• Journal of the Korea Society for Simulation
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• v.21 no.2
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• pp.1-9
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• 2012

Subterranean termites forage by constructing tunnel networks in soil and encounter food resources during tunnel excavation. Some species of termites can travel up to 150 m underground. They often travel to the surface to find wood cellulose to feed their colony, which in turn causes extensive damage to wooden architecture, such as timber-frame houses. This type of damage has been constantly increasing along with global warming because higher temperatures provide an ecological niche for termites. The damage is closely related to termite territory size and distribution. Recently, as a way to research termite control, the necessity of a mathematical model to simulate termite territory formation in relation to damage has increased. So far, however, few studies have been conducted on the development of a model because it is difficult to quantify or characterize the relationship between territorial behavior and field conditions including complicated environmental factors. In the present study, we suggest a simulation model of the territoriality of the Formosan subterranean termites, Coptotermes formosanus (Shiraki), and Reticulitermes flavipes (Kollar), based on empirical data. The model consists of 2 procedures. One describes tunnel network growth for each colony, and the other represents territoriality based on tunnel-tunnel interactions between different colonies. Using the model, we show changes in territorial competition according to the termination probability of tunnel growth.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Steel and Composite Structures
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• v.16 no.6
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• pp.703-718
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• 2014

The initial clamping forces of high strength bolts subjected to different faying surface conditions drop within 500 hours regardless of loading, any other external force or loosening of the nut. This study develops a mathematical model for relaxation confined to creep on a coated faying surface after initial clamping. The quantitative model for estimating relaxation was derived from a regression analysis for the relation between the creep strain of the coated surface and the elapsed time for 744 hours. This study establishes an expected model for estimating the relaxation of bolted joints with diverse coated surfaces. The candidate bolts are dacro-coated tension control bolts, ASTM A490 bolt, and plain tension control bolts. The test parameters were coating thickness, species of coating. As for 96, 128, 168, and $226{\mu}m$ thick inorganic zinc, when the coating thickness was increased, relaxation after the initial clamping rose to a much higher range from 10% to 18% due to creep of the coating. The amount of relaxation up to 7 days exceeded 85% of the entire relaxation. From this result, the equation for creep strain can be derived from a statistical regression analysis. Based on the acquired creep behavior, it is expected that the clamping force reflecting relaxation after the elapse of constant time can be calculated from the initial clamping force. The manufacturer's recommendation of inorganic zinc on faying surface as $75{\mu}m$, appears to be reasonable.

• Journal of the Korean School Mathematics Society
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• v.15 no.2
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• pp.331-348
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• 2012

With a gradual increase in research on teaching and learning calculus, there have been various studies about students' thinking about the derivative. This paper reviews the results of the existing empirical studies published in Korean and English. These studies mainly have shown that how students think about the derivative is related to their understanding of the related concepts and the representations of the derivative. There are also recent studies that emphasize the importance of how students learn the derivative including different applications of the derivative in different disciplines. However, the current literature rarely addressed how students think about the derivative in terms of the language differences, e.g., in Korean and English. The different terms for the derivative at a point and the derivative of a function, which shows the relation between concepts, may be closely related to students' thinking of the derivative as a function. Future study on this topic may expand our understanding on the role language-specific terms play in students' learning of mathematical concepts.

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.1
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• pp.37-43
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• 2016

Recently, it is emphasized importance of family. The new family organize including husband and wife are created by caused marriage, they organize new family including wife's home and husband's home. As a result, they may experience about conflict or peace between new family and previous family. The research of family mainly have been studied in the social science side. However, because researchers of social science deals with linguistic emotion status, there is no mathematical modeling for family relationship. In this paper, one of the nonlinear research for social subject, we modify love model of Romeo and Juliet. Then we propose novel family relationship model for parent-in-law and daughter (or son)-in- law relation. We also confirm chaotic behavior or nonlinear behavior by time series and phase portrait.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.807-825
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• 2010

Educational interest has been paid to ADHD students. Because of being easily distracted, lacking concentration, and committing hyperactive acts, they lag much behind other students in academic grades and their teachers have many difficulties in teaching them. This study aims to provide a case of enhancing an ADHD student's fraction-related achievement. To do this, we investigated his mathematical abilities in a preliminary study, devised an individualized teaching for the fractions unit, and applied them to him. And analyzing the results from observations and interviews of the student we can induce the following results: First, the ADHD student showed such types of errors in relation to fraction as lack of the concept of dividing into equal parts, lack of the concept of numerator and denominator, and errors in adding or subtracting fractions anc mixed fractions whose denominators were the same. And secondly, the fraction-related achievements of the ADHD student have improved thanks to the systematic teaching plan based on the accurate understanding of his academic gap relative to other students, his learning attitude, and his time difference. In addition, this study suggests several implications for ADHD students' learning of fractions.

• Korean Journal of Food Science and Technology
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• v.12 no.4
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• pp.285-291
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• 1980

The hydration and cooking rate of two rice varieties, Akibare (Japonica) and Milyang 23 (Indica), were investigated in terms of mathematical rate equations. The hydration rate at temperatures of $10{\sim}40^{\circ}C$ was examined by weighing method. The absorption of liquid water by rice grain was directly proportional to the square root of the hydration time. The diffusion coefficient was given by the Arrhenius relation : $D=3.151{\times}10^{-3}\exp\;(-4000/RT)$ for Akibare and $D=5.853{\times}10^{-3}\exp\;(-5700/RT)$ for Milyang 23. Milyang 23 was cooked at a faster rate than Akibare. The activation energies for cooking were in the range of 18 000 cal/mole at $90{\sim}100^{\circ}C$ and 9,000cal/mole at $100{\sim}120^{\circ}C$. However, Milyang 23 showed slightly higher activation energy of cooking at $90{\sim}100^{\circ}C$. Adhesiveness and amylograph viscosities at all reference points for Milyang 23 were higher than those for Akibare.

• Education of Primary School Mathematics
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• v.14 no.3
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• pp.261-275
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• 2011

We observed the process for solving linear equations of two 5th grade elementary students, who do not have any pre-knowledge about solving linear equation. The way of students' usage of fractional schemes and manipulations are closely observed. The change of their scheme adaptation are carefully analyzed while the coefficients and constants become complicated. The results showed that they used various fractional scheme and manipulations according to the coefficients and constants. Noticeably, they used repeating fractional schemes to establish the equivalence relation between unknowns and the given quantities. After establishing the relationship, equivalent fractions played important role. We expect the results of this study would help shorten the gap between the arithmetic and the algebraic thinking.

• Applied Biological Chemistry
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• v.26 no.1
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• pp.1-7
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• 1983

The hydration of two japonica(Akibare and Milyang 15) and four indica(Milyang 30, Suweon 287, Suweon 294 and Iri 342) rice varieties was investigated in terms of mathematical rate equation. The hydration rate at temperatures of $4{\sim}32^{\circ}C$ was examined by a weighing method. The absorption of water was directly proportiponal to the square root of the hydration time(t) and was described by the diffusion equation: $1-\bar{M}=(2/\sqrt{\pi})(S/V)\;\sqrt{Dt},\;where\;\bar{M}$ is dimensionless moisture ratio, S/V is the surface-to-volume ratio and D is diffusion coefficient. The average D value was given by the Arrhenius relation: $D=D_0\;\exp(-E_a/TR)$. The activation energy was $4{\sim}5kcal/mole$. The rice samples could be classified into three groups based on hydration kinetics: Milyang 30-Suweon 287; Akibare-Milyang 15; and Suweon 294-Iri 342.

• Journal of the Korean Society of Hazard Mitigation
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• v.3 no.2 s.9
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• pp.119-125
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• 2003

Water flow in unsaturated soils is affected by two mathematical equations called soil water-characteristic curve and permeability-suction relationship. Soil water-characteristic curve is an equation showing volumetric water content-suction relationship. Many researchers have presented equations for the relationships. This paper illustrates the importance of correctly determining the two relationships when analyzing unsaturated water flows. Results from two methods, Gardner (1958) and Fredlund et al. (1994), are used for comparison purposes. Numerical simulations of water flow by finite element method are performed using the two methods. The results by the numerical simulations are compared with the field data which was obtained from time-domain reflectometry (TDR) probes in Delaware County, Ohio. This data was obtained by the Seasonal Instrumentation Program which is included as a part of the Strategic Highway Research Program (SHRP).