• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.695-708
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• 2024

In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.25-45
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• 2022

In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.629-645
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• 2020

A uniformly convergent numerical method is developed for solving singularly perturbed 1-D parabolic convection-diffusion problems. The developed method applies a non-standard finite difference method for the spatial derivative discretization and uses the implicit Runge-Kutta method for the semi-discrete scheme. The convergence of the method is analyzed, and it is shown to be first order convergent. To validate the applicability of the proposed method two model examples are considered and solved for different perturbation parameters and mesh sizes. The numerical and experimental results agree well with the theoretical findings.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.623-641
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• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• Wind and Structures
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• v.5 no.2_3_4
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• pp.317-328
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• 2002

A numerical investigation on the turbulent flows over a three-dimensional steep hill is presented. The numerical model developed for the present work is based on the finite volume method and the SIMPLE algorithm with a non-staggered grid system. Standard $k-{\varepsilon}$ model and Shih's non-linear model are tested for the validation of the prediction accuracy in the 3D separated flow. Comparisons of the mean velocity and turbulence profiles between the numerical predictions and the measurements show good agreement. The Shih's non-linear model is found to predict mean flow and turbulence better than the Standard $k-{\varepsilon}$. Flow patterns have also been examined to explain the difference in the cavity zone between 2D and 3D hills.

• Journal of the Korea Safety Management & Science
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• v.3 no.3
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• pp.175-190
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• 2001

We propose, a new process capability index $C_{psk}$(WV) applying the weighted variance control charting method for non-normally distributed. The main idea of the weighted variance method(WVM) is to divide a skewed or asymmetric distribution into two normal distributions from its mean to create two new distributions which have the same mean but different standard deviations. In this paper we propose an example, a distributions generated from the Johnson family of distributions, to demonstrate how the weighted variance-based process capability indices perform in comparison with another two non-normal methods, namely the Clements and the Wright methods. This example shows that the weighted valiance-based indices are more consistent than the other two methods in terms of sensitivity to departure to the process mean/median from the target value for non-normal processes. Second method show using the percentage nonconforming by the Pearson, Johnson and Burr systems. This example shows a little difference between the Pearson system and Burr system, but Johnson system underestimated than the two systems for process capability.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.10 no.16
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• pp.183-195
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• 1987

The effectiveness of quality control is contingent to adaptability to the present circumstance. The objectives of this study are to provide empirical data to carry out qualify control effectively. To accomplish this purpose, an empirical study was made by questionaire (mailing survey method, Feb. to Mar. in 1987). The sample is the 167 companies in Korean manufacturing industry. The main findings out of the analysis are as follows the stage of quality control is concentrated in appraisal phase, the company standard is equiped gradually in non-KS marked company and the need of economic evaluation about quality control is increased gradually. With a view to analysing of relationship between quality control and it's effect factors (company standard, KS mark, computer based information system), the methods of $\chi$$^2$ test are used. The company standard have a significant difference in top manager's altitude to duality control, operation stage of quality control. operation scope of qualify control and quality budgeting system but is insignificant with economic evaluation about duality control. Otherwise, KS mark is insignificant with the equality control activity except for operation scope. The quality information system based in computer have a significant difference in operation stage, operation scope and economic evaluation. Therefor, for the purpose of attaining effectiveness of quality control through the economic evaluation about quality control, the company standard and computer based duality information system must be utilized in quality control activity.

• Journal of Korean Academy of Fundamentals of Nursing
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• v.6 no.3
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• pp.359-368
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• 1999

Background : The purpose of this study was to determine whether cleansing the perineum and urethral meatus and using midstream urine affect the rate of bacterial contamination of urine specimens, and to determine the optimum urine collection method. We studied 41 asymptomatic healthy nursing school students. Women who were menstruating were not excluded from this study. Method : The first and midstream urine samples were collected during consecutive urinationsby each woman. The first sample was not a clean-catch specimen, and the second one was a clean-catch specimen. Both specimens were studied by urinalysis and bacterial culture with standard methods. Results : 41 women met the study criteria and 39 successfully completed the study. None of the urine cultures were positive. 68.3% of the non clean-catch first urine cultures, 53.7% of the non clean-catch midstream cultures, 33.3% of the first clean-catch urine culteres and 30.8% of the midstream clean-catch urine were found to be contaminated. There was a significant difference in the bacterial contamination rates between the first and midstream urine, and the clean-catch and non clean-catch urine(p=0.035, p =0.001 respectively). On urinalysis, 7.3% of the non clean-catch first urine, 7.3% of the non clean-catch midstream urine, 2.6% of the clean-catch first urine and 2.6% of clean-catch midstream urine were found to be above grade 2. Conclusions : According to our results, the bacterial contamination rate was the lowest in midstream and clean catch urine specimens. Threrfore it is recommended that the midstream clean-catch technique is the standard practice for collecting urine specimens for bacterial culture in women.

• Journal of Information Processing Systems
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• v.19 no.4
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• pp.527-539
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• 2023

In the positioning algorithm of two-dimensional planar sensor array, the estimation error of time difference-ofarrival (TDOA) algorithm is difficult to avoid. Thus, how to achieve accurate positioning is a key problem of the positioning technology based on planar array. In this paper, a method of sensor reliability discrimination is proposed, which is the foundation for selecting positioning sensors with small error and excellent performance, simplifying algorithm, and improving positioning accuracy. Then, a positioning model is established. The estimation characteristics of the least square method are fully utilized to calculate and fuse the positioning results, and the non-uniform weighting method is used to correct the weighting factors. It effectively handles the decreased positioning accuracy due to measurement errors, and ensures that the algorithm performance is improved significantly. Finally, the characteristics of the improved algorithm are compared with those of other algorithms. The experiment data demonstrate that the algorithm is better than the standard least square method and can improve the positioning accuracy effectively, which is suitable for vibration detection with large noise interference.

• Journal of radiological science and technology
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• v.42 no.5
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• pp.345-350
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• 2019

Liver biopsy is the gold standard for diagnosing liver fibrosis, but it is invasive and has a risk for complications. For this reason, recently, study has been actively conducted on non-invasive liver fibrosis evaluation method. But, there is no established standard for the type of diffuse liver disease. Therefore, this study was suggest the usefulness and cut-off values of Fibroscan, FIB-4, APRI and AAR of patients with hepatitis C in Korea. According to the diagnosis, 240 people in hepatitis C are classified into fatty liver, chronic hepatitis, and liver cirrhosis. The statistical analysis was performed by ANOVA to verify difference between groups. The ROC curve was analyzed to determine the usefulness and practical cut-off value. As a result, for all diseases, the AUC value for Fibroscan was 0.8 over and the APRI was 0.7 over. Cut-off value of serum based liver fibrosis markers was increased in order of fatty liver, chronic hepatitis and liver cirrhosis. If Fibroscan and serological liver fibrosis markers are applied to predict liver fibrosis, it is expected that excessive liver biopsy can be reduced.