• Communications of Mathematical Education
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• v.25 no.3
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• pp.607-627
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• 2011

The purpose of this study is to analyse teaching and learning effects of the structural-mapping used instruction and to find out the characteristics of problem solving process in permutation and combination. For this study, two classes of 11th grade students(67 students) were randomly selected from S high school in D city. One of them was assigned to the experimental group and the other to the control group, respectively. Four lectures of the structural-mapping used instruction were carried out in the experimental group and same amount of lectures of the text book oriented instruction were carried out in the control group. The research findings are as follows. First, the structural-mapping used instruction is shown to be more effective in achievement than the traditional textbook-oriented instruction. Second, the ball-box model is found out to be easier and simpler than the selection-distribution model. Third, students who used the ball-box model are properly able to use both model.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.257-276
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• 2020

In this study, the MKT level of pre-service mathematics teachers in the area of permutations and combinations was investigated, and MKT-Development Program(MKT-DP) focused on improving the MKT of pre-service mathematics teachers was developed and implemented to examine the effects of the program on the MKT in the area of permutations and combinations. Twenty-nine pre-service mathematics teachers participated in a four-week MKT-DP and MKT pre and post tests. According to the MKT pre test results for permutation and combination areas, pre-service teachers who participated in this study showed low levels of MKT in the permutation and combination areas, especially, the level of SCK and KCT was quite low. In order to examine the effects of MKT-DP, the results of pre- and post-MKT tests were analyzed, and a significant difference between pre- and post-tests was found only in the KCT sub-category. This shows that the MKT-DP developed in this study is effective in improving pre-services teachers' KCT in the area of permutation and combination. Although there were no statistically significant differences between the three remaining sub-categories(CCK, SCK, and KCS), the positive influence of MKT-DP can be expected throughout MKT, as a result of some level increase in post-test compared to the pre-test.

• Computers and Concrete
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• v.34 no.1
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• pp.79-91
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• 2024

In symmetric cryptography, a cryptographically secure Substitution-Box (S-Box) is a key component of a block cipher. S-Box adds a confusion layer in block ciphers that provide resistance against well-known attacks. The generation of a cryptographically secure S-Box depends upon its generation mechanism. In this paper, we propose a novel framework for the construction of cryptographically secure S-Boxes. This framework uses a combination of linear fractional transformation and permutation functions. S-Boxes security is analyzed against well-known security criteria that include nonlinearity, bijectiveness, strict avalanche and bits independence criteria, linear and differential approximation probability. The S-Boxes can be used in the encryption of any grayscale digital images. The encrypted images are analyzed against well-known image analysis criteria that include pixel changing rates, correlation, entropy, and average change of intensity. The analysis of the encrypted image shows that our image encryption scheme is secure.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.863-874
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• 2021

In this paper, we propose a post-selection inference procedure for the fused lasso signal approximator (FLSA). The FLSA finds underlying sparse piecewise constant mean structure by applying total variation (TV) semi-norm as a penalty term. However, it is widely known that this convex relaxation can cause asymptotic inconsistency in change points detection. As a result, there can remain false change points even though we try to find the best subset of change points via a tuning procedure. To remove these false change points, we propose a post-selection inference for the FLSA. The proposed procedure applies a permutation test based on CUSUM statistic. Our post-selection inference procedure is an extension of the permutation test of Antoch and Hušková (2001) which deals with single change point problems, to multiple change points detection problems in combination with the FLSA. Numerical study results show that the proposed procedure is better than naïve z-tests and tests based on the limiting distribution of CUSUM statistics.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.61-68
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• 1983

A parallel flats fraction for the $3^n$ factorial experiment is defined as the union of flats, ${t$\mid$At=C_i(mod 3)}, i=1,2,\cdot,f$, in EG(n,3) and is symbolically written as At=C where A is of rank r. The A matrix partitions the effects into u+1 alias sets where $u=(3^{n-r}-1)/2$. For each alias set the f flats produce an alias component permutation matrix (ACPM) with elements from $S_3$. In this paper, a detection vector of the ACPM was constructed for each combination of k or fewer two-factor interactions. Also the relationship between the detection vectors has been shown.

• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.67-82
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• 2014

The term "objectification" has various definitions or perspectives. Nevertheless, it's pursued commonly by groups from various perspectives who emphasize the activities of becoming aware of a process as a totality, realizing that transformations can act on that totality, that is, turning processes into object. The purpose of this study is to identify how students objectify the concept of repetition regarding permutation and combination and find difficulties of objectification focusing on teacher's and students' discourse from common emphasis on previous researches associated with objectification. Students objectified the concept of repetition by replacing talk about processes with talk about objects regarding repetition and using discursive forms that presented phenomena in an impersonal way. The difficulties of objectification were derived from close linkage between the way of using keywords regarding repetition and everyday language.

• Research in Mathematical Education
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• v.16 no.1
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• pp.79-90
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• 2012

This research investigated if the embodied symbol using a turtle metaphor in a microworld environment works as a cognitive tool to mediate the learning of combinatorics. It was found that students were able to not only count the number of cases systematically by using the embodied symbols in a situated problem regarding Permutation and Combination, but also find the rules and infer a concept of Combination through the activities manipulating the symbols. Therefore, we concluded that the embodied symbol, as a bridge that connects learners' concrete experiences with abstract mathematical concepts, can be applied to introduction of various mathematical concepts as well as a combinatorics concept.

• Journal of the Korean Society of Safety
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• v.21 no.6 s.78
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• pp.74-81
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• 2006

Probabilistic Risk Assessment considering statistically random variables is performed for the preliminary design of a Arch Bridge. Component reliabilities of girders have been evaluated using the response surfaces of the design variables at the selected critical sections based on the maximum shear and negative moment locations. Response Surface Method(RSM) is successfully applied for reliability analyses for this relatively small probability of failure of the complex structure, which is hard to be obtained by Monte-Carlo Simulations or by First Order Second Moment Method that can not easily calculate the derivative terms of implicit limit state functions. For the analysis of system reliability, parallel resistance system composed of girders is changed into parallel series connection system. The upper and lower probabilities of failure for the structural system have been evaluated and compared with the suggested prediction method for the combination of failure modes. The suggested prediction method for the combination of failure modes reveals the unexpected combinations of element failures in significantly reduced time and efforts compared with the previous permutation method or system reliability analysis method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.295-300
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• 2007

Probabilistic Risk Assessment considering statistically random variables is performed for the preliminary design of a Arch Bridge. Component reliabilities of girders have been evaluated using the response surfaces of the design variables at the selected critical sections based on the maximum shear and negative moment locations. Response Surface Method (RSM) is successfully applied for reliability analyses for this relatively small probability of failure of the complex structure, which is hard to be obtained by Monte-Carlo Simulations or by First Order Second Moment Method that can not easily calculate the derivative terms of implicit limit state functions. For the analysis of system reliability, parallel resistance system composed of girders is changed into parallel series connection system. The upper and lower probabilities of failure for the structural system have been evaluated and compared with the suggested prediction method for the combination of failure modes. The suggested prediction method for the combination of failure modes reveals the unexpected combinations of element failures in significant]y reduced time and efforts compared with the previous permutation method or system reliability analysis method.

• Annual Conference of KIPS
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• 2016.04a
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• pp.83-85
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• 2016

C-RAN (Cloud Radio Access Network) structure is the most popular approach for 5G stander, it employs CoMP (Coordinated Multiple Points Transmission/Reception) to enhance frequency utilization and increase throughput for cell-edge users. C-RAN mainly includes two parts: baseband units (BBU) and remote radio heads (RRH). In this paper we propose a new resource block allocation (spectrum allocation) scheme by the permutation and combination of BBUs, and we also use the CoMP (Coordinated Multiple Points Transmission/Reception) technique according to the different environment to improve the spectrum utilization and reduce resource waste in different environment. The simulation results expound that the scheme significantly enhances throughput and improves the spectrum utilization.