• Communications of Mathematical Education
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• v.38 no.1
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• pp.49-67
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• 2024

Recent interest in the diverse applications of artificial intelligence (AI) language models has highlighted the need to explore didactical uses in mathematics education. AI language models, capable of natural language processing, show promise in solving mathematical word problems. This study tested the capability of ChatGPT, an AI language model, to solve word problems from elementary school textbooks, and analyzed both the solutions and errors made. The results showed that the AI language model achieved an accuracy rate of 81.08%, with errors in problem comprehension, equation formulation, and calculation. Based on this analysis of solution processes and error types, the study suggests implications for the didactical application of AI language models in education.

• Magazine of the Korean Society of Agricultural Engineers
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• v.39 no.2
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• pp.74-85
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• 1997

This study aims at the development of a mathematical approach for the optimal water allocation in the river basin where available water is not in sufficient. Its optimal allocation model is determined from the comparison and analysis of mathematical programming techniques such as transportation programming and dynamic programming models at its optimal allocation models. The water allocation system used in this study is designed to be the optimal water allocation which can satisfy the water deficit in each district through inter-basin water transfer between Kumho river basin which is a tributary catchment of Nakdong river basin, and the adjacent Hyungsan river basin, Milyang river basin and Nakdong upstream river basin. A general rule of water allocation is obtained for each district in the basins as the result of analysis of the optimal water allocation in the water allocation system. Also a comparison of the developed models proves that there is no big difference between the models Therefore transportation programming model indicates most adequate to the complex water allocation system in terms of its characteristics It can be seen, however, that dynamic programming model shows water allocation effect which produces greater net benefit more or less.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.23-37
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• 2020

The quadratic error metric (QEM) algorithm has been frequently used for simplification of triangular surface models that utilize the vertex-pair algorithm. Simplified models obtained using such algorithms present the advantage of smaller storage capacity requirement compared to the original models. However, a number of cases exist where significant features are lost geometrically, and these features can generally be preserved by utilizing the advantages of the curvature-weighted algorithm. Based on the vertex-based geometric features, a method capable of preserving the geometric features better than the previous algorithms is proposed in this work. To validate the effectiveness of the proposed method, a simplification experiment is conducted using several models. The results of the experiment indicate that the geometrically important features are preserved well when a local feature is present and that the error is similar to those of the previous algorithms when no local features are present.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.1
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• pp.130-140
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• 1998

This paper presents a method to estimate subpixel accuracy motion vectors using a mathermatical model withoug interpolation. the proposed method decides the coefficients of mathematical model, which represents the motion vector which is achieved by full search. And then the proposed method estimates subpixel accuracy motion vector from achieved mathematical model. Step by step mathematical models such as type 1, type 2, type 3, modified bype 2, modified type 3, and Partial Interpolation type 3 are presented. In type 1, quadratic polynomial, which has 9 unknown coefficients and models the 3by 3 pixel plane, is used to get the subpixel accuracy motion vectors by inverse matrix solution. In type 2 and 3, each quadratic polynomial which is simplified from type 1 has 5 and 6 unknown coefficients and is used by least square solution. Modified type 2 and modified type 3 are enhanced models by weighting only 5 pixels out of 9. P.I. type 3 is more accurate method by partial interpolation around subpixel which isachieved by type 3. LThese simulation results show that the more delicate model has the better performance and modified models which are simplified have excellent performance with reduced computational complexity.

• Journal of the Korean Society for Library and Information Science
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• v.14
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• pp.93-130
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• 1987

Scientific communication is an information exchange activity between scientists. Scientific communication is carried out in a variety of informal and formal ways. Basically, informal communication takes place by word of mouth, whereas formal communication occurs via the written word. Science is a highly interdependent activity in which each scientist builds upon the work of colleagues past and present. Consequently, science depends heavily on scientific communication. In this study, three mathematical models, namly Brillouin measure, logistic equation, and Markov chain are examined. These models provide one with a means of describing and predicting the behavior of scientific communication process. These mathematical models can be applied to construct quality filtering algorithms for subject literature which identify synthesized elements (authors, papers, and journals). Each suggests a different type of application. Quality filtering for authors can be useful to funding agencies in terms of identifying individuals doing the best work in a given area or subarea. Quality filtering with respect to papers can be useful in constructing information retrieval and dissemination systems for the community of scientists interested m the field. The quality filtering of journals can be a basis for the establishment of small quality libraries based on local interests in a variety of situations, ranging from the collection of an individual scientist or physician to research centers to developing countries. The objective of this study is to establish the theoretical framework for informetrics which is defined as the quantitative analysis of scientific communication, by investigating mathematical models of scientific communication.

• Genomics & Informatics
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• v.20 no.2
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• pp.22.1-22.9
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• 2022

The rise of newer coronavirus disease 2019 (COVID-19) variants has brought a challenge to ending the spread of COVID-19. The variants have a different fatality, morbidity, and transmission rates and affect vaccine efficacy differently. Therefore, the impact of each new variant on the spread of COVID-19 is of interest to governments and scientists. Here, we proposed mathematical SEIQRDVP and SEIQRDV3P models to predict the impact of the Omicron variant on the spread of the COVID-19 situation in South Korea. SEIQEDVP considers one vaccine level at a time while SEIQRDV3P considers three vaccination levels (only one dose received, full doses received, and full doses + booster shots received) simultaneously. The omicron variant's effect was contemplated as a weighted sum of the delta and omicron variants' transmission rate and tuned using a hyperparameter k. Our models' performances were compared with common models like SEIR, SEIQR, and SEIQRDVUP using the root mean square error (RMSE). SEIQRDV3P performed better than the SEIQRDVP model. Without consideration of the variant effect, we don't see a rapid rise in COVID-19 cases and high RMSE values. But, with consideration of the omicron variant, we predicted a continuous rapid rise in COVID-19 cases until maybe herd immunity is developed in the population. Also, the RMSE value for the SEIQRDV3P model decreased by 27.4%. Therefore, modeling the impact of any new risen variant is crucial in determining the trajectory of the spread of COVID-19 and determining policies to be implemented.

• East Asian mathematical journal
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• v.32 no.4
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• pp.443-464
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• 2016

The purpose of ths study is to compare and analyze the sequence of teaching multiplication facts in the elementary school mathematics. Generally, the multiplication in the elementary school mathematics is composed of the followings; concepts of multiplication, situations involving multiplication, didactical models for multiplication, and multiplication strategies for teaching multiplication facts. This study is focusing to multiplication facts, especially to the sequence of teaching and multiplication strategies. The method of this study is a comparative and analytic method. In order to compare textbooks, we select the Korean elementary mathematics textbooks(1st curriculum~2009 revised curriculum) and the 9 foreign elementary mathematics textbooks(Japan, China, Germany, Finland, Hongkong etc.). As results of comparative investigation, the sequence of teaching multiplication facts is reconsidered on a basis of elementary students' mathematical thinking. And the connectivity of multiplication facts is strengthened in comparison with the foreign elementary mathematics textbooks. Finally multiplication strategies for teaching multiplication facts are discussed for more understanding and reasoning the principles of multiplication facts in the elementary school mathematics.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.885-897
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• 2006

A new mathematical model of pumping heart coupled to lumped compartments of blood circulation is presented. This lumped pulsatile cardiovascular model consists of eight compartments of the body that include pumping heart, the systemic circulation, and the pulmonary circulation. The governing equations for the pressure and volume in each vascular compartment are derived from the following equations: Ohm's law, conservation of volume, and the definition of compliances. The pumping heart is modeled by the time-dependent linear curves of compliances in the heart. We show that the numerical results in normal case are in agreement with corresponding data found in the literature. We extend the developed lumped model of circulation in normal case into a specific model for arrhythmia. These models provide valuable tools in examining and understanding cardiovascular diseases.

• Journal of Welding and Joining
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• v.15 no.3
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• pp.118-127
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• 1997

With the trend towards welding automation and robotization, mathematical models for studying the influence of various variables on the weld bead geometry in gas metal arc (GMA) welding process are required. Partial penetration, single-pass bead-on-plate welds using the GMA welding process were fabricated in 12mm mild steel plates employed four different process variables. Experimental results has been designed to investigate the analytical and empirical formulae, and develop mathematical equations for understanding the relationship between process variables and weld bead geometry. The relationships can be usefully employed not only for open loop process control, but also for adaptive control provided that dynamic sensing of process output is performed.

• Proceedings of the KWS Conference
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• 1997.10a
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• pp.229-233
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• 1997

The demand to increase productivity and quality, the shortage of skilled labour and the strict health and safety requirements have led to the development of the automated welding process to deal with many of the present problems of welded fabrication. To make effective use of the automated arc welding process, it is imperative that a mathematical model, which can be programmed easily and fed to the robot, should be developed. The objectives of the paper are to develop the mathematical equations (linear and curvilinear) for study of the relationship between process variables and bead geometry by employing a standard statistical package program, SAS and to choose the best model for automation of the $CO_2$ gas arc welding process. Mathematical models developed from experimental results can be employed to control the process variables in order to achieve the desired bead geometry based on weld quality criteria. Also these equations may prove useful and applicable for automatic control system and expert systems.