• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.215-222
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• 2019

The heat conduction problem with discontinuous material coefficients generally consists of the conservative equation, boundary condition, and interface condition, which should be additionally satisfied in the solution procedure. This feature often makes the development of new numerical schemes difficult as it induces a layered singularity in the solution fields; thus, a special approximation is required to capture the singular behavior. In addition to the approximation, the construction of a total system of equations is challenging. In this study, a wedge function is devised for enriching the approximation, and the interface condition itself is embedded in the moving least squares(MLS) derivative approximation to consistently satisfy the interface condition. The heat conduction problem is then discretized in a strong form using the developed derivative approximation, which is named as the interface immersed MLS difference method. This method is able to efficiently provide a numerical solution for such interface problems avoiding both numerical quadrature as well as extra difference equations related to the interface condition enforcement. Numerical experiments proved that the developed numerical method was highly accurate and computationally efficient at solving the heat conduction problem with interfacial jump as well as the problem with a geometrically induced interfacial singularity.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.215-231
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• Proceedings of the Korean Magnestics Society Conference
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• 2013.05a
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• pp.19-20
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• 2013

Thermoelectic properties of the typical thermoelectric host materials, the tellurides and selenides, are known to be noticeably changed by their volume change due to the strain [1]. In the bismuth telluride ($Bi_2Te_3$) crystal, a substitution of rare-earth element by replacing one of the Bi atoms may cause the change of the lattice parameters while remaining the rhombohedral structure of the host material. Using the first-principles approach by the precise full potential linearized augmented plane wave (FLAPW) method [2], we investigated the Ce substitution effect on the thermoelectric transport coefficients for the bismuth telluride, employing Boltzmann's equation in a constant relaxation-time approach fed with the FLAPW wave-functions within the rigid band approximation. Depending on the real process of re-arrangement of atoms in the cell to reach the equilibrium state, $CeBiTe_3$ was found to manifest a metal or a narrow bandgap semiconductor. This feature along with the strong correlation effect originated by the 4f states of Ce affect significantly on the thermoelectric properties. We showed that the position of the strongly localized f-states in energy scale (Fig. 1, f-states are shaded) was found to alter critically the transport properties in this material suggesting an opportunity to improve the thermoelectric efficiency by tuning the external strain which may changing the location of the f-sates.

• Geomechanics and Engineering
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• v.5 no.2
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• pp.165-185
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• 2013

In the present study, the numerical and experimental investigations were performed on the backfill- exterior wall-fluid interaction systems in case of empty and full tanks. For this, firstly, the non-linear three dimensional (3D) finite element models were developed considering both backfill-wall and fluid-wall interactions, and modal analyses for these systems were carried out in order to acquire modal frequencies and mode shapes by means of ANSYS finite element structural analysis program. Secondly, a series of field tests were fulfilled to define their modal characteristics and to compare the results from proposed approximation in the selected structures. Finally, comparing the theoretical predictions from the finite element models to results from experimental measurements, a close agreement was found between theory and experiment. Thus, it can be easily stated that experimental verifications provide strong support for the finite element models and the proposed procedures themselves are the meritorious approximations to the real problem, and this makes the models appealing for use in further investigations.

• Proceedings of the Korean Vacuum Society Conference
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• 2012.08a
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• pp.111-111
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• 2012

In this talk, we represent a novel approach to investigating intra-nanorod surface plasmon coupling with control over block compositions. The multi-component rod-like nanostructures, which consist of optically active components (Au and Ag) and optically less active component (for example, Ni) in UV-vis-NIR spectral window, showed interesting optical response depending on each block length and the total length of the structure. By controlling the composition and relative lengths of the blocks that comprise these structures, we can tailor the overall optical properties. Depending on the relative fraction of Au and Ag blocks, the intensity of the transverse modes varied without noticeable peak shifts. However, the strong intraparticle surface plasmon coupling resulted in the collective appearance of longitudinal LSP modes, including higher-order modes. The experimental observations were confirmed by theoretical calculation, using a discrete dipole approximation method. In addition, we will briefly discuss how single nanorod solar cells can be synthesized by using by using electrochemical deposition and AAO hard templates.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Journal of The Korean Astronomical Society
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• v.20 no.1
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• pp.27-47
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• 1987

In the present study a two-mode, separately concurring resonant cavity model is proposed for theoretical interpretation of the 3 minute umbral oscillation. The proposed model has been investigated by calculating the transmission coefficients of the waves propagating through the umbral photosphere (photospheric weak-field cavity) and chromosphere (chromospheric strong-field cavity) into the corona, for 3 different umbral model atmospheres by Staude (1982), Beebe et al. (1982) and Avrett (1981). In computing the transmission coefficients we made use of multi-layer approximation by representing the umbra] atmosphere by a number of separate layers with (1) temperature varying linearly with depth and (2) temperature constant within each layer. The medium is assumed to be compressible, non-viscous, perfectly conducting under gravity. The computed resonant periods, transmission spectra, phase spectra, and kinetic energy density of the waves associated with the oscillations are presented in comparison with the observations and their model dependent characteristics are discussed.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.11a
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• pp.93-96
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• 2003

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We establish some necessary and sufficient conditions for a gknap to admit a fully polynomial approximation scheme, or FPTAS, To do so, we recapture the scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a condition that a gknap does not have an FP-TAS. This condition is more general than the strong NP-hardness.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.225-239
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• 2006

In [5], Csorgo and Zitikis exposed the strong $uniform-over-[0,\;{\infty}]$ consistency, and weak $uniform-over-[0,\;{\infty}]$ approximation of the empirical mean residual life process by employing weight functions. We carry on the uniform asymptotic behaviors of the empirical mean residual life process over the whole positive half line by representing the process as an integral form. We compare our results with those of Yang [15], Hall and Wellner [8], and Csorgo and Zitikis [5].

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.107-121
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• 2013

The purpose of this paper is to investigate the demiclosed principle, the existence theorems and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. The structure of fixed point set of such mappings is also studied. Our results generalize, unify and extend several comparable results in the existing literature.