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Teaching and Learning Models for Mathematics using Mathematica (I)

  • Kim, Hyang-Sook
    • Research in Mathematical Education
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    • v.7 no.2
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    • pp.101-117
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    • 2003
  • In this paper, we give examples of models we have created for use in university mathematics courses. We explain the concept of linear transformation, investigate the roles of each component of 2 ${\times}$ 2 and 3 ${\times}$ 3 transformation matrices, consider the relation between sound and trigonometry, visualize the Riemann sum, the volume of surfaces of revolution and the area of unit circle. This paper illustrates how one can use Mathematica to visualize abstract mathematical concepts, thus enabling students to understand mathematics problems effectively in class. Development of these kinds of teaching and learning models can stimulate the students' curiosity about mathematics and increase their interest.

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Effect of Mix Proportion on the Flowing Characteristics of Super-flowing Concrete (초유동 콘크리트의 유동 성능에 미치는 배합요인의 영향)

  • 노재호;한정호;백명종;이보근;박기청
    • Proceedings of the Korea Concrete Institute Conference
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    • 1994.10a
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    • pp.115-120
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    • 1994
  • Recently super-flowing concrete has been developed and used in many construction sites in Japan. It is believed that super-flowing concrete will change the construction method and contribute to the durability of concrete structures. In this study the effect of mix proportion on the flowing characteristics of super-flowing concrete was investigated to establish the mix design method. From the result we have found that self-compactability of super-flowing concrete was greatly affected by the unit gravel volume and paste/gravel volume ratio. Therefore the two parameters can be used in mix design of super flowing concrete.

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A Fundamental Study on the Development of Fire Resistance Filling of Friendly Environment Using Aerated Concrete (기포콘크리트를 이용한 친환경 내화충전제개발에 관한 기초적 연구)

  • Lee, jong-il;Lim, Nam-Gi
    • KIEAE Journal
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    • v.7 no.4
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    • pp.119-126
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    • 2007
  • In this study, we processed two procedures of application test of filler for fire-resistance utility that are new application methods of aerated concrete and properties test of aerated concrete according to mixing ratio because we investigated the better use of aerated concrete as filler for fireproof safety and we proposed basic data about standardization of mixing of aerated concrete. We measured flow and volume change of aerated concrete. And if its volume doesn't change, we added measuring unit weight and compressive strength. To test application of aerated concrete as filler for fireproof safety, we filled up aerated concrete to fireproof safety according to suitable mixing ratio. Then we measured maximum temperature of inner part of fireproof safety in accordance with the standard test of fireproof. According to the results, aerated concrete as filler for fireproof safety could be possibly used. So when we make aerated concrete, we should consider using an adding agent as well as a foaming agent.

An Experimental Study on the Freezing and Thawing of Concrete Mixed with Steel Slag (제강 슬래그를 이용한 콘크리트의 동결융해에 대한 실험적 연구)

  • 정원섭;조성현;권기주;박성우;김진만
    • Proceedings of the Korea Concrete Institute Conference
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    • 2003.11a
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    • pp.48-53
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    • 2003
  • The steel slag, a by-product which is produced on the process of manufacturing steel by refining pig iron is mainly used as road materials after aging it. It is necessary to age steel slag for long time in air because the reaction with water and free-CaO in steel slag could make the volume expanded. Due to this reason it prevents steel slag from being used as aggregate of concrete. But steel slag used in this study is controled by a air-jet method which rapidly cools substance melted at a high temperature. Rapid cooling prevents from generating of free-CaO in steel slag. In this study, it was investigated that steel slag manufactured by air-jet method affects on concrete in the freezing and thawing. As results of this study, concrete mixed with steel slag was worse in the freezing and thawing than concrete mixed with sand in spite of using air entraining agent. To obtain durability of concrete in the freezing and thawing, it is desirable to mix 50% of steel slag in concrete per unit weight of volume.

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Research of Sludge Quantity and Evaluation of Sludge Handling Facilities in Water Treatment Plants (정수 슬러지 발생량 조사 및 슬러지 처리시설의 공정평가)

  • Moon, Seong-Yong;Kim, Seung-Hyun
    • Journal of Korean Society of Water and Wastewater
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    • v.18 no.3
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    • pp.279-290
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    • 2004
  • Sludge quantity has increased at "A"water treatment plant due to deterioration of raw water quality and GAC installation. Increased sludge resulted in overloading on sludge handling facilities. The object of this study is to survey sludge quantity and capacity of sludge handling facilities at "A"water treatment plant. Measured quantity of sedimentation sludge considerably exceeded the design capacity of sludge holding basin. Sludge holding basin was properly designed, but low concentration of sludge discharged from sedimentation basin caused production of large volume of the sludge. Timer operated control system for sludge withdrawal unit and leakage through a control valve were suspected to cause the low concentration. Augmentation of the control system by a turbidity meter and addition of a new control valve successfully reduced the sludge volume enough to satisfy the design capacity of sludge holding basin. Unlike sedimentation sludge, measured quantity of washwater was considerably less than the design capacity of washwater basin because it was over-designed.

A Study on the Residential Appropriateness for User-Centered Housing Unit of Apartment (거주자 중심의 아파트 단위주호 계획을 위한 주거환경 적합성에 관한 연구)

  • Yoo, Seo-Yeon;Lee, Yeun-Sook
    • Proceeding of Spring/Autumn Annual Conference of KHA
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    • 2004.11a
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    • pp.141-146
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    • 2004
  • Apartment, which have become the major housing style in Korea, have contributed to the development of housing culture as well as achieved a growth in volume. However, the demands and characteristics of residents have not been reflected in the apartment. because it has been developed only for a growth in volume. In this society, apartments need to be developed for resident. Therefore, the purpose of this study is analyzing apartment design factors and examining the appropriateness of apartment residents. To do so, questionnaire research is conducted and 90 questionnaires are analyzed for this study. The questionnaire mainly consists of questions about residential appropriateness of each space, and reaction and coping behavior on the inappropriate residential environment.

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Evaluation of the Fluidity and Compressive Strength of Mortar Containing High Volume Blast Furnace Slag by Replacement Ratio of Lightweight Fine Aggregate (경량잔골재 치환율에 따른 고로슬래그 대량사용 모르타르의 유동성 및 압축강도 평가)

  • Kim, Do-Bin;Kim, Young-Uk;Kim, Sung-Jin;Kim, Jeong-Hyeon;Ban, Jun-Mo;Choi, Se-Jin
    • Proceedings of the Korean Institute of Building Construction Conference
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    • 2017.05a
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    • pp.208-209
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    • 2017
  • This study analyzed the fluidity and strength properties of mortar containing high volume blast furnace slag by replacement ratio of lightweight fine aggregate for reducing the unit weight of concrete structures.

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RELATIVE ISOPERIMETRIC INEQUALITY FOR MINIMAL SUBMANIFOLDS IN SPACE FORMS

  • Seo, Keomkyo
    • Korean Journal of Mathematics
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    • v.18 no.2
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    • pp.195-200
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    • 2010
  • Let C be a closed convex set in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$. Assume that ${\Sigma}$ is an n-dimensional compact minimal submanifold outside C such that ${\Sigma}$ is orthogonal to ${\partial}C$ along ${\partial}{\Sigma}{\cap}{\partial}C$ and ${\partial}{\Sigma}$ lies on a geodesic sphere centered at a fixed point $p{\in}{\partial}{\Sigma}{\cap}{\partial}C$ and that r is the distance in ${\mathbb{S}}^m$ or ${\mathbb{H}}^m$ from p. We make use of a modified volume $M_p({\Sigma})$ of ${\Sigma}$ and obtain a sharp relative isoperimetric inequality $$\frac{1}{2}n^n{\omega}_nM_p({\Sigma})^{n-1}{\leq}Vol({\partial}{\Sigma}{\sim}{\partial}C)^n$$, where ${\omega}_n$ is the volume of a unit ball in ${\mathbb{R}}^n$ Equality holds if and only if ${\Sigma}$ is a totally geodesic half ball centered at p.

Reliability Evaluation of Ceramic Structures Under Thermal Shocks (열충격이 작용하는 세라믹구조의 신뢰성 평가)

  • 김종태;심확섭;장건익;이치우;이환우
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1996.11a
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    • pp.954-958
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    • 1996
  • An analysis method for the reliability of ceramic structures subjected to thermal shocks is presented, Flaws with the size of given probability distribution function are assumed to be distributed at random with a certain density per unit volume in the structures. Criterions for crack instability are derived for brittle solids under general thermal stresses. A probabilistic failure model is presented to study the probability of crack instability for blittle solids containing cracks with uncertain crack size. The reliabilities of brittle structures are evaluated based on the weakest-link hypothesis, which states that a structure fails when the cracks in any differential volume become unstable. A numerical example is given to demonstrate the application of the proposed method.

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Development of Durability Estimation and Design Systems of Worm Gears (웜기어의 강도평가 및 설계시스템 개발에 관한 연구)

  • 정태형;백재협
    • Transactions of the Korean Society of Automotive Engineers
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    • v.5 no.1
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    • pp.207-216
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    • 1997
  • We developed the durability estimation and design systems to minimize the volume, considering the durability, efficiency, and design requirements of worm gears. That is, we consider each kind of factors affecting on durability on the basis of AGMA Standard for the cylindrical and double-enveloping worm gears. We also estimate input power on the basis of wear and durability, bending strength and deflection of worm shaft, and we developed the durability estimation and design systems of power transmission worm gears introducing the optimal design method on the personal computer to be easily used in field. Also, we developed a method which converts the design variables obtained from the optimal design method to integer values(number of worm threads, number of worm threads, number of worm wheel teeth, etc.,) to be used in real design and production. The developed durability estimation and design method can be easily applied to the design of worm gears used as power transmission devices in machineries and is expected to be used for weight minimization of worm gear unit.

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