• Journal of Internet Computing and Services
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• v.14 no.4
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• pp.25-33
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• 2013

The procedure of the arbitration which is the tag collision is essential because the multiple tags response simultaneously in the same frequency to the request of the Reader. This procedure is known as Anti-collision and it is a key technology in the RFID system. In this paper, we propose the 4-Bit Pattern Slot Allocation(4-BPSA) algorithm for the high-speed identification of the multiple tags. The proposed algorithm is based on the tree algorithm using the time slot and identify the tag quickly and efficiently through accurate prediction using the a slot as a 4-bit pattern according to the slot allocation scheme. Through mathematical performance analysis, We proved that the 4-BPSA is an O(n) algorithm by analyzing the worst-case time complexity and the performance of the 4-BPSA is improved compared to existing algorithms. In addition, we verified that the 4-BPSA is performed the average 0.7 times the query per the Tag through MATLAB simulation experiments with performance evaluation of the algorithm and the 4-BPSA ensure stable performance regardless of the number of the tags.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.59-81
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• 2021

This study aimed to investigate how the learners' mathematics learning processes change with repeatedly reading mathematical text. As a way to teach and learn mathematics, we also wanted to examine the effect of repeated reading and to explore the implications for a more efficient teaching and learning strategy. To help us with this study, we mainly used eye tracking and heart rate (HR) measurement. There were four cycles in a cycle of repeated reading, and the number of repeated readings for all cycles was fixed to three times. Eight prospective mathematics teachers in the Department of Mathematics Education of a National University in South Korea participated. Data were analyzed in five aspects: (1) the total reading time per round, the total reading time per slide; (2) the change trends of total reading time per round and slide; (3) the order of slides read; (4) the change trends of HR per round. We found that most participants read in a similar pattern in the first reading, but the second and third reading patterns appeared more diverse for each learner. Also, the first reading required the most time regardless of the repeat cycle, and the time it took to repeatedly read afterward varied depending on the individual. Based on the findings of this study, the most primary conclusion is that self-directed mathematics learning by using repeated reading is effective regardless of cycle. In addition, we suggested four strategies to improve the efficiency of this teaching and learning method.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.679-710
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• 2021

We study the tensor product algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m), where P_k(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of P_k(n₁) ⊗ P_k(n₂) ⊗ ⋯ ⊗ P_k(n_m) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γ_k^m, Γ_k^m = {[λ] = (λ₁, λ₂, …, λ_m)|λ_i ∈ Γ_k, i ∈ {1, 2, …, m}} where Γ_k = {λ_i ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f^[λ]m_k^[λ] where m_k^[λ] is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f^[λ] is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.

• Journal of the Korean association of regional geographers
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• v.3 no.2
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• pp.151-162
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• 1997

Although modern versions of the traditional Von $Th{\ddot{u}}nen$ theory have contributed to a description of spatial organization in agriculture, they did not incorporate the market mechanism as an integral part of location theory. This deficiency has been indicated and new mathematical structure has been proposed elsewhere by the author. The closed model, which simultaneously considered a basic principle of supply and demand, exposed a computational complexity. Based on the problem, this study attempts to extend market mechanism in order to consider the influence of city (market) size in agricultural location theory. To theoretically explore the economic relationship in a location theory, this study simplifies agricultural activity as just two activities in one-dimensional spatial economy. The problem has been solved by equating total supply and demand of agricultural products, and then by determining each agricultural price from the relationship. All of the mathematical problems have been arranged in matrix form. First, the traditional model and closed model have been compared by quantitative comparative statics which provides the sensitivity test for each model. The results have shown that the traditional model shows a relatively excessive change in land use, besides the deficiency of a constant agricultural price. Second, the effects of the size of market town and its population increase were examined, using the closed model. In this case, the price of agricultural product is increased, and the land use is extended outward. This proves that locational rent is related to the expansion of land use. Third, environmental uncertainty was associated with the closed model, in order to further consider the difference of farmers attitude in strategic perspective. In this study, two extreme attitudes, which reflects the maximum average expected returns and the maximum guaranteed returns, were examined in their land use and their effects on the prices of agricultural products. It was shown that the two farmers attitudes can be interconnected with location theory. Due to the exogenous data, the differences in the area of land use and total quantities of agricultural products were not clearly shown in this study. However, it was shown that the land use pattern is very different. That is, maximum guaranteed return model reveals a mixed land use pattern around the market town. Basically, this study shows some spatial and economic implications related to Von $Th{\ddot{u}}nen$ model.

• Journal of Science Education
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• v.45 no.2
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• pp.247-256
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• 2021

Visual representation has been a useful tool in mathematical problem solving because it vividly express and structure the variables in the problem. But its effects may vary according to the types of problems. So, this study analyzes the survey results on the 5^th graders' visual representations using questionnaire consisting of the routine problems and the non-routine problems. The results are follows: The rate of correct answers in routine problems was higher than that of the non-routine problems. Even though the subjects were asked to solve the problem using visual representations, the ratio of solving the problem using the numerical expression was high in the routine problems. On the other hand, the rate of solving the problem using visual representation was high in the non-routine problems. The number of respondents who used visual representation in the non-routine problems was twice as many as that of the routine problems. But, among the subjects who used visual representation in the non-routine problems, the proportion of incorrect answers was also high, which resulted in using visual pictures. So, it is necessary to provide an experience that can use various types of the visual representations for problem solving and pay attention to the process of converting problems into visual representations.

• Journal of Science Education
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• v.45 no.2
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• pp.257-273
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• 2021

This study explores classes for pre-service mathematics teachers. The purpose of this study is to examine the differences between 'non-face-to-face' classes & 'face-to-face' classes, as well as the differences in learning outcomes between these two methods. A Professors' Learning Group was formed to effectively carry out this study. Through this learning group, we shared how to plan and operate the lecture. The subjects of this study are 'non-face-to-face calculus courses & face-to-face calculus courses' and 'non-face mathematics education theory courses & face-to-face mathematics education theory courses." Specifically, in these two pairs of courses, we analyze the differences in course management and the differences in the outcomes of students' assessments. Non-face-to-face classes were planned, developed, implemented and evaluated based on the 'non-face class design model.' The results of this study are as follows: First, we explored the differences between 'non-face-to-face classes/mixed classes' and 'face-to-face classes.' Second, the achievement results in calculus courses were higher in face-to-face classes than in non-face classes. Third, the results of achievements in mathematics education theory courses were higher in mixed classes than in face-to-face classes. Through the results of this study, we hope that the non-face-to-face class capabilities can be improved in pre-service mathematics teacher training.

• Journal of Science Education
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• v.44 no.3
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• pp.331-344
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• 2020

This study aims to find meaningful implications for the development of Korean elementary school math education courses and textbooks by comparing and analyzing the number and arithmetic areas of Korean and Canadian math textbooks in fifth and sixth grades. To this end, the textbook composition system of Korean and Canadian elementary schools was compared and analyzed, and the number and timing of introduction of math textbooks and math textbooks by grade, and the number in fifth and sixth grade and the learning contents of math textbooks were compared and analyzed. The following conclusions were obtained from this study: First, it is necessary to organize a textbook that can solve the problem in an integrated way by introducing the learned mathematical concepts and computations naturally in the context of problems closely related to real life, regardless of the type of private calculation or mathematics area. Second, it is necessary to organize questions using materials such as real photography and mathematics, science, technology, engineering, art, etc. and to organize textbooks that make people feel the necessity and usefulness of mathematics. Third, sufficient learning of the principles of mathematics through the use of various actual teaching aids and mathematical models, and the construction of textbooks focusing on problem-solving strategies using engineering tools are needed. Fourth, in-depth discussions are needed on the timing of learning guidance for fractions and minority learning or how to organize and develop learning content.

• Journal of Soil and Groundwater Environment
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• v.12 no.4
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• pp.54-59
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• 2007

In this study, a semi-analytical model to address groundwater level fluctuations in response to precipitations and its infiltration is developed through mathematical modeling based on water balance equation. The developed model is applied to a prediction of groundwater level fluctuations in Hongcheon area. The developed model is calibrated through a nonlinear parameter estimator by using daily precipitation rates and groundwater fluctuations data of a same year 2003. The calibrated input parameters are directly applied to the prediction of groundwater fluctuations of year 2004 and the simulated curve successfully mimics the observed. The developed model is also applied to practical problems such as a prediction of a effect of reduced recharge due to surface coverage change and a induced water level reduction. Through this study, we found that recharge to precipitation ratio is not a constant and may be a function of a precipitation pattern.

• Journal of Astronomy and Space Sciences
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• v.27 no.1
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• pp.1-10
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• 2010

The distance distribution in our planetary system has been a controversial matter. Two kinds of important issues on Titius-Bode's relation have been discussed up to now: one is if there is a simple mathematical relation between distances of natural bodies orbiting a central body, and the other is if there is any physical basis for such a relation. We have examined, by applying it to exo-planetary systems, whether Titius-Bode's relation is exclusively applicable to our solar system. We study, with the $X^2$ test, the distribution of period ratios of two planets in multiple planet systems by comparing it with that derived from not only Titius-Bode's relation but also other forms of it. The $X^2$ value between the distribution of the orbital period derived from Titius-Bode's relation and that observed in our Solar system is 12.28 (dof=18) with high probability, i.e., 83.3 %. The value of $X^2$ and probability resulted from Titius-Bode's relation and observed exo-planetary systems are 21.38 (dof=26) and 72.2 %, respectively. Modified forms we adopted seem also to agree with the planetary system as favorably as Titius-Bode's relation does. As a result, one cannot rule out the possibility that the distribution of the ratio of orbiting periods in multiple planet systems is consistent with that derived from Titius-Bode's relation. Having speculated Titius-Bode's relation could be valid in exo-planetary systems, we tentatively conclude it is unlikely that Titius-Bode's relation explains the distance distribution in our planetary system due to chance. Finally, we point out implications of our finding.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.12
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• pp.1106-1114
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• 2012

To achieve synchronized motion between a wearable robot and a human user, the redundancy must be resolved in the same manner by both systems. According to the seven DOF (Degrees of Freedom) human arm model composed of the shoulder, elbow, and wrist joints, positioning and orientating the wrist in space is a task requiring only six DOFs. Due to this redundancy, a given task can be completed by multiple arm configurations, and thus there exists no unique mathematical solution to the inverse kinematics. This paper presents analysis on the kinematic and dynamic aspect of the human arm movement and their effect on the redundancy resolution of the human arm based on a seven DOF manipulator model. The redundancy of the arm is expressed mathematically by defining the swivel angle. The final form of swivel angle can be represented as a linear combination of two different swivel angles achieved by optimizing different cost functions based on kinematic and dynamic criteria. The kinematic criterion is to maximize the projection of the longest principal axis of the manipulability ellipsoid for the human arm on the vector connecting the wrist and the virtual target on the head region. The dynamic criterion is to minimize the mechanical work done in the joint space for each two consecutive points along the task space trajectory. As a first step, the redundancy based on the kinematic criterion will be thoroughly studied based on the motion capture data analysis. Experimental results indicate that by using the proposed redundancy resolution criterion in the kinematic level, error between the predicted and the actual swivel angle acquired from the motor control system is less than five degrees.