• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.719-725
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• 2013

A domain is called an LPI domain if every locally principal ideal is invertible. It is proved in this note that if D is a LPI domain, then D[X] is also an LPI domain. This fact gives a positive answer to an open question put forward by D. D. Anderson and M. Zafrullah.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.649-657
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• 2018

Let R be a commutative ring. In this paper, the w-projective Basis Lemma for w-projective modules is given. Then it is shown that for a domain, nonzero w-projective ideals and nonzero w-invertible ideals coincide. As an application, it is proved that R is a Krull domain if and only if every submodule of finitely generated projective modules is w-projective.

• Research in Mathematical Education
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• v.7 no.1
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• pp.41-58
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• 2003

This study firstly examined 18 prospective secondary mathematics teachers' understanding of the nature of definitions and the use of the dynamic geometry software Sketchpad to not only improve their understanding of definitions, but also their ability to define geometric concepts themselves. Results indicated that the evaluation of definitions by accurate construction and measurement enabled students to achieve a better understanding of necessary and sufficient conditions, as well as the ability to more readily find counter-examples, and to recognize uneconomical definitions, and improve them.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.1045-1049
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• 2001

Before building houses or apartments, we need to predict noise propagation to eliminate possible noise problems to residents. However, we do not try to predict noise propagation during estimation of noise effect for the developing area since we did not have a good mathematical model to predict noise level due to a traffic noise. In this article, an adequate mathematical model has been developed and proved to predict noise effect to living area due to a traffic noise.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.87-94
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• 2002

Trot(1999) considered how to calculate the expected area of a random triangle in the unit square $[0,1]{\times}[0,1]$. He used the Mathematica software package for the computational part. In this article, we study various aspects of the probability distribution of a triangle randomly chosen inside the circle of radius r. A simulation activity that can be conducted in statistics and probability classrooms is also considered.

• The Mathematical Education
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• v.42 no.4
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• pp.561-577
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• 2003

Because statistical concepts are important parts in school mathematics, mathematics teachers have trained by special education model. In this study, a desirable direction of curriculum on probability and statistics at pre-service for mathematics teacher is considered. We proposed four subjects as Exploration and Analysis of Data for Mathematics Teacher, Probability and Statistics I, II for Mathematics Teacher and Statistical Software for Mathematics, and suggested the constituents and something being kept in mind for each subject.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.297-306
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• 2007

In this paper, we present a new kind of duality between intersection bodies and projection bodies. Furthermore, we establish some counterparts of dual Brunn-Minkowski inequalities for intersection bodies.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.176-181
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• 2001

Analysis technology is widely accepted and quite popular these days. Incorporation of the analysis result into design process is a key factor for the success of the analysis area. A few design software products have been commercialized. Generally, they are trying to make an interface between various design methods and analysis software. Optimization is a representative design method. The products are investigated and compared for the aspects of user convenience and algorithm performance. A few popular products are selected. Graphic user interface (GUI) is compared for the function and efficiency. The performances of the optimization algorithms are tested by mathematical and engineering examples. The results are discussed.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.45-63
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• 2003

This study is a research about the effect on achievement, retention and attitude of learning descriptive statistics with the computer software. For this study, 60 students are randomly divided two groups, one is an experimental group using software, the other one is a control group using lecture type of learning statistics. For the analysis, both groups are divided three subgroups according to mathematical ability. Also the topic "descriptive statistics" is divided by 5 subtopics. The test is divided three parts(computation, concept and application) according to knowledge type. The attitude toward statistics is investgated with questionaire and interview with both groups. The achievement test is taken after 8 class periods. The retention test were administered together six weeks after achievement test. The experimental group achieved significantly better than in concept type while the control group performed significantly better than the experimental group in computation type. With respect to the attitude toward statistics, lower ability students may have been negatively affected by the use of software.

• Journal of Korean Society for Quality Management
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• v.30 no.3
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• pp.186-194
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• 2002

In this paper we introduce formulae for estimating the failure rate of a large scaled software by using the Bayesian rule when a black-box random testing which selects an element(test case) at random with equally likely probability, is performed. A program or software can be treated as a mathematical function with a well-defined (input)domain and range. For a large scaled software, their input domains can be partitioned into multiple subdomains and exhaustive testing is not generally practical. Testing is proceeding with selecting a subdomain, and then picking a test case from within the selected subdomain. Whether or not the proportion of selecting one of the subdomains is assumed probability, we developed the formulae either case by using Bayesian rule with gamma distribution as a prior distribution.