• Journal of Welding and Joining
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• 제8권2호
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• pp.53-57
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• 1990

Analytic solutions of heat conduction during welding which were first found by Resenthal have some restrictions. One of these is that models to which analytic solutions can be applied must have simple geometric shape, and another is that quasi-stationary state must be created. On the other hand, computational methods developed recently with the aid of the computer can overcome these shortcomings, but the methods raise problems from economic point of view when they are applied to 3 dimensional problems. Taking account of these problems, a new method combinig the analytic method with the computational one is proposed. This method can be ued in weldments with complicated geometric shape in non-stationary state, but with the aid of the analytic method can reduce the computing time.

• Journal of applied mathematics & informatics
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• 제38권3_4호
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• pp.311-334
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• 2020

The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that arises in the elliptic interface problems are very complex. In this article we propose an exponentially accurate nonconforming spectral element method for these problems based on [7, 18]. A geometric mesh is used in the neighbourhood of the singularities and the auxiliary map of the form z = ln ξ is introduced to remove the singularities. The method is essentially a least-squares method and the solution can be obtained by solving the normal equations using the preconditioned conjugate gradient method (PCGM) without computing the mass and stiffness matrices. Numerical examples are presented to show the exponential accuracy of the method.

• 대한지리학회지
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• 제46권3호
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• pp.366-381
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• 2011

일반적으로 이산적 입지 공간에서 경쟁적 입지 문제는 입지 후보지에 따라 수많은 조합의 경우가 발생하는 의사결정 문제이기 때문에, 수리적으로 계산하기가 쉽지 않다. 따라서 본 연구에서는 결정적 배분 형태를 가정한 이산적 입지 공간의 경쟁적 입지 문제를 보다 효율적으로 해결하기 위한 대안적 방법에 대해 논의한다. 제안된 방법론의 핵심은 입지 문제의 크기와 관련되는 잠재적 입지후보지의 개수를 기하학적 개념을 이용하여 줄이는 것이다. 사례 분석으로 경쟁이 가열화되고 있는 초고속 인터넷 시장을 대상으로 제안된 방법론을 적용하였는데 두 가지 다른 크기의 문제, 즉 연구 지역 전체에 대해 정의된 잠재적 입지 후보지와 GIS 기반의 기하학적 알고리즘에 의해 추출된 보다 적은 수의 잠재적 입지 후보지에 대해 계산 결과와 공간적 배열을 비교하였다. 사례 분석 결과, 두 문제 모두 고객 유치를 최대화시키는 동일한 최적 입지를 보여주는 한편, 적은 수의 잠재적 입지 후보지를 가진 경쟁적 입지 모델이 보다 효율적으로 해결될 수 있었다.

• 대한수학회지
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• 제24권2호
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• pp.217-237
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• 1987

• 한국수학교육학회지시리즈A:수학교육
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• 제46권3호
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• pp.245-261
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• 2007

This paper deals with the possible problems which may arise when students learn the names of elementary geometric figures in the languages of Korean, Chinese, English. The names of some simple geometric figures in these languages are analyzed, and a specially designed test was administered to some grade eight students from the three language groups to explore the possible influence of the characteristics of the languages on students' capability in identifying the figures, the way students define the figures, and students' understanding of the inclusive relationship among figures. It was found that the usage of the terms to describe geometric figures may indeed have affected students' understanding of the figures. The names of geometric figures borrowed from those of everyday life objects may cause students to fix on some attributes of the objects which may not be consistent with the definition of the figures. Even when the names of the geometric figures depict the features of the figures, the words used in the naming of the figures may still affect students' understanding of the inclusive relations. If there is discrepancy between the definition of a geometric figure and the features that the name depicts, it may affect students' understanding of the definition of the figure, and if there is inconsistency in the classification of figures, it may affect students' understanding of the inclusive relationship involving those figures. Some implications of the study are then discussed.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권4호
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• pp.353-369
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• 2018

This study started with the following questions. Suppose that students do not accept various forms of geometric series tasks as the same task. Also, let's say that the approach was different for each task. Then, when they realize that they are the same task, how will students connect the different approaches? This study is a process of pro-actively confirming whether or not such a question can be made. For this purpose, three students in the second grade of high school participated in the teaching experiment. The results of this study are as follows. It also confirmed how the students think about the various types of tasks in the geometric series. For example, students have stated that the value is 1 in a series type of task. However, in the case of the 0.999... type of task, the value is expressed as less than 1. At this time, we examined only mathematical expressions of students approaching each task. The problem of reachability was not encountered because the task represented by the series symbol approaches the problem solved by procedural calculation. However, in the 0.999... type of task, a variety of expressions were observed that revealed problems with reachability. The analysis of students' expressions related to geometric series can provide important information for infinite concepts and limit conceptual research. The problems of this study may be discussed through related studies. Perhaps more advanced research may be based on the results of this study. Through these discussions, I expect that the contents of infinity in the school field will not be forced unilaterally because there is no mathematical error, but it will be an opportunity for students to think about the learning method in a natural way.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1992년도 추계학술대회논문집; 반도아카데미, 20 Nov. 1992
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• pp.117-123
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• 1992

In recent years, the finite element method has become one of the most popular numerical technique for obtaining solutions of engineering science problems. However, there exist various uncertainties in modeling the problems, such as the dimensions(geometry shape), the material properties, boundary conditions, etc. The consideration for the uncertainties inherent in the problems can be made by understanding the influences of uncertain parameters[1]. Determining the influences of uncertainties as statistical quantities using the standard finite element method requires enormous computing time, while the probabilistic finite element method is realized as an efficient scheme[2,3] yielding statistical solution with just a few direct computations. In this paper, a formulation of the probabilistic fluid-structure interaction problem accounting for the first order perturbation of geometric shape is derived, and especially probabilistical acoustic pressure scattering from the structure with surrounding fluid is focused on. In Section 2, governing equations for the fluid-structure problems are given. In Section 3, a finite element formulation, based on the functional, is presented. First order perturbation of geometric shape with randomness is incorporated into the finite element formulation in conjunction with discretization of the random fields in Section 4 and 5. Finally, the proposed formulation is applied to a acoustic pressure scattering problem from an infinitely long cylindrical shell structure with randomness of radial perturbation.

• 한국수학사학회지
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• 제20권1호
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• pp.57-72
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• 2007

최근 수학교육에서 펜토미노와 같은 절단 퍼즐들을 학습에 많이 활용하고 있다. 그러나 이런 퍼즐들의 개발 배경과 수학적 활용 방법에 대한 연구 부족으로 수학적 개념 도입이나 문제해결을 위한 소재로서 다양하게 사용되고 있지 못한 실정이다. 이 논문은 펜토미노를 수학 학습에서 효과적으로 활용하기 위하여 펜토미노와 같은 절단 퍼즐의 배경이 되는 기하학적 문제와 펜토미노의 개발에 관한 수학사적 배경을 알아보고, 제 7차 초등학교 교육과정의 수학 교과서에서 활용할 수 있는 단원과 여러 문헌에서 펜토미노를 활동한 자료를 조사하여 체계적인 수학 학습자료를 개발하는 기초 자료와 방향을 제시하는 데 그 목적이 있다.

• 한국수학사학회지
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• 제17권1호
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• pp.87-96
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• 2004

This article dealt with two approaches, algebraic and geometric approaches in terms of Pythagoreans theorem. As mathematics evolves, many theorems had been developed beginning with geometric approaches. However, the algebraic techniques that survive these days are so powerful and generalized in school curriculum. So, if students have more chances to see mathematical properties in geometrical ways, they can experience how beautiful and meaningful they are through the process of the advent of them. Also, it was to try to develop an insight into their applications to other problems.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1473-1479
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• 2009

We introduce the resistant length and examine its properties. We also consider the geometric applications of resistant length to the boundary behavior of analytic functions, conformal mappings and derive the theorem in connection with the fundamental sequences, purely geometric problems. The method of resistant length leads a simple proofs of theorems. So it shows us the usefulness of the method of resistant length.