• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.2
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• pp.181-186
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• 2022

Poisson-Boltzmann equation (PBE) is used to model problems arising from various disciplinary including bio-pysics and colloid chemistry. Therefore, to predict a numerical solution of PBE is an important issue. The authors proposed deep learning based methods to solve PBE while the computational time to generate finite element method (FEM) solutions were bottlenecks of the algorithms. In this work, we shorten the generation time of FEM solutions in two directions. First, we experimentally find certain penalty parameter in a bilinear form. Second, we applied algebraic multigrids methods to the algebraic system so that condition number is bounded regardless of the meshsize. In conclusion, we have reduced computation times to solve algebraic systems for PBE. We expect that algebraic multigrids methods can be further employed in various disciplinary to generate deep learning samples.

• School Mathematics
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• v.9 no.1
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• pp.141-160
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• 2007

The purpose of this paper was to evaluate how students apply prior knowledge or experience in solving algebra word problems from the chain of signification-based perspective. Three middle school students were evaluated in this case study. The results showed that the subjects formed similarities in the process of applying knowledge needed for solving a problem. The student A and C used semi-open-end formulas and closed formulas as solutions. They then formed concrete shape for each solution using the chain of signification that was applied for solution by forming procedural similarity. At this time, the chain of signification could be the combination of numbers, words, and pictures (such as diagrams or graphs) or just numbers or words. On the other hand, the student C who recognized closed formulas and her own rule as a solution method could not formulate completely procedural similarity due to many errors arising from number information. Nonetheless, all of the subjects showed something in common in the process of coming up with a algorithm that was semi-open-end formula or closed formula.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.3
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• pp.697-703
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• 2000

As device dimensions are lastly scaled down, impact ionization(I.I.) events are very important to analyze hot carrier transport in high energy region, and the exact model of impact ionization is demanded on device simulation. We calculate full band model by empirical pseudopotential method and the impact ionization rate is derived from modified Keldysh formula. We calculate impact ionization coefficients by full band Monte Carlo simulator to investigate temperature dependent characteristics of impact ionization for GaAs as a function of field. Resultly impact ionization coefficients are in good agreement with experimental values at look. We how energy is increasing along increasing the field, while energy is decreasing along increasing the temperature since the phonon scattering rates for emission mode are very high at high temperature. The logarithmic fitting function of impact ionization coefficients is described as a second orders function of temperature and field. The residuals of the logarithmic fitting function are mostly within 5%. We Dow, therefore, the logarithm of impact ionization coefficients has quadratic dependence on temperature, and we can save time of calculating the temperature dependent impact ionization coefncients as a function of field.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.

• Proceedings of the Korea Air Pollution Research Association Conference
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• 1999.10a
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• pp.194-196
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• 1999

대기나 수용액 속에 부유 입자는 서로 충돌하여 합쳐져서 그 크기가 커지게 된다. 이러한 과정을 응집(Coagulation)이라고 하며, 이는 대기중 부유입자의 농도 및 크기분포의 변화, 구름 속에서의 빗방울형성 등에 매우 중요한 기작 중의 하나이다. 응집방정식은 일반적으로 비선형 편미적분 방정식으로 표현되어 일반 해를 구하는 것은 불가능하다. 이러한 이유로 응집방정식을 풀 때에는 수치 해석적인 방법이 주로 이용되고 있다.(Tolof, 1977; Gelbard and Seinfeld, 1978; Reed ea al., 1980; Mick et al., 1991).(중략)

• The Science & Technology
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• v.29 no.4 s.323
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• pp.68-69
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• 1996

숫자를 헤아리는 방법은 민족마다 또 문화권에 따라 서로 다르다. 서양에는 피코, 마이크로, 밀리, 윈, 헌드레드, 밀리언 등이 있고 동양에서는 일, 십, 백, 천, 억, 조, 경 등을 기본적인 숫자의 단위로 쓰고 있다. '불가사의', '무량대수' 등도 숫자의 단위이며 소수점 이하는 푼, 리를 비롯해 '순식', '찰나' 등 다양하다. 우리가 흔히 쓰는 '순식'은 숨을 한번 쉬는 3초를, 그리고 불교에서의 '일겁'은 우주의 일생을 일컫는다. 이렇듯 흥미롭고 신비로운 숫자의 세계를 풀어본다.

• Communications of Mathematical Education
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• v.10
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• pp.505-517
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• 2000

수학 학습에서 컴퓨터와 계산기의 활용은 시각화의 강화로부터 직관력과 사고력의 향상을 가져왔다. 컴퓨터 대수체계(Computer Algebra System)가 탑재된 수학 학습용 컴퓨터 프로그램과 계산기가 활발히 사용되고 있으며, 교수매체로서의 활용은 지식 정보전달 체계와 학습자의 지식 구성방법에 새로운 패러다임을 형성하였다. 특히 수학학습용 그래픽 계산기(Graphing Calculator)는 휴대형(Hand-held Technology)으로 학습공간의 이동(Mobil Education)이 가능하며, 수학학습 전용기라는데 의미를 둘 수 있다. Symbolic Graphing Calculator를 활용한 수업에서 학습자는 계산기를 가지고, 기호연산 실행 조작을 통해 자신의 사고과정을 표현하고, Symbolic Graphing Calculator는 실행 조작에 즉각적으로 과정과 결과를 제공하며, 다른 표상과 상호작용을 함으로써 학습자 스스로의 규제가 강화된 과정을 통해 지식을 구성하게 된다. 이때 교사는 지식 정보전달 체계인 대화형 실행매체(IMTs)를 작성하여 학습자의 지식 형성에 안내자의 역할을 하게 된다. 이번 워크샵에서는 CASIO fx 2.0을 활용한 교실 수업모형을 그래프 표상과 연계한 방정식의 풀이과정을 통해 알아본다.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2000.05a
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• pp.451-454
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• 2000

The impact ionization(I.I.) is necessary to analyze carrier transport properties under the influence of high electric field. The full band I-k relation and Fermi's golden rule are used for the calculation of impact ionization rate. We have investigated the temperature- and field-dependent impact ionization coefficient for silicon using full band Monte Carlo simulation. The impact ionization coefficients calculated by our impact ionization model are agreed with experimental data at look. We know that impact ionization coefficients and electron energies are decreasing along increasing temperature due to increase of phonon scattering, especially by emission. The logarithm of impact ionization coefficients are fitted to linear function for temperature and field. The residuals of linear function are within the error bound of 5%. We know logarithmic impact ionization coefficients are linearly dependent on temperature and field.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.411-429
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• 2015

In this study we investigated the effects of using GSP in solving geometric problems. Especially we focused the effects of GSP in leveled students' connection of geometry and algebra. High leveled students prefer to use algebraic formula to solve geometric problems. But when they did not know the geometric meaning of their algebraic formula, they could recognize the meaning after using GSP. Middle and low leveled students usually used GSP to obtain hints to solve the problems. For the low leveled students GSP was usually used to understand the meaning of the problem, but it did not make them solve the problem.

• Journal of the Korean School Mathematics Society
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• v.18 no.2
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• pp.223-240
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• 2015

This paper deals with how to design and develop white-box based e-learning contents which are equipped with conceptual understanding and step-by-step computational procedures for studying vector calculus for science-engineering majors who might need supplementary mathematics learning. Noting that rewriting rules are often used in school mathematics for students' problem solving, the theoretical aspects of rewriting rules are reviewed for developing supplementary e-learning contents for them. The software design of step-by-step problem solving requires careful arrangement of rewriting rules and pattern matching techniques for white-box procedures using a computer algebra system such as Mathematica. Several modules for step-by-step problem solving as well as producing dynamic display of e-learning contents was coded by Mathematica in order to find the length of a curve in vector calculus after implementing several rules for differentiation and integration. The developed contents are equipped with diagnostic modules and immediate feedback for supplementary learning in terms of a tutorial. At the end, this paper indicates the strengths and features of the developed contents for college students who need to increase math learning capabilities, and suggests future research directions.