• KOREAN JOURNAL OF PACKAGING SCIENCE & TECHNOLOGY
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• v.4 no.1
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• pp.23-32
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• 1997

The change in moisture content of moisture sensitive products in moisture-semipermeable packages was investigated for the purpose of predicting the shelf life of a product-package combination. A mathematical model, and a computer program based on the physiochemical properties of the product and the moisture permeability of the package was developed. The moisture content for products in moisture-semipermeable packages was determined under various environmental conditions and the results were compared with the predicted values by means of the simulation model. These experimental studies demonstrated that the prediction of the change in moisture content of packaged products over time by the simulation model is accurate, within a practical range of temperature and relative humidity values. The developed semi-empirical model is considered to have applications in industry, since it provides product shelf life information for a range of temperature and relative humidity conditions, with a limited number of experimentally obtained data points.

• Advances in nano research
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• v.13 no.6
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• pp.561-574
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• 2022

The stability of protein tissues and protein fibers in the human muscle is investigated in the presented paper. The protein fibers are modeled via tube structures embedded in others proteins fibers like the elastic substrate. Physical sport and physical exercise play an important role in the stability of synthesis and strength of the protein tissues. In physical exercise, the temperature of the body increases, and this temperature change impacts the stability of the protein tissues, which is the aim of the current study. The mathematical simulation of the protein tissues is done based on the mechanical sciences, and the protein fibers are modeled via wire structures according to the high-order theory beams. The thermal stress due to the conditions of the sport is applied to the nanoscale protein fibers, then the stability regarding the frequency analysis is investigated. Finally, the impact of temperature change, physical exercise, and small-scale parameters on the stability of the protein tissues are examined in detail.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.553-567
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• 2023

There are real life situations in our lives where the things are changing continuously or from time to time. It is a very important problem for one whether to continue the existing relationship or to form a new one after some occasions. That is, people, companies, cities, countries, etc. may change their opinion or position rapidly. In this work, we think of the problem of changing relationships from a mathematical point of view and think of an answer. In some sense, we comment these changes as power changes. Our number theoretical model will be based on this idea. Using the convolution sum of the restricted divisor function E, we obtain the answer to this problem.

• Smart Structures and Systems
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• v.33 no.4
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• pp.281-290
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• 2024

This work investigates the mechanical energy harvesting from smart and adaptive devices using magnetic interactions. The energy harvester is built from an elastic beam connected to an electric circuit by a magnetostrictive material that promotes energy transduction. Besides, magnetic interactions define the system stability characterizing multistable configurations. The adaptiveness is provided by magnets that can change their position with respect to the beam, changing the system configuration. A mathematical model is proposed considering a novel model to describe magnetic interactions based on the single-point magnet dipole method, but employing multiple points to represent the magnetic dipole, which is more effective to match experimental data. The adaptive behavior allows one to alter the system stability and therefore, its dynamical response. A nonlinear dynamics analysis is performed showing the possibilities to enhance energy harvesting capacity from the magnet position change. The strategy is to perform a system dynamical characterization and afterward, alter the energetic barrier according to the environmental energy sources. Results show interesting conditions where energy harvesting capacity is dramatically increased by changing the system characteristics.

• Journal of Educational Research in Mathematics
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• v.14 no.3
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• pp.221-237
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• 2004

This research analyzed mathematical discourse of the students in an RME-based differential equations course at a university in order to investigate the social transformation of the students' conceptual model of differential equations. The analysis focused on the change in the students' use of conceptual metaphor for differential equations and pedagogical factors promoting the change. The analysis shows that discrete and quantitative conceptual model was prevalent in the beginning of the semester However, continuous and qualitative conceptual model emerged through the negotiation of mathematical meaning based on the inquiry of context problems. The participation in the project class has a positive impact on the extension of the students' conceptual model of differential equations and increases the fluency of the students' problem solving in differential equations. Moreover, this paper provides a discussion to identify the pedagogical factors Involved with the transformation of the students' conceptual model. The discussion highlights the sociocultural aspect of teaching and learning of mathematics and provides implications to improve teaching of mathematics in school.

• Nuclear Engineering and Technology
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• v.28 no.2
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• pp.103-117
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• 1996

A mathematical model of vapor explosion propagation is presented. The model predict two-dimensional, transient flow fields and energies of the four fluid phases of melt drop, fragmented debris, liquid coolant and vapor coolant by solving a set of governing equations with the relevant constitutive relations. These relations include melt fragmentation, coolant-phase-change, and heat and momentum exchange models. To allow thermodynamic non-equilibrium between the coolant liquid and vapor, an equation of state for oater is uniquely formulated. A multiphase code, TRACER, has been developed based on this mathematical formulation. A set of base calculations for tin/water explosions show that the model predicts the explosion propagation speed and peak pressure in a reasonable degree although the quantitative agreement relies strongly on the parameters in the constitutive relations. A set of calculations for sensitivity studies on these parameters have identified the important initial conditions and relations. These are melt fragmentation rate, momentum exchange function, heat transfer function and coolant phase change model as well as local vapor fractions and fuel fractions.

• The Mathematical Education
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• v.57 no.2
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• pp.157-177
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• 2018

The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

• Journal of Educational Research in Mathematics
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• v.21 no.3
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• pp.295-311
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• 2011

The importance of problem solving in mathematics education has been emphasized and many studies related to this issue have been conducted. But, studies of problem solving in the aspect of affect domain are lacked. This study found the changing pattern of emotions that occur in process of a problem solving. The results are listed below. First, students experienced a lot of change of emotions and had a positive emotion as well as negative emotion during solving problems. Second, students who solved same problems through same methods experienced different change patterns of emotions. The reason is that students have different mathematical beliefs and think differently about a difficulty level of problem. Third, whether students solved problems with positive emotion or negative emotion depends on their attitude of mathematics. Fourth, students who thought that a difficulty level of problem was relatively high experienced more negative affect than students who think a difficulty level of problem is low experienced.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.739-744
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• 2002

Recently we have discovered that sediments should be separated from lithosphere, and soil should be separated from biosphere, both sediment and soil will be mixed sediments-soil-sphere (Seso-sphere), which is using particulate mechanics to be solved. Erosion and sediment both are moving by particulate matter with water or wind. But ancient sediments will be erosion same to soil. Nowadays, real soil has already reduced much more. Many places have only remained sediments that have ploughed artificial farming layer. Thus it means sediments-soil-sphere. This paper discusses sediments-soil-sphere erosion modeling. In fact sediments-soil-sphere erosion is including water erosion, wind erosion, melt-water erosion, gravitational water erosion, and mixed erosion. We have established geographical remote sensing information modeling (RSIM) for different erosion that was using remote sensing digital images with geographical ground truth water stations and meteorological observatories data by remote sensing digital images processing and geographical information system (GIS). All of those RSIM will be a geographical multidimensional gray non-linear equation using mathematics equation (non-dimension analysis) and mathematics statistics. The mixed erosion equation is more complex that is a geographical polynomial gray non-linear equation that must use time-space fuzzy condition equations to be solved. RSIM is digital image modeling that has separated physical factors and geographical parameters. There are a lot of geographical analogous criterions that are non-dimensional factor groups. The geographical RSIM could be automatic to change them analogous criterions to be fixed difference scale maps. For example, if smaller scale maps (1:1000 000) that then will be one or two analogous criterions and if larger scale map (1:10 000) that then will be four or five analogous criterions. And the geographical parameters that are including coefficient and indexes will change too with images. The geographical RSIM has higher precision more than mathematics modeling even mathematical equation or mathematical statistics modeling.

• Communications of Mathematical Education
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• v.34 no.4
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• pp.525-544
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• 2020

There are many factors that affect academic achievement, and the influences of those factors are also complex. Since the factors that influence mathematics academic achievement are constantly changing and developing, longitudinal studies to predict and analyze the growth of learners are needed. This study uses longitudinal data from 2014 (second year of middle school) to 2017 (second year of high school) of the Seoul Education Longitudibal Study, and divides it into groups with similar longitudinal patterns of change in mathematics academic achievement. The longitudinal change patterns and direct influence of mood and satisfaction were examined. As a result of the study, it was found that the mathematics academic achievement of the first group (1456 students, 68.3%) including the majority of students and the second group (677 students) of the top 31.7% had a direct influence on the mathematics class attitude. It was found that the mood and satisfaction of mathematics classes did not have a direct effect. In addition, the influence of mathematics class attitude on mathematics academic achievement was different according to the group. In addition, students in group 2 with high academic achievement in mathematics showed higher mathematics class attitude, mood, and satisfaction. In addition, the attitude, atmosphere, and satisfaction of mathematics classes were found to change continuously from the second year of middle school to the second year of high school, and the extent of the change was small.