• Journal for History of Mathematics
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• v.21 no.4
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• pp.61-78
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• 2008

In this paper, we discuss about De Morgan's view on the development of algebra according to following distinctions: arithmetic, universal arithmetic, symbolic algebra, significant algebra. De Morgan thought that the differences between arithmetic and universal arithmetic lie in the usage of letters and the immediate performance of computation. In his viewpoint, universal arithmetic is a transitional phase, in which absurd phenomena occur, from arithmetic to algebra and these absurd phenomena call for algebra. The feature of De Morgan's view on the development of algebra is that symbolic calculus which consist of symbol system without symbol's meaning is acquired, then as extended meanings are furnished to symbols, symbolic calculus become logical so significant calculus is developed. For example, Single algebra is developed, as an extended meaning is furnished to a symbol -1, and double algebra is developed, as an extended meaning is furnished to a symbol $\sqrt{-1}$. According to De Morgan, a symbol system is derived from the incompleteness of a prior symbol system.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.26-36
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• 1999

A general procedure for determining the optimum location of suspension hard points with respect to kinematic design parametes is presented. Suspensions are modeled as connection of rigid bodies by ideal kinematic joints. Constraint equations of the kinematic joints are expressed in terms of the generalized coordinates and hard points. By directly differentiating the constraint equations with respect to the hard points, kinematic sencitivity equations are obtained. In order to cope with algebraic complexity associated with the differentiation process, a symbolic computation technique is used. A performance index is defined in terms of static design parameters such as camber, caster, toe, ect.. Gradient of the performance index can be analytically computed from the kinematic sensitivity equations. Optimization results show the effectiveness and validity of the procedure, which is applicable to any type of suspension if its kinematic configurations are given.

• Journal of the Korea Convergence Society
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• v.8 no.12
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• pp.283-289
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• 2017

In this study, a general program has been developed to calculate the static design factor of a vehicle suspension system. The partial derivatives of Jacobians for constraint equations are calculated using the symbolic technique. In the commercial program, finite difference method is used to calculate the Jacobian matrix of Jacobian. But in this study, it is calculated by using the symbol calculation method to precisely consider it. The calculated Jacobian matrix for the system has proved its accuracy through the solution of the numerical example. A simulation was performed for a double wishbone suspension of a 1/4 vehicle. The result can be used to calculate the static design factor of the suspension, and also add a convergence module that can perform virtual tests.

• Journal of the Korean Institute of Telematics and Electronics
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• v.13 no.6
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• pp.20-23
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• 1976

A boolean algebra method for computing the reliability in a communication network is prosented. Given the set of all simple paths between two nodes in a network, the terminal reliability can be symbolically computed by the Boolean operation which is named parallel operation. The method seems to be promising for both oriented and nonoriented network.

• Applied Biological Chemistry
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• v.20 no.3
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• pp.285-291
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• 1977

In this paper the new statistical method called "New Modified Triangle Test" is studied. This method is to test the null hypothesis based on the result which comes from evaluating sample size "t", where $t{\geqq}3$, by using Triangle Preference Scale Test. It a confirmed that "New Modified Scheffe's Method 1" can be used for appraising "New Modified Triangle Test". In this report, the weight fraction of in-correct oddity chosen to correct oddity chosen is made 1/2 in terms of chance probability.

• Communications of Mathematical Education
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• v.16
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• pp.109-122
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• 2003

현재 초, 중, 고등학교의 수학교육 현실은 수학 개념의 정확한 이해에 초점을 맞추지 못하고 공식의 암기와 그것을 이용하여 단순한 문제 풀이에 시간을 많이 할애함으로써 수학의 기본적인 개념이나 기호의 정확한 사용법을 인지하지 못하고 계산 기능적인 면으로 치우치는 경향이 많이 나타나며, 문제 풀이의 창의적인 상황이 제시되지 않는 상태에서 교사 중심의 문제풀이 방법에만 의존하고 있다. 이러한 문제점 속에서 창의적인 문제 해결 방안을 구상할 수 있는 사고력의 배양에 소홀함이 있다고 볼 수 있다. 따라서 학생 스스로 의미를 파악하여 학습 할 수 있는 교수 방법이나 학습 방법에 대한 연구는 현실적으로 매우 시급한 상황에 처해있다. 이러한 상황에서 많은 수학교육자들은 학생들이 좀 더 쉽게 수학의 개념에 접근 할 수 있게 하기 위하여 많은 노력을 하고 있다. 그러한 노력 중의 하나로 테크놀러지를 이용한 수학교육을 말 할 수 있는데, 이는 실제로 수학교육에 긍정적인 영향을 준다고 알려져 있다. 본 논문은 현 고등학교 수학I의 등차수열에 관한 내용을 Mathematica를 이용하여 다각수(도형수)로부터 등차수열의 개념을 유도하였다.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.1-19
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• 2016

This study investigated the mathematical notation used today in terms of skip ping the parenthesis. At first we have studied the elementary and secondary curriculum content related to omitted rules. As a result, it is difficult to find explicit evidence to answer that question 'What is the calculation of the $48{\div}2(9+3)$?'. In order to inquire the notation fundamentally, we checked the characteristics on prefix, infix and postfix, and looked into the advantages and disadvantages on infix. At the same time we illuminated the development of mathematical notation from the point of view of skipping the parenthesis. From this investigation, we could check that this interpretation was smooth in the point of view that skipping the parentheses are the image of the function. Through this we proposed some teaching methods including 'teaching mathematical notation based on historic genetic principle', 'reproduction of efforts to overcome the disadvantages of infix and understand the context to choose infix', 'finding the omitted parentheses to identify the fundamental formula' and 'specifying the viewpoint that skipping the multiplication notation can be considered as an image of the function'.

• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.444-448
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• 2007

자연하천에서 단위구간(측선)의 연직선상 평균유속산정을 위한 일반적인 측정방법으로는 표면유속법, 1점법, 2점법, 3점법, 4점법, 5점법, 6점법, 연직 유속분포법 등이 있으며, 본 연구에서는 지난 1년간 낙동강유역 이안, 신풍, 성덕(무계), 성덕(보현)지점에서 회전식유속계로 측정한 유속자료를 이용하여 측선별 연직분포곡선을 작성한 후 측정지점 횡단면상 수심이 얕은 양안과 상류 제약조건(수풀 또는 돌출된 바위 등)으로 인해 측선의 흐름이 왜곡되는 지점을 제외한 측선별 연직유속분포곡선을 평균하여 지점별 대표 연직유속분포곡선을 작성하였다. 지점별 대표 연직유속분포 곡선을 작성하여 평균유속을 산정한 값을 기준으로 하천유량 측정시 일반적 평균유속 산정방법인 1, 2, 3점법 및 표면유속법에 대한 변동계수를 분석한 결과 1점법은 0.064, 2점법은 0.027, 3점법은 0.043, 표면유속법은 0.126으로 1, 2, 3 점법에서는 지점별 변화가 비교적 작게 나타났으며 표면유속법에서는 유량측정 지점별 변화가 큰 것으로 나타났다. 또한, 낙동지점에서 ADCP를 이용한 유량측정시 수집된 측선별 연직유속분포자료를 이용, 측정지점의 유량별 대표 연직유속분포 곡선을 작성, 실제 하천유량측정에 널리 쓰이고 있는 평균유속 측정방법을 비교 분석하였다. 분석결과, 1점법에서는 평균유속대비 1.076, 2점법에서는 1.026, 3점법에서는 0.051로서 2, 3점법이 대체로 양호한 결과를 보이며 이는 Hulsing 등의 연직유속분포곡선을 이용하여 계산한 1점법에서 1.020, 2점법, 1.010, 3점법 1.015의 결과 추세와도 일치하였다.

• Journal of Sericultural and Entomological Science
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• v.36 no.2
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• pp.138-146
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• 1994

The structural characteristics of Antheraea yamamai and Antheraea pernyi silk were investigated by using x-ray diffraction method, IR spectroscopy and polarizing microscopy. The amino acid composition, fiber density, thermal decomposition temperature and glass transition temperature were also measured for relating these physical properties to the structure in comparison with those of Bombyx mori silk fiber. There was no significant structural difference between A. yamamai and A. pernyi silk fiber on an examination of x-ray diffraction curve and IR spectrum. Both of these wild silk fibers showed double diffraction peaks at the Bragg angle 2Θ16.7˚ and 20.5˚by x-ray diffraction analysis as well as IR absorption peaks for the bending vibration of specific groups related to ala-ala amino acid sequence. On the other hand, the x-ray diffraction curve and IR spectrum of Bombyx mori silk fiber are different from those of wild silk fibers, indicating different crystal structure as well as amino acid sequences. It showed under the polarizing microscope examination that the birefringence and optical orientation factor of wild silk fibers are much lower than those of B. mori silk. Also, the surface of degummed wild silk fibers was characterized by the longitudinal stripes of microfibrils in the direction of fiber axies. The amino acid composition, which is strongly related to the fine structure and properties, was not significantly different between these two wild silk fibers. However, the alanine content was somewhat less and polar amino acid content more for A. yamamai. As a result of fiber density measurement, the specific gravities of B. mori, A. pernyi and A. yamamai were 1.355~1.356, 1.308~1.311, 1.265~1.301g/㎤ in the order, respectively. The calculated crystallinity(%) was 64% for B. mori and 51~52% for wild silk fibers, which showed same trend by IR method in spite of somewhat higher value. The thermal decomposition behaviour was examined by DSC and TGA, showing that the degradation temperature was in the order of B mori, A. prernyi and A. yamamai at around 350$^{\circ}C$. It was also observed by TGA that the decomposition seems to proceed step by step according to their specific regions in the fiber structure, resulting the difference in their thermal stabilities. The glass transition temperature was turned out to be 220$^{\circ}C$ for B. mori, 240$^{\circ}C$ A. yamamai and 255$^{\circ}C$ A. pernyi by the dynamic mechanical analysis. It is expected that the chemical properties are affected by the dynamic mechanical behavior in accordance with their structural characters.

• Korean Journal of Food Science and Technology
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• v.31 no.4
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• pp.957-963
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• 1999

Effects of cryoprotectants on protein denaturation of soybean curd, tofu, during frozen storage were examined. A whole-coagulated non-press tofu was prepared by adding 2% of isolated soybean protein to soy milk in order to prevent loss of added cryoprotectants. The cryoprotectants added were glocose, glycerol, sorbitol, propylene glycol, and tripolyphosphate. The texture characteristics of soybean curds before and after frozen storage were measured by sensory evaluation and Texture analyzer, and the results were evaluated by response surface methodology (RSM). Glucose, glycerol, sorbitol, and sodium tripolyphosphate were effective as single cryoprotectant, and the mixtures of glucose and sodium tripolyphosphate, and sorbitol and propylene glycol were also effective in minimizing textural change during freezing. Overall, the mixture of cryoprotectants were more effective than single cryoprotectant. According to the RSM, the maximum effect of cryoprotectants in minimizing textural changes during freezing was obtained with the mixture of 2.1% glucose, 6.7% glycerol, 2.1% sorbitol, 0.4% propylene glycol, and 0.3% sodium tripolyphosphate. However, considering the sensory acceptability, the optimum use of cryoprotectants in frozen tofu was 1% glucose, 2% glycerol, 1% sorbitol, 0.2% propylene glycol, and 0.5% sodium tripolyphosphate.