• 충청수학회지
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• 제7권1호
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• pp.123-139
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• 1994

In this paper we are concerned with optimal control problems whose costs are quadratic and whose states are governed by linear delay differential equations and general boundary conditions. The basic new idea of this paper is to introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• 경영과학
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• 제29권2호
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• pp.143-155
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• 2012

The purpose of this study is to formulate and solve the scheduling problem to heat-treatment process in forging process and apply it to industries. Heat-treatment is a common process in manufacturing heavy forged products in ship engines and wind power generators. Total complete time of the schedule depends on how to group parts and assign them into heat furnace. Efficient operation of heat-treatment process increases the productivity of whole production system while scheduling the parts into heat-treatment furnace is a combinatorial problem which is known as an NP-hard problem. So the scheduling, on manufacturing site, relies on engineers' experience. To improve heat-treatment process schedule, this study formulated it into an MIP mathematical model which minimizes total complete time. Three methods were applied to example problems and the results were compared to each other. In case of small problems, optimal solutions were easily found. In case of big problems, feasible solutions were found and that feasible solutions were very close to lower bound of the solutions. ILOG OPL Studio 5.5 was used in this study.

• Biotechnology and Bioprocess Engineering:BBE
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• 제4권1호
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• pp.51-58
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• 1999

A mathematical model for a three phase fluidized bed bioreactor (TFBBR) was proposed to describe oxygen utilization rate, biomass concentration and the removal efficiency of Chemical Oxygen Demand (COD) in wastewater treatment. The model consisted of the biofilm model to describe the oxygen uptake rate and the hydraulic model to describe flow characteristics to cause the oxygen distribution in the reactor. The biofilm model represented the oxygen uptake rate by individual bioparticle and the hydrodynamics of fluids presented an axial dispersion flow with back mixing in the liquid phase and a plug flow in the gas phase. The difference of setting velocity along the column height due to the distributions of size and number of bioparticle was considered. The proposed model was able to predict the biomass concentration and the dissolved oxygen concentration along the column height. The removal efficiency of COD was calculated based on the oxygen consumption amounts that were obtained from the dissolved oxygen concentration. The predicted oxygen concentration by the proposed model agreed reasonably well with experimental measurement in a TFBBR. The effects of various operating parameters on the oxygen concentration were simulated based on the proposed model. The media size and media density affected the performance of a TFBBR. The dissolved oxygen concentration was significantly affected by the superficial liquid velocity but the removal efficiency of COD was significantly affected by the superficial gas velocity.

• 한국수학교육학회지시리즈A:수학교육
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• 제40권1호
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• pp.15-25
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• 2001

The purpose of this thesis is to search the situation of an outbreak of the fallacy and methods of its treatment. We regard intuition as origins of genuine knowledge, but it sometimes raises the fallacy by intrinsic characters of itself. It makes an examination of the fallacy of the sense of sight like an optical illusion to instance that of sense. The sense of sight is an important factor in an intuitive cognition. However, its activity without thinking raises the fallacy of intuition in the process to observe and judge the things. I point out the fallacy of intuition which originates from terms and concepts in mathematical problems. The concept of mean velocity is representative. In this case, students make a mistake which means velocity can be solved by dividing the sum of v$_1$ and v$_2$ into two. The methods which overcome the fallacy of intuition are balance of intuition and logic, overcome of functional fixedness, the development of intuitive models and the development of metacognitive ability.

• 대한수의학회지
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• 제60권1호
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• pp.15-18
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• 2020

Canine heartworm disease is a vector-borne disease that is transmitted from dog to dog by mosquitoes. It causes epidemics that disrupt the health environments of dogs and are burdensome for many dog owners. Recent trends of changing temperatures and weather conditions in South Korea may have an impact on the population of mosquitoes, and it affects the population of dogs at risk of heartworm infection. Mathematical modeling has become an important measure for analyzing the epidemiological characteristics of infectious diseases. However, canine heartworm infection transmission has not been reported yet through mathematical modeling. We develop a mathematical model of canine heartworm infection to predict the population of infected dogs depending on the vector (mosquito) population using a susceptible, exposed, infected, and recovered model. Simulation results show that after 1 year, 3,289 dogs out of 73,602 (about 4.5%) are exposed and 134 (about 0.2%) are infected. Only 0.2% of susceptible dogs become infected after 1 year. However, if all exposed dogs are maintained in the same circumstances without any treatment, then the number of infected subjects will increase over time. This may increase the possibility of other dogs, especially dogs that live outside, being infected.

• East Asian mathematical journal
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• 제40권2호
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• pp.149-166
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• 2024

This study is to establish the domains and the standards of instructional evaluation on the teacher knowledge dealing with the knowledge of 'teaching and learning methods and assessment'. Especially, in this study, the instruction assessment standards are developed focused on the five types of mathematics competencies such as problem solving, communication, reasoning, connection, information and handling, which were emphasized in the mathematical curriculum revised in 2022. By the result, ten domains such as an instruction involving instruction goal and content, problem-solving competency, data treatment competency, learners' achievement level and attitude, communication competency, reasoning competency, connection competency, the assessment method and procedure based on the competency, the assessment tool development based on the competency, assessment result based on the competency were new established. According to those domains, the total 20 instructional evaluation standards were developed. This study is limited to consider the domain of 'teaching and learning methods and assessment' among the domains of teacher knowledge, while dealing with the elements of mathematics competencies in the standards. However, instructional evaluation standards reflecting these competencies should be developed in the other diverse domains of teacher knowledge.

• Coupled systems mechanics
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• 제8권6호
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• pp.489-500
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• 2019

With drinking water standards becoming more rigorous and increasing demands for additional water quantities, while water resources are becoming more polluted, mathematical models became an important tool to improve water treatment processes performance in the water supply system. Water treatment processes models reflect the knowledge of the processes and they are useful tools for water treatment process optimization, design, operator training for decision making and fundamental research. Unfortunately, in the current practice of drinking-water production and distribution, water treatment processes modeling is not successfully applied. This article presents a review of some existing water treatment processes simulators and the experience of their application and indicating the main weak points of each process. Also, new approaches in the modeling of water treatment are presented and recommendations are given for the work in the future.

• 환경위생공학
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• 제15권1호
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• pp.14-24
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• 2000

The water treatment by ozone was performed to remove VOC and organic substances in the multistage ozone contactor. This paper is secondary paper about the theme of ozone treatment since the first paper (Kor. Sanitary J., 15, 1(2000)) publicized, it was compared experimental results with theoretical those which were derived from the mathematical model associated with chemical reactions and mass transfer. Basic designing factors were determined as an optimal conditions for the removal rate of VOCs as follows: ozone input concentration in the contactor was 2mg/L, ozone contact time was 7 min and number of contactor was three-layered.

• Coupled systems mechanics
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• 제4권2호
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• pp.157-172
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• 2015

Control of potable water treatment plant (PWTP) is nowadays based on experience. The aim of this article is to show that model based control of treatment process is more efficient than process operation based on experience. Stimela environment is used for modeling of processes of potable water treatment. Application of the model was conducted on PWTP "Crkvice" in Zenica (BiH). This plant has used conventional rapid sand filters. By effective application of the model it is determined the optimal filter run time for different input turbidity of raw water. This results in the possibility of reducing the consumption of backwashing water, lower costs for its pumping and reducing the amount of coagulants. In the existing practice, based on experience, these benefits are not used.

• 한국초지조사료학회지
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• 제37권4호
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• pp.350-357
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• 2017

Near infrared spectroscopy (NIRS) is a rapid and accurate method for analyzing the quality of cereals, and dried animal forage. However, one limitation of this method is its inability to measure fermentation parameters in dried and ground samples because they are volatile, and therefore, respectively lost during the drying process. In order to overcome this limitation, in this study, fresh coarse haylage was used to test the potential of NIRS to accurately determine chemical composition and fermentation parameters. Fresh coarse Italian ryegrass haylage samples were scanned at 1 nm intervals over a wavelength range of 680 to 2500 nm, and optical data were recorded as log 1/reflectance. Spectral data, together with first- and second-order derivatives, were analyzed using partial least squares (PLS) multivariate regressions; scatter correction procedures (standard normal variate and detrend) were used in order to reduce the effect of extraneous noise. Optimum calibrations were selected based on their low standard error of cross validation (SECV) values. Further, ratio of performance deviation, obtained by dividing the standard deviation of reference values by SECV values, was used to evaluate the reliability of predictive models. Our results showed that the NIRS method can predict chemical constituents accurately (correlation coefficient of cross validation, $R_{cv}^2$, ranged from 0.76 to 0.97); the exception to this result was crude ash ($R_{cv}^2=0.49$ and RPD = 2.09). Comparison of mathematical treatments for raw spectra showed that second-order derivatives yielded better predictions than first-order derivatives. The best mathematical treatment for DM, ADF, and NDF, respectively was 2, 16, 16, whereas the best mathematical treatment for CP and crude ash, respectively was 2, 8, 8. The calibration models for fermentation parameters had low predictive accuracy for acetic, propionic, and butyric acids (RPD < 2.5). However, pH, and lactic and total acids were predicted with considerable accuracy ($R_{cv}^2$ 0.73 to 0.78; RPD values exceeded 2.5), and the best mathematical treatment for them was 1, 8, 8. Our findings show that, when fresh haylage is used, NIRS-based calibrations are reliable for the prediction of haylage characteristics, and therefore useful for the assessment of the forage quality.