• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.15-29
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• 2007

In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

• Journal for History of Mathematics
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• v.28 no.4
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• pp.167-179
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• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.329-342
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• 2008

There have been many experimental and observational evidences which indicate the predator response to prey density needs not always monotone increasing as in the classical predator-prey models in population dynamics. Holling type functional response depicts situations in which sufficiently large number of the prey species increases their ability to defend or disguise themselves from the predator. In this paper we investigated the stability and instability property for a Holling type predator-prey system of a generalized form. Hopf type bifurcation properties of the non-diffusive system and the diffusion effects on instability and bifurcation values are studied.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.253-270
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• 2015

Two major simultaneous attack strategies have been introduced, as one of cooperative attack of multiple missiles. One strategy is an undesignated time attack, in which the missiles communicate among themselves to synchronize the arrival times by reducing the mutual differences of times-to-go of multiple missiles during the homing. The other is a designated time attack, in which a common impact time is commanded to all members in advance, and thereafter each missile tries to home on the target on time independently. For this individual homing, Impact-Time-Control Guidance (ITCG) law is required. After introducing cooperative proportional navigation (CPN) for the first strategy, this article presents a new closed-form ITCG guidance solution for the second strategy. It is based on the linear formulation, employing base trajectories driven by PNG with various navigation constants. Nonlinear simulation of several engagement situations demonstrates the performance and feasibility of the proposed ITCG law.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1567-1579
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• 2020

Let R ⊂ S be a Frobenius extension of rings and M a left S-module and let 𝓧 be a class of left R-modules and 𝒚 a class of left S-modules. Under some conditions it is proven that M is a 𝒚-Gorenstein left S-module if and only if M is an 𝓧-Gorenstein left R-module if and only if S ⊗_R M and Hom_R(S, M) are 𝒚-Gorenstein left S-modules. This statement extends a known corresponding result. In addition, the situations of Ding modules, Gorenstein AC modules and projectively coresolved Gorenstein flat modules are considered under Frobenius extensions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.2
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• pp.71-76
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• 2011

The problem of decision making under imprecise environments are widely spread in real life decision situations. We present a method of object recognition from imprecise multi observer data, which extends the work of Roy and Maji [J Compu. Appl. Math. 203(2007) 412-418] to generalized intuitionistic fuzzy soft set theory. The method involves the construction of a comparison table from a generalized intuitionistic fuzzy soft set in a parametric sense for decision making.

• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.175-189
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• 2019

The problem of the estimation of quantitative sensitive variable using the item sum technique (IST) on successive occasions has been discussed. IST difference, IST regression, and IST general class of estimators have been proposed to estimate quantitative sensitive variable at the current occasion in two occasion successive sampling. The proposed new estimators have been elaborated under Trappmann et al. (Journal of Survey Statistics and Methodology, 2, 58-77, 2014) as well as Perri et al. (Biometrical Journal, 60, 155-173, 2018) allocation designs to allocate long list and short list samples of IST. The properties of all proposed estimators have been derived including optimum replacement policy. The proposed estimators have been mutually compared under the above mentioned allocation designs. The comparison has also been conducted with a direct method. Numerical applications through empirical as well as simplistic simulation has been used to show how the illustrated IST on successive occasions may venture in practical situations.

• Research in Mathematical Education
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• v.24 no.2
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• pp.111-130
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• 2021

This exploratory study focuses on analyzing three mathematics textbooks in Germany, Singapore and South Korea to reveal similarities and differences in their introductions of fraction concepts. Findings reveal that all three countries' textbooks introduce fraction concepts predominantly by using pictorial representations such as area models, but the introductions of multiple fraction constructs vary. The Singaporean and South Korean textbooks predominantly used a part-whole construct to introduce fractional concepts while the German textbook introduced various constructs sequentially in the first pages using several scenarios from different real-life situations. The findings were represented using visual representations, which we called textbook signatures. The textbook signatures provided configurations of the textbook features across the three countries. At the end of paper, we share insights and limitations about the use of textbook signatures in the research on textbook analysis.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.81-109
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• 1999

This study aims to reflect the basic principles and teaching-teaming principles of Realistic Mathematics Education in order to suppose an way in which mathematics as an activity is carried out in primary school. The development of what is known as RME started almost thirty years ago. It is founded by Freudenthal and his colleagues at the former IOWO. Freudenthal stressed the idea of matheamatics as a human activity. According to him, the key principles of RME are as follows: guided reinvention and progressive mathematisation, level theory, and didactical phenomenology. This means that children have guided opportunities to reinvent mathematics by doing it and so the focal point should not be on mathematics as a closed system but on the process of mathematisation. There are different levels in learning process. One should let children make the transition from one level to the next level in the progress of mathematisation in realistic contexts. Here, contexts means that domain of reality, which in some particular learning process is disclosed to the learner in order to be mathematised. And the word of 'realistic' is related not just with the real world, but is related to the emphasis that RME puts on offering the students problem situations which they can imagine. Under the background of these principles, RME supposes the following five instruction principles: phenomenological exploration, bridging by vertical instruments, pupils' own constructions and productions, interactivity, and interwining of learning strands. In order to reflect how to realize these principles in practice, the teaming process of algorithms is illustrated. In this process, children follow a learning route that takes its inspiration from the history of mathematics or from their own informal knowledge and strategies. Considering long division, the first levee is associated with real-life activities such as sharing sweets among children. Here, children use their own strategies to solve context problems. The second level is entered when the same sweet problems is presented and a model of the situation is created. Then it is focused on finding shortcomings. Finally, the schema of division becomes a subject of investigation. Comparing realistic mathematics education with constructivistic mathematics education, there interaction, reflective thinking, conflict situation are many similarities but there are alsodifferences. They share the characteristics such as mathematics as a human activity, active learner, etc. But in RME, it is focused on the delicate balance between the spontaneity of children and the authority of teachers, and the development of long-term loaming process which is structured but flexible. In this respect two forms of mathematics education are different. Here, we learn how to develop mathematics curriculum that respects the theory of children on reality and at the same time the theory of mathematics experts. In order to connect the informal mathematics of children and formal mathematics, we need more teachers as researchers and more researchers as observers who try to find the mathematical informal notions of children and anticipate routes of children's learning through thought-experiment continuously.

• Education of Primary School Mathematics
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• v.15 no.1
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• pp.41-52
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• 2012

The korean mathematics textbooks according to the 2007 revised mathematics curriculum and the MiC textbooks are similar in that they introduce mathematical materials in real life situations and are composed in such a way that require students to form their own mathematical concepts. However the MiC textbooks are focus more on situation-centered problems and context-centered problems where a set of procedures need to be followed in order to arrive at an answer. So, this paper is aim at comparing the units of statistics in the korean mathematics textbooks and the MiC textbooks in order to find the implications for writing textbook. By comparing the specific content and the used methods, I found Korean textbooks focused on understanding concepts and spending less time surveying and collecting data. On the other hand, MiC textbooks used activities that real mathematicians would be involved with, such as surveying and analyzing data to compose mathematical concepts.