• East Asian mathematical journal
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• v.25 no.3
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• pp.247-262
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• 2009

Permutation and combination are the part of mathematics which can be introduced the pliability and diversity of thought. In prior studies of permutation and combination, there treated difficulties of learning, strategy of problem solving, and errors that students might come up with. This paper provides the method so that meaningful teaching and learning might occur through the systematic approach of permutation and combination. But there were little prior studies treated counting numbers that basic of mathematics' action. Therefore this paper tries to help the understanding of permutation and combination with the process of changing from informal knowledge to formal knowledge.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.3
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• pp.1451-1458
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• 2013

This paper deals with the programs and algorithms that generate the full data set that satisfy the basic combinatorial requirement of combination, permutation, partial permutation or shortly r-permutation, which are used in the application of the total data testing or the simulation input. We search the programs able to meet the rules which is permutations and combinations, r-permutations, select the fastest program by field. With further study, we developed a new program reducing the time required to processing. Our research performs the following pre-study. Firstly, hundreds of algorithms and programs in the internet are collected and corrected to be executable. Secondly, we measure running time for all completed programs and select a few fast ones. Thirdly, the fast programs are analyzed in depth and its pseudo-code programs are provided. We succeeded in developing two programs that run faster. Firstly, the combination program can save the running time by removing recursive function and the r-permutation program become faster by combining the best combination program and the best permutation program. According to our performance test, the former and later program enhance the running speed by 22% to 34% and 62% to 226% respectively compared with the fastest collected program. The programs suggested in this study could apply to a particular cases easily based on Pseudo-code., Predicts the execution time spent on data processing, determine the validity of the processing, and also generates total data with minimum access programming.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.329-339
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• 2018

In this study, we propose tests for equality of several variances with the normality assumption. First of all, we propose the likelihood ratio test by applying the permutation principle. Then by using the p-values for the pairwise tests between variances and combination functions, we propose combination tests. We apply the permutation principle to obtain the overall p-values. Also we review the well- known test statistics for the completion of our discussion and modify a statistic with the p-values. Then we illustrate proposed tests by numerical and simulated data and compare their efficiency with the reviewed ones through a simulation study by obtaining empirical p-values. Finally, we discuss some interesting features related to the resampling methods and tests for equality among several variances.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.261-279
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• 2009

Permutation and combination are the subjects that most teachers feel difficult to teach in Mathematics. This paper investigated evaluation items and factors of anxiety of students for permutation and combination, and further examined the way to lessen the factors of anxiety. Two high school students participated for over a year from December 2007 to February 2008. Also, two teachers joined for the analysis of evaluation items. We found that the ill-structured problems and word problems are the main factors to bring about the anxiety, whereas cooperative learning with high intelligent peers, practice to read word problems and write the process of problems solving are helpful in lessening the mathematical anxieties. Further we propose that the study of appropriate teaching and learning method for permutation and combination should be performed in the future.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.19-38
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• 2021

The purpose of this study is to examine pre-service teachers' noticing when evaluating peers' mathematical problem posing tasks. To this end, 46 secondary pre-service teachers were asked to create real-world problems related to permutation and combination and randomly assigned to evaluate peers' problems. As a result, the pre-service teachers were most likely to notice the difficulty of their peers' mathematics problems. In particular, the pre-service teachers tended to notice particular conditions in order to increase the difficulty of a problem. In addition, the pre-service teachers noticed the clarity of a question and its solution, novelty of the problem, the natural connection between real-world contexts and mathematical concepts, and the convergence between mathematical concepts.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.563-574
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• 2016

In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.

• The Mathematical Education
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• v.48 no.2
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• pp.113-139
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• 2009

In this study, we apply the discovery method in the instruction of Permutation and Combination, and examine the effect upon the student's emotion after the instruction change. The research progressed through the instruction by the discovery method for two students of highschool Y. This research has been done for about one and half year from November 2006 to February 2008. We draw our research results through a series of processes consisted of videotaping a classroom activities, recording interview details and writing an observation diary, with the aim of the experimental instruction. In the end, we get to the conclusion that students showed a strong positive attitude on the discovery instructional method and that diverse discovery method has supplementary relation in classwork.

• Journal of Internet Technology
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• v.21 no.4
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• pp.1013-1024
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• 2020

In this paper, we introduce an image encryption algorithm that can be used in combination with compression algorithms. Existing encryption algorithms focus on either encryption strength or speed without compression, whereas the proposed algorithm improves compression efficiency while ensuring security. Our encryption algorithm decomposes images into pixel values and pixel intensity subsets, and computes the order of permutations. An encrypted image becomes unpredictable after permutation. Order permutation reduces the discontinuity between signals in an image, increasing compression efficiency. The experimental results show that the security strength of the proposed algorithm is similar to that of existing algorithms. Additionally, we tested the algorithm on the JPEG and the JPEG2000 with variable compression ratios. Compared to existing methods applied without encryption, the proposed algorithm significantly increases PSNR and SSIM values.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.47-47
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• 1989

This paper considers the parallel machines scheduling problem characterized as a multi-objective combinatorial problem. As this problem belongs to the NP-complete problem, genetic algorithms are applied instead of the traditional analytical approach. The purpose of this study is to show how the problem can be effectively solved by using genetic algorithms with a permutation approach. First, a permutation representation which can effectively represent the chromosome is introduced for this problem . Next, a schedule builder which employs the combination of scheduling theories and a simple heuristic approach is suggested. Finally, through the computer experiments of genetic algorithm to test problems, we show that the niche formation method does not contribute to getting better solutions and that the PMX crossover operator is the best among the selected four recombination operators at least for our problem in terms of both the performance of the solution and the operational convenience.

• Korean Management Science Review
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• v.14 no.2
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• pp.47-61
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• 1997

This paper considers the parallel machines scheduling problem characterized as a multi-objective combinatorial problem. As this problem belongs to the NP-complete problem, genetic algorithms are applied instead of the traditional analytical approach. The purpose of this study is to show how the problem can be effectively solved by using genetic algorithms with a permutation approach. First, a permutation representation which can effectively represent the chromosome is introduced for this problem . Next, a schedule builder which employs the combination of scheduling theories and a simple heuristic approach is suggested. Finally, through the computer experiments of genetic algorithm to test problems, we show that the niche formation method does not contribute to getting better solutions and that the PMX crossover operator is the best among the selected four recombination operators at least for our problem in terms of both the performance of the solution and the operational convenience.