• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.823-833
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• 2009

It is well-known that if a convex hyperbolic polygon is constructed as a fundamental domain for a subgroup of the modular group, then its translates by the group elements form a locally finite tessellation and its side-pairing transformations form a system of generators for the group. Such hyperbolically convex polygons can be obtained by using Dirichlet's and Ford's polygon constructions. Another method of obtaining a fundamental domain for subgroups of the modular group is through the use of a right coset decomposition and we call such domains standard fundamental domains. In this paper we give subgroups of the modular group which do not have hyperbolically convex standard fundamental domain containing only inequivalent cusps.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.569-579
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• 2019

Cusp (parabolic) points in the extended modular group ${\bar{\Gamma}}$ are basically the images of infinity under the group elements. This implies that the cusp points of ${\bar{\Gamma}}$ are just rational numbers and the set of cusp points is $Q_{\infty}=Q{\cup}\{{\infty}\}$.The Farey graph F is the graph whose set of vertices is $Q_{\infty}$ and whose edges join each pair of Farey neighbours. Each rational number x has an integer continued fraction expansion (ICF) $x=[b_1,{\cdots},b_n]$. We get a path from ${\infty}$ to x in F as $<{\infty},C_1,{\cdots},C_n>$ for each ICF. In this study, we investigate relationships between Fibonacci numbers, Farey graph, extended modular group and ICF. Also, we give a computer program that computes the geodesics, block forms and matrix represantations.

• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.225-238
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• 2014

We apply modular function theory to find the relation among t-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in [1] because their relations are linear for t = 3 or 5.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.107-116
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• 2005

We show an algorithm to draw the famous picture of Kleinian modular group PSL(2, $\mathbb{Z}$), which appears in describing the moduli space of elliptic curves.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.7
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• pp.2610-2630
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• 2021

The aim of this paper is to propose the alternative algorithm to finish the process in public key cryptography. In general, the proposed method can be selected to finish both of modular exponentiation and point multiplication. Although this method is not the best method in all cases, it may be the most efficient method when the condition responds well to this approach. Assuming that the binary system of the exponent or the multiplier is considered and it is divided into groups, the binary system is in excellent condition when the number of groups is small. Each group is generated from a number of 0 that is adjacent to each other. The main idea behind the proposed method is to convert the exponent or the multiplier as the subtraction between two integers. For these integers, it is impossible that the bit which is equal to 1 will be assigned in the same position. The experiment is split into two sections. The first section is an experiment to examine the modular exponentiation. The results demonstrate that the cost of completing the modular multiplication is decreased if the number of groups is very small. In tables 7 - 9, four modular multiplications are required when there is one group, although number of bits which are equal to 0 in each table is different. The second component is the experiment to examine the point multiplication process in Elliptic Curves Cryptography. The findings demonstrate that if the number of groups is small, the costs to compute point additions are low. In tables 10 - 12, assigning one group is appeared, number of point addition is one when the multiplier of a point is an even number. However, three-point additions are required when the multiplier is an odd number. As a result, the proposed method is an alternative way that should be used when the number of groups is minimal in order to save the costs.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.601-618
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• 2004

Throughout this paper, we will consider that R is a near-ring and G an R-group. We initiate the study of monogenic, strongly monogenic R-groups, 3 types of nonzero R-groups and their basic properties. At first, we investigate some properties of D.G. (R, S)-groups, faithful R-groups, monogenic R-groups, simple and R-simple R-groups. Next, we introduce modular right ideals, t-modular right ideals and 3 types of primitive near-rings. The purpose of this paper is to investigate some properties of primitive types near-rings and their characterizations.

• Journal of Korean Institute of Industrial Engineers
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• v.36 no.1
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• pp.22-31
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• 2010

In R&D project evaluation, we consider the technical couple. And we set technology modular alternatives, after evaluating technical group based on technical couple. So we solve the problem extracted from existing research of R&D project evaluation. We use Conjoint Analysis(CA) for this research. CA is usually used for confirming customers' preference. However we use it for researchers' preference in the side of technology. This research is followed by the next 4 steps. (1) Hierarchical model of goal technology (2) Composition model of modular alternatives (3) Evaluation model of modular alternatives (4) Setting model of technology modular alternatives.

• The Journal of Korean Association of Computer Education
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• v.22 no.1
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• pp.79-86
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• 2019

This study examines the impact of modular robot programming education on middle school informatics curriculum learning motivation. For this purpose, the experiment was conducted with a experimental group of 25 people and a control group of 25 people, and modular robot programming education and learning motivation test were used as research tools. As a result of processing the results of the learning motivation test paper with the independent sample t-test and the paired t-test, the experimental group had 9.36 points higher learning motivation than the control group and 15.44 points higher than the pre-test. In particular, it significantly affected the improvement of all the sub-components of the learning motivation, and among them, it greatly affected the enhancement of attention, relevance and satisfaction. In conclusion, it can be seen that modular robot programming education has a positive effect on improving students' motivation to learn the informatics curriculum.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2016.05a
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• pp.19-20
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• 2016

Domestic construction industry has experienced many difficulties as it has been on a downward. It's a way that active modular structure market to solve this problem. However, as Modular structure technical standard in Korea is in the early stages, our modular factory maufactured rate is almost 40% lower than overseas. Besides, there is less design diversity so it just applies for a few buildings like low-rise building and general group barrackes. To deal with these problems, it is essential to modulating the equipment which can improve the production rate. This will help to ensure the quality, shortening of the construction period, the reduction of labor costs. We have defined the name of segmented by each installation location of the equipment to modulating equipment. And it was examined the suitability of the modulating of the location-specific utility system. The results of the analysis are discussed on the page.

• Hwankyungkyoyuk
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• v.16 no.2
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• pp.51-64
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• 2003

The ultimate objective of environmental education is to develop characteristics of the affective domain being the basis for environmental behavior. As this need, the researchers developed a modular program for environmental values education suited elementary school's actuality. In practice of program development, researchers analyzed the contents of environmental education in current curriculum. Researchers set up development principles of modular program according to the level of elementary moral development. The system of this modular program consists of three levels like environmental awareness, environmental literacy, environmental responsibility, and each module is made up of three subjects representing these levels. So this modular program is classified with three level's modular group like low grade, center grade, and high grade. And set in array after selecting value strategies suited each grade level. The expectant effects of this program for environmental values education are as follows: Students form sound environmental values and attitudes for environment through various strategies that develop environmental awareness and environmental literacy. And those strategies provides various experiences to construct knowledge, value, and attitude about environment by oneself working together with teacher. So teacher and students can utilize easily at school or in nature. Besides, since it relates with single environmental problem from awareness to participation about environment, teachers can conduct elementary environmental curriculum more systematically and effectively.