• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.597-610
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• 2024

Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].

• Journal of the Korean Society for Precision Engineering
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• v.8 no.2
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• pp.27-35
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• 1991

We propose the crack growth rate equation which applied over three regions (threshold region, stable region, unstable region) of fatigue crack propagation. Constant stress amplitude fatigue tests are conducted for four materials under three stress ratios of R=0.05, R=0.2 and R=0.4. Materials which have different mechanical properties i.e. stainless steel, low carbon steel, medium carbon steel and aluminum alloy are used. The fatigue crack growth rate equation is given by $da/dN={\beta} (1-R)^{\delta}\({\DELTA}K-{\DELTA}K_t)^{\alpha} / (K_{cf}-K_{max})$${\alpha}, {\beta}$ , and ${\delta}$ are constants, and ${\Delta}K_t$ is stress intensity factor range at low ${\Delta}K$ region. The constants are obtained from nonlinear least square method. $K_{ef}$is critical fatigue stress intensity factor. The relation between half crack length and number of cycles obtained by integrating the crack growth rate equation is in agreement with the experimental data. It is also experimented with constant maximum stress and decreasing stress ratios, and the fatigue growth rate of each material is in accord with the proposed equation.

• Journal of Ocean Engineering and Technology
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• v.6 no.1
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• pp.105-112
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• 1992

The main purpose of this study is to derive a law of fatigue crack growth rate in the region of elastic or elasto-plastic fracture mechanics at elevated temperatures through the application of dimensional analysis. An equation of elasto-plastic fatigue crack growth rate at elevated temperatures appeared a new Arrhenius type equation containing J-integral range and absolute temperature. The elastic or elasto-plastic crack growth rate equation shows a fairly good agreement with the experimental results for Cr-Mo-V rotor steel and Hastelloy-X alloy in the comparatively wide temperature ranges.

• Journal of Microbiology and Biotechnology
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• v.13 no.5
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• pp.641-646
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• 2003

An accurate and efficient method for measuring the mass of hairy roots using conductometry is established. A conductivity equation expressed in terms of the concentration of the ion species in the medium is suggested. By using this equation, the effect of the individual ions on the total conductivity can be quantitatively analyzed. An equation for the in situ estimation of the cell growth coefficient for determining the mass of hairy roots is established based on measurements of the nitrogen concentration and conductivity during cultivation. The proposed equation does not require preliminary experiments to determine the cell growth coefficient. Instead, the physiological characteristics of the plant species are reflected by introducing the cellular nitrogen content. Since the cell growth coefficient is determined by measuring the major ionic nutrient concentrations, it is more effective to express the dynamics of an actual culture system. This improved method for determining the mass of hairy roots was successfully utilized in a fed-batch culture system.

• Journal of Distribution Science
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• v.14 no.3
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• pp.39-44
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• 2016

Purpose - The purpose of this research is to investigate whether Korea's economic growth can be explained by the endogenous growth theory. Specifically, we test whether R&D expenditure has a positive and significant effect on the economic growth. Research design, data, and methodology - We hypothesize that R&D expenditure has a positive effect on the economic growth after adding control variables in the growth equation. Korean annual data from 1963 to 2011 from Science and Technology Annual of the Ministry of Education, Science and Technology, the Bank of Korea, etc. are used. We estimate the growth equation by GMM in addition to OLS. Results - We found that R&D expenditure has a positive and significant effect on the economic growth after adding the ratio of investment to GDP, the ratio of FDI to GDP, the ratio of government expenditure to GDP, inflation and the ratio of trade openness to GDP as control variables in the growth equation. Conclusions - Our results show that Korea's rapid economic growth for the past five decades can be explained by the R&D-based endogenous economic growth theory. Our results suggest that the policy attention of the Korean government be paid to R&D promotion.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.421-434
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• 2016

The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.

• Journal of Korean Society of Forest Science
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• v.87 no.1
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• pp.40-49
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• 1998

This study aimed to provide a strategy for selecting an adequate combination of growth intervals(i.e. times between age $T_1$ and age $T_2$) to be used to improve the reality of the growth equation through obtaining better precision of parameter estimates. Variety of growth functions were fitted to the data and one equation which best fitted the data was chosen for the analysis. A modified Schumacher projection equation, selected as a best equation, that included dummy variables representing locality as a predictor variable was fitted for basal area and height equations with nonoverlapping growth interval and all possible growth interval data sets of Douglas-fir(Pseudotsuga menziesii Mirb.Franco). The data were measured in all parts of the South Island of New Zealand. It was found that the precision of parameter estimates was increased in both basal area and height equations by using data set which contained a range of measurement intervals from short to long term.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.53 no.4
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• pp.471-475
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• 2017

This study aims to suggest the methodology to improve to estimate back-calculated fish growth parameters using weighted average. It is to contribute to correct errors in the calculation of back-calculated growth equation with unequal numbers of sample by age. If the numbers of sample were evenly collected by age, each back-calculated length at age was equal between arithmetic and weighted averages. However, most samples cannot be evenly collected by age in reality because of different catchability by fishing gear and limitation of environment condition. Therefore, the estimation of back-calculated length by weighted average method is essential to calculate growth parameters. There were some published growth equations from back-calculated length using a simple arithmetic average with different numbers of samples by age when searching for back-calculated growth equations from 91 relevant papers. In this study, the process of deriving growth equation was investigated and two different average calculations were applied to a fish growth equation, for example of Acheilognathus signifer. Growth parameters, such as $L_{\infty}$, k and $t_0$, were estimated from two different back-calculated averages and the growth equations were compared with growth performance index. Based on the correction of back-calculated length using weighted average by age, the changes by female and male were -14.19% and -5.23% for $L_{\infty}$, and 59.28% and 18.91% for k, respectively. The corrected growth performance index by weighted average improved at 7.05% and 2.46% by female and male, respectively, compared to the arithmetic averages.

• Journal of the Korean Ceramic Society
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• v.36 no.8
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• pp.871-875
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• 1999

Theoretical equation to calculate thermal fatigue life was derived in which slow crack growth theory was adopted. The equation is function of crack growth exponent n. Cyclic thermal fatigue tests were performed at temperature difference of 175, 187 and 200$^{\circ}C$ respectively. At each temperature difference critical thermal fatigue life cycles of the alumina ceramics were 180,37 and 7 cycles. And theoretical thermal fatigue life cycles were calculated as 172, 35 and 7 cycles at the same temperature difference conditions. Therefore thermal fatigue behavior of alumina ceramics can be represented by derived equation. Also theoretical single cycle critical thermal shock temperature difference can be calculated by this equation and the result was consistent with the experimental result well.

• Korean Journal of Materials Research
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• v.24 no.2
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• pp.87-92
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• 2014

The Notched Ring Test(NRT) has proven to be very useful in determining the slow crack growth behavior of polyethylene pressure pipes. In particular, the test is simple and an order of magnitude shorter in experimental times as compared to the currently used Notched Pipe Test(NPT), which makes this method attractive for use as the accelerated slow crack growth test. In addition, since the NRT specimen is taken directly from the pipe, having maintained the cross-section, processing induced artifacts that would affect the slow crack growth behavior are not altered. This makes the direct comparison to the slow crack growth specimen in pipe from more meaningful. In this study, for comparison with other available slow crack growth methods, including the NPT, the stress intensity factor equation for NRT specimen was developed and demonstrated of its accuracy within 3% of that obtained from the finite element analysis. The equation was derived using a flexure formula of curved beam bending along with numerically determined geometric factors. The accuracy of the equation was successfully tested on 63, 110, 140, 160, 250, and 400 mm nominal pipe diameters, with crack depth ranging from 15 % to 45 % of the pipe wall thickness, and for standard dimensional ratio(SDR) of 9, 11, and 13.6. Using this equation the slow crack results from 110SDR11 NRT specimen were compared to that from the NPT specimen, which demonstrated that the NRT specimen was equivalent to the NPT specimen in creating the slow crack, however in much shorter experimental times.