• Journal of Radiation Protection and Research
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• v.36 no.1
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• pp.1-7
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• 2011

A simple mathematical model of simultaneous combined action of environmental agents has been proposed to describe the synergistic interaction of microwave and high ambient temperature treatment on animal heating. The model suggests that the synergism is caused by the additional effective damage arising from an interaction of sublesions induced by each agent. These sublesions are considered to be ineffective if each agent is taken individually. The additional damage results in a higher body temperature increment when compared with that expected for an independent action of each agent. The model was adjusted to describe the synergistic interaction, to determine its greatest value and the condition under which it can be achieved. The prediction of the model was shown to be consistent with experimental data on rabbit heating. The model appears to be appropriate and the conclusions are valid.

• Environmental Engineering Research
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• v.14 no.2
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• pp.71-78
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• 2009

A review of stormwater quantity and quality in the urban environment is presented. The review is presented in three parts. The first part reviews the mathematical methods for stormwater quantity and has been undertaken by examining a number of stormwater models that are in current use. The important feature of models, their applications, and management has been discussed. Different types of stormwater management models are presented in the literatures. Generally, all the models are simplified as conceptual or empirical depending on whether the model is based on physical laws or not. In both cases if any of the variables in the model are regarded as random variables having a probability distribution, then the model is stochastic model. Otherwise the model is deterministic (based on process descriptions). The analytical techniques are presented in this paper.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.05a
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• pp.1-16
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• 2006

The purpose of this study is to investigate how fifth and sixth graders recognize average and to find out suggestions for teaching/learning methods of average by examining which difference there is depending on the way of the word problem presentation. To solve these study questions, With the way of the word problem presentation set up as experimental treatment experiment was conducted to analyze these. In conclusion, since students who did not learn the regular course of average values had various informal concepts already, it is needed to consider handling more various concepts of average in order to enable students to expand flexible thoughts. And informal concepts of average students showed were the same or similar to types of formalized concepts and had logicality and propriety in their own way. Compared with fifth graders, sixth graders showed a wide difference in informal concepts of average depending on the way of the word problem presentation.

• East Asian mathematical journal
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• v.26 no.4
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• pp.463-485
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• 2010

The purpose of this paper is to investigate if the instruction using GSP to 4th graders for them to explore 'rectangles and making them' have an influence of understanding and retention of the knowledge, generation of the knowledge which is not dealt with during experimental treatment, and if they can reason based on what they have learned about it and about what has not been learned. According to the result from the data gained, learners in the experiment group show that they can retain, generate, reason better than ones in the comparison group.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.29-36
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• 2013

In the treatment of the sequential beta-protection procedure, we define the reasonable stopping time and investigate that for the stopping time Wijsman's requirements, coverage probability and beta-protection conditions, are satisfied in the estimation for the mean vector ${\mu}$ by the sample from the multivariate normal distributed population with unknown mean vector ${\mu}$ and a positive definite variance-covariance matrix ${\Sigma}$.

• The Mathematical Education
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• v.40 no.2
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• pp.291-315
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• 2001

There are some problems in the introduction of proof in middle school mathematics. Among the problems, one is the use of postulates and the another is the methods of proof how to connect a statement with others. The first case has been treated mainly in this note. Since proof means to state the reason logically why the statement is true on the basis of others which have already been known as true and basic properties, in order to prove logically, it is necessary to take the basic properties and the statement known already as true. But the students don't know well what are the basic properties and the statement known already as true for proving. No use of the term postulation(or axiom) cause the confusion to distinguish postulation and theorem. So they don't know which statements are accepted without proof or not accepted without proof, To solve this problems, it is necessary to use the term postulate in middle school mathematics. In middle school mathematics, we present same model of the introduction of proof which are used the postulates needed for the proof.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.281-295
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• 2023

This study aims to establish and analyze a mathematical model for the transmission dynamics of male adolescent smoking and to determine an optimal control strategy to reduce male adolescent smoking. We consider three groups in the population: smokers, non-smokers, and temporary nonsmokers. In our model to which optimal control theory was applied, the number of smokers decreased sharply and the number of non-smokers increased significantly. Our simulation results under various control scenarios reveal that integrated control measures(such as prevention, education, and treatment) may be necessary to reduce the growth rate of adolescent smoking. Moreover, we concluded that efforts to encourage current smokers and temporary quitters to quit should be sustained longer than efforts to reduce the rate at which nonsmokers become smokers through smoking prevention education.

• Environmental Engineering Research
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• v.20 no.4
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• pp.392-396
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• 2015

This work aims to investigate the oily wastewater treatment by the electrocoagulation-flotation (ECF) and propose a mathematical model for the efficiency prediction. Cutting oil was used to prepare the synthetic oily wastewater with submicron droplet sizes. The chemical coagulation by aluminium sulfate was firstly tested following by the electrocoagulation-flotation with aluminium electrodes. Both processes gave the effective treatment performance with the efficiencies higher than 90%. However, the ECF consumed less aluminium dosage as well as produced less sludge, which were its advantage on the chemical coagulation. The performance of the ECF was found to be affected by the current density, oil concentration, and reaction time according to the analysis by the design of experiment (DOE). Finally, the prediction model was proposed by two approaches, including linear and logarithm function. The latter model gave more accuracy prediction results in terms of treatment efficiency and duration in the lag and stable stages.

• Journal of Korean Society of Water and Wastewater
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• v.27 no.4
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• pp.457-468
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• 2013

Based on the activated sludge model(ASM), a mathematical model which represents the aerobic sludge digestion by sequencing batch reactor(SBR) combined with ultrasonic treatment was composed and performed in this study. Aerobic digestion using sequencing batch reactor(SBR) equipped with ultrasound treatment was also experimented for the purpose of parameter calibration. Most of the presented kinetic parameters in ASM or ASM2 could be used for the aerobic digestion of sludge but the parameters related in hydrolysis and decay rate needed modification. Hydrolysis rate constant of organic matter in aerobic condition was estimated at $0.3day^{-1}$ and the maximum growth rate for autotrophs in aerobic condition was $0.618day^{-1}$. Solubilization reactions of particulate organics and nitrogen by ultrasonication was added in this kinetic model. The solubilization rate is considered to be proportional to the specific energy which is defined by specific ultrasound power and sonication time. The solubilization rate constant by ultrasonication was estimated at $0.202(W/L)^{-1}day^{-1}$ in this study. Autotrophs as well as heterotrophs also decomposed by ultrasonic treatment and the nitrification reaction was limited by the lack of autotrophs accumulation in the digester.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.693-722
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• 2016

In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.