• 한국CDE학회논문집
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• 제2권1호
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• pp.11-18
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• 1997

Scientific volume visualization addresses the representation, manipulation, and rendering of volumetric data sets, providing mechanisms for looking closely into structures and understanding their complexity and dynamics. In the past several years, a tremendous amount of research and development has been directed toward algorithms and data modeling methods for a scientific data visualization. But there has been very little work on developing a mathematical volume model that feeds this visualization. Especially, in flow visualization, the volume model has long been required as a guidance to display the very large amounts of data resulting from numerical simulations. In this paper, we focus on the mathematical representation of volumetric data sets and the method of extracting meaningful information from the derived volume model. For this purpose, a B-spline volume is extended to a high dimensional trivariate model which is called as a flow visualization model in this paper. Two three-dimensional examples are presented to demonstrate the capabilities of this model.

• The Journal of the Acoustical Society of Korea
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• 제18권1E호
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• pp.37-43
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• 1999

This paper deals with a hybrid finite element method for wave scattering problems in infinite domains. Scattering of waves involving complex geometries, in conjunction with infinite domains is modeled by introducing a mathematical boundary within which a finite element representation is employed. On the mathematical boundary, the finite element representation is matched with a known analytical solution in the infinite domain in terms of fields and their derivatives. The derivative continuity is implemented by using a slope constraint. Drilling degrees of freedom at each node of the finite element model are introduced to make the numerical model more sensitive to the transverse component of the elastodynamic field. To verify the effects of drilling degrees freedom and slope constraints individually, reflection of normally incident P and SV waves on a traction free half spaces is considered. For the P-wave incidence, the results indicate that the use of slope constraint is more effective because it suppresses artificial reflection at the mathematical boundary. For the SV-wave case, the use of drilling degrees freedom is more effective by reducing numerical error at irregular frequencies.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권3호
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• pp.177-194
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• 2012

What strategies are used to help students understand quadratic functions in mathematics classroom? In specific, how does Chinese teacher highlight a connection between algebraic representation and graphic representation? From October to November 2009, an experienced teacher classroom was observed. It was found that when students started learning a new type of quadratic function in lessons, the teacher used two different teaching strategies for their learning: (1) Eliciting students to plot the graphs of quadratic functions with pointwise approaches, and then construct the function image in their minds with global approaches; and (2) Presenting a specific mathematical problem, or introducing conception to elicit students to conjecture, and then encouraging them to verify it with appoint approaches.

• 대한수학교육학회지:학교수학
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• 제12권4호
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• pp.507-530
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• 2010

본 연구는 지역별 우수수업 동영상에서 나타나는 수학적 의사소통이 어떻게 이루어지고 있는지를 분석하여 양질의 수업을 찾아 교사의 수업 관행에 도움을 주고자한 것이다. 교사와 교실 전체 간에 이루어지는 담화를 중심으로 수업을 분석하기 위해 다음과 같은 연구문제를 설정하였다. 첫째, 지역별 우수수업 동영상의 수학적 의사소통 수업유형은 무엇인가? 둘째, 지역별 우수수업은 의사소통이 어떻게 이루어지고 있는가? 셋째, 담화중심 수업의 수학적 의사소통 수준은 어떠한가? 공개된 24개의 수업을 수업 유형에 따라 분류한 결과 초등학교 수학 수업의 특성상 조작 중심수업 유형이 가장 많은 것으로 나타나 다른 유형의 수업도 좀 더 이루어질 필요가 있음을 알 수 있었다. 그리고 교수 학습 지도안에서 수학적 의사소통 능력을 고려한 수업은 5개이며 이 중 1개 수업만이 수학적 의사소통 능력을 인지적 영역에 포함시키고 있어, 수학적 의사소통 능력에 대해 교사가 정확히 알 필요가 있었다. 또한, 학생 간 질문하기를 수업에 반영할 필요가 있었다.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.651-662
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• 1998

Mathematics is means for making sense of one's experiential world and products of human activities. A usefulness of mathematics is derived from this features of mathematics. Keeping the meaning of situations during the mathematizing of situations. However, theories about the development of mathematical concepts have turned mainly to an understanding of invariants. The purpose of this study is to show the possibility of computer in representing situation and phenomena. First, we consider situated cognition theory for looking for the relation between various representation and situation in problem. The mathematical concepts or model involves situations, invariants, representations. Thus, we should involve the meaning of situations and translations among various representations in the process of mathematization. Second, we show how the process of computational mathematization can serve as window on relating situations and representations, among various representations. When using computer software such as ALGEBRA ANIMATION in mathematics classrooms, we identified two benifits First, computer software can reduce the cognitive burden for understanding the translation among various mathematical representations. Further, computer softwares is able to connect mathematical representations and concepts to directly situations or phenomena. We propose the case study for the effect of computer software on practical mathematics classrooms.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제18권5호
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• pp.1163-1185
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• 2024

With the sharp increase in the volume of literature data, researchers must spend considerable time and energy locating desired papers. A paper recommendation is the means necessary to solve this problem. Unfortunately, the large amount of data combined with sparsity makes personalizing papers challenging. Traditional matrix decomposition models have cold-start issues. Most overlook the importance of information and fail to consider the introduction of noise when using side information, resulting in unsatisfactory recommendations. This study proposes a paper recommendation method (PR-SLSMF) using document-level representation learning with citation-informed transformers (SPECTER) and low-rank and sparse matrix factorization; it uses SPECTER to learn paper content representation. The model calculates the similarity between papers and constructs a weighted heterogeneous information network (HIN), including citation and content similarity information. This method combines the LSMF method with HIN, effectively alleviating data sparsity and cold-start issues and avoiding topic drift. We validated the effectiveness of this method on two real datasets and the necessity of adding side information.

• Korean Journal of Mathematics
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• 제18권3호
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• pp.243-252
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• 2010

In this paper we extend the projective properties of representations of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as left R-modules to the projective properties of representations of quiver $Q={\bullet}{\rightarrow}{\bullet}$ as left $R[x]$-modules. We show that if P is a projective left R-module then $0{\rightarrow}P[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules. And we show $0{\rightarrow}L$ is a projective representation of $Q={\bullet}{\rightarrow}{\bullet}$ as R-module if and only if $0{\rightarrow}L[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules. Then we show if P is a projective left R-module then $R[x]\longrightarrow^{id}P[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules. We also show that if $L\longrightarrow^{id}L$ is a projective representation of $Q={\bullet}{\rightarrow}{\bullet}$ as R-module, then $L[x]\longrightarrow^{id}L[x]$ is a projective representation of a quiver $Q={\bullet}{\rightarrow}{\bullet}$ as $R[x]$-modules.

• 한국학교수학회논문집
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• 제24권2호
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• pp.217-241
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• 2021

본 연구에서는 삼각함수의 모델링을 통한 그래픽 과정의 효과를 알아보기 위한 실험연구로 실험과정의 분석을 질적연구 방법으로 처리했다. 이를 위해 수학적 모델링의 절차를 세분하여 기존의 모델에 두 단계, 즉, 질문의 생성과 아이디어 교환을 강조하는 놀이실험단계와 컴퓨터 그래픽 과정의 단계를 추가했다. 실험은 고등학교 2학년을 대상으로 실험반(TMG) 26명이 참여했고, 데이터의 질적분석을 위해 활동지, 면담 및 실험과정의 관찰자료를 분석하였다. 국내외 대부분의 연구가 통계적 방법을 이용한 양적 분석 방법이기 때문에 교사들에게는 모델링 수업에 큰 도움을 주지 못한다. 연구결과로 (1) 기존의 수학적 모델링의 절차에 두 개의 단계를 추가하여 보다 세분화한 모델링의 과정은 질문생성, 아이디어교환, 동료들과 소통 등에서 긍정적인 결과를 볼 수 있었다. (2) 실험학교의 수학과 수업에 컴퓨터 그래픽을 포함한 테크놀로지의 도입은 양과 수(Quantity) 교육에 매우 적절함을 보여주었다.

• 대한수학회지
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• 제51권6호
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• pp.1177-1187
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• 2014

In the current paper we study absolutely pure representations of quivers. Then over some nice quivers including linear quivers some sufficient conditions guaranteeing a representation to be absolutely pure is characterized. Furthermore some relations between atness and absolute purity is investigated. Finally it is shown that the absolutely pure covering of representations of linear quivers (including $A^-_{\infty}$, $A^+_{\infty}$ and $A^{\infty}_{\infty}$) by R-modules whenever R is a coherent ring exists.

• East Asian mathematical journal
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• 제19권1호
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• pp.133-150
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• 2003

This paper will show that the relation (1.1) $$L^1({\Omega}){\subset}C_0(\bar{\Omega}){\subset}H_{p,q}$$ if 1/p'-1/n(1-2/q')<0 where p'=p/(p-1) and q'=q/(q-1) where $H_{p.q}=(W^{1,p}_0,W^{-1,p})_{1/q,q}$. We also intend to investigate the control problems for the retarded systems with $L^1(\Omega)$-valued controller in $H_{p,q}$.