• 한국수학교육학회지시리즈D:수학교육연구
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• 제13권4호
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• pp.309-330
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• 2009

The article aims to present findings of a study which has examined the ability of elementary school mathematics teachers and of teacher-trainees in other disciplines to solve irregular challenging problems of sequences in general rather than numerical sequences only. The findings show that mathematics teachers succeed to cope with unusual assignments when the requirements of the problems presented to them are analogous to irregular problems. However, when the problems require a change in the thinking procedure in the direction of creative thinking, there is a considerable decrease in performance. Another finding shows that, although teacher-trainees succeed less in solving the presented problems, they give incorrect solutions which do indicate creative thinking. An inevitable conclusion based on the research findings is that teacher training institutions should enhance and reinforce multi-directional. branching out and creative thinking competences.

• 대한수학회지
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• 제53권6호
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• pp.1371-1389
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• 2016

In this paper, we propose a new rank two quasi-Newton method based on adjoint Broyden updates for solving symmetric nonlinear equations, which can be seen as a class of adjoint BFGS method. The new rank two quasi-Newton update not only can guarantee that $B_{k+1}$ approximates Jacobian $F^{\prime}(x_{k+1})$ along direction $s_k$ exactly, but also shares some nice properties such as positive deniteness and least change property with BFGS method. Under suitable conditions, the proposed method converges globally and superlinearly. Some preliminary numerical results are reported to show that the proposed method is effective and competitive.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권4호
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• pp.327-336
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• 2021

In this paper, we will introduce the image processing methods for the remote pupillary light reflex measurement using the video taken by a general smartphone camera without a special device such as an infrared camera. We propose an algorithm for estimate the size of the pupil that changes with light using image data analysis without a learning process. In addition, we will introduce the results of visualizing the change in the pupil size by removing noise from the recorded data of the pupil size measured for each frame of the video. We expect that this study will contribute to the construction of an objective indicator for remote pupillary light reflex measurement in the situation where non-face-to-face communication has become common due to COVID-19 and the demand for remote diagnosis is increasing.

• 대한수학회지
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• 제56권4호
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.263-279
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• 2022

This paper presents an automatic inspection of defects in semiconductor images. We devise a statistical method to find defects on homogeneous background from the observation that it has a log-normal distribution. If computer aided design (CAD) data is available, we use it to construct a signed distance function (SDF) and change the pixel values so that the average of pixel values along the level curve of the SDF is zero, so that the image has a homogeneous background. In the absence of CAD data, we devise a hybrid method consisting of a model-based algorithm and two neural networks. The model-based algorithm uses the first right singular vector to determine whether the image has a linear or complex structure. For an image with a linear structure, we remove the structure using the rank 1 approximation so that it has a homogeneous background. An image with a complex structure is inspected by two neural networks. We provide results of numerical experiments for the proposed methods.

• 대한수학회보
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• 제59권2호
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• pp.303-318
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• 2022

n-writhes denoted by J_n(K) are virtual knot invariants for n ≠ 0 and are closely associated with coefficients of some polynomial invariants of virtual knots. In this work, we investigate the variations of J_n(K) under arc shift move and conclude that n-writhes J_n(K) vary randomly in the sense that it may change by any random integer value under one arc shift move. Also, for each n ≠ 0 we provide an infinite family of virtual knots which can be distinguished by n-writhes J_n(K), whereas odd writhe J(K) fails to do so.

• 대한수학회보
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• 제61권2호
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• pp.541-556
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• 2024

In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain $-{\Delta}u+V(x)u-{\frac{u}{\sqrt{1-u^2}}}{\Delta}{\sqrt{1-u^2}}={\lambda}{\mid}u{\mid}^{p-2}u$, x ∈ ℝ^N, where 2 ≤ p < 2^*, N ≥ 3. By the Ekeland variational principle, the cut off technique, the change of variables and the L^∞ estimate, we study the existence of positive solutions. Here, we construct the L^∞ estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.

• Journal of Obesity & Metabolic Syndrome
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• 제27권4호
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• pp.203-212
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• 2018

Dynamic energy balance can give clinicians important answers for why obesity is so resistant to control. When food intake is reduced for weight control, all components of energy expenditure change, including metabolic rate at rest (resting energy expenditure [REE]), metabolic rate of exercise, and adaptive thermogenesis. This means that a change in energy intake influences energy expenditure in a dynamic way. Mechanisms associated with reduction of total energy expenditure following weight loss are likely to be related to decreased body mass and enhanced metabolic efficiency. Reducing calorie intake results in a decrease in body weight, initially with a marked reduction in fat free mass and a decrease in REE, and this change is maintained for several years in a reduced state. Metabolic adaptation, which is not explained by changes in body composition, lasts for more than several years. These are powerful physiological adaptations that induce weight regain. To avoid a typically observed weight-loss and regain trajectory, realistic weight loss goals should be established and maintained for more than 1 year. Using a mathematical model can help clinicians formulate advice about diet control. It is important to emphasize steady efforts for several years to maintain reduced weight over efforts to lose weight. Because obesity is difficult to reverse, clinicians must prioritize obesity prevention. Obesity prevention strategies should have high feasibility, broad population reach, and relatively low cost, especially for young children who have the smallest energy gaps to change.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제15권2호
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• pp.107-134
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• 2012

수학적 모델링은 일반적으로 수학적인 방법으로 해석되고 이해되어야 하는 실제적인 문제 상황을 해결하기 위해 상황에 대한 적절한 수학적 모델을 구성하여 문제를 해결하는 일련의 과정이라고 할 수 있다. 문장제는 실제적인 측면과 형식적인 측면, 모두를 포함하고 있으므로 수학적 모델링 활동에 이상적인 도구가 될 수 있다. 이에 본 연구는 실세계의 맥락을 고려해야 하는 진정성있는 문장제를 바탕으로 한 수학적 모델링 학습이 문장제 해결 행동, 문장제 해결에서 실생활 경험을 활용하는 능력, 문장제에 대한 신념 등에 미치는 영향을 조사하였다. 연구 결과 문장제에 대한 수학적 모델링 학습은 직접번역 접근(DTA) 대신에 의미기반 접근(MBA)으로 문장제 해결 행동을 이끄는데 효과적이었으며, 문장제를 해결하는데 있어서 실생활 맥락을 고려하는 태도에 긍정적인 영향을 미쳤다. 또한 수학적 모델링 학습은 문장제에 대한 긍정적인 신념을 형성하는데 중요한 역할을 했음을 알 수 있었다. 이와 같은 연구 결과를 바탕으로 초등학교에서 문장제를 어떻게 다루어야 하는지에 대한 시사점을 살펴보았다.

• 한국학교수학회논문집
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• 제4권2호
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• pp.61-74
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• 2001

The purposes of this study are to develop the mathematical performance assessment tasks and to apply them to the middle school students. And I also intend to know the students' inclination and learning attitude to mathematics. In order to satisfy this study, I developed the performance assessment tasks and the standard program of marking about the mathematical function and statistics for the first grade students at middle school. After examining the students' basic investigation, their inclination and learning attitude to mathematics, I applied these developed tasks to them After that I put both classes and performance assessment into operation in all 15 periods. I set up two classes of the first grade students (49 students) at J middle school in Kongju, Chungcheongnam-do as a model group. The results of this study are as follows: First, owing to the developed performance assessment tasks of function and statistics, the teachers can operate the assessment system as a process of teaching and learning. Second, because of the application of mathematical performance assessment tasks, we can change the students' inclination and learning attitude to mathematics affirmatively. And by using these tasks, we can help the students to think mathematically. In this way, the students will be able to realize the real value of mathematics and have a growing interest in mathematics through all these meaningful processes. Judging from this study, we can elevate the students' abilities of problem solving and reasoning and improve teaching-learning method by applying the performance assessment tasks to them. Thanks to these tasks, the students will be changed affirmatively in their inclination and learning attitude to mathematics. I think that these tasks are very good assessment method which can call forth curiosity and interest. Besides, they can also help the students realize the real value of mathematics.