• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.329-334
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• 2007

By the works of Levine [2] and Rolfsen [5], [6], it is known that a local move called a crossing-change is strongly related to the Alexander invariant. In this note, we will consider to what degree the relationship is strong. Let K be a knot, and $K^{\times}$ the set of knots obtained from a knot K by a single crossing-change. Let MK be the Alexander invariant of a knot K, and MK the set of the Alexander invariants $\{MK\}_{K{\in}\mathcal{K}}$ for a set of knots $\mathcal{K}$. Our main result is the following: If both $K_1$ and $K_2$ are knots with unknotting number one, then $MK_1=MK_2$ implies $MK_1^{\times}=MK_2^{\times}$. On the other hand, there exists a pair of knots $K_1$ and $K_2$ such that $MK_1=MK_2$ and $MK_1^{\times}{\neq}MK_2^{\times}$. In other words, the Gordian complex is not homogeneous with respect to Alexander invariants.

• Proceedings of the KOSOMBE Conference
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• v.1998 no.11
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• pp.177-178
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• 1998

This paper is a study on compensation for error in estimation of mean pressure according to the change of arterial pressure shape. Because arterial pressure shape affects the mean pressure and blood volume which are important factors for measurement of blood pressure(BP), change of arterial pressure shape cause BP measurement error. In order to solve this problem, we add the compensation function C($\alpha$), depending on arterial pressure shape, to mathematical oscillometric model. Consequently, we could accurately estimate the blood pressure by correcting of the error using compensation function.

• Journal of Biosystems Engineering
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• v.42 no.2
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• pp.86-97
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• 2017

Purpose: This study aims to evaluate the applicability of a tractor-baler system equipped with a newly developed round baler by conducting stability analyses via static-state mathematical simulations and verification experiments for the tractor equipped with a loader. Methods: The centers of gravity of the tractor and baler were calculated to analyze the transverse overturning of the system. This overturning of the system was analyzed by applying mathematical equations presented in previous research and comparing the results with those obtained by the newly developed mathematical simulation. For the case of the tractor equipped with a loader, mathematical simulation results and experimental values from verification experiments were compared and verified. Results: The center of gravity of the system became lower after the baler was attached to the tractor and the angle of transverse overturning of the system steadily increased or decreased as the deflection angle increased or decreased between $0^{\circ}$ and $180^{\circ}$ on the same gradient. In the results of the simulations performed by applying mathematical equations from previous research, right transverse overturning occurred when the tilt angle was at least $19.5^{\circ}$ and the range of deflection angles was from $82^{\circ}$ to $262^{\circ}$ in counter clockwise. Additionally, left transverse overturning also occurred at tilt angles of at least $19.5^{\circ}$ and the range of deflection angles was from $259^{\circ}$ to $79^{\circ}$ in counter clockwise. Under the $0^{\circ}$ deflection angle condition, in simulations of the tractor equipped with a loader, transverse overturning occurred at $17.9^{\circ}$, which is a 2.3% change from the results of the verification experiment ($17.5^{\circ}$). The simulations applied the center of gravity and the correlations between the tilt angles, formed by individual wheel ground contact points excluding wheel radius and hinge point height, which cannot be easily measured, for the convenient use of mathematical equations. The results indicated that both left and right transverse overturning occurred at $19.5^{\circ}$. Conclusions: The transverse overturning stability evaluation of the system, conducted via mathematical equation modeling, was stable enough to replace the mathematical equations proposed by previous researchers. The verification experiments and their results indicated that the system is workable at $12^{\circ}$, which is the tolerance limit for agricultural machines on the sloped lands in South Korea, and $15^{\circ}$, which is the tolerance limit for agricultural machines on the sloped grasslands of hay in Japan.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.34 no.5
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• pp.3-11
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• 2018

Since the tensegrity structure is flexible and variable, the study on the mobility to the tensegrity has been conducted. However, it is difficult to apply the tensegrity to the architecture field due to several limits. This paper describes the methodology for the analysis of the shape change process of single prism tensegrity structure as an initial study. To apply the tensegrity structure to the architectural field, the assemblage and mathematical formulation procedures of the single prism tensegrity structures are carried out. And single prism tensegrity are presented to the computational strategies for simulate the shape change of those structures. Next, the investigation of structural behaviors through various cases of target displacements is described. Also, the summary of these methods in algorithms is illustrated. As a result it is confirmed that the single prism tensegrity structure model converges 99% on average to a given target node by using the proposed algorithm. Therefore, it is confirmed that the proposed algorithm and program are suitable for shape change analysis of single prism tensegrity structure model.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.525-547
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• 2015

This study analyzed the written texts of textbook and the teacher's discourse explaining 'the relationship between quadratic functions and quadratic equations' in the 9th grade high school mathematics class. Data consisted of the lecture recordings and the textbooks were analyzed based on the Halliday's systemic functional linguistics. According to the results, the written texts of the textbook used lexico-grammatical strategies such as generalization using hyponomy of meanings, mathematical objectification through nominalization and materialization of meaning through change in themes to compose mathematical concepts. The textbook generalized from an example in the description of formulating mathematical concepts, and in this process the organizational interactions of discourse-semantic level and lexico-grammartical level appeared. On the other hand, the teacher's doscourse appeared the change in transitivity and the addition of the reasons and the process. Also the teacher used explanation process of formulating the relationship between quadratic functions and quadratic equations. The linguistic characteristics of the teacher were linguistic implication and omission of lexemes due to contextual ommission. And there was no use of structural lexico-grammatical resources that influence the discourse-semantic level. This results provide a new framework for analyzing mathematical discourse, and suggest the lexico-grammatical strategies that can be used to explain mathematical concepts by teachers in math classrooms.

• Education of Primary School Mathematics
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• v.1 no.2
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• pp.85-95
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• 1997

Recently, by the popularization of computers and the development of many kinds of information transmission software, the living pattern in business offices and in home-life have changed rapidly. Because of the great progression of today's science technology, the influence of social education on the children is larger than that of the traditional school.. By a rapid change in the social atmosphere, there are some people who insist the traditional school education system is of no use any more. There have been many calls for reform of traditional schooling and in particular there has been major rethinking of school mathematics. The initial demand for change in elementary school mathematics is because of the poor achievement of students. There are even more compelling reasons for change. For example today's science technology society requires a different mathematical literacy for its citizens than that of the past. The importance of problem-solving based on interest and progress is more important than just paper-pencil computation in elementary schools. And also the increasing information wave of today's society demands that the school accept the long-distance education which could not be imagined in the past. Taking account of this variety, school education in the future should willingly introduce and apply the open education system to keep pace with today's society. To accept society demands actively, today's schools are going to accept and apply the idea of the open education. In this viewpoint, the purpose of the paper is to analyze the causes of under-achievement in mathematics teaming, the directions of school mathematics education, the system of textbooks and the problems of teaching-learning programs and paper-pencil test.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.

• The Mathematical Education
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• v.58 no.2
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• pp.299-317
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• 2019

In this study, we analyzed the change of teacher knowledge through task design in the teacher-researcher community focused on knowledge of students in the area of derivatives application. The following subjects were studied. First, we have analyzed the focus of the discussion related to teacher knowledge of students within the teacher-researcher community. Second, we have analyzed the change of teacher knowledge of students according to the focus. The results of this study are as follows. First, community member' different knowledge of students led the discussion on the task solving paths. The main focus of the discussion was the possibility in inducing responses and motivation. Second, the process of reviewing and evaluating task solving paths and reaching consensus led the improvement of teacher knowledge. Teachers and researchers led changes of teacher knowledge by sharing the knowledge based on previous research and experience, respectively. This ultimately shows the necessity of co-learning between teachers and researchers in teacher education.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.161-161
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• 2023

Bias correction of values is a necessary step in downscaling coarse and systematically biased global climate models for use in local climate change impact studies. In addition to univariate bias correction methods, many multivariate methods which correct multiple variables jointly - each with their own mathematical designs - have been developed recently. While some literature have focused on the inter-comparison of these multivariate bias correction methods, none have focused extensively on the effect of diverse configurations (i.e., different combinations of input variables to be corrected) of climate variables, particularly high-dimensional ones, on the ability of the different methods to remove biases in uni- and multivariate statistics. This study evaluates the impact of three configurations (inter-variable, inter-spatial, and full dimensional dependence configurations) on four state-of-the-art multivariate bias correction methods in a national-scale domain over South Korea using a gridded approach. An inter-comparison framework evaluating the performance of the different combinations of configurations and bias correction methods in adjusting various climate variable statistics was created. Precipitation, maximum, and minimum temperatures were corrected across 306 high-resolution (0.2°) grid cells and were evaluated. Results show improvements in most methods in correcting various statistics when implementing high-dimensional configurations. However, some instabilities were observed, likely tied to the mathematical designs of the methods, informing that some multivariate bias correction methods are incompatible with high-dimensional configurations highlighting the potential for further improvements in the field, as well as the importance of proper selection of the correction method specific to the needs of the user.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.519-538
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• 2013

The purpose of this study, for each section of high school mathematics I help to verify the utillization of instructional class in the formation of students' academic achievement and mathematical beliefs. For this purpose we construct an experimental class and then analyse the students' change in those aspects after applying concept learning hand-out and colleage feedback on their works those students are in the experimental class. As a result of the experiment, we find that concept learning hand-out activity and colleague feedback made some significant changes on the students achievement in mathematics and mathematical beliefs. Therefore, in this study I want to solve the concrete problems are as follows. First, utilizing the concepts of mathematics tutoring lessons to improve students' academic achievement is it effective? Second, utilizing the concepts of mathematics tutoring classes does have a positive impact on students' mathematical beliefs? Third, utilizing the concepts of mathematics tutoring lessons for students what is the reaction?