• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.127-133
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• 1996

Let $\Omega_n$ be the polyhedron of $n \times n$ doubly stochastic matrices, that is, nonnegative matrices whose row and column sums are all equal to 1. The permanent of a $n \times n$ matrix $A = [a_{ij}]$ is defined by $$ per(A) = \sum_{\sigma}^ a_{1\sigma(a)} \cdots a_{n\sigma(n)} $$ where $\sigma$ runs over all permutations of ${1, 2, \ldots, n}$.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.2
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• pp.156-160
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• 2008

A localization system to estimate the position as well as movement direction of mobile robots is proposed in this paper. This system implements a camera fixed on a robot and color patches evenly distributed and mounted on the planar ceiling. Different permutations of patch colors code information about robot localization. Thus, extraction of color information from patch images leads to estimation of robot position. Additionally, simple geometric indicators are combined with patch colors to estimate robot's movement direction. Since only the distribution of patch colors has to be known, the analysis of patch images to is relatively fast and simple. The proposed robot localization system has been successfully tested for navigation of sample mobile robot. Obtained test results indicate the robustness and reliability of proposed technique for robot navigation.

• Journal of Electrical Engineering and information Science
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• v.2 no.5
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• pp.121-128
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• 1997

This paper proposes a class of rearrangeable networks, called generalized rearrangeable networks(GRNs). GRNs are obtained from the Benes network by rearranging the connections between states and the switches within each stage. The GRNs constitute all of the rearrangeable networks which have the recursive decomposition structure and can be routed by the outside-in decomposition of permutations as the Bene network. This paper also presents a necessary condition for a network to be a GRN and a network labeling scheme to check if a network satisfies the condition. the general routing algorithm for the GRNs is given by modifying slightly the looping algorithm of the Benes network.

• Journal of Korea Society of Digital Industry and Information Management
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• v.10 no.4
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• pp.117-125
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• 2014

In this paper, a novel hardware architecture of the LT codec is presented where non-BP based decoding algorithm is applied. Novel LT codec architecture is designed with an efficient degree distribution unit using Verilog HDL. To perform permutation operation, different initial valued or time shifted counters have been used to get pretty well permutations and an effect of randomness. The codec will take 128 bits as input and produce 256 encoded output bits. The simulation results show expected performances as the implemented distribution and the original distribution are pretty same. The proposed LT codec takes 257.5 cycle counts and $2.575{\mu}s$ for encoding and decoding instead of 5,204,861 minimum cycle counts and 4.43s of the design mentioned in the previous works where iterative soft BP decoding was used in ASIC and ASIP implementation of the LT codec.

• 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.

• 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.

• The Mathematical Education
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• v.63 no.2
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• pp.187-207
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• 2024

In this study, we explored the feasibility of automatically scoring descriptive assessment items using GPT-4 based ChatGPT by comparing and analyzing the scoring results between teachers and GPT-4 based ChatGPT. For this purpose, three descriptive items from the permutation and combination unit for first-year high school students were selected from the KICE (Korea Institute for Curriculum and Evaluation) website. Items 1 and 2 had only one problem-solving strategy, while Item 3 had more than two strategies. Two teachers, each with over eight years of educational experience, graded answers from 204 students and compared these with the results from GPT-4 based ChatGPT. Various techniques such as Few-Shot-CoT, SC, structured, and Iteratively prompts were utilized to construct prompts for scoring, which were then inputted into GPT-4 based ChatGPT for scoring. The scoring results for Items 1 and 2 showed a strong correlation between the teachers' and GPT-4's scoring. For Item 3, which involved multiple problem-solving strategies, the student answers were first classified according to their strategies using prompts inputted into GPT-4 based ChatGPT. Following this classification, scoring prompts tailored to each type were applied and inputted into GPT-4 based ChatGPT for scoring, and these results also showed a strong correlation with the teachers' scoring. Through this, the potential for GPT-4 models utilizing prompt engineering to assist in teachers' scoring was confirmed, and the limitations of this study and directions for future research were presented.

• Ecology and Resilient Infrastructure
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• v.4 no.2
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• pp.93-96
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• 2017

Spatial variations of physicochemical and microbiological variables were examined to understand spatial heterogeneity of those variables in intertidal flat. Variograms were constructed for understanding spatial autocorrelations of variables by a geostatistical analysis and spatial correlations between two variables were evaluated by applications of a Cross-Mantel test with a Monte Carlo procedure (with 999 permutations). Water content, organic matter content, pH, nitrate, sulfate, chloride, dissolved organic carbon (DOC), four extracellular enzyme activities (${\beta}-glucosidase$, N-acetyl-glucosaminidase, phosphatase, arylsulfatase), and bacterial diversity in soil were measured along a transect perpendicular to shore line. Most variables showed strong spatial autocorrelation or no spatial structure except for DOC. It was suggested that complex interactions between physicochemical and microbiological properties in sediment might controls DOC. Intertidal flat sediment appeared to be spatially heterogeneous. Bacterial diversity was found to be spatially correlated with enzyme activities. Chloride and sulfate were spatially correlated with microbial properties indicating that salinity in coastal environment would influence spatial distributions of decomposition capacities mediated by microorganisms. Overall, it was suggested that considerations on the spatial distributions of physicochemical and microbiological properties in intertidal flat sediment should be included when sampling scheme is designed for decomposition processes in intertidal flat sediment.

• MALSORI
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• no.38
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• pp.71-97
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• 1999

In this paper I have surveyed vowel phonemes in a variety of English accents and have proposed the vowel systems of English. The English accents covered in this paper include General American English, Northeastern American English, Western American English, Southern British English, Northern British English, Scottish English, Southern Irish English, Northern Irish English, Australian English, and New Zealand English. The vowel systems proposed here reflect the acoustic information of vowels and phonological aspects of English. This paper offers an Optimality Theory-based analysis of the English vowel systems by appealing to independently motivated constraints. This paper, following Flemming(1995), makes an assumption that the vowel system in question is selected in output as an optimal candidate by a given constraint ranking, the assumption which is different from the view that the vowel system is fixed in input. The analysis proposed here gives an answer to why a specific vowel system is selected and why dialectal variations come about. It is shown in this paper that the vowel system selected in a specific dialect comes from an optimal satisfaction of a given constraint ranking and that dialectal differences result from dynamic permutations of the same constraints. The constraint-based analysis proffered here accounts well for the similarities and differences among dialects in regard to the vowel system.

• Journal of the Korea Computer Industry Society
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• v.2 no.2
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• pp.203-210
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• 2001

To estimate relational models and test the theoretical hypotheses of binary tree search algorithms, we built binary search trees with random permutations of n (number of nodes) distinct numbers, which ranged from three to seven. Probabilities for building binary search trees corresponding to each possible height and balance factor were estimated. Regression models with variables of number of nodes, height, and average number of comparisons were estimated and the theorem of O(1g(n)) was accepted experimentally by a Lack of Test procedure. Analysis of Variance model was applied to compare the average number of comparisons with three groups by height and balance factor of the trees to test theoretical hypotheses of a binary search tree performance statistically.