• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.139-147
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• 2005

It is interesting to locate homogeneous segments within a DNA sequence. Suppose that the DNA sequence has segments within which the observations follow the same residue frequency distribution, and between which observations have different distributions. In this setting, change points correspond to the end points of these segments. This article explores the use of a binary segmentation procedure in detecting the change points in the DNA sequence. The change points are determined using a sequence of nested hypothesis tests of whether a change point exists. At each test, we compare no change-point model with a single change-point model by using the Bayesian information criterion. Thus, the method circumvents the computational complexity one would normally face in problems with an unknown number of change points. We illustrate the procedure by analyzing the genome of the bacteriophage lambda.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.77-87
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• 2015

Parallel lines are often used to increase production rate in many manufacturing systems where the main line splits into several lines in parallel, and after some operations, they merge into a main line again. Queueing networks with finite buffers have been widely used for modeling and analyzing manufacturing systems. This paper provides an approximation technique for multi-server two-stage networks with merge configuration and blocking which will be a building block for analysis of general manufacturing systems with parallel lines and merge configuration. The main idea of the method is to decompose the original system into subsystems that have two service stations with multiple servers, two buffers and external arrivals to the second stage are allowed. The subsystems are modeled by level dependent quasi-birth-and-death (LDQBD) process.

• 한국수학사학회지
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• 제27권2호
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• pp.139-152
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• 2014

This paper aims to compare and contrast Kierkegaard and Turing, whose birth dates were one hundred years apart, analyzing them from the perspective of the limit. The model of analysis is two concentric circles and movement in them and on the boundary of outer circle. In the model, Kierkegaard's existential stages have 1:1 correspondences: aesthetic stage, ethical stage, religious stage A and religious stage B correspond to inside of the inner circle, outside of the inner circle, the boundary of the outer circle and the outside of the outer circle, respectively. This paper claims that Turing belongs to inside of the outer circle and moves to the center while Kierkegaard belongs to outside of the outer circle and moves to the infinity. Both of them have movement of potential infinity but their directions are opposite.

• 한국수학교육학회지시리즈A:수학교육
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• 제43권1호
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• pp.70-85
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• 2004

Comparing to the other subject, hierarchy among mathematical contents is strong from the perspective of knowledge order as grades go up. That is, the knowledge that students already have learned, are learning and will learn are closed related from grade to grade. We expect students to be proactive and creative in studying mathematics, which is the goal of 21th century, analyzing their. knowledge structure based on the hierarchy of knowledge through assessment. Especially, using computer system we provide students with substantial feedback for the assessment as well as objective validity is increased along with speedy and exact process in a bid to help students' mathematical understanding grow. This paper seeks to analyze the assessment data by applying knowledge spaces to computer system and develops efficient methods based on the analyzed results, to diagram each student's knowledge structure.

• East Asian mathematical journal
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• 제36권2호
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• pp.317-330
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• 2020

The purpose of this action research project was to study the effects of incorporating coding into the middle school math classroom affected student dispositions with math and their understanding of mathematical concepts. The project, involving a total of 107 US middle school students, used five data sources to examine these effects: a survey, a chart measuring student engagement, a pre- and post-assessment before and after the coding project, and teacher observation with reflection forms. After analyzing the data, it was found that incorporating coding into the middle school math classroom could have a positive impact on student math dispositions and their understanding of math concepts.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권3호
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• pp.777-792
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• 2010

경쟁력 있는 지식기반 사회를 구축하기 위해서 다양한 교수법을 구안하고자 하는 노력과 더불어 우리나라 현실에 맞는 교수법 구안 연구도 함께 진행되어야 할 필요성이 있다. 이에 따라 본고에서는 설명식 수업을 통하여 학생들이 수학을 이해하고 의미 있게 받아드리기 위한 방안으로 Ausubel의 유의미 학습을 재조명하였다. Ausubel의 유의미 학습의 의의와 조건 그리고 유의미 학습의 방법 등을 분석함으로써 수학교육에서 유의미 설명식 학습 활용이 보다 용이하게 활용될 수 있도록 하였다.

• 대한수학회지
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• 제49권4호
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• pp.715-731
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• 2012

This paper considers the stability of positive steady-state solutions bifurcating from the trivial solution in a delayed Lotka-Volterra two-species predator-prey diffusion system with a discrete delay and subject to the homogeneous Dirichlet boundary conditions on a general bounded open spatial domain with smooth boundary. The existence, uniqueness and asymptotic expressions of small positive steady-sate solutions bifurcating from the trivial solution are given by using the implicit function theorem. By regarding the time delay as the bifurcation parameter and analyzing in detail the eigenvalue problems of system at the positive steady-state solutions, the asymptotic stability of bifurcating steady-state solutions is studied. It is demonstrated that the bifurcating steady-state solutions are asymptotically stable when the delay is less than a certain critical value and is unstable when the delay is greater than this critical value and the system under consideration can undergo a Hopf bifurcation at the bifurcating steady-state solutions when the delay crosses through a sequence of critical values.

• International Journal of Reliability and Applications
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• 제2권1호
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• pp.1-26
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• 2001

The purpose of this paper is to introduce a proportional reversed hazard rate model, in contrast to the celebrated proportional hazard model, and study some of its structural properties. Some criteria of ageing are presented and the inheritance of the ageing notions (of the base line distribution) by the proposed model are studied. Two important data sets are analyzed: one uncensored and the other having some censored observations. In both cases, the confidence bands for the failure rate and survival function are investigated. In one case the failure rate is bathtub shaped and in the other it is upside bath tub shaped and thus the failure rates are non-monotonic even though the baseline failure rate is monotonic. In addition, the estimates of the turning points of the failure rates are provided.

• 공학교육연구
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• 제22권3호
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• pp.41-48
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• 2019

The purpose of this study is to examine how academic achievement in college math courses differ depending on when the course takes place. As a result, based on years of data analyses on students' academic achievement, it was affirmed that achievement levels differ due to environmental factors despite the diverse efforts of instructors and students. By further analyzing the causes of these differences, this study suggests solutions for improving the different academic achievement levels.

• 대한수학회지
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• 제56권2호
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• pp.353-385
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• 2019

In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers for commutation classes [${\tilde{w}}]$ of w in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order ${\prec}_{[{\tilde{w}}]}$ on the subset ${\Phi}(w)$ of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection functors, we can apply their properties to the representation theory of KLR algebras and dual PBW-basis associated to any commutation class [${\tilde{w}}_0$] of the longest element $w_0$ of any finite type.