• The Mathematical Education
• /
• v.42 no.3
• /
• pp.403-417
• /
• 2003

The purpose of this study is to analyze the effects of the use of calculators in elementary school mathematics education. For this purpose, we established the subject matters of the research as folloows; (1) to develop the lesson plan and the students' activity sheet related to the use of calculators. (2) to analyze the effects of the use of calculators when we applied the materials developed. Four classes of sixth grade students were sampled two elementary schools in D city. Two of them were assigned to the calculator group and the others to traditional group. The experiment was conducted for 10 class times. Two kinds of test instruments were used: pretest and post test. The pretest scores guaranteed that both groups were homogeneous. Post-test was used to identify the effect of use of calculator and the post-test scores were analyzed by t-test. We also used questionnaire to identify the students' change of attitude toward mathematics. The results of this study as fellows: (1) The calculator group got scores significantly higher than the traditional group on the test. (2) The students' attitude in calculator group was changed a little positively.

• Bulletin of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.35-44
• /
• 1994

In this paper we study exponential growth of Betti numbers over artinian local rings. By the Change of Tor Formula the results in the paper extend to the asymptotic behavior of Betti numbers over Cohen-Macaulay local rings. Using the length function of an artinian ring we calculate an upper bound for the number of generators of modules, this is then used to maximize the number of generators of sygyzy modules. Finally, applying a filtration of an ideal, which we call a Loewy series of an ideal, we derive an invariant B(R) of an artinian local ring R, such that if B(R)>1, then the sequence $b^{R}$$_{i}$ (M) of Betti numbers is strictly increasing and has strong exponential growth for any finitely generated non-free R-module M (Theorem 2.7).).

• Research in Mathematical Education
• /
• v.13 no.4
• /
• pp.309-330
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1371-1389
• /
• 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
• /
• v.25 no.4
• /
• pp.327-336
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.857-867
• /
• 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
• /
• v.26 no.4
• /
• pp.263-279
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.303-318
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.541-556
• /
• 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
• /
• v.27 no.4
• /
• pp.203-212
• /
• 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.