• The Mathematical Education
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• v.45 no.1 s.112
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• pp.61-74
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• 2006

The ability of understanding the number and number systems, grasping the properties of number systems, and manipulating number systems is the foundation to understand algebra. It is useful to deepen students' mathematical understanding of number systems and operations. The authentic understanding of numbers and operations can make it possible for the students to manipulate algebraic symbols, to represent relationship among sets of numbers, and to use variables to investigate the properties of sets of numbers. The high school students need to understand the number systems from more abstract perspective. The purpose of this study is to study on understanding and application ability of eleventh graders of basic properties of operations with real numbers.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1559-1568
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• 2015

The relative class number $H_d(f)$ of a real quadratic field $K=\mathbb{Q}(\sqrt{m})$ of discriminant d is the ratio of class numbers of $O_f$ and $O_K$, where $O_K$ denotes the ring of integers of K and $O_f$ is the order of conductor f given by $\mathbb{Z}+fO_K$. In a recent paper of A. Furness and E. A. Parker the relative class number of $\mathbb{Q}(\sqrt{m})$ has been investigated using continued fraction in the special case when $(\sqrt{m})$ has a diagonal form. Here, we extend their result and show that there exists a conductor f of relative class number 1 when the continued fraction of $(\sqrt{m})$ is non-diagonal of period 4 or 5. We also show that there exist infinitely many real quadratic fields with any power of 2 as relative class number if there are infinitely many Mersenne primes.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.427-429
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• 2005

This paper presents the use of Point Number Algorithm (PNA) for real-time image processing for position identification of mobile robot. PNA can get how many points in the image gotten from the robot vision and can calculate the distance between the robot and the wall by the number of the points. The algorithm can be applied to a robot vision system enable to identify where it is in the workspace. In the workspace, the walls are made up by white background with many black points on them evenly. The angle of the vision is set invariable. So the more black points in the vision, the longer the distance is from the robot to the wall. But when the robot does not face the wall directly, the number of the black points is different. When the robot faces the wall, the least number of the black points can be gotten. The simulation results are presented at the end of this paper.

• Journal of the Ergonomics Society of Korea
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• v.36 no.3
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• pp.197-211
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• 2017

Objective: We propose to apply color information to facilitate finding books in the library. Background: Currently, books are classified in the basis of a decimal classification system and a call number in the library. Users find a book using the call number. However, this classification system causes various difficulties. Method: In a process analysis and survey study, we identify what the real problem is and where the problem is occurred. To solve the real problems, we derived a new search method using color information. We conducted a comparative experiment with 48 participants to see whether the new method can show higher performance. Results: The new method using color information showed faster time and higher subjective rating scores than current call number method. Also, the new method showed faster time regardless of the skill level while the call number method showed time differences in terms of the skill level. Conclusion: The effectiveness of the proposed method was verified by experiments. Users will be able to find the desired book without difficulty. This method can improve the quality of service and satisfaction of library use. Application: Our book search method can be applied as a book search tool in a real public library. We hope that the method can provide higher satisfaction to users.

• School Mathematics
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• v.4 no.4
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• pp.643-655
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• 2002

In this paper we emphasize the introduction of ‘incommensurability’ on the teaching and learning the irrational number because we think of the origin of number as ‘ratio’. According to Greek classification of continuity as a ‘never ending’ divisibility, discrete number and continuous magnitude belong to another classes. That is, those components were dealt with respectively in category of arithmetic and that of geometry. But the comparison between magnitudes in terms of their ratios took the opportunity to relate ratios of magnitudes with numerical ratios. And at last Stevin coped with discrete and continuous quantity at the same time, using his instrumental decimal notation. We pay attention to the fact that Stevin constructed his number conception in reflecting the practice of measurement : He substituted ‘subdivision of units’ for ‘divisibility of quantities’. Number was the result of such a reflective abstraction. In other words, number was invented by regulation of measurement. Therefore, we suggest decimal representation from the point of measurement, considering the foregoing historical development of number. From the perspective that the conception of real number originated from measurement of ‘continuum’ and infinite decimals played a significant role in the ‘representation’ of measurement, decimal expression of real number should be introduced through contexts of measurement instead of being introduced as a result of algorithm.

• Journal of Korean Society of Water and Wastewater
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• v.18 no.3
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• pp.312-319
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• 2004

The optimum dosage control is presumably the goal of every water treatment plant. However it is difficult to determine the dosage rate of coagulant, due to nonlinearity, multivariables and slow response characteristics, etc. To deal with this difficulty, the real number genetic-fuzzy system was used in determining the dosage rate of the coagulant. The genetic algorithms are excellently robust in complex optimization problems. Since it uses randomized operators and searches for the best chromosome without auxiliary informations from a population which consists of codings of parameter set. To apply this algorithms, we made the real number rule table and membership function from the actual operation data of the water treatment plant. We determined optimum dosages of coagulant(LAS) using the fuzzy operation and compared them with the dosage rate of the actual operation data.

• Journal of the Korea Society for Simulation
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• v.6 no.2
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• pp.105-115
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• 1997

Fuzzy simulation predicts the behaviors of real system based on a model by qualitative reasoning methods and simulates the representation of ambiguous values on the real system variables using the theory of fuzzy sets. During the simulation, however, unnecessary behaviors due to the fuzzy representation are created, and the number of states of system variables changing temporally in the time axis is drastically increased. In this paper, we present a new algorithm which eliminates the spurious behaviors from the great number of result values due to the results of the fuzzy operation, and reduces the number of the states by transforming the complex state transition rules. This paper also shows the easy implementation of the simulation by using the existing package while it is difficult on the PC due to the complexities of the calculation.

• Proceedings of the Korea Institute of Fire Science and Engineering Conference
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• 2008.11a
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• pp.363-370
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• 2008

The present study has been performed to investigate the effect of statistical number of droplets on the simulation of the sprinkler spray using fire field model. In order to simulate the sprinkler spray characteristics, the present study uses NIST Fire Dynamics Simulator version 5.2. A group of Lagrangian particle with similar droplet characteristics, such as diameter, velocity, temperature and so on, is represented by parcel concept to decrease the total number of droplets tracked in the simulation. The present study introduces a new parameter to represent the ratio between real number of droplets and computational parcels. The dependency of the number of parcels on the fire suppression characteristics and spray patterns is quantitatively examined for different ratio between the real number of droplets and computational parcels.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.219-226
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• 2014

In this paper we study the infiniteness of Hilbert 2-class field towers of real quadratic function fields over $\mathbb{F}_q(T)$, where q is a power of an odd prime number.

• Journal of the Ergonomics Society of Korea
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• v.26 no.2
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• pp.15-20
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• 2007

The purpose of this study is to compare assessment techniques for Korean characters entry methods of mobile phones. This study was performed based on survey of relevant existing studies. The assessment techniques were classified into three: 1) predicting entry time using conceptual models such as Fitts' law, Hick-Hyman's law and KLM-GOMS model (conceptual model); 2) counting the number of pressing button(number of pressing button); and 3) measuring performance or rating subjective measures using real mobile phones(real mobile phone). The comparison revealed that the assessment results were different depending upon the techniques used. The results from the conceptual model using only Fitts' law and the number of pressing button were opposite to those from techniques of the real mobile phone and conceptual model using Fitts' and Hick-Hyman's laws. Based on this result and suggestions provided by the literature, it is recommended that for more precisely assessing interfaces of mobile phones such as Korean characters entry method, real mobile phones be used instead of the conceptual models.