• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.827-841
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• 2022

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions f(z) and g(z) of the following complex difference equation A₁(z)f(z + 1) + A₀(z)f(z) = F(z)e^𝛼(z) when they share 0, ∞ CM, where A₁(z), A₀(z), F(z) are non-zero polynomials, 𝛼(z) is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

• Journal of Korean Society on Water Environment
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• v.23 no.5
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• pp.683-688
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• 2007

Water flow into unsaturated soils is most often modeled by Richards equation consisting of the mass conservation law and Darcy's law. Three standard forms of Richards equation are presented as the head (${\Psi}$)-based form, the moisture content (${\theta}$) based form, and the mixed form. Numerical solutions of these partial differential equations with highly nonlinear terms can cause poor results along with significant mass balance errors. The numerical solution based on the mixed form of Richards equation is known that the mass is perfectly conserved without any additional computational efforts. The aim of this study is to develop fully implicit numerical scheme of Richards equation for one-dimensional vertical unsaturated flow in homogeneous soils using the finite difference approximation, and then to perform sensitivity analysis of infiltration to the variations in the unsaturated soil properties and to different soil types.

• Journal of the Korean Society of Tobacco Science
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• v.22 no.1
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• pp.76-83
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• 2000

This study was carried out to predict blending ratio of cut tobacco(CT), expanded stem(ES), and expanded cut tobacco(ECT) in cigarettes. CT, ES, and ECT samples from A brand were, ground and blended with reference to A blending ratio, and scanned by near infrared spectroscopy(NIRSystem Co., Model 6500). Calibration equations were developed and then determined blending ratio by NIRS. The standard error of calibration(SEC) and performance(SEP) of C factory samples between NIRS and known blending ratio were 0.97%, 1.93% for CT, 0.50%, 1.12 % for ES and 0.68%, 1.10% for ECT, respectively. The SEP of CT, ES and ECT of Band D factory samples determined by C factory calibration equation were more inaccurate than those of C factory samples determined by C factory calibration equations. These results were caused by the difference of CT, ES and ECT spectra followed by each factory. The SEP of CT, ES and ECT of Band D factories determined by calibration equations derived from each factory samples were more accurate than those of determined by calibration equation derived from C factory samples. Each factory SEP of CT, ES and ECT determined by calibration equation derived from all calibration samples(B+C+D factory) was similar to that determined by calibration equation derived from each factory samples. To improve the analytical inaccuracy caused by spectra difference, we need to apply a specific calibration equation for each factory sample. Data in development of specific calibrations between sample and NIRS spectra might supply a method for rapid determination of blending ratio of CT, ES, and ECT.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.29-38
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• 2016

For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.

• Journal of Advanced Marine Engineering and Technology
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• v.18 no.3
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• pp.94-101
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• 1994

To develope the new simulator for the analysis of fluid flow information, the influence of various convective difference schemes were evaluated. General curvilinear coordinate system with nonorthogonal grids was adopted for the successful analysis of various complex geometries. Computation results show that if we can not obtain full grid numbers within available computational environment, we need to use higher order finite difference schemes to keep the prediction accuracy.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.125-138
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• 2003

Some Riccati type difference inequalities are established for the second-order nonlinear difference equations with negative neutral term $\Delta$(a(n)$\Delta$(x(n) - px(n-$\tau$))) + f(n, x($\sigma$(n))) = 0 using these inequalities we obtain some oscillation criteria for the above equation.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.473-481
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• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.593-610
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• 2023

In view of Nevanlinna theory, we investigate the meromorphic solutions of q-difference differential equations and our results give the estimates about counting function and proximity function of meromorphic solutions to these equations. In addition, some interesting results are obtained for two general equations and a class of system of q-difference differential equations.

• Journal of Korea Water Resources Association
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• v.50 no.12
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• pp.863-875
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• 2017

In this study, the effects of potential evapotranspiration method on drought index results were evaluated using SC-PDSI. Monthly heat index method, Penman-Monteith method, and Hargreaves equation were used as potential evapotranspiration method. SC-PDSI was calculated using three potential evapotranspiration method at 56 stations and compared the results. As a result, it was confirmed that the results by Penman-Monteith method and Hargreaves equation showed similar SC-PDSI calculation results without much difference, and the result by monthly heat index method showed a relatively large difference. It was confirmed that the results of SC-PDSI and drought situation judgment for the period of spring and winter season showed a big difference by the month. In conclusion, when calculating PDSI in Korea, using Penman-Monteith method and Hargreaves equation will be able to express the drought situation well.

• Proceedings of the Korea Concrete Institute Conference
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• 1992.10a
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• pp.155-160
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• 1992

In this study , the size effect on diagonal shear failure of reinforced high strength concrete beams was investigated, For this purpose, ten singly reinforced high strength concrete beams without web reinforcement were tested for five different dimensions of effective depth which were varied from 67mm to 915mm. The compressive strength of concrete used in this study was 53.7 MPa. One type of reinforcing bar with nominal yield strength of 400 MPa was used. Test results were analyzed and compared with strength predicted by ACI code equation, Zutty's equation and Bazant &Kim's equation. As the results, ACI code equation was seriously unconservative for beams with d of 915mm. Bazant & Kim's equation predicted well the trend of test data. Within the scope of this study, there was no clear difference in size effect with variation of compressive strength of concrete.