• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.1-25
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• 2013

In this paper we have developed a mathematical model of alcohol abuse. It consists of four compartments corresponding to four population classes, namely, moderate and occasional drinkers, heavy drinkers, drinkers in treatment and temporarily recovered class. Basic reproduction number $R_0$ has been determined. Sensitivity analysis of $R_0$ identifies ${\beta}_1$, the transmission coefficient from moderate and occasional drinker to heavy drinker, as the most useful parameter to target for the reduction of $R_0$. The model is locally asymptotically stable at disease free or problem free equilibrium (DFE) $E_0$ when $R_0$ < 1. It is found that, when $R_0$ = 1, a backward bifurcation can occur and when $R_0$ > 1, the endemic equilibrium $E^*$ becomes stable. Further analysis gives the global asymptotic stability of DFE. Our aim of this analysis is to identify the parameters of interest for further study with a view for informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.

• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.119-132
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• 2022

Virotherapy is an effective method for the treatment of cancer. The oncolytic virus specifically infects the lyse cancer cell without harming normal cells. There is a time delay between the time of interaction of the virus with the tumor cells and the time when the tumor cells become infectious and produce new virus particles. Several types of viruses are used in virotherapy and the delay varies with the type of virus. This delay can play an important role in the success of virotherapy. Our present study is to explore the impact of this delay in cancer virotherapy through a mathematical model based on delay differential equations. The partial success of virotherapy is guarenteed when one gets a stable non-trivial equilibrium with a low level of tumor cells. There exits Hopf-bifurcation by considering the delay as bifurcation parameter. We have estimated the length of delay which preserves the stability of the non-trivial equilibrium point. So when the delay is less than a threshold value, we can predict partial success of virotherapy for suitable sets of parameters. Here numerical simulations are also performed to support the analytical findings.

• 제어로봇시스템학회논문지
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• 제10권6호
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• pp.475-486
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• 2004

The interaction of HIV and human immune system was studied in the perspective of dynamics. We summarized the recent researches on drug scheduling using optimal control theory for HIV treatment. The drug treatment to make immune system to work properly is investigated based on mathematical models including memory CTLp. In the simulation results, it was verified that stopping medication after a certain period of treatment can lead a patient to be cured naturally by one s immune system. Also, we summarized and categorized the advantages and disadvantages of each HIV drug scheduling method. In conclusion, model-based predictive control is more efficient for making decision of drug dose than other methods, when there exist uncertainties on model parameters or state variables.

• 제어로봇시스템학회논문지
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• 제15권5호
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• pp.555-561
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• 2009

The established mathematical modeling methods have limitation to know the hydraulic characteristics at the wastewater treatment plant which are complex and nonlinear systems. So, an artificial neural network (ANN) model based on hydraulic characteristics is applied for modeling wastewater quality of a full-scale wastewater treatment plant using DNR (Daewoo nutrient removal) process. ANN was trained using data which are influents (TSS, BOD, COD, TN, TP) and effluents (COD, TN, TP) components in a year, and predicted the effluent results based on the training. To raise the efficiency of prediction, inputs of ANN are added the influent and effluent information that are in yesterday and the day before yesterday. The results of training data tend to have high accuracy between real value and predicted value, but test data tend to have lower accuracy. However, the more hydraulic characteristics are considered, the results become more accuracy.

• 열처리공학회지
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• 제32권1호
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• pp.17-28
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• 2019

Jominy hardenability curves of low alloy steel containing less than 5 wt.% of alloying elements in total were calculated by applying Scheil's rule of additivity to pre-calculated isothermal transformation curve. Isothermal transformation curve for each phase in steel was approximated as a simple mathematical equation by using Kirkaldy's approach and all coefficients in the equation were estimated from experimental temperature-time-transformation (TTT) and/or continuous cooling transformation (CCT) data in the literature. Then jominy test with simple boundary conditions was performed in computer by applying the finite difference scheme. The resultant cooling curves at each location along a longitudinal direction of Jominy bar were applied to calculate phase fractions as well as mechanical properties such as micro Vickers hardness. The simulated results were compared with experimental CCT data and Jominy curves in the literature.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권4호
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• pp.509-524
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• 2014

This study was to investigate the types of errors and the frequency of errors to understand students' solving process on the descriptive items with the students of an excellent high school which located in a non-leveling local school district of Gyunggi Province. All 11 items were developed in the equation of a circle and 120 students who attended this high school participated in solving them. The result showed a tendency as follows: Logically invalid inference(Type A, 38.83%) of errors, Omission error of the problem solving process(Type B, 25%), Technical error(Type C, 15.67%), Wrong conclusion(Type D, 11.94%), Use of wrong theorem(Type E, 5.97%), and Use of wrong picture(Type F, 2.61%). The logically invalid inference the students showed with a largest tendency was made because of the lack of reflection. This meant that this error could be corrected in a little treatment of carefulness.

• 상하수도학회지
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• 제24권4호
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• pp.387-394
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• 2010

The influent COD of municipal wastewater has been divided into 4 fractions; readily soluble biodegradable, slowly particulate biodegradable, soluble and particulate unbiodegradable COD. The mathematical modeling of biological wastewater treatment processes and the design and operation of nutrient removal plants require a reliable and accurate estimate of the composition of influent wastewater COD. COD utilization rate is proportional to the oxygen uptake rate(OUR), so a batch biodegradation test with OUR measurement has been effectively used for the determination of COD fractionation. But the mathematical model of COD utilization and heterotrophs synthesis is essential to interpret the OUR measurement. Mamais method is another method for determining readily biodegradable soluble COD. Like the OUR test method, batch biodegradation test is necessary but it does not require mathematical model. These two methods for determining COD fractionation are introduced here in detail. Experimental results showed that COD composition by Mamais method is not different to that by OUR test method so, either of them can be used.

• Tuberculosis and Respiratory Diseases
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• 제86권4호
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• pp.251-263
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• 2023

The stethoscope has long been used for the examination of patients, but the importance of auscultation has declined due to its several limitations and the development of other diagnostic tools. However, auscultation is still recognized as a primary diagnostic device because it is non-invasive and provides valuable information in real-time. To supplement the limitations of existing stethoscopes, digital stethoscopes with machine learning (ML) algorithms have been developed. Thus, now we can record and share respiratory sounds and artificial intelligence (AI)-assisted auscultation using ML algorithms distinguishes the type of sounds. Recently, the demands for remote care and non-face-to-face treatment diseases requiring isolation such as coronavirus disease 2019 (COVID-19) infection increased. To address these problems, wireless and wearable stethoscopes are being developed with the advances in battery technology and integrated sensors. This review provides the history of the stethoscope and classification of respiratory sounds, describes ML algorithms, and introduces new auscultation methods based on AI-assisted analysis and wireless or wearable stethoscopes.

• 한국식품과학회지
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• 제24권5호
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• pp.408-413
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• 1992

신속간편법으로서 식품의 성분함량 측정에 이용되는 근적외 반사분광분석에서 문제가 되고 있는 시료의 균질도의 차이가 흡광도에 미치는 영향을 조사하고 흡광도로 나타난 수치를 수학적으로 처리함으로써 예측의 오차는 다음과 같이 감소하였다. 1. 세절도가 일정한 시료의 흡광도를 무변형, 1차 미분 및 2차 미분하여 calibration한 후 세절도가 다양한 시료의 성분을 예측한 결과 예측오차(standard error of prediction)는 수분함량에 있어서 1.478%, 0.658% 및 0.580%, 지방함량의 예측오차 0.949%, 0.637%, 및 0.527%이었으며 단백질 측정시 각각 0.514%, 0.493% 및 0.394%로 2차 미분의 예측오차가 모든 성분측정에서 가장 낮음을 알 수 있었다. 2. 세절도가 다양한 시료의 무변형, 1차 미분 및 2차 미분처리한 calibration을 이용하여 세절도가 다양한 시료의 성분을 예측한 결과 수분함량 예측오차는 각각 1.026%, 0.589% 및 0.568%, 지방함량 예측오차는 각각 0.828%, 0.639% 및 0.602% 이었으며 단백질함량 예측오차는 0.860%, 0.557% 및 0.399%로서 역시 2차 미분, 1차 미분, 무변형의 순으로 정확성이 높았다. 결과를 종합할 때 흡광도를 수학적으로 처리하여 calibration에 이용하므로서 calibration시료의 세절도에 관계없이 측정결과의 정확성은 높아졌다.

• 상하수도학회지
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• 제28권6호
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• pp.735-745
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• 2014

This paper presents PKES(PuKyung -Excel based Simulator) for WWTPs(wastewater treatment plants) by using MS Excel and VBA(Visual Basic for Application). PKES is a user-friendly simulator for the design and optimization of the whole plant including biological and physico-chemical processes for the wastewater and sludge treatment. PKES calculates the performance under steady or dynamic state and allows changing the mathematical model by the user. Mathematical model implemented in PKES is a improved integration model based on ASM2d and ADM1 for simulation of AS(activated sludge) and AD(anaerobic digestion). Gaseous components of $N_2$, $N_2O$, $CO_2$ and $CH_4$ are added for estimation of GHGs(greenhouse gases) emission. The simulation results for comparison between PKES and Aquasim(EAWAG) showed about the same effluent concentrations. As a result of verification using by measured data of BOD, TSS, TN and TP for 2 years of operation, calculated effluent concentrations were similar to measured effluent concentrations. The values of average RMSE(root mean square error) were 1.9, 0.8, 1.6 and 0.2 mg/L for BOD, TSS, TN and TP, respectively. Total GHGs emission of WWTP calculated by PKES was 138.5 ton-$CO_2$/day and GHGs emissions of $N_2O$, $CO_2$ and $CH_4$ were calculated at 21.7, 28.9 and 87.9 ton-$CO_2$/day, respectively. GHGs emission of activated sludge was 32.5 % and that of anaerobic digestion was 67.5 %.