• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1673-1685
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• 2023

Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

• Journal of the Korean Society of Tobacco Science
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• v.2 no.2
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• pp.44-50
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• 1980

The growth of flue-cured tobacco was analyzed with the mathematical treatment. The results are summarized as followings: 1. The growth curve was fitted to the quadratic polynomial equation in improved-mulching cultivation, blot to the Gompertz equation in the other cultivations. 2. The initial point of the maximum growth phase for dry weight was about 50 days after transplanting in improved-mulching cultivation, but about 40 days in the other cultivations, and the maximum growth period was for 25 days in all cultivations. 3. The growth rate of the maximum growth period in dry weight decreased in the order of improved-mulching cultivation, mulching cultivation, and non-mulching cultivation. 4. A relative growth amount in the maximum growth period was higher in later sowing. 5. The length of maximum growth was 5 days shorter in leaf area than in dry weight. The maximum growth phase was 7 days earlier in leaf area than in dry weight.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.1
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• pp.19-26
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• 2004

The growth of solid particles in TiC-XC-2vo1.% and TiC-XC-30vo1.% Ni alloys, (where X=Zr, W or Mo) was fitted to the equation of the form $d^3$-${do}^3$=Kt during the liquid phase sintering at 1,673K. Also, the grain growth behavior decreased markedly with the addition of ${MO}_2$C or WC and increased with the addition of zrC. The contiguity was greater in the alloys with a smaller growth rate constant and especially, decreased by increasing the Ni content in the TiC-${MO}_2$C-Ni alloy. In addition, the effect of the addition of carbide on the grain growth of 2 vo1.% Ni alloys was found to be similar to that of 30vo1.% Ni alloys. Consequently, the grain growth mechanism cannot be explained by the usual solution / reprecipitation process, but can be explained in terms of a new growth velocity equation, which includes the effects of contiguous carbide grain boundaries in restricting the overall grain growth, as well as the area of the solid / liquid interface in the alloy.

• Journal of the Korean Society of Safety
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• v.9 no.3
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• pp.13-21
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• 1994

Effects of tensile and compression residual stresses in the welded SS41 and A17075-76 on fatigue crack propagation behavior are investigated when a crack propagates from residual stresses region. We propose the fatigue crack growth equation on tensile and compression residual stresses in welded metal. The results obtained in this experimental study are summarized as follows . 1 ) A fatigue crack growth equation which applied fatigue fracture behavior of the welded metal is proposed. (equation omitted) where, $\alpha$, $\beta$, ${\gamma}$ and $\delta$ are constants, and R$_{eff}$ is effective stress ratio [R$_{eff}$=(Kmin+Kres)/(Kmax+Kres)], Kcf is critical fatigue stress intensity factor. The constants are obtained from nonlinear least square method. The relation between crack length and number of cycles obtained by integrating the fatigue crack growth rate equation is in agreement with the experimental data. 2) The experimental results confirmed that the cause of crack extension and retardation by residual stresses has relation to the phenomenon of crack closure. 3) The relaxing trend of residual stresses by the crack propagation was greater In case of compressive residual stress than that of tensile residual stress in the welded metal.tal.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2007.05a
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• pp.107-110
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• 2007

It has been reported that the permanent strain could happen during recrystallization and grain growth even under the externally applied stress which is much lower than yield stress. In this study, we performed dilatometry experiments under the various compressive stresses and measured the amount of recrystallization and grain growth induced permanent strain. A new constitutive equation based on the concept of boundary migration induced plasticity was suggested to describe the recrystallization and grain growth induced plasticity. This equation was verified by comparing the calculated values with dilatometric experimental data under the various compressive stresses.

• Journal of Ocean Engineering and Technology
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• v.12 no.1
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• pp.39-49
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• 1998

In this work, fatigue tests by axial loading were carried out to investigate the effect of stress ratio on the growth behaviors of surface fatigue crack for SM45C steel and Al 2024-T4 alloy. The growth behaviors of surface crack have been monitored during fatigue process by measuring system attached CCTV and monitor. When the growth rates of surface crack were investigate by the concept of LEFM based on Newman-Raju's .DELTA.K, the dependence of stress ratio appears both SM45C steel and Al 2024-T4 alloy. Therefore, modified stress intensity factor range, .DELTA.K' [=(1+R)/sup n/.DELTA.K] are intorduced to eliminate the dependence of stress ratio. Using .DELTA.K', it is found that the dependence of stress ratio disappears both SM45C steel and Al 2024-T4 alloy.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.235-240
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• 2003

Methods to predict fatigue crack growth are compared in a quantitative manner for crack growth test data of 2024-T351 aluminum alloy under narrow and wide band random loading. In order to account for the effect of load ratio, crack closure model, Hater's equation and NASGRO's equation have been employed. Load interaction effect under random loading has been considered by crack closure model, Willenborg's model and Wheeler's model. The prediction method using the measured crack opening results provides the best result among the prediction methods discussed for narrow and wide band random loading data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.10
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• pp.1785-1792
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• 2003

Methods to predict fatigue crack growth are compared in a quantitative manner for crack growth test data of 2024- T351 aluninum alloy under narrow and wide band random loading. In order to account for the effect of load ratio, crack closure model, Hater's equation and NASGRO's equation have been employed. Load interaction effect under random loading has been considered by crack closure model, Willenborg's model and Wheeler's model. The prediction method using the measured crack opening results provides the best result among the prediction methods discussed for narrow and wide band random loading data.

• Journal of the Korean Ceramic Society
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• v.32 no.5
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• pp.587-593
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• 1995

Abnomal grain growth behavior of BaTiO3 ceramics was investigated with addition of seed grains. It was foudn that the nucleation rate of abnormal grain was constant and growth of abnormal grain was linearly increased with sitnering time, regardless of amount of seed grains. These facts were also confirmed by fitting of the volume fraction of abnormal grain vs. sintering time using Avrami type equation (n=4). It was suggested that seed grains did not change the nucleation rate or growth mechanism of abnormal grain but increase the number of abnormal grains at initial stage of sintering and then it led to fine microstructure of BaTiO3 ceramics.

• East Asian Economic Review
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• v.21 no.4
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• pp.295-315
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• 2017

This paper derives the gravity equation with intermediate goods trade. We extend a standard monopolistic competition model to incorporate intermediate goods trade, and show that the gravity equation with intermediates trade is identical to the one without it except in that gross output should be used as the output measure instead of value added. We also show that the output elasticity of trade is significantly underestimated when value added is used as the output measure. This implies that with the conventional gravity equation, the contribution of output growth can be substantially underestimated and the role of trade costs reduction can be exaggerated in explaining trade expansion, as we demonstrate for the case of Korea's trade growth between 1995 and 2007.