied the low noise transformers which have the predicted noise level. As the result, we are able to satisfy the noise regulation through measuring 43.6dBA at the boundary of substation. It is confirmed that the average error rate of prediction was within 3 percent.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Coupled systems mechanics
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• v.10 no.1
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• pp.21-38
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• 2021

This work is an attempt to design a dynamic model for a non local bio-thermoelastic medium with diffusion. The system of governing equations are formulated in terms of displacement vector field, chemical potential and the tissue temperature in the context of non local dual phase lag (NL DPL) theories of heat conduction and mass diffusion. Based on this considered model, we study the fundamental solution and propagation of plane harmonic waves in tissues. In order to analyze the behavior of the NL DPL model, we construct basic theorem in the terms of elementary function which determine the existence of three longitudinal and one transverse wave. The effects of various parameters on the characteristics of waves i.e., phase velocity and attenuation coefficients are elaborated by plotting various figures of physical quantities in the later part of the paper.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.79-86
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• 1996

A boundary element method which utilizes the fundamental solution in the half plane is developed to analyze the multi-layered elastic media. The objective of this study is to derive numerically the fundamental solutions and to apply those to the exterior multi-layered domain problems. To obtain numerical fundamental solutions of multi-layered structural system, the same number of solutions as that of layers in Fourier transform domain are employed. The numerical integration technique is used in order to inverse the Fourier transform solution to real domain. To verify the proposed boundary element method, two examples are treated: (1) a circular hole near the surface of a half plane; and (2) a circular cavity within one layer of four layered half plane.

• Smart Structures and Systems
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• v.21 no.4
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• pp.469-477
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• 2018

This paper presents a numerical solution for the thick cylinders made of functionally graded materials (FGMs) with a constant Poisson's ratio and an arbitrary Young's modulus. We define two fundamental solutions which are derived from an ordinary differential equation under two particular initial boundary conditions. In addition, for the single layer case, we can define the transfer matrix N. The matrix gives a relation between the values of stress and displacement at the interior and exterior points. By using the assumed boundary condition and the transfer matrix, we can obtain the final solution. The transfer matrix method also provides an effective way for the solution of multiply layered cylinder. Finally, a lot of numerical examples are present.

• East Asian mathematical journal
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• v.31 no.5
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• pp.727-735
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• 2015

We introduce the fundamental theorem of upper and lower solutions for a class of singular ($p_1,\;p_2$)-Laplacian systems and give the proof by using the Schauder fixed point theorem. It will play an important role to study the existence of solutions.

• Steel and Composite Structures
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• v.12 no.6
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• pp.541-548
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• 2012

This paper deals with the applicability of extended layerwise optimization method (ELOM) for frequency optimization of laminated composite plates. The design objective is the maximization of the fundamental frequency of the laminated plates. The fibre orientations in the layers are considered as design variables. The first order shear deformation theory (FSDT) is used for the finite element solution of the laminates. Finally, the numerical analysis is carried out to show the applicability of extended layerwise optimization algorithm of laminated plates for different parameters such as plate aspect ratios and boundary conditions.