• Honam Mathematical Journal
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• v.35 no.1
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• pp.101-107
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• 2013

The Gamma function ${\Gamma}$ which was first introduced b Euler in 1730 has played a very important role in many branches of mathematics, especially, in the theory of special functions, and has been introduced in most of calculus textbooks. In this note, our major aim is to explain the convergence of the Euler's Gamma function expressed as an improper integral by using some elementary properties and a fundamental axiom holding on the set of real numbers $\mathbb{R}$, in a detailed and instructive manner. A brief history and origin of the Gamma function is also considered.

• The Mathematical Education
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• v.47 no.2
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• pp.155-168
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• 2008

The theory of representation, which has been an important topic of epistemology, has long history of study. But it has diverse meaning according to the fields of argument. In this paper the author set the meaning of mathematical representation as the interrelation of internal and external representations. With this concept, the following items were studied. 1. Survey on the concepts of mathematical representations. 2. Investigation of pedagogical significance of the mathematical representations, taking into account the characteristics of school mathematics. 3. Recommendation of principles for teaching representation to cope with the problems that are related with cause of disliking each domain of the secondary school mathematics. This study is expected to enable the development of teaching methods to help students strengthening their ability to comprehend mathematical sentences.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.1-7
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• 2005

The genomes of organism are being published in an enormous speed. The genomes has a lot of intronic regions, and repeats constitute a substantial part of that. Repeats playa crucial role in DNA finger-printing, and detecting certain genomic diseases, such as Huntington disease, which has a high number of CAG repeats. Also, they throw important clues about the evolutionary history. Repeats are in two types, Tandem Repeats and Interspersed Repeats. In this paper we address ourselves to the problem of detecting Primary Tandem Repeats, which are tandem repeats that are not contained in any tandem repeats. We show that our algorithm takes O(n log n) time, where n is the length of genome.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.125-136
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• 2008

There are different perspectives on a function graph. For instance, a parabola is defined by movement of a ball in physics and by quadratic function in mathematics. This study deals with the turtle motion, which is local and intrinsic, and the construction of function graphs with mathematical experiments in a microworld. This paper concerns with a function graph which is in the curriculum or in the history of mathematics. In view of pre-calculus, we introduce activities of mathematization about formalizing of length and area of function graphs without knowledge of calculus.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.457-472
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• 2002

In this paper, we deal with the algebraic thinking from the perspective of ‘process’ and ‘object’ aspects. Generally, mathematical concepts have come from the concrete process. We consider the origin of algebra as the arithmetic calculations. Also, the concept of school arithmetic is beginning from actions or procedures. However, in order to develop the alge- braic thinking and to apply this thinking, we have to see the history of algebraic thinking, and find this duality. Next we investigate various researches relating to the ‘process-object duality’. Theses studies suppose that the concept formation and thinking process should be stared from the process-object duality. Finally, we reinterprete many difficulties in algebra - equals sign, variables, algebraic expressions, and linear equations, the principle of permanence of form- from the perspective of the process-object duality.

• Journal of Gifted/Talented Education
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• v.14 no.3
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• pp.19-40
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• 2004

This paper reports on current work using the Purdue Three-Stage Model to create enrichment classes in science, technology, engineering, and mathematics (the STEM disciplines). First, the history of the Purdue Three-Stage Model and general principles of curriculum and instruction for gifted and talented learners in math/science are reviewed. Then a detailed description of the Model is presented. Following the general description, five specific teacher applications of the Model are presented and compared with respect to the STEM disciplines and developmental levels addressed, and the relative emphasis of each unit on the different stages of the Model. Finally, the advantages of the Model as a framework for curriculum development in science, technology, engineering, and mathematics classes for talented youth are discussed.

• The Mathematical Education
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• v.47 no.4
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• pp.447-465
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• 2008

The purpose of this study is to suggest effective teaching methods on the concept of infinity for students to obtain the right concept in the middle school curriculum. Many people have thought that infinity is something vouge and unapproachable. But, nowadays it is rather something with a precise definition that lies at the core of modern mathematics. To understand mathematics and science very well, it is necessary to comprehend the concept of infinity. But students tend to figure out the properties of infinite objects and limit concepts only through their experience closely related to finite process, and so they are apt to have their spontaneous intuition and misconception about it. Since most of them have cognitive obstacles in studying the infinite concepts and misconception, mathematics teachers need to help them overcome the obstacles and establish the right secondary intuition for the concepts through good examples and appropriate explanation. In this study, we consider the developing process of the concept of infinity in human history and give some comments and suggestions in teaching methods relative to that concept with new suitable examples.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.495-507
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• 1998

This article intends to review what problems the terms in calculus have and how those problems are caused. For this purpose We make examinations on the considerations in the analysis of mathematical terminology, which includes the problems of general and technical terms, the meaning and the boundary of words, their consistency, the name and meaning, concept and their concept images, translations and qwerty effects. And in chapter 3, We analyse the textbook which are currently used, through which I was able to find out that the terms in calculus have some problems, In other words, the key terms such as "differentiable", "differential coefficient", "differential" have their roots in the term "differential" but the term "derived function" is very distinct from other terms and thus obstructs the consistency of terms. And the central term "differential" is being used without clear definition. In particular, the fact that "differential", when used in its arbitrary definition, has the image of "splitting minutely" can be an obstacle to understanding the exact concepts of calculus. In chapter 4, We make a review on the history of calculus and the term "differential" currently used in modern mathematics so that I can identify the origin of the problem connected with the usage of the term "differential". We should recognize the specified problems and its causes and keep their instructional implications in mind. Furthermore, following researches and discussions should be made on whether the terminology system of calculus should be reestablished and how the reestablishment should be made.e terminology system of calculus should be reestablished and how the reestablishment should be made.

• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1237-1242
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• 2010

Based on the detailed travel history of cases from 2006 to 2008 who reside in non-malarious areas, statistical estimates of the incubation periods were obtained. The data suggest that cases fall into two categories with short- and long-term incubation periods, respectively. 72 and 25 cases successfully met our criteria for inferring the durations of short- and long-term incubation periods. The mean short- and long-term incubation periods were estimated to be 25.42 days and 328.6 days weeks, respectively.

• Journal of Information Processing Systems
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• v.13 no.1
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• pp.152-173
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• 2017

Mobile phones are the most common communication devices in history. For this reason, the number of mobile subscribers will increase dramatically in the future. Therefore, the determining the location of a mobile station will become more and more difficult. The mobile station must be authenticated to inform the network of its current location even when the user switches it on or when its location is changed. The most basic weakness in the GSM authentication protocol is the unilateral authentication process where the customer is verified by the system, yet the system is not confirmed by the customer. This creates numerous security issues, including powerlessness against man-in-the-middle attacks, vast bandwidth consumption between VLR and HLR, storage space overhead in VLR, and computation costs in VLR and HLR. In this paper, we propose a secure authentication mechanism based new mobility management method to improve the location management in the GSM network, which suffers from a lot off drawbacks, such as transmission cost and database overload. Numerical analysis is done for both conventional and modified versions and compared together. The numerical results show that our protocol scheme is more secure and that it reduces mobility management costs the most in the GSM network.