• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.569-580
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• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

• Proceedings of the Korean Information Science Society Conference
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• 2010.06c
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• pp.323-327
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• 2010

본 논문은 차분 진화 알고리즘의 최적해 탐색 능력을 향상시키기 위해 병렬 처리기법을 적용한 기법을 제안한다. 이를 위해서 기존의 개체군들을 5개의 그룹으로 나누어서 독립적으로 최적화 과정을 하도록 하여 일정한 확률에 의해서 각 그룹이 다른 그룹의 Best individual들을 변이 과정에서 참조하도록 하였다. 이러한 방식을 통해서 기존 차분 진화 알고리즘이 가지고 있는 지역해 수렴 문제를 해결하는 할 수 있도록 하였다. 실험을 통해서 제안된 차분 진화 알고리즘(P-DE)의 탐색 능력을 비교 및 분석 하였다. 실험 결과 제안된 차분 진화 알고리즘(P-DE)이 지역해 수렴 문제를 충분히 해결함으로써 기존의 알고리즘에 비해서 우수한 성능을 보이는 것을 확인 하였다.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.613-623
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• 2020

The notion of quasi-Einstein metric in theoretical physics and in relation with string theory is equivalent to the notion of Ricci soliton in differential geometry. Quasi-Einstein metrics or Ricci solitons serve also as solution to Ricci flow equation, which is an evolution equation for Riemannian metrics on a Riemannian manifold. Quasi-Einstein metrics are subject of great interest in both mathematics and theoretical physics. In this paper the notion of Ricci 𝜌-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3-dimensional almost Kenmotsu Einstein manifold M is a 𝜌-soliton, then M is a Kenmotsu manifold of constant sectional curvature -1 and the 𝜌-soliton is expanding with λ = 2.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.877-888
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• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.

• Transactions of Materials Processing
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• v.14 no.3 s.75
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• pp.215-223
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• 2005

A numerical analysis program is developed by FDM scheme for the prediction of microstructural transformation during heat treatment of steels. In this study, multi-phase model was used fur description of diffusional austenite transformations in low-alloy hypoeutectoid steels during cooling after austenitization. A fundamental property of the model consisting of coupled differential equations is that by taking into account the rate of austenite grain growth, it permits the prediction of the progress of ferrite, pearlite, and bainite transformations simultaneously during quenching and estimate the amount of martensite also by using K-M eq. In order to simulate the microstructural evolution during tempering process, another Avrami-type eq. was adopted and method for vickers hardness prediction was also proposed. To verify the developed program, the calculated results are compared with experimental ones of casting product. Based on these results, newly designed heat treatment process is proposed and it was proved to be effective for industry.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.3
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• pp.143-151
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• 1995

The electrochemical impulse oscillations of the cathodic currents at the platinum group (Pt, Pd) electrode/(0.05M KHC$_{8}H_{4}O_{4}$) buffer solution interfaces have been studied using voltammetric, chronoamperometric, and electrochemical impedance methods. The periodic impulses of the cathodic currents are the activation controlled currents due to the hydrogen evolution reaction, and depend on the fractional surface coverage of the adsorbed hydrogen intermediate and potential. The oscillatory mechanism of the cathodic current impulses is connected with the unstable steady state of negative differential resistance. The widths and periods of the cathodic current impulses are 4ms or 5ms and 152.5ms or 305ms, respectively. The H$^{+}$ discharge reaction step is 38 or 61 times faster thatn the recombination reaction steps and the H$^{+}$ mass transport processes. The atom-atom recombination reaction step is twice faster thatn the atom-ion recombination reaction step. The two kinds of active sites corresponding to the atom-atom and atom-ion recombination reaction steps exist on the platinum group electrode surfaces.

• Proceedings of the KWS Conference
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• 1994.05a
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• pp.44-47
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• 1994

The ageing behavior of Cu-bearing HSLA steels was studied by using Differential scanning calorimetry(DSC), Transmission electron microscopy and hardness tester. Two heat evolution peaks were observed during DSC scans over the temperature range of 25～590$^{\circ}C$ at a heating rate of 5$^{\circ}C$/min. The peaks appeared in low (241∼319$^{\circ}C$ : HSLA-A, 224∼310$^{\circ}C$ : HSLA-B) and high temperature (514∼590$^{\circ}C$ : HSLA-A, 451∼558$^{\circ}C$ : HSLA-B) are attributed to the formation of coherent Cu-clusters and noncoherent $\varepsilon$-Cu phase, respectively. It was confirmed that as ageing proceeds, the coherent bcc Cu-clusters transform to noncoherent fcc $\varepsilon$-Cu phase. In the case of the ageing to peak hardness at 300$^{\circ}C$ and 400$^{\circ}C$, the coherent Cu-clusters contributed to the hardening. As ageing time and temperature increase over peak hardness, noncoherent $\varepsilon$-Cu are formed and hardness decreases.

• Steel and Composite Structures
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• v.5 no.6
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• pp.421-441
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• 2005

The present work reports on a numerical simulation of a compartment fire. The fire was modeled using a simplified approach, where combustion is simulated as a volumetric heat release. Computations were performed with the commercial code CFX 5.6. Radiation was modeled with a differential approximation (P1 model), while turbulence effects upon the mean gas flow were dealt with a SST turbulence model. Simulations were carried out using a transient approach, starting at the onset of ignition. Results are provided for the temperature field time evolution, thus allowing a direct comparison with the analytical and experimental data. The high spatial resolution available for the results proved to be of great utility for a more detailed analysis of the thermal impact on the steel structure.

• Macromolecular Research
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• v.14 no.1
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• pp.45-51
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• 2006

We conducted simultaneous, small-angle, X-ray scattering/differential scanning calorimetry (SAXS/DSC) and simultaneous, wide-angle, X-ray scattering (WAXS)/DSC measurements for a polymer blend of poly($\varepsilon$-caprolactone)/poly(ethylene glycol)(PCL/PEG). The time-dependent SAXS/DSC and WAXS/DSC results, measured while the system was quenched below the melting temperature of PCL from a melting state, revealed the competitive behavior between liquid-liquid phase separation and crystallization in the polymer blend. The time-dependent structural evolution extracted from the SAXS/WAXS/DSC results can be characterized by the following four stages in the PCL crystallization process: the induction (I), nucleation (II), growth (III), and late (IV) stages. The influence of the liquid-liquid phase separation on the crystallization of PCL was also observed by phase-contrast microscope and polarized microscope with 1/4$\lambda$ compensator.

• Bulletin of the Korean Chemical Society
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• v.32 no.1
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• pp.145-148
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• 2011

The thermal behavior of lithiated Si anodes has been investigated using differential scanning calorimetry (DSC). In particular, the effect of Si particle size on the thermal stability of a fully lithiated Si electrode was investigated. For DSC measurements, a lithiated Si anode was heated in a hermetically sealed high-pressure pan with a polyvinylidene fluoride (PVDF) binder and a 1 M $LiPF_6$ solution in an ethylene carbonate (EC)-diethyl carbonate (DEC) mixture. The thermal evolution around $140^{\circ}C$ increases with lithiation and with decreasing particle size; this phenomenon is attributed to the thermal decomposition of the solid electrolyte interface (SEI) film. Exothermic peaks, following a broad peak at around $140^{\circ}C$, shift to a lower temperature with a decrease in particle size, indicating that the thermal stability of the lithiated Si electrode strongly depends on the Si particle size.