• Research in Mathematical Education
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• v.26 no.3
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• pp.167-202
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• 2023

A central problem of mathematics teaching worldwide is probably the insufficient adaptive handling of tasks-especially in computational practice phases and modeling tasks. All students in a classroom must often work on the same tasks. In the process, the high-achieving students are often underchallenged, and the low-achieving ones are overchallenged. This publication uses different modeling of the tennis serve as an example to show a possible solution to the problem and develops and discusses one adaptive task each for middle school, high school, and college using three mathematical models of the tennis serve each time. From model to model within the task, the complexity of the modeling increases, the mathematical or physical demands on the students increase, and the new modeling leads to more realistic results. The proposed models offer the possibility to address heterogeneous learning groups by their arrangement in the surface structure of the so-called parallel adaptive task and to stimulate adaptive mathematics teaching on the instructional topic of mathematical modeling. Models A through C are suitable for middle school instruction, models C through E for high school, and models E through G for college. The models are classified in the specific modeling cycle and its extension by a digital tool model, and individual modeling steps are explained. The advantages of the presented models regarding teaching and learning mathematical modeling are elaborated. In addition, we report our first teaching experiences with the developed parallel adaptive tasks.

• Journal of Korean Society for Quality Management
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• v.7 no.2
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• pp.17-21
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• 1979

There are many kinds of the mathematical models which are developed for choosing the economic inspection plan. The aim of this paper is to classify these mathematical models, and to examine their characteristics. The mathematical models for choosing the economic inspection plan can be classified into three groups. The first of it is the break-even analysis, the second group of the model is to choose the inspection plan so as to minimize total sampling inspection cost function, and the third group of it is the model to choose the inspection plan which maximize the profit function of the sampling inspection. As a result of examining the characteristics of this classified group of the models the model to choose the inspection plan which minimize total sampling inspection cost is more economical than the other models.

• Coupled systems mechanics
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• v.12 no.6
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• pp.539-555
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• 2023

Although some prediction models have successfully developed for ultra-high performance concrete (UHPC), they do not provide insights and explicit relations between all constituents and its consistency, and compressive strength. In the present study, based on the experimental results, several mathematical models have been evaluated to predict the consistency and the 28-day compressive strength of UHPC. The models used were Linear, Logarithmic, Inverse, Power, Compound, Quadratic, Cubic, Mixed, Sinusoidal and Cosine equations. The applicability and accuracy of these models were investigated using experimental data, which were collected from literature. The comparisons between the models and the experimental results confirm that the majority of models give acceptable prediction with a high accuracy and trivial error rates, except Linear, Mixed, Sinusoidal and Cosine equations. The assessment of the models using numerical methods revealed that the Quadratic and Inverse equations based models provide the highest predictability of the compressive strength at 28 days and consistency, respectively. Hence, they can be used as a reliable tool in mixture design of the UHPC.

• Electronics and Telecommunications Trends
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• v.38 no.6
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• pp.1-11
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• 2023

Large language models seem promising for handling reasoning problems, but their underlying solving mechanisms remain unclear. Large language models will establish a new paradigm in artificial intelligence and the society as a whole. However, a major challenge of large language models is the massive resources required for training and operation. To address this issue, researchers are actively exploring compact large language models that retain the capabilities of large language models while notably reducing the model size. These research efforts are mainly focused on improving pretraining, instruction tuning, and alignment. On the other hand, chain-of-thought prompting is a technique aimed at enhancing the reasoning ability of large language models. It provides an answer through a series of intermediate reasoning steps when given a problem. By guiding the model through a multistep problem-solving process, chain-of-thought prompting may improve the model reasoning skills. Mathematical reasoning, which is a fundamental aspect of human intelligence, has played a crucial role in advancing large language models toward human-level performance. As a result, mathematical reasoning is being widely explored in the context of large language models. This type of research extends to various domains such as geometry problem solving, tabular mathematical reasoning, visual question answering, and other areas.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.39-61
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• 2012

Mathematical creativity is essential in school mathematics and mathematics curriculum and ensures the growth of mathematical ability. Therefore mathematics educators try to develop students' creativity via mathematics education for a long time. In special, 2011 revised mathematics curriculum emphasizes mathematical creativity. Yet, it may seem like a vague characterization of mathematical creativity. Furthermore, it is needed to develop the methods for developing the mathematical creativity. So, the goal of this paper is to search for teaching and learning models for developing the mathematical creativity. For this, I discuss about issues of mathematical creativity and extract the factors of mathematical creativity. The factors of mathematical creativity are divided into cognitive factors, affective factors and attitude factors that become the factors of development of mathematical creativity in the mathematical instruction. And I develop 8-teaching and learning models for development of mathematical creativity based on the characters of mathematics and the most recent theories of mathematics education. These models make it crucial for students to develop the mathematical creativity and create the new mathematics in the future.

• East Asian mathematical journal
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• v.16 no.2
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• pp.251-266
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• 2000

The problem of solution uniqueness to the task of determining unknown parameters of mathematical models from input-output observations is studied. This problem is known as structural identifiability problem. We offer a new approach for testing structural identifiability of linear state space models. The approach compares favorably with numerous methods proposed by other authors for two main reasons. First, it is formulated in obvious mathematical form. Secondly, the method does not involve unfeasible symbolic computations and thus allows to test identifiability of large-scale models. In case of non-identifiability, when there is a set of solutions to the task, we offer a method of computing functions of the unknown parameters which can be determined uniquely from input-output observations and later used as new parameters of the model. Such functions are called parametric functions capable of estimation. To develop the method of computation of these functions we use Lie group transformation theory. Illustrative example is given to demonstrate applicability of presented methods.

• Journal for History of Mathematics
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• v.29 no.6
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• pp.353-363
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• 2016

In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1527-1575
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• 2017

In a spirit of Givental's constructions Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested Landau-Ginzburg models for smooth Fano complete intersections in Grassmannians and partial flag varieties as certain complete intersections in complex tori equipped with special functions called superpotentials. We provide a particular algorithm for constructing birational isomorphisms of these models for complete intersections in Grassmannians of planes with complex tori. In this case the superpotentials are given by Laurent polynomials. We study Givental's integrals for Landau-Ginzburg models suggested by Batyrev, Ciocan-Fontanine, Kim, and van Straten and show that they are periods for pencils of fibers of maps provided by Laurent polynomials we obtain. The algorithm we provide after minor modifications can be applied in a more general context.

• Ocean and Polar Research
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• v.41 no.1
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• pp.19-34
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• 2019

The present study obtained universal mathematical models of all elements and characteristics regarding hook and line fishing systems. To describe the hook and line fishing systems on site we used three kinds of coordinate systems: the earth based coordinate system, natural coordinate system, and flow (velocity) coordinate system. Mathematical models presented in this article allow us to define the shape of the fishing gear, the tension of the rope at different points, hydrodynamic resistance, diameter of the hook's wire, immersion depth of the fishing hooks, distance from hooks to the ground and the required lifting force of the floats. These models allow for the performance of computer simulations regarding any kinds of hook and line gears in still water or water where flow occurs.

• The Korean Journal of Physiology and Pharmacology
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• v.23 no.5
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• pp.305-310
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• 2019

The physiomic approach is now widely used in the diagnosis of cardiovascular diseases. There are two possible methods for cardiovascular physiome: the traditional mathematical model and the machine learning (ML) algorithm. ML is used in almost every area of society for various tasks formerly performed by humans. Specifically, various ML techniques in cardiovascular medicine are being developed and improved at unprecedented speed. The benefits of using ML for various tasks is that the inner working mechanism of the system does not need to be known, which can prove convenient in situations where determining the inner workings of the system can be difficult. The computation speed is also often higher than that of the traditional mathematical models. The limitations with ML are that it inherently leads to an approximation, and special care must be taken in cases where a high accuracy is required. Traditional mathematical models are, however, constructed based on underlying laws either proven or assumed. The results from the mathematical models are accurate as long as the model is. Combining the advantages of both the mathematical models and ML would increase both the accuracy and efficiency of the simulation for many problems. In this review, examples of cardiovascular physiome where approaches of mathematical modeling and ML can be combined are introduced.