• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.319-339
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• 2014

Recently, the discussion about division and partition of fraction increases in Korea's national curriculum documents. There are varieties of assertions arranging from the opinion that both interpretations are unintelligible to the opinion that both interpretations are intelligible. In this paper, we investigated a possibility that division and partition interpretation of fraction become valid. As a result, it is appeared that division and partition interpretation of fraction can be defined reasonably through expansion of interpretation of natural number. Besides, division and partition interpretation of fraction can be work in activity, such as constructing equation from sentence problem, or such as proving algorithm of fraction division.

• Education of Primary School Mathematics
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• v.22 no.2
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• pp.113-127
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• 2019

The purpose of this study is to justify the fraction division algorithm in elementary mathematics by applying the definition of natural number division to fraction division. First, we studied the contents which need to be taken into consideration in teaching fraction division in elementary mathematics and suggested the criteria. Based on this research, we examined whether the previous methods which are used to derive the standard algorithm are appropriate for the course of introducing the fraction division. Next, we defined division in fraction and suggested the unit-circle partition model and the square partition model which can visualize the definition. Finally, we confirmed that the standard algorithm of fraction division in both partition and measurement is naturally derived through these models.

• Journal of the Korean Home Economics Association
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• v.40 no.12
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• pp.159-170
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• 2002

This study, with a view to establishing the objective and concrete methodology of partition of properly by the married couple in the process of divorce, is to suggest the calculation method of impartial division of property by means of applying the system to division of remainder used in Germany. Generally, the process of estimating the amount of partitioned property has two steps, the first of which is to calculate the remainder of the husband and the wife each. The second step is to compare the remainders of the couple and calculate the difference in order for the spouse who has more to claim the payment of a half of the difference. This method has the advantage of dividing impartially the remainder obtained by labor in the married life.

• Bulletin of the Korean Chemical Society
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• v.5 no.4
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• pp.145-149
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• 1984

The entropy and heat capacity are calculated for the Morse oscillator model in order to test the quality of the partition function recently deduced by two of us. It is found that these analytical expressions are more reliable than the usually accepted one and give better results in the calculation of thermodynamic properties.

• Korean Journal of Soil Science and Fertilizer
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• v.36 no.4
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• pp.200-209
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• 2003

Distribution coefficient ($K_d$) is an universal parameter estimating cadmium partition for a soil-water-crop system in agricultural lands. This study was performed to find some factors affecting soil-water partition coefficients for cadmium in some Korean soils. The distribution coefficients ($K_d$) of cadmium for the 15 series of agricultural soils were measured at quasi-steady state in the pH ranges from 2 to 11. The adsorption data of the selected soils showed a linear relationship between log $K_d$ and pH, which was well agreed with theoretically expected results ; $log\;K_d=0.6339pH+0.5532(r^2=0.70^{**})$. Normalization of the partition coefficients were performed in a range of pH 3.5 ~ 8.5 to minimize adverse effects of Al dissolution, cationic competition, and organic matter dissolution. The $K_d$-om, partition coefficients normalized for organic matter, improved this linearity to the pH of soils. The values of $K_d$-om measured from the field samples were significantly correlated with those of $K_d$ predicted from the sorption-edge experimental data ($r^2=0.68^{**}$).

• Macromolecular Research
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• v.15 no.7
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• pp.682-687
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• 2007

The equation of state developed herein is predicated on a hard-sphere reference with perturbations introduced via a potential function to account for electrostatic forces and for attraction between protein particles. During this process, the generalized Lennard-Jones (GLJ) pair potential function is employed. The GLJ pair potential function is employed to represent the protein-protein interaction in two-protein systems. Via the use of the relation between the equation of state and the chemical potential, the phase behavior in the aqueous two-protein system can be estimated. The partition coefficients can be obtained via these processes. The calculated values of the coefficients agree fairly well with the experimental data in the given pH and ionic strength range, with no additional adjustable model parameters.

• Environmental Analysis Health and Toxicology
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• v.20 no.4 s.51
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• pp.351-358
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• 2005

The n -octanol/water partition coefficient (Pow) is one of the most important parameters employed for estimating a chemiral's environmental fate and toxicity. The shake-flask method, one direct experimental method, i.1 prone to experimental artifacts for highly hydrophobic compounds. Thus, a valid method for direct determination of the Pow of highly hydrophobic compounds is needed. The slow -stirring method has been demonstrated to provide reliable log Pow data to log Pow greater than 5. This study was performed to evaluate the accuracy of slow- stirring experiment for determination of log Pow, particularly for highly hydrophobic compounds. 1, 2, 3, 4-tetrachlorobenzene, hexachlorobezene, 2, 2', 3, 3', 5, 5', 6, 6'-octachlorobiphenyl, decachlorobiphenyl, and p, p'-DDT (4.5$\times$0.02, 5.41$\times$0.06, 7.26$\times$0.04, 7.87$\times$0.10, and 6.03$\times$0.06, respectively. The octanol/water partition coefficient by the slow-stirring method were very similar to the literature values. These results indicate that the slow- stirring method allows for reliable determination of log Pow of highly hydrophobic chemicals.

• Education of Primary School Mathematics
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• v.27 no.1
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• pp.91-110
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• 2024

The purpose of this study is to explore visual models for deriving the fractional division algorithm, to see how students understand this integrated model, the rectangular partition model, when taught in elementary school classrooms, and how they structure relationships between fractional division situations. The conclusions obtained through this study are as follows. First, in order to remind the reason for multiplying the reciprocal of the divisor or the meaning of the reciprocal, it is necessary to explain the calculation process by interpreting the fraction division formula as the context of a measurement division or the context of the determination of a unit rate. Second, the rectangular partition model can complement the detour or inappropriate parts that appear in the existing model when interpreting the fraction division formula as the context of a measurement division, and can be said to be an appropriate model for deriving the standard algorithm from the problem of the context of the inverse of a Cartesian product. Third, in the context the inverse of a Cartesian product, the rectangular partition model can naturally reveal the calculation process in the context of a measurement division and the context of the determination of a unit rate, and can show why one division formula can have two interpretations, so it can be used as an integrated model.

• Korean Journal of Heritage: History & Science
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• v.55 no.4
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• pp.196-209
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• 2022

This study compared and analyzed the spatial division function and role of partitions by comparing the entire space and the spatial changes before and after the installation of partitions in <Donggwoldo>, which was manufactured in the late Joseon Dynasty. As a research method, a set standard was prepared to decompose the space of <Donggwoldo> into a unit space, and the standard was set according to the role and height of the space by classifying it into a main space, sub space, and transition space. Two convex maps were prepared according to before and after the installation of the Panjang, and the values of connectivity, control, and integration, which are spatial syntax variables, were calculated and analyzed. The results of the study are as follows. First, the partition in <Donggwoldo(東闕圖)> did not affect the overall spatial arrangement and control or connection of Donggwol, but the movement and access of space is limited to specific areas. Second, the partition was a facility intensively distributed in Naejeon(內殿) and Donggung(東宮) to be used actively in the way of space utilization. It shows that the unit space increased rapidly due to the installation of the partition. Since the partition was installed in the spaces that were open and under high control in the case of Naejeon(內殿), it helped to secure private spaces as closed ones under low control. On the other hand, for Donggung(東宮), the spaces were compartmented and divided with the partition to guide the movement path through narrow gates of the partition and increase the depth of the space. This helped to create spaces that are free and can be hidden as it increased the number of spaces coming through. Third, In addition to the functions of "eye blocking, space division, and movement path control" revealed in prior research, the partition has created a "space that is easy to control" within a specific area. The installation of the partition reduced the scale through the separation of spaces, but it occurred the expansion of the movement path and space. Also, the partition functioned to strengthen hiding and closure or increase openness as well through space division. This study is significant in that it revealed the value of the spatial control function of panjang through the analysis of spatial control and depth by analyzing the function of the partition with a mathematical model in addition to the analysis and study of the function and role of panjang. In addition, it is valuable in that it has prepared a framework for analysis tools that can be applied to traditional residential complexes similar to palaces by applying space syntax to <Donggungdo> to create convex spaces according to unit space division and connection types of palace architecture and landscape elements.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.657-659
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• 1998

In order to optimize fuzzy modeling of nonlinear system, we proposed a optimal fuzzy model according to the characteristic of I/O relationship, HCM method, the genetic algorithm, and the objective function with weighting factor. A conventional fuzzy model has difficulty in definition of membership function. In order to solve its problem, the premise structure of the proposed fuzzy model is selected by both the partition of input space and the analysis of input-output relationship using the clustering algorithm. The premise parameters of the fuzzy model are optimized respectively by the genetic algorithm and the consequence parameters of the fuzzy model are identified by the standard least square method. Also, the objective function with weighting factor is proposed to achieve a balance between the performance results for the training and testing data.